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CONTENTS

Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013

of the South African Institution of Civil EngineeringVolume 55 No 1 April 2013 ISSN 1021-2019

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© South African Institution of Civil Engineering

2 Estimating car ownership and transport energy consumption:

a disaggregate study in Nelson Mandela Bay

C J Venter, S O Mohammed

11 Experimental and numerical investigation of the natural frequencies

of the composite profi led steel sheet dry board (PSSDB) system

F A Gandomkar, W H Wan Badaruzzaman, S A Osman, A Ismail

22 Improving water quality in stormwater & river systems:

an approach for determining resources

N Nel, A Parker, P Silbernagl

36 Design implications on capital and annual costs of smallholder irrigator projects

A F Hards, J A du Plessis

45 A model for the drying shrinkage of South African concretes

P C Gaylard, Y Ballim, L P Fatti

60 Pile design practice in southern Africa Part I: Resistance statistics

M Dithinde, J V Retief

72 Pile design practice in southern Africa Part 2: Implicit reliability of existing practice

J V Retief, M Dithinde

80 Optimising dosage of Lytag used as coarse aggregate in lightweight aggregate concretes

S Ahmad, Y S Sallam, I A R Al-Hashmi

85 Centrifuge modelling of a soil nail retaining wall

S W Jacobsz

94 2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings

of mass concrete considering contact interface and variations of material properties:

Part 1: Thermal analysis

S Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian

104 2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings

of mass concrete considering contact interface and variations of material properties:

Part 2: Stress Analysis

S Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian

114 Discussion:

Weak interlayers in fl exible and semi-fl exible road pavements: Part 1

Comment by Dr CJ Semmelink and response by Dr Frank Netterberg and Dr Morris de Beer

116 Discussion:

The eff ects of placement conditions on the quality of

concrete in large-diameter bored piles

Comment by Prof Mark G Alexander


TECHNICAL PAPER

JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING

Vol 55 No 1, April 2013, Pages 2–10, Paper 777

PROF CHRISTO VENTER is an Associate Professor

of Transportation Engineering in the

Department of Civil Engineering at the

University of Pretoria. His teaching, research and

consulting activities focus on public transport,

transport planning, travel demand modelling,

and social aspects of mobility. He is registered

as a professional civil engineer.

Contact details:

Associate Professor

Department of Civil Engineering


Pretoria

South Africa

0002

T: +27 12 420 2184

F: +27 12 362 5218

E: [email protected]

SEMIRA MOHAMMED is currently a researcher at

the CSIR Built Environment (Council for Scientifi c

and Industrial Research) where she has been

working for the last eight years. She completed

her BSc Civil Engineering degree at the

University of Asmara, Eritrea, and her MSc

Transportation Planning at the University of

Pretoria, South Africa. She has been involved in

a number of research projects ranging from traffi c management to

passenger transport, with emphasis on transport energy, the environment

and road safety.

Contact details:

Researcher

Built Environment Unit

CSIR

PO Box 12417

Hatfi eld, Pretoria

0028

South Africa

T: +27 12 841 3991

F: +27 12 841 4044


Keywords: travel behaviour, energy consumption, land use, vehicle ownership

model, travel demand management

INTRODUCTION

Transport energy consumption is emer-

ging as a major area of public and political

concern worldwide. The transport sector is

a significant consumer of energy – estimates

for Cape Town, for instance, indicate that

transport accounts for just over half of all

energy consumed in the city (SEA 2003).

Given that about 97% of transport energy

in South Africa comes from liquid fuels, of

which the lion’s share is refined imported

crude (Cooper 2007), concerns centre around

energy security, the exposure of the economy

to international oil price volatility, and the

environmental impacts of transport fuel use.

Potential strategies to reduce the trans-

port sector’s dependence on oil include

technological improvements such as increas-

ing the energy efficiency of the vehicle parc,

behaviour change, reducing the demand for

travel by individual commuters, or shifting

towards less energy-intensive modes of travel

(Vanderschuren et al 2008). Behavioural

change objectives are being pursued through

the various public transport upgrading and

travel demand management strategies being

implemented in South African cities (DOT

2007). What complicates these efforts is the

extent to which energy concerns are inter-

woven with many other social and economic

goals, from urban restructuring and poverty

relief to industrial development. There is

thus increasing interest in understanding

the drivers of energy use, and their linkages

with other urban processes. Local empirical

studies of transport energy consumption

have tended to focus at the city or provincial

level (e.g. Cooper 2007; SEA 2003; Maré

& Van Zyl 1992), typically using aggregate

fuel sales data. Goyns (2008) analysed fuel

consumption and emissions in Johannesburg

for a sample of instrumented vehicles under

various vehicle, driving and traffic condi-

tions, but could not link it to demographic

or land use variables. Goyns’s work showed

that, as travel demand and conditions vary at

a fine grain across space and time, patterns of

transport energy consumption vary consider-

ably at the intra-metropolitan level. A greater

understanding is needed of the relationships

between transport energy consumption and

the socio-economic, land use, and transport

supply characteristics in cities before the

energy and sustainability impacts of urban

management policies can be predicted; and

before effective policies and interventions can

be fashioned that are aimed specifically at

addressing energy concerns.

With that in mind, the paper aims to

answer the following questions:

■ Can detailed and disaggregate informa-

tion on transport energy use be derived

from available travel survey data?

■ Which socio-economic and land use

variables significantly influence energy

consumption in personal transport?

Estimating car ownership and transport energy consumption: a disaggregate study in Nelson Mandela Bay

C J Venter, S O Mohammed

This paper investigates energy consumption patterns by households and individuals during travel on a typical day. A methodology is developed to estimate trip-by-trip energy consumption using standard 24-hour travel survey data, and applied to the Nelson Mandela Metropolitan Area using their 2004 household travel survey. Baseline energy consumption patterns by different modes, times of day, and user groups are established. Across the population, energy use is very skewed: 20% of people consume about 80% of transport energy, mainly due to the disproportional contribution of car use to energy expenditure. We then estimate a disaggregate vehicle ownership model and link it to a model of household transport energy consumption to explore the underlying socio-economic and land use variables driving energy consumption. Land use factors (especially job accessibility) significantly affect energy use, but do so differently for low and for high-income households, suggesting that accessibility-enhancing land use and transport measures could have unintended consequences for overall energy and environmental management.

Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 3

■ How do these variables affect household

car ownership and transport energy use?

■ What are the implications for urban

policy and management?

The data is taken from the Nelson Mandela

Metropolitan Area Travel Survey (NMMM

2004) conducted in 2004, supplemented by

transport supply data. The study is restricted

to personal surface transport modes and

excludes freight and commercial transport.

The focus is furthermore on the end-user

consumption of energy only, in terms of the

marginal amount of fuel (in the case of road

transport) or electricity (in the case of rail)

consumed by a traveller during each trip.

Full accounting of energy use could include

the energy used in the construction of infra-

structure and the manufacture of vehicles,

but such life-cycle assessments (e.g. Chester

& Horvath 2008) fall outside the scope of

this paper.

The following section provides a brief

introduction to previous work on the rela-

tionships between transport energy, land use,

and travel behaviour, followed by a descrip-

tion of the research design and methodology

used. The final sections describe the results

of the analysis, including two disaggregate

models estimated on car ownership and

energy use. Lastly, conclusions are drawn as

to the meaning of the findings for strategies

to reduce or manage energy use in the pas-

senger transport sector.

TRANSPORT ENERGY

CONSUMPTION, LAND USE

AND TRAVEL BEHAVIOUR

The links between land use, travel

behaviour and energy consumption

Relationships between land use and energy

use have been studied widely internation-

ally. The earliest studies focused on urban

density. In perhaps the most well-known

(although not uncontested) work, Newman

and Kenworthy (1989) measured per capita

petroleum consumption and population

densities in a number of large cities around

the world, and found a clear negative

relationship between the two. Car usage

was lower and provision of public transport

higher in the cities with the highest densities.

Others have argued that the transport policy

environment accompanying higher densities

– including parking management and fuel

pricing – often contribute as much to the

achievement of high public transport shares

as density per se (e.g. Gomez-Ibanez 1991).

In recent years a significant body of

research has emerged around the links

between land use and travel behaviour. Travel

behaviour – the amounts, types, lengths and

modes of travel undertaken by trip-makers

with various characteristics – is important

as an intermediate factor determining the

amount of energy consumed during travel.

The range of land use variables examined

has also broadened from aggregate density

towards more microscopic factors reflecting

the quality of the urban environment, includ-

ing neighbourhood safety, attractiveness

for walking and bicycling, block sizes and

mixed land uses (e.g. Crane & Crepeau 1998;

Zegras 2010). The general conclusion has

been that land use variables account for some

variation in travel patterns, but that socio-

economic characteristics and preferences

are at least as important in determining the

desire and opportunity for travel (e.g. Ewing

& Cervero 2001; Banister 2005). Among the

most important socio-economic variables

identified were car ownership and employ-

ment – travel patterns and distances tend to

change significantly once a household owns a

motor vehicle.

Models of vehicle ownership

Vehicle ownership models, central to the

analysis of transport energy consumption,

have a long history. Mokonyama and Venter

(2007) provide a brief overview of modelling

approaches used in South Africa, and discuss

the limitations of conventional ownership

models using time-series or income variables

only (e.g. Sweet 1988). In short, significant

evidence exists of the benefits of using pric-

ing, land use and demographic factors to

help explain vehicle ownership. Disaggregate

choice models of the kind used in this paper

are ideally suited to this task, provided the

data is available at the household or indi-

vidual level. One local application has been

found of a logit model used to investigate

the choice between petrol and diesel vehicles

(Naude 2002), but the model did not go so

far as to examine the initial vehicle purchase

decision.

Methodologies for studying land

use / transport energy relationships

Studies of the effects of urban form on vehi-

cle usage and energy consumption can be

divided into aggregate and disaggregate stud-

ies. Aggregate studies use spatially defined

averages for all variables, with observations

usually at the city or metropolitan level.

Besides the work by Newman and Kenworthy

(1989), recent applications of this approach

include comparisons of transport energy

consumption across cities in developed and

developing countries (Daimon et al 2007).

A major problem with cross-sectional

aggregate approaches is the difficulty in

controlling for cultural, political, historical

and economic differences. Handy (1996)

reviewed many studies, and concluded that

aggregate studies are generally not capable of

uncovering true relationships between land

form measures and travel.

Disaggregate studies, on the other

hand, use household observations of

vehicle usage and city-wide, zonal or

neighbourhood averages for urban form

variables. These allow energy use for

transport to be compared to characteristics

of the household and the residential area

(e.g. Golob & Brownstone 2005; Lindsey

et al 2011). For example, Naess et al (1995)

used data collected from 321 households

in 30 residential areas in Greater Oslo to

investigate variations in travel distances,

modal splits and energy use, and found that

residents of high-density, centrally located

communities travel considerably shorter

distances and use considerably less energy

per capita than those who live in low-density,

outer areas. A similar approach is applied in

this paper to the Nelson Mandela Bay area.

RESEARCH DESIGN

Background and study area

The study area is the Nelson Mandela

Metropolitan Area located in the Eastern

Cape Province. It has a population of

approximately 1.5 million and a land area of

1 845 square kilometres (NMMM 2004). The

metropolitan boundary includes the city of

Port Elizabeth, its surrounding low-income

residential areas, and the nearby towns of

Despatch and Uitenhage. Thirty-four per

cent of households have access to one or

more cars, very similar to the average of 36%

for other metropolitan areas in South Africa

(DOT 2005). Nelson Mandela Bay is fairly

well served by public transport. Minibus

taxis transport about 20% of daily trips,

while the Algoa Bus Company, the sole bus

operator in the area, serves about 6% of all

trips on a fairly extensive bus route network

connecting outlying areas with the Port

Elizabeth (CBD) Central Business District

(NMMM 2005). A single commuter rail line

connects the CBD with Uitenhage, but trans-

ports less than 1% of trips. The overall split

between public and private modes is 40:60

(excluding walking).

Although the modal mix and mode

shares in Nelson Mandela Bay are typical of

metropolitan areas in South Africa, it has

some unique topographical features. These

include the coastline which directs growth

towards the north and north-west, and the

Swartkops River to the north of the metro,

both of which might lead to longer travel

distances than in other comparable-sized

metros.


Travel survey data

In 2004, the Nelson Mandela Metropolitan

Municipality undertook a travel survey to

determine travel demand characteristics in

the area. A total of 2 828 randomly chosen

households (10 200 individuals) were included

in the survey. The survey included a 24-hour

weekday travel diary. As one of the first travel

surveys in South Africa that extended beyond

peak periods it offered much more complete

travel data than traditional survey sources.

Data on standard vehicle ownership and

demographics was also collected.

To estimate energy consumed for trans-

port, the data on trip distances and public

transport occupancies was obtained from

secondary sources. Trip distances were

extracted from a zonal distance matrix

based on shortest route road distances

between zone centroids. Public transport

occupancy figures were obtained from the

municipality’s Current Public Transport

Record (CPTR), which recorded bus and taxi

occupancies by route and time of day.

Land use data and

accessibility measures

The land use intensity variables that we used

included population density and a job acces-

sibility index. The population density per

residence zone was derived from the 2001

national census data.

The accessibility of a household in a par-

ticular zone is generally defined as the ease

of reaching opportunities in the surrounding

area, and is affected both by the location of

the household relative to potential destina-

tions, and the quality of the transport system

available. In order to test our hypothesis that

the amount of transport energy consumed

is affected by the level of accessibility a

household enjoys, we constructed an acces-

sibility index for each home zone. A standard

gravity-based measure was used (El-Geneidy

& Levinson 2007), defined as follows:

Ai = ∑dj ∙ f(wij)

∑dj

(1)

where:

Ai = accessibility index of zone i to

opportunities;

dj = the amount of job opportunities

available at zone j;

f(wij) = an impedance function expressing

the increasing difficulty of travel-

ling between i and j as the distance

increases;

wij = the road distance between zones i

and j.

We used a locally calibrated impedance func-

tion of f(wij) = e–0.15wij obtained from the trip

distribution model of the NMMM strategic

transport model; it thus reflects the actual

sensitivity of trip makers in the area to travel

distance, averaged over trip purpose and

income levels (NMMM 2004). Two assump-

tions are that access to jobs reflects the level

of access to other opportunities (including

shopping, social, and business opportunities);

and that road distance as a proxy for travel

friction captures the main effect of interest,

even though it ignores congestion.

Estimating transport

energy consumption

The transport energy estimation process

requires determining the energy intensity

for each individual trip made. Studies have

shown that fuel consumption per vehicle-

kilometre depends on many factors, inclu ding

vehicle engine size, fuel type, traffic condi-

tions, environmental conditions and driving

style (Goyns 2008; Wong 2000). We used

average fuel consumption figures for passen-

ger vehicles and for minibuses as suggested

by Schutte and Pienaar (1997), and averaged

across petrol and diesel vehicles according

to the number of each fuel type registered in

the Nelson Mandela Metropolitan Area. The

figures for passenger vehicles accord with

fuel consumption rates measured by Wong

(2000) in coastal regions of South Africa.

Sivanandan and Rakha (2003) showed that

energy intensity estimates based on an aver-

age composite vehicle tend to produce con-

clusions that are consistent with the explicit

modelling of the various vehicle types.

The average fuel consumption estimates

for buses were obtained from the Algoa Bus

Company. A summary of the final fuel inten-

sity figures (in litres per 100 veh-km) used for

each mode in the survey is given in Table 1.

The fuel consumption for each trip made

by each individual interviewed during the

survey was calculated as:

l/person-trip = km × l/veh-km

vehicle occupancy (2)

where:

l/person-trip = fuel consumption

km = distance

l/veh-km = fuel consumption intensity

Trip distances were estimated from the

shortest-path route between the origin

and destination of each trip. Equation (2)

is applicable to all modes of travel, except

for passenger rail. Rail transport in Nelson

Mandela Metropolitan Area uses electric

power. In order to convert the electric

power consumption to the same unit as the

other modes, the energy consumption and

maximum occupancy figures (for 9 M com-

muter rail trains) suggested by Del Mistro &

Aucamp (2000) were used, namely 10.3 MJ/

coach-km and 255 passengers respectively.

The average occupancy per coach, based on

100% occupancy in peak direction and 20%

in the opposite direction, is taken as 60%.

Thus the energy consumption per rail pas-

senger trip was calculated as:

MJ/person-trip)

= km × Mj/coach-km

60% × maximum occupancy per coach (3)

where:

MJ/person-trip = energy consumption

km = distance

Mj/coach-km = energy consumption

intensity

Results from Equation (2) were converted to

Megajoules (MJ) to enable comparison across

different modes using a conversion factor of

36.7 MJ/litre of fuel. The final step was the

summation of the energy consumption by

trip according to the levels of analysis.

Modelling disaggregate energy

consumption: analytical issues

When attempting to model the relationship

between transport energy consumption and

household, individual or spatial explanatory

Table 1 Fuel consumption and energy intensity rates used to estimate energy consumption

Mode usedFuel consumption

(litres/100 veh-km)Energy intensity

(Megajoules/100veh-km)

Walk 0 0

Bicycle 0 0

Motor cycle 2.8 102.8

Bakkie taxi 12.3 451.4

Minibus taxi 14.0 513.8

Commuter rail --- 10.3 (MJ per couch-km)

Bus 47.5 1 833.5

Motor vehicle 10.8 396.4

Note: See text for data sources


variables, one is confronted with a number of

analytical problems. The first relates to the

problem of self-selection bias. This kind of

problem occurs when cross-sectional data is

used to assess how land use variables, such

as density or accessibility, influence people’s

travel behaviour (see Mokhtarian & Cao 2008)

or travel energy consumption. Self-selection

refers to the fact that households are not ran-

domly distributed across space: households

who prefer (or are unable) to own a car may

choose to locate in an area that provides

opportunities for walking and public trans-

port use. If statistical analysis then identifies a

correlation between being located in an acces-

sible neighbourhood and high use of public

transport, it is not clear that this behaviour

can be attributed to the neighbourhood

features rather than to preference variables.

In other words, causality is unclear. Methods

exist for dealing with problems of simultane-

ity (see for instance Mokhtarian & Cao 2008),

but these require more advanced research

designs involving control groups that are not

available for this study. We do not correct for

self-selection bias here. The results, therefore,

must be interpreted with caution: we can, at

best, infer association between land use and

energy consumption, rather than causality.

A second problem relates to endogene-

ity, in this case with respect to the effect of

unobserved taste variations on car ownership

and energy use. We expect (and will later

prove) that income (and the values and life-

style choices normally associated with a cer-

tain income level) strongly affects the deci-

sion to buy a motor vehicle. The same values

and preferences also affect the amount of

travel undertaken (and therefore the amount

of energy consumed). For statistical reasons

we cannot specify a single regression model

of transport energy consumption containing

the household’s number of motor vehicles as

an independent variable, as this variable may

be correlated with the unobserved values and

preferences (and thus with the regression

model’s error term). Instead we develop an

instrumental variable, the predicted number

of cars in a household, and use this predicted

value rather than the observed number of

cars owned as the explanatory variable in the

regression model (see Zegras 2010).

What the need for an instrumental

variable implies is that a separate model of

household car ownership choice must first

be estimated on the data set, before energy

consumption can be modelled. We therefore

specify a multinomial logit (MNL) model to

capture the household decision of whether

to own zero, one, or two or more vehicles, as

a function of demographic and spatial vari-

ables. Apart from its usefulness in supplying

the instrumental variable for the energy

use model, the MNL model also provides

additional insight into the factors affecting

a household’s decision of whether or not to

buy a car.

A third problem relates to the use of the

energy consumption metric as a dependent

variable, as the variable is calculated across

all persons and households in the sample,

and therefore includes many zero observa-

tions. In fact, the data shows that 34% of

individuals consumed no energy during

travel, as their trips consisted exclusively of

walking or bicycle trips on the survey day.

The data is thus left-censored, with many

observations clustered at zero, and can

not be modelled using a simple linear OLS

model for continuous dependent variables.

This would produce biased and inconsist-

ent parameter estimates (Washington et al

2003). The solution is to use a Tobit model

(a model formulation developed specifically

to deal with such cases), and estimated

Maximum Likelihood methods. The Tobit

model is encountered in the travel behaviour

literature in the analysis of travel expendi-

ture data, which is frequently left-censored

when no money is spent on transport (e.g.

Thakuriah & Liao 2005). The paper does not

elaborate on the specification or estimation

of the Tobit model; suffice to say that Tobit

model results and test statistics can be inter-

preted in the same way as those of ordinary

least squares models.

ENERGY CONSUMPTION

PATTERNS ACROSS SUB-

GROUPS OF THE POPULATION

We look firstly at patterns of daily transport

energy consumption by aggregating our

trip-level energy consumption estimates by

mode used, by time of day, and by zone. We

then aggregate across demographic charac-

teristics, such as gender and occupation, in

order to examine intergroup differences in

energy use.

Transport energy use by

mode and time of day

Figure 1 plots the distribution of daily

transport energy consumption per person.

It is clearly a very skew distribution, with

about 34% of individuals in the sample using

no fuel, and 83% consuming less than 40 MJ

per day to travel (40 MJ is approximately the

energy consumed during one 10-kilometre

long car trip made by a single occupant). The

cumulative distribution in Figure 1 shows

Figure 1 Daily and cumulative daily energy consumption by persons in the sample

(unweighted, n = 7 000 persons)

500

450

400

350

300

250

200

150

100

50

0

MJ

pe

r p

ers

on

pe

r d

ay

Cu

mu

lati

ve %

of

tota

l d

ail

y e

ne

rgy

con

sum

pti

on

100

90

80

70

60

50

40

30

20

10

0

Percentage of individuals

0 20 40 60 80 100

Daily transport energy consumption Cumulative transport energy consumption


that 80% of residents in Nelson Mandela Bay

contribute only 22% to the overall energy bill,

with the remaining 20% of people consuming

78% of the total.

The reason for this skewness is apparent

from Table 2, which shows the distribution

of trips by mode in the sample. Almost half

of all trips are made on foot or on bicycles.

The car is used in a quarter of person-trips,

but these trips consume three to five times

the amount of energy as trips by motorcycle,

minibus taxi or bus. This is due to the car’s

low occupancy rather than to long trip

distances; mean car trip lengths are similar

to trip lengths by taxi, and less than trip

lengths by bus and train. Surprisingly, the

mean energy consumption per bus trip

is about 50% higher than that per trip in

a minibus taxi. Two reasons account for

this: buses have an energy intensity that is

more than three times higher than that of

minibuses (Table 1); and bus passengers tend

to make longer trips than taxi passengers.

When controlling for trip distance, however,

the energy consumed per bus passenger on a

per-kilometre basis is about equal to that of a

minibus taxi passenger. The higher carrying

capacity of buses offsets their higher energy

intensity, but perhaps not to the extent

expected. Trains are by far the most efficient

mode due to their high passenger capacities.

When comparing transport energy con-

sumption across different times of the day,

marked differences are observed. As shown in

Table 3, average energy use of trips made dur-

ing peak hours is 60% higher than that of trips

made during the rest of the day. Both occu-

pancies and trip distances vary depending on

the time of the day. Table 2 shows that only

buses are significantly fuller during the peaks

than during the off-peaks; minibus taxis have

about the same average occupancy through-

out the day, while private cars actually have

lower occupancy during peaks – an indication

that the car trip to work tends to be predomi-

nantly single-occupancy. Furthermore, mean

trip distances are higher during the peak than

the off-peak (Tables 2 and 3), contributing

further to peak period energy use.

Spatial patterns of

transport energy use

Figure 2 shows the zonal average household

transport energy consumption, plotted

on the transport analysis zones used by

NMMM. The figure indicates how demo-

graphic, spatial and transport supply factors

interact to determine energy consumption

patterns in the study area. High transport

energy consumption is recorded in outlying

areas towards the north (around Coega) and

south, but these are in fact sparsely popu-

lated areas of low significance. Low income

residential areas that are well-served by pub-

lic transport, such as Motherwell, iBhayi and

Kwanobuhle, have relatively low transport

energy consumption; so do the Despatch and

Uitenhage areas which are close to the rail

line and to local factory jobs. Higher-income

areas such as Bluewater Bay, Summerstrand

and the PE central suburbs are located closer

to the Port Elizabeth CBD, but have higher

energy consumption – this despite having

relatively good taxi and bus coverage. The

metro’s unique topography may also contrib-

ute to higher energy consumption across the

river to the north, from where residents have

longer travel distances to access major work

nodes to the south.

Table 2 Comparison of transport energy use by travel mode

Mode of travelNumber of

person-trips observed

Percentage of trips

Mean energy use

(MJ/person-trip)

Average occupancy(persons/vehicle)

Average trip distance (km/trip)

Time of day Time of day

Off-peak Peak Off-peak Peak

Non-motorised 9 785 46.1 0.0 1.00 1.00 1.8 1.9

Motor cycle 50 0.2 5.6 1.03 1.00 5.9 4.7

Motor vehicle 5 333 25.1 25.8 2.02 1.95 8.3 10.2

Minibus taxi 4 751 22.4 4.8 9.30 9.43 8.0 9.5

Bakkie taxi 89 0.4 11.1 4.67 4.87 12.9 10.9

Bus 1 120 5.3 7.1 32.94 44.38 12.3 14.6

Train 57 0.3 1.7 51.0a 255.0a 32.0 23.8

Other 45 0.2 8.9 2.80 2.81 5.9 7.0

Notes: Sources: Mean energy use estimated. Average occupancy of motor vehicle trips as reported in survey. Average occupancy of public transport trips obtained from Current Public Transport Record, 2004. a = Train occupancies based on national averages. Average occupancy shown per coach.

Table 3 Comparisons of transport energy use by time of day

Period Mean energy use (MJ/person-trip) Mean trip distance (km/trip)

Peak period 9.7 6.9

Off-peak period 6.0 5.2

All trips in sample 8.1 6.1

Notes: Peak period is defined as 6:00-9:00 and 15:00-18:00. Off-peak period is all the other hours of the day

Figure 2 Estimated average daily household transport energy consumed (MJ), shown per

transport analysis zone

Uitenhage

KwaNobuhle Despatch

Ibhayi

Motherwell

Coega

PE Central

Summerstrand

Bus routeRail routeTaxi route

Average Transport Energy (MJ/HH)

0–5050–100100–250>250N/A

0 3.75 7.5 15 kilometres


TRANSPORT ENERGY USE BY

GENDER AND EMPLOYMENT STATUS

To examine patterns of transport energy use

across segments of the population, trip-level

consumption figures are aggregated for

each individual and grouped by gender and

employment status (see Table 4). Gender is

considered here as it relates to the different

roles played by men and women in society,

and has frequently been found to account for

significantly different travel patterns across a

population (e.g. Turner & Fouracre 1995). In

this sample, the mean energy consumption

by male travellers is significantly higher than

that of women. Men make slightly fewer trips

per day than women, but, on average, travel

longer distances. This is consistent with

previous findings indicating that, compared

to men, women tend to make more non-work

trips, and tend to visit destinations closer to

the home (e.g. Venter et al 2007). Men also

tend to use cars more: 28% of all trips by

men are made by car, compared to 22% for

women.

A similar grouping by occupation type

shows the importance of employment status

as a predictor of transport energy consump-

tion. People who are employed and travel to

work consume 47 MJ during travel per day,

compared to 14 MJ for unemployed people

or homemakers, and 9 MJ for students and

scholars. Thus giving one unemployed

person a job would tend to increase their

transport energy use more than three-fold,

everything else being equal, as employment

is associated with both longer travel dis-

tances and more frequent use of the car. The

strength and nature of the income effect on

energy consumption is examined further in

the following section.

DISAGGREGATE RELATIONSHIPS

BETWEEN LAND USE,

DEMOGRAPHICS AND TRANSPORT

ENERGY CONSUMPTION

The objective here is to assess to what extent

energy use during travel is affected by a

household or individual’s own characteristics

(such as income and gender), by zone-level

land use characteristics (such as density), and

by zone-level accessibility to surrounding

opportunities. Some of the variables were

already examined in the previous section,

but we now include them in a multivariate

model to assess the relative strength of

each in explaining variations in energy use.

Theory suggests that higher incomes are

associated with higher energy use, as both

car ownership and travel activity tend to

increase as incomes grow. Higher densities

are associated with lower energy use, all else

being equal, because opportunities for walk-

ing and reducing trip lengths grow as more

activities are available close to home. The

influence of accessibility is unpredictable;

being located in more accessible areas close

to the city centre might lead to reduced trip

lengths and thus reduced energy require-

ments, but it might equally lead to increased

trip making as the opportunities for interac-

tion improve.

As explained earlier, we first estimate a

model of household vehicle ownership choice

to examine the factors driving the decision

to purchase a vehicle, and to supply an

instrumental variable of predicted car own-

ership that can be used in the subsequent

energy use models.

Household vehicle ownership choice

A multinomial logit (MNL) model of vehicle

ownership choice was estimated, using a

category-dependent variable with three

potential outcomes, namely zero cars (the

base case), one car, or two and more cars

in a household. Household characteristics

tested as explanatory variables included

the monthly household income reported by

respondents, the number of workers in the

household, and household size, which was

interacted with income to test the possibil-

ity that household size has a differential

effect on vehicle ownership depending on

socio-economic status. All correlations

among explanatory variables are below 0.5,

indicating sufficient independence. Zonal

population density and job accessibility

index variables were included as land use

descriptors.

Table 5 shows the parameter estimates

and the t-values for each coefficient, as well as

the goodness-of-fit statistics. Almost all coef-

ficients are significant, and the adjusted rho-

squared value of 0.31 is good for disaggregate

Table 4 Comparisons of transport energy use and travel, by gender and occupation

GroupMean energy use (MJ/person/day)

Mean number of trips (trips/person/day)

Mean daily travel distance

(km/person/day)

Gender

Female 20.8 3.1 18.0

Male 28.9 2.9 19.3

Employment status

Working outside home 46.9 3.3 27.8

Not working outside home 13.8 3.3 14.7

Scholars and students 8.8 2.7 11.8

All individuals in sample 24.7 3.0 18.6

Notes: ‘Working outside home’ includes part and full-time workers. ‘Not working outside home’ includes people working from home, home-makers, unemployed, retired.

Table 5 Estimation results: Multinomial logit model of vehicle ownership choice

Variables0 vehicles

(base)

1 vehicle 2+ vehicles

Beta T-value Beta T-value

Household characteristics

No of workers 0.353 4.69** 0.703 6.79**

HH income (R’000s) 0.149 5.67** 0.264 9.57**

HH size (low incomea) –0.138 –3.92** –0.146 –2.50**

HH size (high incomea) 0.001 0.025 –0.047 –0.86

Zone characteristics

Population densityb –0.148 –9.183** –0.366 –11.945**

Job access indexc 6.847 4.476** 6.720 3.491**

Constants –1.003 –5.87** –1.898 –7.72**

Number of observations 1 648 534 411

Likelihood ratio test (full model)Chi-squared =

1 475**

Adjusted rho-squared 0.314

** = Significant at 95%a = Low-income households are below the median income of R2 500 per month; high-income is aboveb = Population density of household zone (in 1 000 persons per square kilometre) c = Accessibility index by road to job opportunities (see text for explanation)


choice models. Household income and the

number of workers show a positive and strong

relationship to vehicle ownership – this can

be expected and agrees with evidence from

previous studies. Household size has an

interesting differential effect on the likelihood

of buying a car, depending on the income. For

low-income households, an increasing house-

hold size is associated with a lower likelihood

of buying a car, even controlling for the level

of income itself. Increasing household sizes

indicate the presence of either more children

or dependent elderly people in the family, who

represent a competing claim on household

resources, leaving less for the purchase and

maintenance of a vehicle. Amongst high-

income households, however, the number of

people in the household has no statistically

significant relationship with the number of

vehicles – evidently, once incomes are high

enough, children’s impact on household

resources is not significant enough to affect

vehicle purchase decisions.

The density of people in a household’s

neighbourhood has a negative association

with the likelihood of buying a vehicle, as

was expected. This strong relationship is,

however, not necessarily an indication that

land use by itself influences car owner-

ship – the problem of self-selection bias

described above prevents us from drawing

any conclusions regarding causality. A look

at population density figures for NMMA

confirms that the highest density zones are

found in lower income townships like Ibhayi

and Motherwell. It is likely, therefore, that

households who cannot afford to buy a vehi-

cle locate in higher density residential areas

for a host of reasons, including historical or

community ties, housing affordability, and,

perhaps, the nearby location of social and

educational opportunities.

The accessibility index, as a measure of

relative location on a metro-wide scale, is

significant and positive. The more accessible

a home is via the road network, the more

likely the household is to own one or more

vehicles. The implication is, once again, not

necessarily one of causality. The result might

as well be an outcome of historic settlement

patterns typical to the South African city:

higher income households have historically

had the opportunity to locate in more cen-

tral, more accessible places with good road

networks, and are also more likely to afford

and own more vehicles. It is important to

note that there is at this stage no evidence

that city-scale accessibility patterns influ-

ence vehicle ownership decisions – a more

detailed investigation, controlling for socio-

economic variables and preferably using

time-series data, is needed to examine such

a question.

Household transport

energy consumption

Table 6 presents the results of a Tobit model

of transport energy consumption estimated

at the household level, and using household

characteristics and spatial properties of the

household’s home zone as independent vari-

ables. Household income is omitted from the

model due to its high correlation with the

expected vehicle ownership variable.

Parameter estimates are largely signifi-

cant and of the expected sign, and the model

performs well according to the likelihood

ratio test. The positive signs of the household

variables indicate that, all else being equal,

households consume more transport energy

if they have more workers or more people

in the household overall. More workers

mean more work trips – which we already

showed tend to be energy intensive – while

bigger households make more trips overall.

Expected vehicle ownership dwarfs all

other variables in the model (looking at the

t-values), confirming that this is the single

most important driver of household trans-

port energy use (Goyns 2008).

The land use variables show interesting

results. Population density of the home zone

is insignificant: by itself it does not explain

household transport energy consumption.

Read in conjunction with the previous

model’s results, this implies that the density

effect is indirect rather than direct: lower

density is associated with higher car owner-

ship, thus indirectly affecting travel patterns

via mode use; but once the car is bought,

lower population density is not associated

with more trip-making. This is consistent

with the findings of Mirrilees (1993) that

factors such as the distribution and distances

between different land uses, the location of

services with respect to one another, and

vehicle ownership play a larger role in trans-

port energy demand than urban density.

The estimates for the job accessibility

variables show that, indeed, a household’s

location relative to job (and by implication

other opportunities in the surrounding

metro area) does affect the amount of

transport energy consumed, even after

controlling for vehicle ownership. The effect

differs, however, across households. In order

to account for a potential accessibility/

income relationship suggested by the MNL

model, the accessibility index was interacted

with a household income dummy which

categorised the household as either below

or above the median income level for the

area. The parameter estimates show that a

household’s accessibility significantly affects

Table 6 Estimation results: Tobit models of transport energy consumption

VariablesHousehold model Individual model

Beta T-value Beta T-value

Household characteristics

No of workers

HH size

Expected vehicles owneda

15.181

2.865

104.54

6.45**

3.19**

20.83** 38.32 27.7**

Individual characteristics

Gender (1 = male)

Age

Employed (1 = employed)

Studying (1 = scholar/student)

3.605

0.593

31.07

–10.48

2.67**

10.41**

16.68**

–4.17**

Zone characteristics

Population densityb 0.964 1.67 –0.066 –0.33

Job access indexc

Low-income HHd

High-income HHd

–31.304

–263.73

–0.55

–4.06**

97.68

–0.186

4.53**

–1.09

Constants –34.971 –5.92** –44.02 –12.80**

Number of observations 2 593 7 000

Number (%) of zero observations 363 (14%) 2 380 (34%)

Likelihood ratio test (full model)Chi-squared =

1 201**Chi-squared =

3 039**

** = significant at 95%Dependent variable = Megajoules of transport energy consumed per day (per individual/household)Empty cells denote variable not used in modela = Estimated as 0*P(0) + 1*P(1) + 2.3*P(2+), where the values of P(n), the probability of owning n vehicles (calculated from the MNL model estimated above), and the value 2.3 is the mean number of vehicles owned by all households in the sample who own two or more vehicles.b = Population density of household zone (in 1 000 persons per square kilometre) c = Accessibility index by road to job opportunities (see text for explanation)d = Low-income households are below the median income of R2 500 per month; high-income is above


transport energy consumption only if the

household is high-income: richer households

tend to consume less transport energy if

they live in more accessible places. This

suggests that, once a vehicle is available,

households benefit from being located in

more central, accessible places by gaining

the ability to reduce their travel distances

and, by extension, their transport energy

consumption. Low-income households do

not gain this benefit from being located in

accessible places (as indicated by the non-

significant parameter estimate). The reason

is probably that low-income households are

more likely to have low transport energy

consumption levels anyway – being more

likely to walk or use public transport – so

that any additional gains in travel distances

do not impact energy expenditures

significantly.

Individual transport energy

consumption

The results of the transport energy con-

sumption model estimated at the individual

level indicate similar findings (see Table 6).

Once again, expected household car owner-

ship is the strongest predictor of energy use.

Personal characteristics also explain energy

use: all else being equal, being male, being

older, and being employed raises a person’s

energy expenditure, while being a student or

scholar reduces energy use (relative to being

unemployed). These findings are consistent

with the results of the bivariate analyses

presented earlier.

Population density is again non-signifi-

cant. However, the interacted access index

variable reverses its significance and sign:

persons living in low-income households

are now more likely to have higher energy

expenditures, while no effect is found among

high-income persons. What this might

indicate is that accessibility is associated

with increased travel activity among lower-

income people, as one might expect if there

was significant latent or suppressed demand

for travel among low-income persons, which

is released once travel becomes easier or less

expensive due to improved accessibility. This

interpretation matches the general finding

regarding the differential benefits of acces-

sibility suggested by the previous model:

that accessibility plays a different role for

different people, depending on their socio-

economic status and the extent of mobility

they already enjoy. Among high-income (car

owning) people, higher levels of access are

associated with travel activity savings and

a reduction in energy use; among lower-

income people, higher access is associated

with increased motorised travel and higher

energy expenditures.

CONCLUSIONS: IMPLICATIONS

FOR URBAN MANAGEMENT

Methodologically the study demonstrated

the feasibility of using travel survey data to

establish disaggregate patterns of transport

energy consumption at the individual, house-

hold or neighbourhood levels. This provides

opportunities for using existing travel data

sources for establishing baseline data to moni-

tor impacts and changes over time. Marginal

methodological improvements might come

from improved data collection (especially the

inclusion of vehicle size and fuel type data in

questionnaires), and marrying travel route

information with more accurate link-level

speed information to improve the accuracy of

vehicle energy consumption estimates.

Our results clearly showed how skewed

energy expenditure is across the population.

Car users, although they make only 25% of

trips, contribute 70% of the passenger trans-

port energy consumption in metropolitan

Nelson Mandela Bay. The strong influence

of car ownership and income level on energy

consumption is a common finding globally.

From the urban policy perspective this high-

lights the challenges inherent in addressing

urban sustainability issues. If the objective

were simply to reduce transport energy use,

the largest pay-off would come from reduc-

ing private vehicle use through, for instance,

the pricing of low-occupancy car travel.

However, energy reduction goals are traded

off against other policy objectives such as job

creation. Workers spend three times more

energy travelling daily than the unemployed;

should residential and work locations remain

fixed, employment gains will result in sig-

nificant increases in South Africa’s energy

needs, unless a significant proportion of

such travel can be shifted to non-motorised

modes or to rail.

What might transport interventions do to

energy consumption? Compared to the dif-

ference between cars and non-car modes, the

difference in energy use between road-based

public transport modes is relatively small.

So is the average difference between peak

and off-peak travel (although this difference

might be larger in cities with higher conges-

tion levels than NMMM). More specifically,

on a per-passenger-kilometre basis, the

energy consumption of minibus taxi trips is

similar to that of bus trips, due to the high

energy efficiency of small vehicles and the

relatively low occupancy of metropolitan

bus services. This suggests that – in energy

terms – little can be gained from travel

demand management (TDM) strategies such

as peak spreading, or from public transport

interventions such as bus rapid transit (BRT),

unless they are coupled with appreciable

increases in bus occupancy, introduction of

more fuel efficient vehicles, significant speed

gains by avoiding congestion, and a signifi-

cant amount of switching from car (rather

than taxi) to BRT. The predominant focus of

first-generation BRT schemes on replacing

minibus-taxi services is likely to do little for

energy and environmental concerns unless

they delay the car purchase decision among

medium-income future car owners. This is a

challenging proposition given the sensitivity

of car ownership to income growth.

A significant element of the urban sustain-

ability agenda is concerned with changing

the density and form of land use in cities.

Our findings suggest that such efforts will

have a variety of impacts on travel behaviour,

energy consumption and sustainability – and

not all of it in a desirable direction. High

neighbourhood densities are correlated with

lower car ownership (and thus with reduced

transport energy use), but the data does not

allow us to establish causality – in other

words to conclude that densification strategies

would necessarily lead to better sustainability

outcomes. Further research using time-series

data (perhaps using repeated panel surveys) is

needed to allow researchers to tease out the

effects of density (and other land use factors)

from other historic and taste-based variables.

Metropolitan-wide accessibility – the

ease of reaching job (and other) opportuni-

ties within a reasonable travel time – does

seem to affect travel behaviour and transport

energy consumption. An important finding

is that this relationship appears to depend on

the socio-economic status of a household or

individual. Among high-income households,

better accessibility is associated with lower

travel. It is likely that access-enhancing strat-

egies, such as those promoting mixed-use

developments in accessible, centrally located

nodes, would reduce driving distances and

the energy and environmental costs of travel.

However, the same accessibility improve-

ments could have the opposite effect on

lower-income (non-driving) households, as

the time or cost savings brought about by

the access improvements could be converted

into increased travel, releasing some of the

pent-up demand for mobility. This is where

coordination between land use and transport

is key: attractive, upgraded public transport

should then be available to capture this

additional demand in energy-efficient ways.

Otherwise, uncoordinated land use measures

could have unintended consequences and

contribute to deteriorating sustainability

outcomes in our cities.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the

help of the Nelson Mandela Metropolitan


Municipality in providing access to the data.

Findings and conclusions are not necessarily

those of the Municipality.

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Chile. Urban Studies, 1–25.


INTRODUCTION

The PSSDB system is a lightweight compos-

ite load-bearing structural system consisting

of profiled steel sheet (PSS) and dry board

(DB). They are attached by self-drilling and

self-tapping screws, as illustrated in Figure 1.

The system was developed by Wright et al

(1989) as a flooring system with many advan-

tages (Wan Badaruzzaman & Wright 1998).

It can be applied in domestic buildings, office

buildings or during renovation (Wright et al

1989) for various structural purposes such as

floors, roofs and walls (Ahmed et al 2000).

According to some researchers on the

static behaviour of the PSSDB system, the

screw spacing has a significant effect on the

stiffness of the system, as a panel with lower

screw spacing is stiffer than a panel with

higher screw spacing (Wan Badaruzzaman et

al 2003; Ahmed et al 1996; Ahmed & Wan

Badaruzzaman 2006). This stiffness has a direct

effect on the natural frequencies of the system.

Soedel (2004) stated that knowledge of

the frequency of a structure is crucial for two

reasons: firstly, from a design point of view,

for example prediction about the occurrence

of resonance conditions on the structure;

and secondly, measurement of natural fre-

quency is needed to obtain forced response

of the structure.

TECHNICAL PAPER



DR FARHAD ABBAS GANDOMKAR obtained his BEng

in Civil Engineering from Shahid Chamran University

of Ahvaz in 1996, his MSc in Structural Engineering

from Isfahan University of Technology in 1999, and his

PhD in Structural Engineering from Universiti

Kebangsaan Malaysia in 2012. He has been a full-time

lecturer at the Ahvaz branch of the Islamic Azad

University, Iran, since 1999 and is a member of the Khouzestan Construction

Engineering Disciplinary Organization. He has more than 13 years’ experience

in teaching, training, research, publication and administration.

Contact details:

Department of Civil & Structural Engineering

Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia

43600 Bangi, Selangor, Malaysia

T: 00603 8925 5760/1492, F: 00603 8925 5703,


PROF WAN HAMIDON WAN BADARUZZAMAN

obtained his PhD in Structural Engineering from the

University of Wales, Cardiff , UK, in 1994. He is Professor

of Structural Engineering at the National University of

Malaysia, where he began his career almost 30 years

ago. His research interest focuses on the profi led steel

sheeting dry board (PSSDB) system, a lightweight

composite structural system that he has developed

over the years. He has published many papers related to research fi ndings on

this patented and award-winning construction system.

Contact details:




T: 00603 8925 5760/1492, F: 00603 8925 5703


PROF SITI AMINAH OSMAN is Associate Professor in

Civil and Structural Engineering, and is a member of

the Board of Engineers Malaysia. She graduated

from Universiti Teknologi Malaysia in 1992 with a

BEng (Hons), MSc in Structural Engineering from the

University of Bradford, UK (1995) and a PhD in Civil

and Structural Engineering from Universiti

Kebangsaan Malaysia (2006). After her undergraduate studies, she started

lecturing at Universiti Kebagsaan Malaysia. Her interests are structural

engineering, wind engineering and industrial building system construction.

Contact details:




T: 00603 8921 6221, F: 00603 8921 6147


PROF AMIRUDDIN ISMAIL obtained his BEng in Civil

Engineering from the University of Pittsburgh, USA, in

1983, his MSc in Transportation and Urban Systems from

the University of Pittsburgh in 1984, and his PhD in

Transportation Engineering from Universiti Kebangsaan

Malaysia in 2002. He is currently Professor in Civil &

Structural Engineering at Universiti Kebangsaan Malaysia, and has more than

25 years’ experience in teaching, training, research, publication and

administration.

Contact details:




T: 00603 8921 6203, F: 00603 8921 6147


Keywords: natural frequency, profi led steel sheet dry board, frequency response

function, low and high frequency fl oors, human comfort

Experimental and numerical investigation of the natural frequencies of the composite profi led steel sheet dry board (PSSDB) system

F A Gandomkar, W H Wan Badaruzzaman, S A Osman, A Ismail

This paper investigates the natural frequencies of the profiled steel sheet dry board (PSSDB) system. Frequency response functions (FRFs), estimated experimentally, were used to determine the natural frequencies of three different PSSDB panels with different screw spacing. Finite element models (FEMs) were developed to predict the natural frequencies of the tested panels. The FEMs were verified by comparing their results with results of the experimental test, and these confirmed the natural frequencies of the system. The effect of screw spacing on the natural frequencies of the system was studied experimentally and numerically. The numerical results uncovered the effect of various parameters, such as the PSS and DB thicknesses and boundary conditions, on the fundamental natural frequency (FNF) of the system. Fifteen finite element models were developed to determine the FNF of the PSSDB system with practical dimensions. When applied as a flooring system these panels are categorised as low-frequency floor (LFF) or high-frequency floor (HFF), to determine occurrence of resonance, design criteria, and whether or not they would be comfortable for humans.

Figure 1 Profiled steel sheet dry board system

Self-drilling and self-tapping screw

Dryboard

Profiled steel sheet

SS/2


Table 1 Characteristics of the experimental samples

Name of sampleScrew spacing

(mm)

Characteristics of samples

PSS DB Screw

PSSDB100 100

Peva45(t = 0.8 mm)

Plywood(18 mm)

DS-FH 432 self-drilling and

self-tappingPSSDB200 200

PSSDB300 300

Figure 3 Placing of selected points in plan to determine FRFs of PSSDB100, PSSDB200 systems

Point1

Point2

Point3

Point4

Point5

Point6

Point7

Point8

Point9

Point10

Point11

200 mm 200200200200200200200200200200200

Many reports and studies are available

to show that the FNF of a floor system is

the most important value to determine its

serviceability for human activities. In this

case Wiss & Parmelee (1974) presented a

response rating formula, Murray (1981)

proposed a formula for the critical damping

ratio, Ellingwood & Talin (1984) predicted

the maximum acceleration of a floor mid-

span, Ebrahimpour & Sack (2005) presented

literature on the critical FNF for wood and

lightweight construction, and Murray et al

(1997) proposed a design criteria graph with

respect to the peak acceleration and FNF of a

floor system.

Over a number of decades studies have

been performed on the dynamic character-

istics of the structural system, focusing on

natural frequencies. Hurst & Lezotte (1970)

conducted an analytical and experimental

study on the natural frequency of the

plywood-joist system, considering the effect

of joist size on the results. In their study ply-

wood was nailed to joists. In the same study,

Filiatrault et al (1990) revealed the natural

frequency and mode shapes of a plywood-

joist system for different boundary conditions

by the finite strip method, which, when

compared, agreed well with experimental

test results. They also discussed the effects of

different parameters on the natural frequency

of the system. Fukuwa et al (1996) evaluated

dynamic properties of a prefabricated steel

building by obtaining the natural frequency

and damping ratio of the system for various

construction stages. Effects of non-structural

members on the results were investigated

in their study. El-Dardiry et al (2002) deter-

mined the natural frequency of a long-span

flat concrete floor by using a suitable FEM

and an experimental heel-drop test. They

considered several FEMs and refined them

by comparing their results with experimental

test results, and then presenting the most

suitable FEM. Ferreira & Fasshauer (2007)

performed a free vibration study on a com-

posite plate by an innovative numerical meth-

od. Results of different thickness-to-length

ratios were determined and discussed in

their study. Ju et al (2008) developed a new

composite floor system, and measured the

natural frequencies and damping ratios of

the system by experimental testing for three

different construction stages: steel erection

stage, concrete casting stage, and finishing

stage. They compared the results with inter-

national codes to evaluate the serviceability

of the proposed floor system and obtained

good vibration characteristics. Xing & Liu

(2009) derived successfully the natural modes

of a rectangular orthotropic plate by exact

solution of mathematical statements for three

different boundary conditions. Two studies

were carried out on the modal analysis of an

orthotropic composite floor slab with profiled

steel deck (De A Mello et al 2008) and a pre-

and post-impacted nano-composite laminates

system (Velmurugan 2011). Both studies were

performed to find dynamic characteristics of

composite floor systems, similar to the study

by Bayat et al (2011) to determine the vibra-

tion frequencies of tapered beams. Honda &

Narita (2012) presented an analytical method

to determine the natural frequencies and

vibration modes of laminated plates having

such cantilever reinforcing fibres.

Figure 2 The PSSDB system with 200 mm

screw spacing during test

Figure 4 Placing of selected points in plan to determine FRFs of PSSDB300 system

Point1

Point2

Point3

Point4

Point5

Point6

Point7

300 mm 300300 300 300 300 300 300

Figure 5 (a) Bruel & Kjaer portable and multi-channel PULSE analyser type 3560D (b) ENDEVCO

uniaxial accelerometer type 751-100 (c) Impact hammer type 2302-10

(a) (b) (c)


Study of the natural frequency of the

PSSDB system is limited to an experimental

study done by Wright et al (1989) to identify

the FNF of the system, considering PMF100

as the PSS and chipboard as the DB. It was

reported that, since the PSSDB system is

slender and flexible by nature, its FNF may

be low. Vibration of such floors during

human activities may therefore be perceiv-

able. It has also been stated that floors with

FNFs lower than approximately 7 Hz are

considered uncomfortable for users (Wright

1989). In addition, Gandomkar et al (2011)

determined the natural frequencies of the

PSSDB system experimentally and numeri-

cally with in-filled concrete in the trough

of the PSS. They also evaluated the effect of

various parameters on the FNF of the men-

tioned system.

There is little energy in high frequency

floors (of approximately 10 Hz) (Middleton

& Brownjohn 2010). A floor is an HFF if it

has an FNF above 10 Hz, but it is known

as an LFF if it is dominated by resonance

from the first four harmonics of a walking

force. Ljunggren et al (2007) stated that

some researchers suggested two different

design criteria for floors: deflection criteria

for HFF and an acceleration limit for LFF.

However, Murray et al (1997) recommended

acceleration limits for LFF and HFF, and a

minimum static stiffness of 1 kN/mm under

concentrated load as an additional check for

HFF. Therefore, knowing the FNF of a floor

system will determine the design of the floor

and whether it should be an LFF or HFF

floor, and hence its level of comfort.

Using non-structural systems, such as

partitions, on a completed floor has an effect

on the damping value of the floor system

(De Silva & Thambiratnam 2009). Knowing

the damping ratio of a bare floor system can

therefore help designers to select a realistic

damping ratio for the dynamic analysis of

the system.

This paper presents natural frequencies

of the PSSDB system, focusing on three

main goals. The first goal is to estimate the

natural frequencies and damping ratios of

the system through experimental study by

considering the effect of different screw

spacing. The natural frequencies and

damping ratios will be used to verify finite

element models (FEMs) and determine

the dynamic response of the system under

human walking load respectively. The

second goal is to develop FEMs to identify

the natural frequencies of various configu-

rations of the PSSDB systems. The third

goal is to determine the effect of various

selected parameters, such as the PSS and

DB thicknesses, and also different bound-

ary conditions, on the FNF of the system

through verified FEMs. The FNFs of panels

with practical dimensions are investigated

for different boundary conditions; then the

panels are categorised as LFF or HFF sys-

tems, which will determine how comfort-

able the panels would be for users.

EXPERIMENTAL DETAILS

In the PSSDB system, the value of partial

interaction between the PSS and DB is

influenced by the screw spacing. The study

of the effect of partial interaction between

the PSS and the DB on the FNF of the PSSDB

system is carried out by experimental tests

to meet the first goal of this paper. For

this purpose, three different samples were

prepared to measure the natural frequencies

and damping ratios of the studied systems

with 100 mm, 200 mm, and 300 mm screw

spacing. The characteristics of the samples

are presented in Table 1.

The length and width of all samples were

selected as 2 400 mm and 795 mm respec-

tively. Figure 2 shows the PSSDB system with

screw spacing of 200 mm during the test.

Natural frequencies of the samples were

measured by estimating their FRFs, as shown

in Figures 3 and 4. Eleven points were select-

ed for the determination of the FNFs of the

PSSDB100 and PSSDB200 samples (Figure

3). In these samples the accelerometer was

fixed very close to Point 10 (Figure 3). In

addition, for sample PSSDB300, seven points

were considered, as illustrated in Figure 4,

and the accelerometer was fixed near Point 6

(Figure 4).

The excitation and response signals

of the studied systems were recorded and

measured. Bruel & Kjaer portable, and

multi-channel PULSE analyser type 3560D

ENDEVCO accelerometers type 751-100,

and impact hammer type 2302-10 were used

as the measuring devices (Figure 5), as well

as the Bruel & Kjaer Pulse LabShop as mea-

surement software. Damping ratios of the

systems were also outcomes of these tests.

STRUCTURAL MODEL

The structural model of the samples is

depicted in Figure 6.

According to Murray et al (1997), the

dynamic modulus of elasticity for steel can

be chosen similar to its static value (BS

5950 Part 4:1994), i.e. 210 GPa. Stalnaker

& Harris (1999) stated that plywood is

nearly isotropic because of its manufacturing

process. Also, Ahmed (1999) declared that,

although dry boards may be found to be

isotropic or orthotropic by nature, they can

easily be modelled as isotropic plates with

very good results. Based on the study carried

out by Narayanamurti et al in Hu (2008),

Matsumoto & Tsutsumi (1968), and Bos &

Bos Casagrande (2003), the dynamic Young’s

modulus of plywood was found to be higher

than its static value. In this study, the static

modulus of elasticity of plywood, available

in the local market, is adopted as 7 164 MPa

(Yean 2006), considering an isotropic sheet-

ing, while the dynamic value is chosen 10%

greater than the static value according to Bos

& Bos Casagrande (2003).

The density of Peva45 and plywood has

been chosen as 7 850 kg/m3 and 600 kg/m3

respectively.

In the PSSDB system, the stiffness of the

screws which is obtained by experimental

push-out tests (Ahmed 1999; Akhand 2001;

Nordin et al 2009) is directly used as input

data for the FEMs (Nordin et al 2009). A

study was performed to identify the connec-

tion stiffness between Peva45-Cemboard,

Cemboard-Timber, and Peva45-Plywood by

push-out tests. Also, the shear connection

stiffness between Peva45 and plywood for

Figure 6 Structural model of the PSSDB100, PSSDB200 and PSSDB300: (a) Longitudinal section (b) Transverse section

(a) (b)

PlywoodPeva45

Screw

Pin support Roller support

Y = 0 Y = 2 400 mm

75 mm75 mm X = 0Peva45

X = 795 mm

Plywood

DS-FH432 screw


the same configuration was found to be

610 N/mm (Nordin et al 2009), which is the

same as in this paper.

COMPUTATIONAL MODEL

To cover the second goal of this paper, three

FEMs were developed to obtain natural

frequencies of the PSSDB100, PSSDB200,

and PSSDB300 systems. The FEMs are

implemented using ANSYS finite element

computer program (ANSYS 2007).

Two methods were used to evaluate the

natural frequencies of the systems. The “Block

Lanczos” and “QR damped” methods were

utilised to extract undamped and damped

natural frequencies of panels respectively.

In the FEMs, the PSS and DB were assigned

by element of SHELL281 (Figure 7) as it is

suitable for analysing thin to moderately thick

shell structures (ANSYS 2007). It comprises

an 8-noded element having six degrees of

freedom at each node: translation in and rota-

tion about the x-, y- and z-axes. In addition,

the screws were represented by an element

of COMBIN14 (Figure 8) as the connection

between Peva45 and plywood. COMBIN14

possesses longitudinal or torsional capability

in 1-D, 2-D or 3-D applications (ANSYS 2007).

The longitudinal spring-damper option is a

uniaxial tension-compression element having

up to three degrees of freedom at each node:

translation in the nodal x-, y- and z-directions.

No bending or torsion is considered. The

spring-damper element has no mass. Mass

can be added by using the appropriate mass

element. The spring or the damping capability

may be removed from the element (ANSYS

2007). In this paper, the capability of damping

was removed (Cv = 0) from the element.

Figure 9 illustrates the procedure of

modelling Peva45 and plywood in a simula-

tion for one bay of the studied system. The

connection between elements of Peva45 and

plywood in the simulation is performed by

using spring element (COMBIN14) in three

directions (X, Y, and Z). In this case, and

according to Figure 9, the nodes D2 and D10

were respectively connected to the nodes P2

and P10 in which stiffness of springs were

adopted as 610 N/mm (Nordin et al 2009) in

X and Y directions, and as 105 N/mm in Z

(vertical) direction (see Figure 9).

OBSERVATION OF RESULTS

AND COMPARISON

Results are presented in two parts – experi-

mental and finite element simulation. Then

the experimental and finite element results

are compared to present the accuracy of

the FEMs.

Experimental results

The FRFs of studied systems are shown in

Figure 10 and according to the figure the

first six natural frequencies (NFs) of the

systems are presented in Table 2. Damping

ratios (DRs) corresponding to the NFs of the

systems are also summarised in Table 2.

The status of the natural frequency in

Table 2 was missing for the mode number 5

while the natural frequency of this mode was

available in its FEM (Table 3). The reason for

this absence has been revealed by evaluation

of its mode shape. This mode was in the

transverse direction of accelerations that

were measured. Therefore, the mode did not

appear in the experiments.

According to earlier studies, the

PSSDB100 is stiffer than PSSDB200, and

Figure 7 SHELL281 (ANSYS 2008)

MN

K

OP

I

J

L

2

6

3

1

4

5

8

4

5

1

2

6

7

3

Z0

X0

Y0

Figure 8 COMBIN14 (ANSYS 2008)

J

K

I

Cv

X

Y

Z

Figure 9 (a) One bay PSSDB structural system (b) Positioning of nodes in elements of one bay PSSDB system

P1 P2 P3

P4 P5

P6

P7 P8

P9 P10 P11

D1 D2 D3 D6 D9 D10 D11

(a) (b)

Plywood

Peva45

Figure 10 Experimental estimation of FRF between excitation at point A and response at point B for (a) PSSDB100 (b) PSSDB200 (c) PSSDB300

0.8

FR

F [

(m/s

2)/

N]

0.6

0.4

0.2

0

(a) (b) (c)

1008060400 20

Frequency (Hz)

0.8

FR

F [

(m/s

2)/

N]

0.6

0.4

0.2

01008060400 20

Frequency (Hz)

0.8

FR

F [

(m/s

2)/

N]

0.6

0.4

0.2

01008060400 20

Frequency (Hz)

Note: The points A (Point 6 in Figure 3 and Point 4 in Figure 4) and B were selected in y = 1 200 and y = 2 200 mm (Figure 6(a)) respectively, along the length and middle

point of width for both points


the latter is stiffer than PSSDB300 due to

the number of screws. On the other hand,

the mass of the PSSDB100, PSSDB200 and

PSSDB300 is almost the same. As a result

it can be predicted that the FNF of the

PSSDB100 should be greater than that of

PSSDB200, and the latter greater than that of

PSSDB300. This issue was verified by results

of the experimental test. Table 2 shows that

the partial interaction between two main

elements of the PSSDB system had an effect

on the natural frequencies of the systems,

as the FNF of the system increased by 3.55%

and 11.24% respectively for changing the

screw spacing from 300 mm to 200 mm, and

300 mm to 100 mm. However, reduction

of the screw spacing decreases the damp-

ing of the system. The FNFs of the studied

panels were measured by the test well above

10 Hz. Therefore all panels fell in the HFF

category (Middleton & Brownjohn 2010) and

were also comfortable for users (Wright et

al 1989).

Finite element results

The experimentally observed FRFs of the

systems presented their damped natural

frequencies. Therefore, in the simulation,

damped natural frequencies of the systems

were determined by the QR damped method

via the ANSYS finite element package. In

the QR damped method, damping of the

system is introduced by the Rayleigh damp-

ing approach (see more detail in Clough &

Penzien 1993). According to Chowhury &

Dasgupta (2003), only the first few modes

of a structure with large degrees of freedom

(around three at minimum and about 25

at maximum) contribute to the dynamic

response of a structure. In this study, the

first six modes are assumed to be significant

in the dynamic behaviour of the system.

Then the Rayleigh damping coefficients were

determined (Chowhury & Dasgupta 2003)

and used in the simulation.

Three finite element models were devel-

oped to identify the natural frequencies of

the PSSDB100, PSSDB200 and PSSDB300

systems. The first six undamped and damped

natural frequencies of the studied systems

are summarised in Table 3.

According to simulation results, the

FNF of the PSSDB100 was greater than the

PSSDB200, and the latter was greater than

PSSDB300. This point is also confirmed by

the experimental results. Table 3 shows small

differences between undamped and damped

natural frequencies of the systems. The

results also show that the undamped natural

frequencies of all systems were greater

than their corresponding damped natural

frequencies. Caughey & O’Kelly (1961) stated

that, in a system with classical normal

modes, the damped natural frequencies

are always less than or equal to their cor-

responding undamped natural frequencies.

Piersol et al (2010) mentioned that generally

classical normal modes exist in a structure

without damping or with particular types

of damping. According to the results of this

study, the measured damping can be consid-

ered as particular damping for each system;

therefore they can be used in the dynamic

analysis of the bare PSSDB systems with dif-

ferent screw spacing.

Comparison of experimental

and finite element results

As stated, the FRFs of the systems present

their damped natural frequencies. However,

undamped and damped natural frequencies

of the studied systems were calculated very

close to one another by the numerical meth-

od. Nevertheless, damped natural frequen-

cies of the systems which were determined

by FEM are compared with their damped

natural frequencies that have been evaluated

by the tests in order to reveal more accurate

errors. The errors of numerical results are

calculated by Eq (1) and presented in Table 4.

Error (%) = T4Ci

= [test value – finite element value]

test value × 100

= [T2Ci – T3Ci]

T2Ci × 100, i = a, b, c (1)

where:

T2Ci: column i = a, b, c of Table 2



Table 2 First six experimental natural frequencies and damping ratios of studied systems

Mode No

PSSDB100 PSSDB200 PSSDB300

NF (Hz)(a) DR (%) NF (Hz)(b) DR (%) NF (Hz)(c) DR (%)

1 18.8 1.230 17.50 1.400 16.9 3.140

2 23.1 1.500 21.3 1.890 21.9 0.984

3 46.9 0.732 46.3 0.840 41.9 0.959

4 55.0 0.936 55.6 0.994 52.5 0.914

5 64.4 0.511 Missing – 62.5 0.767

6 81.3 0.43 67.5 0.884 68.8 1.06

Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T2Ca, T2Cb & T2Cc in the following. T2Ca means Table 2 Column a.

Table 3 First six numerical undamped and damped natural frequencies of the studied systems

Mode No

PSSDB100 PSSDB200 PSSDB300

Undamped Damped(a) Undamped Damped(b) Undamped Damped(c)

1 18.072 (Hz) 18.070 (Hz) 17.563 17.561 17.410 17.402

2 23.207 23.206 22.026 22.024 22.303 22.295

3 46.790 46.788 44.851 44.848 44.481 44.465

4 60.053 60.049 57.233 57.228 57.303 57.276

5 62.887 62.882 57.278 57.273 58.639 58.611

6 76.707 76.700 69.880 69.873 74.025 73.978

Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T3Ca, T3Cb & T3Cc in the following.

Table 4 Error of numerical method in the studied systems (%)

Mode No PSSDB100(a) PSSDB200(b) PSSDB300(c)

1 3.88 0.35 2.97

2 0.46 3.40 1.80

3 0.24 3.13 6.12

4 9.18 2.93 9.10

5 2.36 – 6.22

6 5.66 3.52 7.53

Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T4Ca, T4Cb & T4Cc in the following.


The mentioned errors show that the FEMs

can predict the natural frequencies of the

PSSDB system with accuracy. Therefore,

performed convergence studies on the finite

element models and selected elements of

the models which were combinations of the

SHELL281 and COMBIN14 elements were

suitable for the purpose of the study. The

difference between the experimental and

FEM results may be due to reasons such as:

■ Finite element method is a numerical

approximate method.

■ Imperfections of the PSS, DB and screws

in the test specimens were not captured

in the FEMs.

PARAMETRIC STUDY

A series of parametric studies based on

the FEMs for the PSSDB200 system were

performed to show the effect of different

conditions on the FNF of the system. The

PSSDB system with a length of 2 400 mm

and a width of 795 mm was chosen as the

control sample, adopting 0.8 mm thick

Peva45 as PSS, 18 mm thick plywood as DB,

DS-FH 432 self-drilling and self-tapping

screws at 200 mm screw spacing as the

connectors, and pin support at Y = 0 and

roller support at Y = 2 400 mm both at the

bottom flange of the PSS (Figure 6(a)). A

series of studies were performed to uncover

the FNF of the PSSDB panels with practical

dimensions. Their categorisation and level of

comfort were also revealed. All supports in

these studies were considered at the bottom

flange of the PSS. Only in one case supports

were assumed at the bottom, top and web of

the PSS (see Figure 12).

Effect of thicknesses of Peva45

and plywood

The thickness of the considered Peva45 is

0.8 mm and 1.0 mm, whilst the thickness

of the plywood is 9.252, 12.7, 18, 23 and

25 mm. Both products are available on the

local market. The effect of the thicknesses

of Peva45 and plywood on the FNF of the

system is presented in Table 5. The percent-

age difference between the FNF of the con-

trol sample and the FNF of the panel with

other thicknesses for Peva45 and plywood

are also presented in Table 5.

According to the results, increasing

the thicknesses of the Peva45 and the

plywood enhanced and decreased the FNF

of the system respectively. By enhancing

the thickness of the Peva45 from 0.8 mm

to 1.0 mm, and the thickness of the

plywood from 9.252 mm to 25 mm the FNF

increased and decreased by an average value

of 4.91% and 18.56% respectively. It can

therefore be seen that the obtained results

are a manifestation of the effect of the mass

and stiffness of Peva45 and plywood on the

FNF of the system. The highest value of the

FNF occurred for the maximum thickness

of Peva45 and minimum thickness of

plywood (20.677 Hz), whilst the lowest

value of the FNF occurred for the minimum

thickness of Peva45 and maximum

thickness of plywood (16.566 Hz).

Therefore, by changing the thickness of

main elements the FNF can be increased by

a maximum value of 24.82%. The minimum

value of the FNF of the studied system

showed well above 10 Hz. The studied

system was therefore in the HFF category

and also comfortable for occupants.

Effect of boundary conditions

The effect of boundary conditions on the

FNF of the system was taken into account

in three situations: effect of sliding and

rotation at the end supports perpendicular

to the strong direction of the PSS (sliding

parallel with Y direction of the plan, Figure

11); effect of locating support under the top

flange and web of the PSS at two ends of

the length (Figure 12); and effect of adding

support parallel with the strong direction of

the PSS (parallel with Y direction of the plan,

Figure 13).

Table 6 FNF of the PSSDB system under different types of end supports perpendicular to the

strong direction of the PSS

Type of support P-R P-P P-F R-F F-F

FNF (Hz) 17.569 23.126 23.214 17.802 23.304

PI (%) 0 31.63 32.13 1.33 32.64

Figure 11 Various end support conditions perpendicular to the strong direction of the PSS

YX Y = 0

R P F F F

P P P R F

Y = 2 400 mm

Table 5 Effect of thickness of Peva45 and plywood on the FNF of PSSDB system

Peva45

Plywood

t = 9.252 mm t = 12.7 mm t = 18 mm t = 23 mm t = 25 mm

FNF (Hz) PD (%) FNF PD FNF PD FNF PD FNF PD

t = 0.8 mm 19.935 13.42 18.826 7.12 17.569 0 16.787 –4.41 16.566 –5.64

t = 1.0 mm 20.677 17.62 19.665 11.88 18.480 5.16 17.710 0.82 17.486 –0.44

PD = Percentage of difference compared with control sample

Figure 12 Illustration of supports under top and bottom flanges and web of the PSS

Top flange Web Bottom flange


Effect of sliding and rotation

of supports

The effect of sliding and rotation at the

end supports perpendicular to the strong

direction of the PSS (X direction, Figure

11) on the FNF of the system is investigated

for various support conditions, as shown in

Figure 11. These involve (i) pin (P) and roller

(R) (control sample), (ii) P-P, (iii) P-F (fixed),

(iv) R-F and (v) F-F end supports.

The FNF results for these conditions are

presented in Table 6. The percentages of the

increase (PI) in the FNF of the various mod-

els over the control sample are also shown in

Table 6.

The results show that if sliding is con-

strained parallel with the strong direction

of the PSS (P-R support converted into

P-P support), then the FNF is increased

significantly. Chao & Chern (2000) and Jalali

(2012) affirmed this observation. On the

other hand, changing a pin support to a fixed

support (P-F instead of P-P, and F-F instead

of P-P) did not show a considerable effect on

the FNF value. Therefore, the control of rota-

tion at the bottom flange of the PSS at the

end support did not significantly affect the

FNF of the system.

Effect of adding support under

top flange and web of PSS

The supports for the control sample were

only considered under the bottom flange

(Case 1) of the PSS. Table 7 shows the FNF

and PI in the FNF for various models over

the control sample of the system if additional

supports are provided at both the top and

bottom flanges of the PSS (Case 2), and at

the top and bottom flanges and the web

(Figure 12) of the PSS (Case 3).

When comparing the results of Cases 1

and 2, it is clear that the FNF of the system

is enhanced significantly if supports are

added at the top and bottom flanges of the

PSS. Also, by comparing the results of Cases

2 and 3, it is demonstrated that additional

supports at the web do not have any signifi-

cant effects on the FNF of the system. This

may be because adding support on the top

flange already prevents rotation of the PSS,

so adding more support on the web does not

make a big difference. By keeping the above-

mentioned three cases in mind, designers

can decide on the shape of supports (beams)

which can be used under the PSS of the

PSSDB floor system to reduce its natural

frequencies.

Effect of adding support parallel

with longitudinal side edges

The supports of the longitudinal side edges

(support in X = 0 and 795 mm parallel with

Y direction of the plan as in Figures 6(b) and

13) for the control sample were considered

free (unconstrained). Various additional sup-

port conditions studied at the longitudinal

side edges are shown in Figure 13. Table 8

shows the FNF and PI in the FNF for various

models in the control sample.

As shown in Table 8, when only one of

the longitudinal side edges was supported

(leaving one side edge free), as in the R-Fr

and P-Fr cases, the FNF increased slightly. It

can be seen that restraining sliding perpen-

dicular to the strong direction of the PSS (X

direction of the plan) would not change the

FNF of the system much (2.8% = 10.59%–

7.79%) if only one of the longitudinal side

edges were supported. However, the increase

in FNF was much more significant, based on

restraining both longitudinal side edges as

in the R-R, P-R and P-P cases. The control of

sliding perpendicular to the strong direction

of the PSS shows a pronounced effect on

increasing the FNF of the system (20.57% =

103.87%–83.30%), where both longitudinal

side edges of the panel were supported (P-P

instead of R-R).

FNF of panels with practical

dimensions

Peva45 is available on the local market in

widths of 795 mm and maximum lengths of

15 m. Also, the maximum length and width

of plywood is 2 400 mm and 1 200 mm

respectively. Therefore, to prepare bigger

practical panels, some pieces of Peva45 and

plywood should be used together. Fifteen

panels in four different lengths of 1 200 mm,

2 400 mm, 3 600 mm and 4 800 mm involv-

ing one, two, three and four repeating sec-

tions of the system were developed, which

were combinations of elements similar to the

control sample, verified by experiments, as

shown in Figure 6(b) and Figures 14–16. In

all fifteen panels, the length and width of all

pieces of plywood were chosen as 2 400 mm

and 795 mm respectively. Also, the length of

Peva45 was used as the length of the panels.

The connection between two adjacent

side-by-side panels (detail A) was represented

Table 7 Effect of adding supports under top flange and web of the PSS on the FNF

Support condition

P-R support in bottom flange only (Case 1)

P-R support in bottom and top flanges (Case 2)

P-R support in bottom and top flanges and web of PSS (Case 3)

FNF (Hz) 17.569 (Hz) 26.256 26.332

PI (%) 0 49.44 49.88

Table 8 Effect of adding supports parallel to the strong direction of the PSS on the FNF

Support condition Fr-Fr R-Fr P-Fr R-R P-R P-P

FNF (Hz) 17.569 (Hz) 18.938 19.430 32.204 33.403 35.818

PI (%) 0 7.79 10.59 83.30 90.12 103.87

Figure 13 Different support conditions parallel to the strong direction of the PSS

Y

X Y = 0

P P

Y = 2 400 mm

P P P P

R R R R R R

Fr Fr R Fr P Fr R R P R P P

Figure 14 The PSSDB panel with two repeating sections

771.5 mm

1 545 mm

Detail A


by a typical lap joint idea as shown in Figure

17. Wright & Evans (1987) presented the

connectivity characteristics of such a joint.

As can be seen in Figure 17, nodes i(2) and

j(2) are connected to node i(3) and node j(3)

respectively, assuming complete freedom in

the longitudinal and rotational directions,

whilst assumed to have complete connection

in the vertical and lateral directions (Wright

& Evans 1987). It should be noted that con-

nections between i(1) and j(1) respectively

to i(2) and j(2) (Peva45 to plywood) are

represented by results of the study by Nordin

et al (2009).

The joint does not exist perpendicularly

to the strong direction. Figure 18 shows the

connection between plywood and Peva45

according to their dimensions.

Table 9 shows the characteristics and the

FNF of the developed panels with practi-

cal dimensions. The categorisation (LFF

or HFF) and level of comfort of the panels

are also undertaken. All panels had pin-

roller supports perpendicular to the strong

direction of the PSS and free-free supports

parallel with the strong direction of the PSS

(Model 0).

The width of the panels with only end

supports perpendicular to the strong direc-

tion of the PSS did not significantly affect

the FNF of the system, as the panels with

the same length and widths of 795 mm,

1 545 mm, 2 295 mm and 3 045 mm had

close values in terms of the FNF. The reason

for this was the enhancement of the stiffness

and mass by increasing the width. However,

Figure 18 Connection between plywood and Peva45 along the panel

Figure 15 The PSSDB panel with three repeating sections

2 295 mm

Detail A

771.5 mm 748 mm

Figure 16 The PSSDB panel with four repeating sections

771.5 mm

Detail A

748 mm

3 045 mm

Figure 17 Detail A: (a) Constructional model (b) Analytical model

(a) (b)

Plywood Plywood Plywood Plywood

Screws

Peva45 Peva45

i(1) j(1)

i(2) j(2)

i(3) j(3)


Table 10 FNF and status of the LFF panels under different models of boundary conditions

Name of Model

Model I Model II Model III

FNF (Hz)Status

FNF (Hz)Status

FNF (Hz)Status

(a) (b) (a) (b) (a) (b)

1PP3LL 24.723 HFF Ok 27.876 HFF Ok 29.425 HFF Ok



2PP4LL 6.8417 LFF Failed 7.1381 LFF Ok 8.1045 LFF Ok

3PP3LL 8.9882 LFF Ok 9.1947 LFF Ok 11.584 HFF Ok

3PP4LL 5.5847 LFF Failed 5.7750 LFF Failed 6.9614 LFF Failed

4PP3LL 8.5472 LFF Ok 8.6555 LFF Ok 11.177 HFF Ok

4PP4LL 5.1182 LFF Failed 5.2264 LFF Failed 6.5480 LFF Failed

(a) Categorisation of the system as LFF or HFF (Middleton & Brownjohn 2010)(b) Level of comfort of the panels for occupants (Wright 1989)

the FNF of the 3 045 mm wide panel was

a bit greater than the FRF of the 2 295 mm

wide panel, etc. This may be due to the

increased stiffness of the panels when using

lap joints in the panels, with two pieces of

Peva45 (one-lap joint), three pieces of Peva45

(two-lap joints), and four pieces of Peva45

(three-lap joints), compared to panels with

one piece of Peva45 without a lap joint

(795 mm wide).

It is obvious that the length of the system

has a direct effect on the FNF of the system.

The results showed that the FNF of a PSSDB

system with a length of more than 3 600 mm

and widths of 795 mm, 1 545 mm, 2 295 mm

and 3 045 mm fell in the LFF category. Also,

panels that were 3 600 mm and 4 800 mm

long, with any widths, were respectively

shown to be comfortable and uncomfortable

for users.

An increase in the FNF of a floor system

(less resonance) is required for user comfort.

If panels are supported on all sides, the FNF

of the system will be higher. This can be

used to increase the FNF (stiffness) of the

panels via boundary conditions. Depending

on the control of sliding at supports, roller or

pin supports can be used on all sides. In this

case, all panels with lengths of 3 600 mm

and 4 800 mm were selected in order to

increase their FNFs through three boundary

conditions as shown in Figure 19. Table 10

summarises the increased FNFs of the panels

corresponding to these boundary conditions

(models I, II, and III). It also illustrates the

level of comfort of the studied panels.

The PI in the FNF of the selected panels

are listed in Table 11 by comparing the FNFs

of the panels under boundary conditions

of models I, II, and III with the FNFs of

the panels under boundary conditions of

model 0.

Table 11 shows that control of sliding

parallel with the strong direction of the PSS

in the multi-panel systems had a significant

Table 9 Characteristics, the FNF, and evaluation of the developed PSSDB models (Model 0)

Name of Model Length (mm) Width (mm) FNF (Hz) (b) (c)

1PP1LL 1 200 795 49.581 HFF Ok

1PP2LL(a) 2 400 795 17.569 HFF Ok

1PP3LL 3 600 795 7.8663 LFF Ok

1PP4LL 4 800 795 4.4606 LFF Failed

2PP1LL 1 200 1 545 52.678 HFF Ok

2PP2LL 2 400 1 545 17.755 HFF Ok

2PP3LL 3 600 1 545 7.9337 LFF Ok

2PP4LL 4 800 1 545 4.4958 LFF Failed

3PP1LL 1 200 2 295 52.733 HFF Ok

3PP2LL 2 400 2 295 17.824 HFF Ok

3PP3LL 3 600 2 295 7.9578 LFF Ok

3PP4LL 4 800 2 295 4.5081 LFF Failed

4PP1LL 1 200 3 045 52.753 HFF Ok

4PP2LL 2 400 3 045 17.859 HFF Ok

4PP3LL 3 600 3 045 7.9700 LFF Ok

4PP4LL 4 800 3 045 4.5143 LFF Failed

(a) Control sample(b) Categorisation of the system as LFF or HFF (Middleton &Brownjohn 2010)(c) Level of comfort of the panels for occupants (Wright 1989)

Figure 19 Model of boundary conditions for increasing the FNF of LFF panels

P

R

R R

X

Y

R

PX

Y

P P

P

P P

X

Y

Model I Model II Model III

P


effect on the FNF of the system. However,

control of sliding perpendicular to the strong

direction of the PSS considerably affected the

FNF of the 795 mm wide panel and did not

have a significant effect on the FNF of the

panels wider than 795 mm. Even by using the

model III boundary condition (pin supports

in all sides), the panels that were 4 800 mm

long, with widths of 1 545 mm, 2 295 mm

and 3 045 mm were still in the category of

LFF. Also, panels with a length of 4 800 mm

and widths of 2 295 mm and 3 045 mm were

not comfortable for users.

CONCLUSIONS

This paper reveals experimentally and numer-

ically the natural frequencies of the PSSDB

system, considering the effect of the level of

interaction between the PSS and the DB. It

is shown that the PSSDB system with lower

screw spacing has higher FNF. The damping

ratio of the PSSDB system is inversely related

to the stiffness of the system, as the damping

ratio of the PSSDB with lower screw spacing

is greater than the system with higher screw

spacing. A series of parametric studies reveal

the effects of different parameters on the FNF

of the system. It is proved that the FNF of

the PSSDB system is significantly influenced

by (i) screw spacing or level of interaction

between the PSS and DB, (ii) thicknesses of

the PSS and DB, (iii) control of sliding along

the strong direction of the PSS, (iv) using sup-

port under both the top and bottom flanges

of the PSS, and (v) the number of side edges

being supported. On the other hand, the FNFs

are not much affected by (i) control of sliding

along the weak direction of the PSS at the side

edge supports, (ii) rotations at all end and side

edge supports, and (iii) the support conditions

under the web of the PSS. Identification of the

FNF of the panels with practical dimensions

with end supports only shows that the FNF of

the panels with the same length and different

widths are very close to one another. However,

a small difference may occur by increasing the

thickness of Peva45 in the location of the lap

joint. It is proved that a significant increase

in the FNF of the PSSDB floor system with

practical dimensions is possible via boundary

conditions.

ACKNOWLEDGEMENTS

The authors would like to acknowledge

the Mechanical Engineering Department

of Universiti Kebangsaan Malaysia for

granting permission to conduct the experi-

mental tests. The authors also express their

gratitude to Mr Alireza Bahrami and Dr

Mohammad Hosseini Fouladi for their con-

tributions to some parts of this study.

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TECHNICAL PAPER



NICOLE NEL received her BSc (Eng) in civil

engineering from the University of Cape Town

in 2003 and went on to complete a Masters in

Development Studies in 2008. She is currently

employed by PD Naidoo & Associates

Consulting Engineers in their Water and Waste

Water Division.

Contact details:

Candidate Engineer

PD Naidoo & Associates Consulting Engineers (Pty) Ltd

PO Box 7786

Roggebaai

8012

South Africa

T: +27 21 440 5060

F: +27 21 418 6440


ABDULLA PARKER obtained a BSc (Eng) and an

MBA from the University of Cape Town. He is

currently head of Catchment Planning for the

City of Cape Town: Catchment Stormwater and

River Management Branch. He previously

worked for the Department of Water Aff airs and

Forestry where he was involved in water use

management, institutional development and

cooperative governance, social and environmental strategies and waterworks

management and development.

Contact details:

Head of Catchment Planning

City of Cape Town: Catchment Stormwater and River Management Branch

PO Box 1694

Cape Town

8000

South Africa

T: +27 21 400 1385

F: +27 21 400 4554


PETER SILBERNAGL (Pr Eng, CEng, Pr CPM), a past

president of Consulting Engineers South Africa)

graduated from UCT with a BSc Eng, GDEng and

an MBA. His fi elds of expertise include project

management, management of multi-

disciplinary teams and subconsultants in

general project management, but particularly in

the areas of water and waste management. He

has developed expertise in human resource and organisational development.

He is currently a director at PD Naidoo & Associates Consulting Engineers.

Contact details:

Director

PD Naidoo & Associates Consulting Engineers (Pty) Ltd

PO Box 7786

Roggebaai

8012

South Africa

T: +27 21 440 5060

F: +27 21 418 6440


Keywords: City of Cape Town, stormwater, pollution, methodology, resources

In the end, all water is stormwater.

– A Parker, 2010

Whatever its origin or use, all water,

whether from roofs, roads, wastewater

treatment works, boreholes or bottles,

becomes stormwater.

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the natural landscape, provide beauty and a

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The impacts of poor water quality may be

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poor quality water used for urban farming

activities may severely compromise food

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many. Ultimately poor water quality poses a

significant threat to human health, aquatic

biodiversity and the added value that good

quality water brings to the economy.

The challenge, therefore, is to protect the

inland waters from the impact of pollution,

and to improve inland water quality to an

acceptable level. Current human and finan-

cial resources to manage pollution in inland

waters are inadequate.

The Catchment, Stormwater and

River Management (CSRM) Branch of the

Transport, Roads, Stormwater and Major

Projects Directorate of the City decided to

launch a project to determine the additional

resources required to manage pollution in

stormwater and river systems to improve

inland water quality compliance to an

“acceptable level”.

This paper is a showcase of the method-

ology used in this multifaceted and inter-

disciplinary project where the causes and

solutions to water pollution are extremely

complex, and large amounts of data, litera-

ture, opinions and information were at hand.

The methods used to achieve the following

project outputs are discussed:

■ Identification of criteria for “acceptable

water quality”

Improving water quality in stormwater & river systems:an approach for determining resources

N Nel, A Parker, P Silbernagl

This paper is a showcase of the approach used to determine the additional resources required to improve inland water quality in the City of Cape Town to an acceptable level. As the improvement of water quality falls in the more complex realm of modern municipal engineering – where many of the issues are so-called “soft” in nature and the problems and solutions are not straightforward – the methods discussed in this paper were instrumental in creating an holistic overview of the state of the rivers and wetlands in the City of Cape Town, highlighting the complexity of the problem and assisting to plot a way forward to provide proactive, sustainable measures for the management of water pollution. The paper discusses: the evaluation of water quality data, catchment analysis and determination of pollution sources, a risk assessment, and a prioritisation exercise, and concludes with the novel points and obstacles encountered. In all, the methods discussed provide a significant contribution towards the quest to improve water quality in the City of Cape Town.


■ Identification of catchment pollution

sources

■ Risk assessment of catchments to deter-

mine their vulnerability

■ Prioritisation of catchments, rivers and

wetlands for intervention

■ Provision of prioritised cost estimates

per district/region/subcouncil for the

management of the various pollution

sources, and identification of implemen-

tation mechanisms/partnerships.

ACCEPTABLE WATER QUALITY

One of the main challenges in the project

was to determine what is meant by “accept-

able water quality” in order to verify practi-

cal and achievable objectives in terms of

water quality and to package vast amounts of

water quality data in a meaningful manner

to achieve the project objectives. Water qual-

ity standards and criteria ultimately drive

the interventions necessary to bring water

quality to a desired level.

City of Cape Town sampling,

monitoring and evaluation

of water quality

An inland surface water monitoring network

with monitoring sites within each of the

major catchment areas is maintained by the

City. There are approximately 100 active

sampling points which are located at strate-

gic locations as indicated in Figure 1. Both

rivers and wetlands are monitored and this

occurs on a monthly basis, with both histori-

cal and current data being available.

Eighteen microbiological and chemical

constituents are measured in inland water

samples. There are therefore, for a 10 year

period, 216 000 data points (18 constituents

for around 100 sampling points taken on a

monthly basis over 10 years). The key is to

present this data in a meaningful way.

Reporting on water quality

For broad reporting purposes, the City

currently assesses these monthly water

quality results for inland waters from two

perspectives: “ecosystem health” and “public

health”. The relevant Department of Water

Affairs and Forestry (DWAF)1 Water Quality

Guideline series provides the basis for this

evaluation.

Aquatic ecosystem health

For ease of reporting, total phosphorus is

used by the City as an “indicator” of general

chemical water quality in inland waters and

provides a proxy measurement of the state of

an aquatic system.

The median2 “total phosphorus” con-

centration is calculated for river and vlei

monitoring points in various systems, and

compared to concentration ranges which

indicate the trophic tendencies and condi-

tions described in Table 1:

Public Health

“Faecal coliforms” is the constituent used by

the City as an indication of the suitability

Table 1 Trophic tendencies for phosphorus concentrations in inland water

Trophic tendency

Phosphorus range (mg/l P)

“Condition”

Oligotrophic <0.005 Excellent: Low levels of nutrients and no water quality problems

Mesotrophic 0.005 – 0.025Good: Intermediate levels of nutrients with emerging water quality problems

Eutrophic

0.025 – 0.125Fair to poor: High levels of nutrients and increasing frequency of water quality problems

0.125 – 0.25

Hypertrophic >0.25Bad: Excessive nutrient levels and water quality problems are almost continuous

Figure 1: City of Cape Town: Inland monitoring network


of inland water for intermediate contact

recreational use (activities involving an inter-

mediate degree of water contact, e.g. sailing,

canoeing and fishing).

The DWAF Water Quality Guideline for

Recreation (DWAF 1996a) sets safe standards

for the limits of pollutants that may be used

for intermediate contact recreational use and

states that samples should not exceed 1 000

faecal coliform organisms per 100 ml. The

percentage of samples with ≤1 000 faecal

coliform counts for the twelve-month period

is thus used as an indication of the level of

compliance.

Table 2 SASS5 categories for the river health programme

Category Description

Natural No or negligible modification (relatively little human impact)

GoodBiodiversity and integrity largely intact (some human-related disturbance but ecosystems essentially in good state)

FairSensitive species may be lost, with tolerant or opportunistic species dominating (multiple disturbances associated with socio-economic development)

PoorMostly only tolerant species present; alien species invasion; disrupted population dynamics; species are often diseased (high human densities of extensive resource exploitation)

UnacceptableRiver has undergone critical modification; almost complete loss of natural habitat and indigenous species with severe alien invasion

Table 3 Public health criteria: ranges for full contact and intermediate contact recreation

Unit

DWAF Recreational Use Guidelines (Vol 2)

Full Intermediate

Ta

rget

Acc

epta

ble

Ris

k

Un

acce

pta

ble

Ta

rget

Acc

epta

ble

Ris

k

Un

acce

pta

ble

Faecal Coliform count / 100 ml

0–130

131–600

601–2 000

>2000

0–1 000

1 001–2 000

2 001–4 000

>4 000

Management 1

Management 2

Management 3

Management 1

Management 2

Management 3

2 001–10 000

10 001–100 000

>100 0004 000–

10 00010 001–

100 000>100 000

E.coli count / 100 ml

0–130

131–200

201–400

>400

No guideline

No guideline

No guideline

No guideline

No guideline

No guideline

Management 1

Management 2

Management 3

401–2 400 2 401–20 000 >20 000

Table 4 Ecosystem health criteria: categories

Variable Units Natural Good Fair Poor Unacceptable Comments

Temperature*# °CDepends on background (Upper boundary = 90th percentile; Lower

boundary = 10th percentile); Good ±2°C; Fair ±4°C; Poor ±>4°CNeed to determine typical background water quality – not essential for prioritisation exercise

Total suspended solids*#

mg/l Depends on background (Not more than 10% higher than background)Need to determine typical background water quality – not essential for prioritisation exercise

Conductivity (EC)*# mS/m Depends on background (not more than 15% different from normal cycles)Need to determine typical background water quality – not essential for prioritisation exercise

pH* units 8–6.59–8 or

6.5–5.7510–9 or 5.75–5

>10; <5Need to determine typical background water quality – not essential for prioritisation exercise

Dissolved oxygen* mg/l >8 8–6 6–4 4–2 <2

Also dependent on background DO levels to some extent. No unacceptable range given but if one selects equal bands then 2 mg/l is the next logical band and is applicable to assessing the actual data

Soluble reactive phorphorus*

mg/l <0.005 0.005 – 0.025 0.025 – 0.125 0.125–0.250 >0.250 Ranges as recommended in the latest water quality benchmarks for the ecological reserve (DWAF 2005)Total inorganic

nitrogen*mg/l <0.25 0.25–1 1–4 4–10 >10

Ammonia (NH3-N)* mg/l <0.015 0.015–0.058 0.058–0.1 0.1–0.2 >0.2No unacceptable range given but if one selects equal bands then 0.2 mg/l is the next logical band and is applicable to assessing the actual data

Blue-green algae toxins (microcystins)@ μg/l <10 10–50 >50

Ranges as recommended in the World Health Organisation (WHO) guidelines

Algae (Chl-a)* μg/l <10 10–20 20–30 30–40 >40No unacceptable range given but if one selects equal bands then 40 μg/l is the next logical band and is applicable to assessing the actual data

# South African Water Quality Guidelines (DWAF 1996b)

* Ecological reserve water quality benchmarks (Jooste & Rossouw 2002)

@ World Health Organisation Recreational Guidelines (2003)


River health programme

The City is a participant in the River Health

Programme (RHP) which is a national bio-

monitoring programme that uses a range of

biological indices for determining the ecologi-

cal health of rivers. The SASS5 index (South

African Scoring System Version 5) is the most

widely utilised bio-monitoring index in the

RHP and consists of an assessment of aquatic

macro-invertebrate communities present to

determine ecological river health.

The local bio-monitoring programme

of the City has been undertaken annually

(where human resources allow) at approxi-

mately 40 river locations. Ideally it should be

undertaken in spring, summer and autumn,

which is now being done (Haskins, personal

communication 2010).

The RHP utilises four descriptive cate-

gories of river condition as shown in Table 2.

The fifth category (“unacceptable”) was

introduced for the purposes of this analysis,

due to the need to address the severely modi-

fied rivers within the municipal boundaries

(Belcher, personal communication 2010).

Methodological approach

for the determination of

acceptable water quality

A Water Quality Sub-Committee was

established in order to determine “accept-

able water quality” criteria and standards.

Participants included the consultant team,

water quality specialists and scientists and

other relevant parties from the City.

The section below discusses the criteria

decided upon, which were used to evalu-

ate and colour-code the water quality data

obtained from the City in order to provide a

visual depiction of the water quality status of

the rivers and wetlands of Cape Town.

Public health criteria

While it is acknowledged that public health

risks associated with recreational water may

be due to the presence and interaction of a

range of constituents, faecal coliforms and

Escherichia coli (E. coli) are considered to be

reasonable “indicator” micro-organisms to

assess health risks, as these are indicators of

probable faecal pollution.

The “target”, “acceptable”, “risk” and

“unacceptable” water quality categories for

faecal coliforms and E. coli for both full con-

tact recreation (swimming) and intermediate

contact recreation (canoeing, waterskiing,

sailing, angling, etc.)3 were based on the

South African Water Quality Guidelines

(DWAF 1996a) (see Table 3).

As many of the E. coli and faecal coliform

counts in the rivers within the municipal

boundaries were found to fall within the

“unacceptable” category (red); subdivisions

of this category named Management 1,

Management 2 and Management 3 were

created. This is intended as a management

tool to help establish the responses and actions

needed, to prioritise rivers and wetlands, and

to help determine the sources of pollution.

For instance, an E. coli count of 1 000 000

is likely to indicate a different source of

pollution (probably a sewer overflow) than

a count of 10 000, even though both are

“unacceptable”.

An analysis of all the E. coli counts for

ten years of water quality data for all of

the monitoring points in the Cape Town

municipal area was undertaken to provide

guidance on what the Management 1 to 3

sub-categories should be. It was found that a

third of the data above the unacceptable (400

E. coli organisms/100ml) limit fell between

400 and 2 400 E. coli organisms/100ml,

a third between 2 400 and 20 000 E. coli

organisms/100ml, and the last third above

Results from Bacteriological Tests (EK19)

DateFaecal Coliforms E. coli

Full Inter mediate Full

12/6/2003 1 300 1 300 700

16/10/2003 17 000 17 000 16 000

18/12/2003 5 400 5 400 3 700

15/1/2004 2 900 2 900 2 100

11/3/2004 48 000 48 000 20 000

10/6/2004 4 000 4 000 4 000

2/9/2004 2 300 2 300 1 800

9/12/2004 20 000 20 000 12 000

13/1/2005 100 000 100 000 100 000

10/3/2005 150 000 150 000 90 000

9/6/2005 15 000 15 000 18 000

8/9/2005 2 000 2 000 1 200

17/10/2005 1 600 1 600 1 700

8/12/2005 1 000 1 000 1 000

12/1/2006 900 900 400

14/3/2006 3 100 3 100 1 700

29/6/2006 15 000 15 000 15 000

21/9/2006 1 400 1 400 1 400

14/12/2006 100 100 100

18/1/2007 400 400 200

8/3/2007 380 380 280

14/6/2007 46 000 46 000 16 000

13/9/2007 330 000 330 000 90 000

6/3/2008 1 000 000 1 000 000 1 000 000

12/6/2008 5 000 5 000 5 000

4/9/2008 32 000 32 000 29 000

4/12/2008 26 000 26 000 17 000

15/1/2009 46 000 46 000 18 000

12/3/2009 1 000 000 1 000 000 1 000 000

18/6/2009 7 900 7 900 1 400

Target Unacceptable (red 1)

Acceptable Unacceptable (red 2)

Risk Unacceptable (red 3)

Table 5 Kuils River colour-coded public health and aquatic ecosystem health water quality results:

monitoring point E19 – northern reaches, upstream of the Bottelary confluence

Results from Aquatic Ecosystem Tests (EK19)

Date DO tpon nh3 srp

12/6/2003 7.1 3.426 0.081 0.125

18/12/2003 5.7 1.35 0.073 0.162

15/1/2004 7.5 0.937 0.083 0.209

11/3/2004 3.3 1.123 0.135 0.263

10/6/2004 7.4 1.229 0.075 0.107

14/10/2004 7.2 1.31 0.056 0.075

9/12/2004 8 2.268 0.107 0.076

13/1/2005 3.5 1.556 0.011 0.186

10/3/2005 5.8 2.244 0.345 0.21

9/6/2005 7.2 2.281 0.065 0.076

8/9/2005 9.7 2.746 0.186 0.105

8/12/2005 8.9 4.889 0.099 0.285

12/1/2006 7.3 1.672 0.302 0.101

14/3/2006 1.1 7.92 6.13 0.044

29/6/2006 5.7 2.79 0.289 0.01

21/9/2006 6.6 2.53 0.13 0.01

14/12/2006 3.1 1.59 0.66 0.041

18/1/2007 3.2 1.747 0.346 <0.001

8/3/2007 4.1 1.366 0.161 0.034

14/6/2007 5.9 3.56 0.761 0.025

13/9/2007 6.2 3.275 0.221 0.051

13/12/2007 1.4 2.809 0.628 0.133

6/3/2008 1.1 1.095 0.016 0.184

12/6/2008 7.7 1.745 0.157 0.066

4/9/2008 7.4 4.25 0.228 0.048

4/12/2008 7 2.805 0.424 0.01

15/1/2009 5.4 1.906 0.12 0.145

12/3/2009 4.7 0.852 0.021 0.066

18/6/2009 6.5 2.591 0.1 0.067

Natural Poor

Good Unacceptable

Fair


20 000 E. coli organisms/100ml. These divi-

sions are purely to guide management and to

assist with the allocation of resources. These

limits were then used for Management 1, 2

and 3 (i.e. the sub-categories of the “unac-

ceptable” range).

The same method was used to determine

the three sub-categories of the “unaccept-

able” range for the faecal coliform counts.

Ecosystem health criteria

The values for the various categories for

the ecosystem health criteria were derived

from both the South African Water Quality

Guidelines (DWAF 1996b) and the ecological

reserve water quality benchmarks (Jooste

& Rossouw 2002). As many of the rivers in

the Cape Town municipal area were found

to fall within the “poor” category (red), an

additional “unacceptable” category (dark red)

was created as a management tool to be able

to prioritise rivers, to establish the responses

needed and to help determine the sources of

pollution (see Table 4).

Temperature, total suspended solids (TSS),

conductivity and pH are dependent on vegeta-

tion, geology etc, and the background levels of

these would need to be determined for each

of the water systems to establish applicable

water quality ranges for each of these constit-

uents within the various categories. Therefore,

for the purposes of the project, the following

constituents (highlighted in blue in Table 4)

were decided upon under the auspices of the

Water Quality Sub-Committee:

■ Dissolved oxygen (DO)

■ Ammonia (NH3)

■ Total inorganic nitrogen (TIN)

■ Soluble reactive phosphorus (SRP)

All of these constituents relay different

information in terms of water quality, and

they would trigger different management

responses. They are, however, all linked

and a particular intervention can often

result in an improvement in all constituent

concentrations.

Algae (A), monitored in some wetlands

(“vleis”), was a further constituent used to

assess water quality specifically within the

vleis. The occurrence of blue-green algae

(Cyanophyceae) – a group known to produce

toxins under certain conditions – is particu-

larly important for assessing potential health

risk.

All the public health and ecosystem

health water quality data for all of the moni-

toring points were colour-coded according to

the categories discussed above.

By way of illustration, Tables 5 – 7 are

examples of colour-coded quarterly data

for three monitoring points along the Kuils

River (a river east of the Cape Town CBD).

The first monitoring point (EK19) is in the



18/1/2000 6.2 2.998 1.929

23/3/2000 5.1 29.18 6.909 2.749

6/6/2000 2.9 21.36 7.846 2.436

21/9/2000 4.1 21.76 12.32 0.23

16/11/2000 9.7 20.54 19.12 2.702

18/1/2001 6.2 22.31 12.59 2.093

15/3/2001 4.5 11.64 1.018 0.348

5/7/2001 8 9.06 1.26 0.681

6/9/2001 9.3 12.29 2.019 0.329

6/12/2001 3.9 23.63 20.84 3.098

24/1/2002 11.8 12.39 9.713 0.977

14/3/2002 8.4 22.68 19.91 15.19

20/6/2002 5 10.26 1.696 1.443

19/9/2002 6.2 20.14 14.87 1.911

12/12/2002 4.6 4.3 1.347

23/1/2003 7.4 8.92 3.475

18/3/2003 5.3 6.157 1.977 1.078

12/6/2003 6.4 16.51 11.48 3.618

18/9/2003 15.8 4.296 0.01 0.192

18/12/2003 5.3 11.69 9.121 4.652

15/1/2004 6.8 11.52 9.117 0.945

11/3/2004 4.5 12.42 8.812 3.997

10/6/2004 6.6 8.598 6.734 1.23

2/9/2004 5.5 16.88 11.15 6.4

9/12/2004 12.8 7.177 2.637

13/1/2005 5.1 16.18 11.72 4.104

10/3/2005 7.3 3.239 0.32 2.272

9/6/2005 8.9 9.924 2.583 1.361

8/9/2005 7.7 18.21 10.12 4.159

8/12/2005 6.3 13 9.728 2.293

12/1/2006 3 7.004 4.977 2.277

14/3/2006 5.5 9.44 2.86 5.77

29/6/2006 6.8 8.51 0.61 2.18

21/9/2006 5.8 10.41 5.65 2.27

14/12/2006 2.4 19.9 19.49 7.63

18/1/2007 4.7 9.421 6.814 1.881

8/3/2007 4.4 11.16 8.58 2.653

14/6/2007 6.1 8.04 2.22 1.06

13/9/2007 6.1 9.519 3.962 1.711

13/12/2007 4.6 26.28 25.25 5.901

6/3/2008 7.6 10.96 7.597 2.084

12/6/2008 4.8 5.794 0.212 1.025

4/9/2008 7.5 7.481 3.537 1.779

4/12/2008 5.3 19.87 18.55 5.421

15/1/2009 2.3 20.94 19.18 3.537

12/3/2009 1.6 22.39 20.68 6.323

Natural Poor

Good Unacceptable

Fair


monitoring point EK09 – middle reaches at Bellville WWTW discharge at Rietvlei Road



Full Intermediate Full

18/1/2000 30 000 30 000 3 000

23/3/2000 4 000 000 4 000 000 3 500 000

6/6/2000 3 100 000 3 100 000 2 200 000

19/10/2000 1 100 000 1 100 000 600 000

18/1/2001 66 000 66 000 58 000

15/3/2001 4 000 4 000 3 000

7/6/2001 6 000 6 000 5 200

6/9/2001 140 000

6/12/2001 100 000 100 000 100 000

24/1/2002 100 000 100 000 100 000

14/3/2002 100 000 100 000 100 000

20/6/2002 82 000 82 000 60 000

19/9/2002 45 000 45 000 26 000

12/12/2002 41 000 41 000 21 000

23/1/2003 66 000 66 000 30 000

18/3/2003 200 000 200 000 160 000

12/6/2003 420 000 420 000 230 000

16/10/2003 34 000 34 000 27 000

18/12/2003 79 000 79 000 39 000

15/1/2004 580 000 580 000 390 000

11/3/2004 170 000 170 000 60 000

10/6/2004 430 000 430 000 190 000

2/9/2004 310 000 310 000 200 000

9/12/2004 25 000 25 000 11 000

13/1/2005 240 000 240 000 130 000

10/3/2005 150 000 150 000 30 000

9/6/2005 5 000 5 000 1 000

8/9/2005 600 000 600 000 270 000

8/12/2005 57 000 57 000 38 000

12/1/2006 150 000 150 000 60 000

14/3/2006 55 000 55 000 10 000

29/6/2006 9 000 9 000 2000

21/9/2006 46 000 46 000 39 000

14/12/2006 65 000 65 000 45 000

18/1/2007 260 000 260 000 80 000

8/3/2007 270 000 270 000 190 000

14/6/2007 13 000 13 000 9 000

13/9/2007 160 000 160 000 60 000

13/12/2007 680 000 680 000 580 000

6/3/2008 180 000 180 000 100 000

12/6/2008 29 000 29 000 11 000

4/9/2008 330 000 330 000 270 000

4/12/2008 960 000 960 000 770 000

15/1/2009 2 300 000 2 300 000 1 600 000

12/3/2009 8 300 000 8 300 000 4 600 000

18/6/2009 46 000 46 000 25 000





northern, upper reaches of the river, upstream

of its confluence with the Bottelary River;

the second point (EK09) is in the middle

reaches at the Bellville Wastewater Treatment

Works (WWTW); and the third point (EK11)

is in the lower reaches downstream of the

Zandvliet WWTW discharge point.

The tables give a visual depiction of the

quality of the water at these particular points

over a 10-year period, thus creating insight

into possible sources of pollution. At moni-

toring point EK19, shown in Table 5, the

“unacceptable” levels of faecal coliforms and

E. coli (reds and dark reds) in recent years in

an area that is relatively affluent, and where

there is no industry and wastewater treat-

ment, is perhaps indicative of leaking sewers

and/or stormwater ingress or infiltration.

Further downstream, at monitoring point

EK09 (Table 6), the water quality worsens

(more reds and dark reds) from both a public

health and ecosystem health perspective.

This is perhaps a result of poor quality efflu-

ent from the Bellville WWTW. Even further

downstream, at monitoring point EK11

(Table 7), the water quality from a public

health perspective improves slightly (more

blues, greens and yellows). It can be conclud-

ed that, in contrast to the concrete-lined sec-

tions higher up in the Kuils River, the natural

wetlands in the vicinity of monitoring point

EK11 are able to attenuate the bacteriological

pollutants. The microbiological constituents,

however, remain “unacceptable”.

CATCHMENT ANALYSIS AND

SOURCES OF POLLUTION

An analysis of each of the catchments, rivers

(including canals) or river reaches, as the

case may be, depending on the water quality

information from the monitoring points, was

undertaken to obtain an understanding of

the situation in each of these discrete units.

A Project Steering Committee (including

any interested parties and all City officials

involved in water quality management)

was established to provide assistance in

this regard. Meetings were held every two

months, or as necessary, and involved work-

shopping of ideas, sharing of knowledge and

findings, and seeking consensus between the

various City Departments.

Field visits to various informal settle-

ments, industries, wastewater treatment

works, pump stations, rivers and wetlands

were held to gain further insight into water

quality issues around Cape Town.

A literature review of previous reports

made available by the City and the evaluation

of historic water quality data created insight

into the state of the rivers and wetlands in

the municipal area of Cape Town.


monitoring point EK11 – lower reaches, downstream of Zandvliet WWTW discharge



Full Intermediate Full

18/1/2000 1 900 1 900 1 600

23/3/2000 4 000 4 000 4 000

6/6/2000 610 610 580

19/10/2000 1 000 1 000 1 000

18/1/2001 680 680 500

15/3/2001 8 000 8 000 6 000

7/6/2001 4 100 4 100 3 600

6/9/2001 300

6/12/2001 1 200 1 200 1 000

24/1/2002 430 430 290

14/3/2002 410 410 240

20/6/2002 13 000 13 000 1 2000

19/9/2002 170 170 170

12/12/2002 850 850 790

23/1/2003 3 200 3 200 2 000

18/3/2003 1 000 1 000 600

12/6/2003 2 800 2 800 2 600

16/10/2003 2 800 2 800 2 600

18/12/2003 640 640 430

15/1/2004 3 800 3 800 3 000

11/3/2004 900 900 700

10/6/2004 350 350 270

8/7/2004 4 400 4 400 3 600

14/10/2004 13 000 13 000 12 000

9/12/2004 2 100 2 100 1 800

13/1/2005 2 100 2 100 900

10/3/2005 25 000 25 000 20 000

9/6/2005 1 500 1 500 1 400

8/9/2005 1 900 1 900 1 900

8/12/2005 520 520 450

12/1/2006 440 440 170

14/3/2006 10 10 10

29/6/2006 350 350 310

21/9/2006 620 620 590

14/12/2006 560 560 410

8/3/2007 500 500 200

12/7/2007 360 360 320

18/10/2007 220 220 160

13/12/2007 4 200 4 200 4 200

6/3/2008 7 200 7 200 1 100

12/6/2008 700 700 200

4/9/2008 80 80 70

4/12/2008 6 200 6 200 3 300

15/1/2009 2 200 2 200 1 300

12/3/2009 8 700 8 700 2 900

18/6/2009 89 000 89 000 41 000






18/1/2000 2.6 3.106 0.744 1.403

23/3/2000 5.468 0.717 1.346

6/6/2000 6.5 7.061 2.924 1.589

21/9/2000 8.1 9.433 0.778 1.537

16/11/2000 4.1 4.724 1.878 1.694

18/1/2001 7.1 6.097 0.512 1.585

15/3/2001 6.4 8.016 4.021 0.037

7/6/2001 8.8 4.527 0.108 1.093

6/9/2001 7.7 3.525 0.03 0.107

6/12/2001 7.3 7.694 2.092 2.307

24/1/2002 5.2 3.868 0.158 1.5

14/3/2002 7.7 5.718 0.426 1.907

20/6/2002 5.6 4.732 0.223 1.25

19/9/2002 5.9 7.074 0.308 1.338

12/12/2002 4.3 0.6 2.17

23/1/2003 4.9 0.081 2.395

18/3/2003 5 6.584 0.072 2.224

12/6/2003 6.9 12.22 0.07 2.53

18/9/2003 5 4.72 0.143 1.629

18/12/2003 6.5 4.662 0.104 3.095

15/1/2004 8 4.964 0.31 3.256

11/3/2004 5.4 4.612 0.137 3.155

10/6/2004 6.8 3.952 0.864 1.544

2/9/2004 6.3 6.496 0.736 2.492

9/12/2004 8 5.489 0.173 1.616

13/1/2005 5.8 5.568 0.06 2.419

10/3/2005 8.8 5.109 0.2 1.944

9/6/2005 6.4 3.691 0.06 0.967

8/9/2005 7.7 4.485 0.064 1.484

8/12/2005 8.689 1.463 2.718

12/1/2006 9.2 5.496 0.778 2.586

14/3/2006 5.4 6.21 1.1 1.82

29/6/2006 5.5 4.85 0.076 1.65

21/9/2006 5.4 5.28 0.09 1.82

14/12/2006 2.6 4.74 2.76 4.66

18/1/2007 3.3 5.561 3.6 4.188

8/3/2007 3.8 6.683 5.979 2.99

14/6/2007 6.3 2.86 0.274 0.749

13/9/2007 4.4 5.106 2.234 1.342

13/12/2007 2.9 23.73 23.2 6.274

6/3/2008 1.6 14.87 12.99 3.429

12/6/2008 4.8 6.665 4.326 1.884

4/9/2008 5.1 4.048 0.601 1.31

4/12/2008 2.2 10.45 9.699 4.935

15/1/2009 2.2 15.55 14.14 4.594

12/3/2009 1.5 21.88 19.09 5.805

18/6/2009 3.5 3.422 1.888 1.028

Natural Poor

Good Unacceptable

Fair


Catchment Workshop November 2009

Name

Surname

Catchment Silvermine

River/Wetland Silvermine River

Monitoring Points sil02, sil04

Water Quality (Bacto)

Water Quality (Eco)

Water Quality over time

Land Use: SANParks, Silvermine Dam, Clovelly residential, public open space, Fishhoek township, Clovelly CC and golf course

Water Use

Possible sources of pollution

Sewer pumps

Golf course runoff

Informal areas

Urban runoff

De

pa

rtm

en

t

Ty

pe

of

Inte

rve

nti

on

Timing Budget

Importance Scale of

1 (Important) to 5 (Not important)

Comments

0–

1y

ea

r

1–

5 y

ea

rs

5–

10

ye

ars

10

–2

0 y

ea

rs

>2

0 y

ea

rs

R0

–R

10

0 0

00

R1

00

00

0–

R1

mil

l

R1

mil

l–R

10

mil

l

R1

0 m

ill–

R1

00

mil

l

>R

10

0 m

ill

Pu

bli

c H

ea

lth

En

vir

on

me

nta

l

Eco

no

mic

Gro

wth

(e

.g.

tou

rism

)

e.g Water and Sanitation

e.g. upgrade WWTW x x 5 5 1

Figure 2 Template used in water quality workshops


Consultations were also held with the

following organisations and entities in the

interest of information-sharing and future

collaboration:

■ DWA

■ South African National Parks (SANParks)

/ Table Mountain National Parks (TMNP)

■ Swartland Municipality

■ Stellenbosch Municipality and

Cape Winelands District Municipality

■ Department of Agriculture

Stakeholder engagement was sought

through a two-day workshop (16 and

17 November 2009). The workshop was held

with various area managers from the City

in order to determine pollution sources,

to suggest possible solutions and to gain

management consensus. Water quality at the

various monitoring points was discussed and

attendees filled out templates as per Figure 2.

Through the process the sources of pol-

lution with respect to water quality in river

systems and stormwater, which stand out

from the many, many types of point or dif-

fuse sources of pollution, were found to be

the following:

■ Perceived major pollutors:

■ Blockages and overflows of sewers

(whether due to extraneous waste

disposed into sewers, illegal rainwater

disposal or previous bad practice in

construction)

■ Greywater and sewage from informal

settlements

■ Sewage pump stations

■ Solid waste in water courses and such

open areas

■ Wastewater treatment works

■ Perceived minor pollutors:

■ Agriculture

■ General urban runoff

■ Golf courses

■ Industry and construction

■ Canalisation of rivers4

RISK ASSESSMENT

The purpose of the risk assessment was to

determine the vulnerability of a catchment

to human and ecological health impacts,

should there be a pollution incident or water

quality-related set of circumstances. It is

not a reflection of what is happening on

the ground, but rather an illustration of the

inherent risk (without a management system

in place) as opposed to the residual risk.

The risk assessment is one of the criteria

that was fed into the catchment prioritisation

exercise, as described later in this paper.

Risk events and their associated con-

sequences were identified by the Project

Steering Committee and Water Quality Sub-

Committee as per Table 8:

Each inland environmental monitoring

point or group of monitoring points (i.e.

river reach) was assessed against the above

risk events. The probability of the event hap-

pening and the potential impact of that risk

were determined. A resultant risk or vulner-

ability score was obtained per river reach, as

shown in Figure 3, where a high probability

and high impact equate to a high vulner-

ability (red); and a low probability and low

impact equate to a low vulnerability (blue).

Table 9 shows how the risk assessment

works, with results for the Hout Bay River,

Hout Bay catchment, as an example of what

was carried out for all of the City’s rivers and

wetlands

Overall, the risk events which resulted in

the highest vulnerability scores included:

■ Ongoing and chronic risk events:

■ Deteriorating municipal infrastructure

■ Increased informal settlement

■ Insufficient maintenance of municipal

infrastructure

■ Sporadic risk events:

■ WWTW breakdown

■ Pipe blockage or overflow

PRIORITISATION OF CATCHMENTS,

RIVERS AND WETLANDS

The catchment prioritisation exercise was

intended to assist the City’s management

structures with the allocation of resources.

The exercise provides guidance on a starting

point for the allocation of resources. Ad hoc

and emergency events that affect water qual-

ity will, however, still need to be attended to

as the need arises.

The methodology, scores, weighting and

input criteria for the prioritisation exercise

were workshopped by the Project Steering

Committee, Water Quality Sub-Committee

and the Consultant Team.

Input criteria

The following criteria were used to prioritise

catchments:

■ Water usage (WU)

■ Public health (PH)

■ Ecosystem health (EH)

■ Risk (R)

■ Downstream impact (DI)5 [rivers] or algae

(A) [wetlands]6

■ Pollution load (PL)7

Initially “cost of intervention” and “time for

implementation” were included as possible

criteria, but after intensive debate at the

various forums, these two criteria were

withdrawn. These could, however, still

be considered at a later stage to further

prioritise catchments for management

interventions.

Table 8 Risk events and risk consequences

Risk event Consequence

WWTW breakdownPartially or untreated sewage effluent (ecosystem and public health risk)

Pipe blockage or overflow Sewage spill (ecosystem and public health risk)

Pump station breakdown & overflow Sewage spill (ecosystem and public health risk)

Agricultural pollution incident Ecosystem and public health risk

Inappropriate disposal of solid waste Aesthetic, ecosystem and public health risk

Long-term degradation of land Increased runoff-flooding, contamination

Densification/hardening of surfaces Increased runoff-flooding, contamination

Increased informal settlements

Less water and sanitation capacity (ecosystem and public health risk), inappropriate greywater disposal, and less solid waste capacity and illegal dumping

Industrial pollution incident Ecosystem and public health risk

Insufficient maintenance of municipal infrastructure

Sewage/stormwater leakage/intrusion (ecosystem and public health risk)

Leaking (i.e. due to ageing) and deteriorating infrastructure (new and old)

Sewage/stormwater leakage/intrusion (ecosystem and public health risk)

Figure 3 Methodology for obtaining the

vulnerability score

Pro

ba

bil

ity

of

risk

eve

nt

100

66

33

00 33 66 100

Impact of risk event

Low

Medium

High


Table 9 Risk assessment results for Hout Bay River, Hout Bay catchment

CatchmentRivers

and Wetlands

Reach/Description

Monitoring point

Risk Event Risk Consequence ProbablityImpact(0/Low/

Med/High)

Priority/Riskiness

(0/Low/Med/High)

Hout BayHout Bay

Upper(Longkloof Rd)

dr04

WWTW breakdown Raw sewage effluent – ecosystem and public health risk

0

Pipe blockage or overflow Sewage spill – public health risk 1 411

P/S breakdown and overflow Sewage spill – public health risk 0

Agricultural pollution incident

Ecosystem health risk 850

Inappropriate disposal of solid waste

Aesthetic, public health and/or ecosystem health risk

850

Long-term degradation of the urban environment

Increased runoff-flooding, contamination

289

Increased densification/hardening of surfaces


289


Less water and sanitation capacity – public health risk

1 411

Industrial pollution incident Ecosystem and public health risk 0

Insufficient maintenance of infrastructure

Sewage/stormwater leakage –ecosystem and public health risk

1 411

Leaking deteriorating infrastructure (new and old)

Sewage/stormwater leakage –ecosystem and public health risk

1 411

MiddleVictoria Rd

dr02


0


P/S breakdown and overflow Sewage spill – public health risk 0


Ecosystem and public health risk 850


Aesthetic, public health and ecosystem health risk

4 150

Long-term degradation of the urban environment


1 411



1 411



6 889



Sewage/stormwater leakage/intrusion – ecosystem and public health risk

4 150


Sewage/stormwater leakag/intrusion – ecosystem and public health risk

4 150

Lower Princess St & estuary

dr05 (bacto)dr01


0


P/S breakdown and overflow Sewage spill – public health risk 6 889


Ecosystem and public health risk 0


Aesthetic, public health and ecosystem health risk

4 150

Long-term degradation of the urbam environment


1 411



1 411



6 889




6 889



6 889


Point scoring system

A point scoring system was then developed

for each of the criteria given above. The

approach for the point allocation was as

shown in Table 10.

Catchments (or river reaches) with good

water quality, low levels of use, low risk of

negative events, low pollution loads and low

downstream impacts would have a lower

priority for intervention than catchments (or

river reaches) where all these attributes would

score badly and thus achieve a higher score.

Each monitoring point or grouping of

monitoring points (i.e. river reach) was

assessed according to the above criteria

and given a score between 1 and 5 as per

Table 10.

The points allocated for Water Usage and

Downstream Impact in each of the rivers

and wetlands were derived from literature,

and in consultation with the Project Steering

Committee, Water Quality Sub-Committee

and through the Consultant Team.

The points for Ecosystem Health, Public

Health and Algae were derived from the

Water Quality Results, whereas the points

for Pollution Load were derived as follows:

■ Pollution Load = {Q (m3/s)*(Ecosystem

Health) (points allocated to the con-

centration (1–5))} + {Q (m3/s)*(Public

Health) (points allocated to the concen-

tration (1–5))} + {Q (m3/s)* (Sandiness

of the area and/or propensity for solid

waste)}

■ Q: Flows for the various rivers and

wetlands within the Cape Town

municipal area were obtained from

reports (Ninham Shand et al 1999),

through personal communication with

City officials (Wood, personal com-

munication 2010) and from low-flow

monitoring undertaken by the City in

May 2002. Outstanding flows were

further derived through inference

of the available flows, the size of the

relevant catchment and the land use

in the catchment.

■ Ecosystem Health and Public

Health: The points allocated for the

Public Health and Ecosystem Health

Water Quality concentration results

(1–5), as described earlier in this

paper, were utilised.

■ Sandiness of the area/propensity for

solid waste: An allocation of 1 to 5

was given according to an area’s sandi-

ness and propensity for litter. A sandy

area with high litter such as Guguletu

obtained a score of 5 and an urban

area with low litter such as Cape Town

CBD obtained a score of 1.8

The final values obtained for the

Pollution Load equation for each of the

Table 10 Points allocation for prioritisation exercise

Water Usage(WU)

Water usage Score

Full contact(formal and informal)

Intensive all yr 5

Intensive part of yr 4

Often used 3

Seldom used 1

Intermediate contact (formal and informal)

Intensive all yr 4

Intensive part of yr 3

Often used 2

Seldom used 1

Irrigation 3

Industry 3

Non-contact 1

Public & Ecosystem Health (PH & EH)

Category Score

Very Bad (mostly red) 5

Bad (yellow/red) 4

Intermediate (all colours) 3

Good (blue/green) 2

Very Good (mostly blue) 1

Risk (R)(Vulnerability Score)

Category Score

Very Bad (reds & oranges) 5

Bad (orange & yellow) 4

Intermediate (yellow/all colours) 3

Good (green) 2

Very Good (blue) 1

Downstream Impact (DI) (rivers only)

Category Score

Large impactLarge population, Blue Flag/intensively used beach, conservation area, tourism, recreational vlei, food source agriculture

5

Medium to large impactFairly large population, beach, sea, vlei, some agriculture

4

Medium impact Medium population size, sea 3

Low to medium impact Small population 2

Low impact No downstream impact 1

Algae (A) (Microcystin Toxins)* (wetlands only)

Category Score

High toxin levels (>50 μg/l) 5

Medium to high toxin levels (25–50 μg/l) 4

Medium toxin levels (10–25 μg/l) 3

Medium to low toxin levels (10–20 μg/l) 2

Low toxin levels (<10 μg/l) 1

Pollution Load (PL)

Category Score

High pollution load 5

Medium to high pollution load 4

Medium pollution load 3

Low to medium pollution load 2

Low pollution load 1

* Microcystin toxin levels measured as a means to monitor the propensity of a wetland to develop harmful algal blooms (HABs)


river reaches and wetlands ranged from 0

to 25. Values from 0 to 5 were then given

a score of 1, values from 6 to 10 a score of

2, values from 11 to 15 a score of 3, values

from 16 to 20 a score of 4, and values

from 21 to 25 a score of 5 as the final

input in the prioritisation exercise. As an

example, Table 11 indicates the Pollution

Load results for the rivers in the Eerste/

Kuils catchment.

■ Points for risk were derived as described

earlier in this paper.

Weighting of criteria

The final scores allocated for each of the

criteria were then weighted as per Table 12

and added to obtain an overall prioritisa-

tion score for each of the river reaches and

wetlands.

The prioritisation scores for each river

reach and wetland within the various catch-

ment areas were added and averaged to

prioritise entire catchments.

Table 11 Pollution Load: Eerste/Kuils catchment

CatchmentRivers/

WetlandsReach/

DescriptionMonitoring

PtLow Flow

(Q)Concentration

PHConcentration

EHSandiness/

LitterPollution

Load

PollutionLoad(1–5)

Eerste/Kuils

Kuils

Upper u/s of Bottelary confluence

ek19 0.05 5 4 3 0.60 1

Bellville WWTW discharge

ek09

0.7 5 4 3 8.40 2(Rietvlei Rd) u/s of Stellenbosch Arterial Rd

ek05

d/s of Baden Powell Bridge

ek08

1.2 4 4 5 15.60 4d/s of Zandtvliet discharge

ek11

Eerste

At N2 freeway-u/s of Kuils confluence

ek13 0.5 3 4 4 5.50 2

Eerste River estuary

ek17 1.5 4 4 4 18.00 4

Kleinvlei Canal

ek 15 0.01 5 4 4 0.13 1

Moddergat-spruit

ek18 0.01 3 4 5 0.12 1

Bottelary At Amandel Road ek03 0.043 3 3 0.26 1

Table 12 Weighting for prioritisation criteria

Criteria Weighting

Public health (PH) 32%

Ecosystem health (EH) 32%

Water usage (WU) 8%

Downstream impact/algae (DI/A) 8%

Risk (R) 8%

Pollution load (PL) 12%

Table 13 Full results for the prioritisation exercise, Hout Bay River

CatchmentRivers/

WetlandsReach/

DescriptionMonitoring

point

Prioritisation criteria

Criteria Points Weighting Score

Hout Bay Hout Bay

Upper(Longkloof Rd)

dr04

PH 1 32.0% 3

EH 2 32.0% 6

WU 1 8.0% 1

DI 5 8.0% 4

R 1 8.0% 1

PL 1 12.0% 1

Total 16

MiddleVictoria Rd

dr02

PH 5 32.0% 16

EH 4 32.0% 13

WU 3 8.0% 2

DI 5 8.0% 4

R 4 8.0% 3

PL 1 12.0% 1

Total 40

Lower Princess St & estuary

dr05(bacto only)dr01

PH 5 32.0% 16

EH 4 32.0% 13

WU 4 8.0% 3

DI 5 8.0% 4

R 5 8.0% 4

PL 1 12.0% 1

Total 41


Table 15 Summary of general recommendations (extract)

RecommendationDuration Benefit

Budget implication (R mill)Priority:

T, H, M, LDescription Capex Opex

Approach to determining resources for stormwater and river systems

Allocate more budget to and prioritise proactive measures

PermanentMore efficient allocation of resources for sustainable water quality improvement; reduces risk in longer term

– – T

Adopt “prevention is better than cure” as guiding principle

PermanentReduction in costly, after-the-event solutions ensuring sustainable water quality improvement

– – T

Institutional issues

Establish inter-departmental water quality forum at senior level

Short-term to permanent

Consolidation of efforts, roles and responsibilities and improved knowledge sharing

– – H

Establish consolidated pollution task teamShort-term to

permanent

Optimisation of resources to address pollution and avoidance of unintended consequences

– – H

Technical issues

Use proactive asset management approach, including audits and inspections for timeous replacement and upgrading of infrastructure

Permanent Greater budget, effort and energy efficiency – – T

Establish programme for eradication of cross-connections, including documentation on GIS

Short- to medium-term

Improved knowledge and records of cross-connections, and therefore improved management response and water quality

R10.0 R5.0 H

Priority range – colour-coding

All the final prioritisation results were

colour-coded in terms of four priority ranges:

■ Red: High priority

■ Yellow: Medium to high priority

■ Green: Low to medium priority

■ Blue: Low priority

These ranges were obtained by determin-

ing the difference between the highest and

lowest priority scores in the prioritisation

exercise and then dividing the number range

into four equal ‘bands’.

Prioritisation results

Table 13 is an example of the working and

final scores for the prioritisation exercise for

the Hout Bay River.

Overall prioritisation results for rivers

were then obtained by averaging the scores

for the various river reaches where applicable.

In such cases it is important to view the river

prioritisation exercise holistically. In the

instance of the Hout Bay River, for example,

it gets a low to medium priority in the overall

river prioritisation exercise; while the middle

to lower reaches are a high priority and the

upper reaches are a very low priority.

By way of example, the prioritisation

results for the vleis/wetlands in the Cape

Town municipal area are shown in Table 14.

Prioritisation: way forward

The prioritisation results are based on a

multi-criteria model using several inputs to

determine those rivers, wetlands and catch-

ments that should receive priority attention

for the proposed interventions.

The prioritisation model, although

rigorous in its composition, can easily be

expanded to include new criteria, or should

a sensitivity analysis be required (to answer

“what if?” questions).

DETERMINATION OF ADDITIONAL

RESOURCES TO MANAGE

POLLUTION IN STORMWATER

AND RIVER SYSTEMS

The methods discussed above culminated in

the determination of interventions, imple-

mentation mechanisms, resources and costs

required by the City to reduce the burden

of pollution in the inland water systems of

the Cape Town municipal area. Proactive,

sustainable measures were recommended as

far as possible and were listed generally and

per catchment.

It was concluded that R675.3 million in

capital or once-off expenditure and R277.15

million in operational expenditure are

required as additional resources to manage

pollution in stormwater and river systems.

General resources applicable throughout

most catchments were discussed under the

following headings:

■ Institutional issues

■ Technical issues

Table 14 Prioritisation results for vleis/wetlands

Catchment Vlei/Wetland Score Priority

Zeekoe Zeekoevlei 49High

Diep Milnerton Lagoon 47

Diep Rietvlei 40

Medium to HighZeekoe Rondevlei 40

Noordhoek Wildevoëlvlei 36

Diep Zoarvlei 34

Low to MediumSand River Die Oog 31

Sand River Little Princessvlei 30

Sand River Langevlei 29

Zeekoe Princessvlei 26

LowSand River Zandvlei 25

Sand River Westlake Wetland 24

South Peninsula Glencairnvlei 19


■ Planning and policy

■ Communication and liaison

Table 15 is an extract of the summary table

used to list general recommendations,

indicating the duration, benefit and budget

implications for each recommendation (an

action and comments column have been

omitted for the sake of clarity).

In addition to the general recommenda-

tions, the resources required to manage water

pollution per catchment were discussed where

catchment-specific details were necessary.

Table 16 is an extract of the summary

table as used to list the catchment-specific

recommendations. The table is in order of

priority, as per the prioritisation exercise.

CONCLUSIONS

This paper discussed the inputs towards

determining resources to manage inland

water pollution in the City of Cape Town.

In the more complex realm of modern

municipal engineering (where many of the

issues are so-called “soft” in nature, and the

problems and solutions are not straightfor-

ward) the methods discussed were instrumen-

tal in creating a holistic overview of the state

of the rivers and wetlands in the City of Cape

Town, highlighting the complexity of the

problem and assisting to plot a way forward

to provide proactive, sustainable measures for

the management of water pollution.

The main obstacle was the time-con-

suming nature of some of the methods. The

colour-coding of data and the compilation of

inputs from the stakeholder workshops were

particularly lengthy.

Another minor obstacle was agreeing on

the points allocated for each of the prioritisa-

tion criteria. There was the later realisation,

however, that the system was fairly robust

and slight deviations in these points made

little or no difference to the ultimate level

of prioritisation of the particular river or

wetland.

Some novel points included: the colour-

coding exercise which helped to convert

vast quantities of hard, scientific data into

something meaningful and tangible to all

involved; the risk assessment and prioritisa-

tion exercise to assist with the allocation of

resources; getting inputs from a vast number

and array of stakeholders; and the ultimate

allotment of actions to City Managers for

each recommendation.

In all, the methods discussed provided a

significant contribution towards the quest

to improve water quality in the City of Cape

Town.

ACKNOWLEDGEMENTS

We wish to thank the following persons for

their valuable contributions throughout this

project:

Table 16 Summary of catchment-specific recommendations (extract)

RecommendationDuration

Budget implication (R mill)Priority

1 – 10 (H – L)Number Description Capex Opex

4.6.1 Diep River catchment: catchment priority: 1

• The recommendations for the Diep River catchment should be read in conjunction with the report for project 233C/2008/09 (Improving the quality of the stormwater discharging into the Diep River – Milnerton), being compiled by iCE Group consulting engineers.

• Appoint additional pollution control inspector for each of five high-priority river reaches where intensive intervention programmes are to be launched

Medium-term – R0.5 1A

• Appoint project manager for each of five identified priority areas to drive integrated improvement programme

Long-term (to move to next priority)

– R0.75 1A

4.6.1.1 Mosselbank River: priority level: high

• Further improvements to Kraaifontein WWTW, including sludge management, phosphate removal, duplicate disinfection unit

Permanent R15.0 R2.0 2

• Implement in Scottsville area in particular findings from a report Advice on the elimination of ingress of stormwater and infiltration of groundwater into the sewer system

Medium-term R1.0 – 3

• Active campaign to reduce agricultural pollution Medium-term – – 6

• Removal of alien vegetation (including aquatic) and restore river banks Long-term R1.0 R0.5 10

• Monitor 15 sewage pump stations for spillage and pollution Permanent – – 5

• Expand solid waste services to areas not currently serviced (e.g. water courses) and increase street sweeping

Permanent – – 4

4.6.1.2 Diep River: priority level: high

• Further upgrade to Potsdam WWTW, including duplicate disinfection unitPermanent R5.0 R1.0 2

• Collaboration with Swartland Municipality and DWA Medium-term – – –

• Provide ablution and car-washing facilities at Bayside Mall taxi rank Medium-term R1.0 R0.1 1B

• Track pollution from Montague Gardens industrial area Short-term – – 7

• Monitor and resolve water quality from Theo Marais Park Short-term R0.5 – 3

• Active campaign to reduce agricultural pollution, including runoff from Milnerton stables

Short-term – – 6

• Monitor nine sewage pump stations for spillage and pollution Permanent – – 5


■ Mr Abdulla Parker for his leadership,

patience, unwavering commitment to the

cause and passion to make a difference.

■ Mr Barry Wood for his invaluable exper-

tise, guidance and support.

■ Ms Candice Haskins for her commitment

and insights into water quality in the City

of Cape Town.

■ Ms Jeanette Kane for her unfailing will-

ingness to help with GIS expertise.

■ Mr Johan Massyn for his willingness to

share his local knowledge and unique

personal experiences.

■ Mr Richard Kotze for his reliability and

for sharing his passion and knowledge.

Many thanks to the project team for their

time, commitment to improving water quality,

enthusiasm, expertise and inspiring insights:

■ Dr Jo Barnes

■ Ms Lyn Viviers

■ Mr Simon Nicks

■ Ms Toni Belcher

Sincere thanks also go to members of the

Steering Committee and the Water Quality

Sub-Committee, and workshop participants.

NOTES

1 The Department of Water Affairs and Forestry

(DWAF) has since become known as the Department

of Water Affairs (DWA)

2 Taken over time

3 It is important to note that while some of the City’s

rivers and water bodies are utilised for formal

full and intermediate contact recreation activities

(e.g. Zandvlei, Milnerton Lagoon, Zeekoevlei and

Rietvlei), the majority of systems are used on a more

informal basis.

4 This is an indirect pollution source, as pollution is

not attenuated in canals as well as it is in natural

rivers, therefore resulting in higher pollution levels.

Furthermore, canals are not as aesthetically pleas-

ing as natural river systems, and may therefore

induce less considerate behaviour towards their

preservation.

5 E.g. Blue Flag beaches, nature reserves, human

habitation, sensitive environment, tourism hotspot

etc, downstream of the water quality monitoring

point.

6 While most wetlands do not have a downstream

impact per se, their algal content (not measured in

the rivers) had to be taken into account as it is an

indication of the propensity for a vlei/wetland to

develop harmful algal blooms (HAB) and therefore

is significant in terms of public health. A distinction

was therefore made between rivers and wetlands

with these criteria.

7 It should be noted that the determination of the pol-

lution load did not form part of the original scope

of works and was later included as an ad hoc inves-

tigation, for which provision existed in the project

budget.

8 Relevant data was obtained from Mr Barry Wood

(CSRM, City of Cape Town).

REFERENCES

Belcher, A (Aquatic water scientist) 2010. Personal

communication.

City of Cape Town (2008) City of Cape Town State of

the Environment Report 2007/8. Cape Town: City of

Cape Town, Environmental Resource Management

Department.

DWAF (Department of Water Affairs and Forestry)

(1996a). South African Water Quality Guidelines,

2nd edition. Vol. 2. Recreational uses. Pretoria: CSIR

Environmental Services.


(1996b). South African Water Quality Guidelines,

2nd edition. Vol. 7. Aquatic ecosystems. Pretoria:

CSIR Environmental Services.

Haskins, C (City of Cape Town) 2010. Personal

communication.

Jooste, S & Rossouw, J N 2002. Hazard-based water

quality ecospecs for the ecological reserve in fresh sur-

face water resources. Report No N/0000/REQ0000,

Pretoria: Department of Water Affairs and Forestry,

Institute for Water Quality Studies.

Ninham Shand, Southern Waters, Cape Metropolitan

Council 1999. Kuils/Eerste River System evaluation

of nutrient flux downstream of Bellville Wastewater

Treatment Works. Report No 3028/8851, Cape Town.

Wood, B (City of Cape Town) 2010. Personal

communication.

World Health Organisation (WHO) 2003. Guidelines

for Safe Recreational Water Environments, Volume 1,

Coastal and Fresh Waters. Geneva.


INTRODUCTION

Irrigation scheme planning and design can

be relatively complex. A scheme’s ultimate

success depends on many things – soils,

water, farmer skills, markets and financing.

By incorporating these factors at the various

design levels, each scheme can be tailored to

the user’s individual circumstances.

The irrigation sector – smallholder irriga-

tors in particular – has been the focus of

much discussion and on-going government

financial assistance. Programmes include

the Revitalisation of Smallholder Irrigation

Schemes of the Limpopo Province and other

ad hoc developments, led by general policy

during the last decade. The Department of

Water Affairs, for instance, has developed a

financial assistance policy for poor farmers

(DWAF 2004), most of whom are small-

holder irrigators.

It is often believed that irrigation is the

key to alleviating poverty, especially in rural

areas. The development of smallholder irri-

gators has a political aspect, because provid-

ing assistance to rural communities through

irrigation aligns directly with national pover-

ty alleviation goals. As a result, governments

place considerable emphasis on smallholder

irrigation, and allocate funds expressly to

develop these irrigators.

By using the correct design philosophy

and optimising the irrigation system, the

project life cycle costs can be minimised

and the best use can be made of the limited

funding.

When designing a new scheme or one

due for revitalisation, two questions arise:

what is the best design approach, and what

will influence the design and profitability?

The answers usually depend on whether

one is designing on a commercial basis, or

altering the design to cater specifically for

the operational needs of the smallholder

irrigator. This paper aims to provide guid-

ance on the expected cost ranges and the

design approach to be adopted under specific

circumstances. The primary aim of the

study is to determine whether an irrigation

scheme’s design should be tailored to the

particular irrigator or broadly structured

Design implications on capital and annual costs of smallholder irrigator projects

A F Hards, J A du Plessis

While agricultural producers on commercially operated irrigation schemes will aim to achieve the recommended high crop yields, those on a smallholder irrigation scheme usually produce moderate to low crop yields. The water demand by these two irrigator types also differs and is reflected in the variations in crop yields. Because smallholder irrigators produce lower crop yields and use less water, they should use a system suited to this lower water demand. Many irrigation schemes have the opportunity for participants to assess their farming objectives and models. The irrigators can then use the assessment results to determine their water demands, reduce their infrastructure capacity and reduce their capital, operation and maintenance costs. On many smallholder schemes, the system has been designed for commercial crop yields and water use. If smallholders never achieve commercial levels of production, they have overcapitalised and subjected themselves to additional operational strain. In this study, six irrigation schemes based in the Eastern Cape were evaluated according to three levels of irrigation supply: a commercial irrigator, a smallholder irrigator and the commercial under-utilised irrigator. The irrigation infrastructure for each of the six schemes was designed, and the associated costs determined, for each level of supply. The study investigates the impact of different designs on the amount of water and land used, and resultant costs of the infrastructure. The results show that a smallholder irrigator using a scheme sized for commercial operation can have significantly higher (between 5% and 29%) annual operation and maintenance costs. The study clearly shows that the farmer type should be considered when designing each irrigation scheme.

TECHNICAL PAPER



ADRIAN HARDS (Pr Eng, MSAICE, MSABI

Designer) has practised in the fi eld of water

engineering for 11 years, gaining most of his

experience in the Eastern Cape. He is particularly

interested in pipeline transient analysis, pump

stations, pipe structural design and irrigation

systems. In 2001 Adrian obtained his BSc in Civil

Engineering from the University of Natal, and in

2008 he obtained Approved Designer status from the South African Irrigation

Institute.

Contact details:


Stellenbosch University

Private Bag X1

Matieland

7602

South Africa

T: +27 21 808 4358

F: +27 21 808 4351


DR KOBUS DU PLESSIS (Pr Eng, MSAICE, MIMESA)

has lectured in hydrology, water engineering

and environmental engineering for the past ten

years at the Stellenbosch University. During his

more than 25 years of experience in the water

sector, he has also worked for the Department

of Water Aff airs, the City of Cape Town and the

West Coast District Municipality. His special

interest is integrated management of water resources in South Africa as

applied by local authorities. He obtained his PhD (Water Governance), MSc

(Water Resource Management) and BEng (Civil) from the Stellenbosch

University.

Contact details:



P/Bag X1

Matieland

7602

T: +27 21 808 4358

F: +27 21 808 4351


Key words: appropriate irrigation design, smallholder irrigators, smallholder

water supply, smallholder production costs


for commercial water use, and whether the

latter, the traditional practice, is the reason

for the high economic risk associated with

smallholder irrigation projects.

LITERATURE REVIEW

Irrigation management

transfer and revitalisation

The most recent stage of smallholder irrigation

in South Africa can be referred to as the era of

irrigation management transfer and revitalisa-

tion (Van Averbeke & Mohamed 2007). The

strategy coincides with the political change in

the country and the ideologies that came with

that change. The planned changes were first

implemented through the Reconstruction and

Development Programme, which was then

followed by the Growth, Employment and

Redistribution Policy.

Existing schemes were targeted first.

Part of the process involved transferring the

responsibility of managing, operating and

maintaining the irrigation scheme from the

state to the farmers. The process is known as

irrigation management transfer (IMT) (Van

Averbeke & Mohamed 2007).

With the current focus on the revitalisa-

tion of irrigation schemes, many lessons can

be learned from previous development mis-

takes. Backeberg (2004) showed that returning

to the previous focus on infrastructure at the

expense of social relationships, land tenure,

water entitlements, economic location and

market access, financial capital and support

services, technical and financial viability, and

resources of households, risks repeating the

mistakes of previous generations.

One of the most comprehensive initiatives

has been the Revitalisation of Smallholder

Irrigation Schemes (RESIS) of the Limpopo

Province (Arcus Gibb 2005). It included the

WaterCare programme and involved revital-

ising the scheme’s infrastructure, leadership,

management and productivity.

The existing smallholder schemes in

South Africa and their characteristics are

summarised in Table 1.

Revitalisation differs from rehabilita-

tion: it does not concentrate solely on the

engineering aspect of the schemes. Denison

(2005) identified that revitalisation takes a

holistic approach in which human develop-

ment (individually and organisationally),

empowerment, access to information, mar-

keting and business strategy development are

given the same emphasis as the engineering

aspects.

Design aspects found in

smallholder irrigation

Each irrigation system installation should

take into account the circumstances and

needs of that scheme. The typical develop-

ment options may need to be adapted to

allow for such issues as:

■ availability of infrastructure for installa-

tion and on-going maintenance

■ availability of support services for main-

tenance of specialist equipment

■ affordability

■ soil and selection of a system that will

prevent soil water management problems

■ the appropriateness of systems such

as short-furrows and the management

requirements needed to ensure their

success.

Productivity of farmers is affected by

education and infrastructure (Fan & Zhang

2004). If inputs and markets are made more

accessible, more rural farmers will be able

to use them, which will lead to greater

productivity (Kamara 2004). However, poor

road conditions, high transport costs and

distant markets prevent good market access

for smallholder irrigators (Nieuwoudt &

Groenewald 2003).

Access to basic general services, such

as finance and communication, affects the

effectiveness of smallholder irrigators and

directly affects their ability to access inputs

and the market in general. Poor access to

services limits the ability of farmers to adopt

new or better technology (Perret & Stevens

2003). Even though they may be regarded

as simple services, they must be remem-

bered during the process of revitalisation

(Chaminuka et al 2008).

Investment costs

The International Water Management

Report (Inocencio et al 2007) investigated

314 projects in 50 countries to find the

factors influencing the cost of revitalising

smallholder irrigation projects. They are:

■ Project size (total irrigated area

benefited by a project)

This is the most important factor

influencing the project costs. The larger

the project, the lower the unit cost; this

is primarily due to the engineering

economies of scale that result from larger

projects.

■ Average area of irrigation systems

involved in a project

As with the project size, larger system

sizes will have lower unit costs than

smaller systems. It was, however, shown

that the larger the system, the lower the

economic performance of the project.

■ Degree of complexity

The degree of complexity does not affect

the development costs of a project.

Increased complexity does, however, have

a negative effect on the rate of return for

the project.

■ Government funding

It was found that the greater the portion

of government funding, the lower the unit

cost for the project.

■ ‘Soft costs’

The ‘soft costs’ include components such

as engineering management, technical

assistance, agricultural support, institu-

tional development, training of staff and

beneficiary farmers. Higher ‘soft costs’

resulted in lower unit costs.

■ Rainfall

The amount of annual rainfall was found

not to have a significant impact on the

costs of projects, but it improved the

economic returns.

■ Macro-economic factors

The greater the gross domestic product

per capita, the higher the unit cost.

■ Farmer contribution to initial costs

No impact was found on the unit cost

where farmers contributed to a project.

When farmers contributed to the initial

costs, the project performance increased.

■ Conjunctive water use

‘Conjunctive water use’ involves the use

of both surface and ground water. It

was found that this did not impact on

Table 1 Categories of existing smallholder irrigation schemes

EraNo of

schemesArea (ha)

Mean area per scheme

(ha)Main technology used

Smallholder canal scheme(1930–1969)

74 18 226 246Gravity-fed surface irrigation

Independent homeland(1970–1990)

62 12 994 210Different forms of overhead irrigation

Irrigation management transfer and revitalisation (1990–present)

64 2 383 37Pump and sprinklers or micro-irrigation

Year of establishment uncertain 117 15 897 136Mostly overhead irrigation

Total 317 49 500 156

Data supplied by Denison (2006)


the unit cost, but increased conjunctive

use did significantly improve project

performance.

■ Operation and maintenance (O&M),

and farmer participation

Three approaches may be taken to

managing O&M – first, through a gov-

ernment agency alone; second, through

a joint venture between government and

farmers; and third, by farmers them-

selves. Farmer-managed systems have

lower unit costs than systems managed

by government agencies. The deeper

involvement of farmers results in tailor-

made, appropriate technology that meets

the farmer’s real needs and reduces the

project costs.

■ Type of crop irrigated

The systems for irrigating rice are sig-

nificantly more expensive than those for

any other crop type. The more valuable

the crop irrigated, the higher the project

performance and profitability. Fruits, veg-

etables and livestock products generally

result in better project performance.

The project size, rainfall and the type of crop

irrigated all affect the costing of the schemes

analysed in the research. Due to the nature

of the study and the engagement of the com-

munity, the degree of complexity, ‘soft costs’

and farmer participation should all result

in lower costs and more efficient schemes.

However, the effect of these items has not

been quantified in this study.

Smallholder production and

reduced crop water requirement

The aim of any irrigation venture is to pro-

duce the best possible crop yield permitted

by the soil, water and fertility (Doorenbos &

Pruitt 1977). Smallholder irrigators tend to

apply significantly less water than commer-

cial irrigators, largely because of their lower

plant densities and low-input cultivation.

Smallholder irrigators farm in a manner

aimed at reducing risk (Perret & Stevens

2003). By reducing risk they lower input

costs. The direct result is reduced crop water

requirements and reduced system capacity.

The reduced system capacity reduces initial

costs and on-going operational costs. If the

system requires less water than its design

requires, its full capability might be underu-

tilised (Crosby et al 2000).

When the system is being designed, the

future needs of the farmer must be deter-

mined. The system can then be designed to

allow flexible operation, and expansion if

required.

Conventional design norms for cal-

culating crop water requirements gener-

ally suit intensive farming practices, and

infrastructure is designed to the peak water

requirement. However, a smallholder irriga-

tor scheme generally has lower yields than an

intensive scheme. When this fact is ignored

and the intensive system is proposed for

the smallholder irrigator, the oversizing can

negatively affect the financial evaluation

of the project; the project might then be

rejected based on sustainability or initial

capital costs. If, when calculating crop water

requirements, crop coefficients were adapted

to reflect the conditions on smallholder

schemes, the proposed infrastructure is

likely to be smaller in capacity and lower in

cost (Crosby et al 2000).

Farmer types and risks

Denison & Manona (2006) and Van Averbeke

& Mohamed (2005) developed farmer

typologies for irrigation schemes. These

typologies are very useful for suiting the

system design to the application. The farmer

types are closely linked to the level of risk

the farmer is willing to accept (i.e. how will-

ing the farmer is to risk losing money). This

willingness to accept risk determines how

farmers operate, another factor in determin-

ing the farmer type. The farmer types also

measure success according to their own

criteria, which might not include financial

aspects. Four farmer types were identified:

■ Business farmer

Business farmers are commercially

oriented producers aiming to produce

an income from their farming activities.

They usually have high skill levels, an

understanding of markets and greater

financial resources. These farmers are

likely to accept higher risks and aim for

higher crop yields.

■ Smallholder farmer

Smallholder farmers are traditionally

plot holders. They do not rely on farm-

ing alone, but generate income from a

variety of livelihoods. As a result, they

rely less on outside markets for their cash

income. They are more risk-averse than

the business farmer and use lower-risk

farming styles. They may struggle to be

financially sustainable on larger schemes

and pump systems with high O&M costs.

Their operations are more suited to

gravity schemes with lower annual costs.

They will generally reduce their inputs

to reduce risk, and consequently achieve

lower yields.

■ Equity labourer

Some large, expensive irrigation schemes

are open to partnerships. They consist of

a number of plot holders who are unable

to farm in a business farmer model.

Instead, an outside commercial partner

operates the scheme and farming enter-

prise, and the plot holders become equity

labourers who make their resources

– soils, water and infrastructure – avail-

able. As equity labourers, the plot holders

enjoy the benefits of employment and

receive dividends from the enterprise

profits.

■ Food producer

Food producers may be plot holders on

a scheme. They have limited access to

resources such as labour and finance.

Generally, food producers are on the pov-

erty line and their objective is simply to

supply their households with food. They

want to avoid risk completely and may

not use irrigation, due to the initial costs,

risks and their low skill level.

One of the most important findings of the

Van Averbeke & Mohamed (2005) study was

the attitude of the farmers. There was no

evidence that farmers of one type aspired

to achieve the higher level of production of

another type. This finding is of particular

importance as it shows that a scheme for

smallholder irrigators should not be designed

on the assumption that they will, over time,

become business farmers. The objectives of

the farmers determine their type. Only when

the objectives of the farmer alter would they

move into a different type.

The scheme design must therefore be

based on direct interaction with the farm-

ers so that the design matches the farmers’

objectives.

METHODOLOGY

The research presented in this paper is based

on the input data from a project undertaken

by ARCUS GIBB for the Department of

Table 2 Pre-feasibility scheme identification

Scheme name Location Size (ha) Water source Existing or proposed

Kama Furrow Zanyokwe 50.90 Keiskamma River Existing bulk

Wolf River Keiskammahoek 25.00 Sandile Dam Proposed

Philane/Ncambedlana Mthatha 85.00 Mtata Dam Existing

Tamboekiesvlei Kat River 33.84 Kat River Dam Proposed

Mantusini Port St Johns 30.00 Mngazi River Proposed

Kruisfontein Ext Humansdorp 19.21 Seekoei River Existing


Water Affairs (Arcus Gibb 2004a–f) in 2003

and 2004 – the Eastern Cape Resource Poor

Farmers Irrigation Pre-Feasibility Study.

However, all cost calculations were based on

2007 values.

The schemes selected to form the basis of

the research are shown in Table 2. Figure 1

shows each scheme schematically.

Design development

The proposed system for each scheme

was developed in consultation with the

beneficiaries and the characteristics of

each scheme. During the study, multiple

development options were evaluated for each

scheme. The economics of these different

options were then evaluated. Only the eco-

nomically most favourable option for each

scheme was used in the analysis presented in

this paper.

The most favourable economic option

was developed for the commercial farmer

and the smallholder irrigator. For each farm-

er type, the water demands were calculated

and the favourable option designed to cater

for the required flow capacity of the system

to meet the irrigation demand. The water

demands were calculated using the SAPWAT

(Crosby & Crosby 1999) software. BEWAB

(Bennie 1993) software was used to estimate

the reduction due to the lower yields and

crop density of smallholder irrigators. For

the purpose of the study, the term ‘level of

supply’ (LOS) has been used to identify the

farmer type and the resulting system capa-

city design.

The calculation of the costs of the

schemes and evaluation does not take into

account everything that affects irrigators.

The initial capital investment in the selected

schemes covers only the construction cost

and related engineering fees. The financial

impacts of training and organisational and

institutional development were excluded.

The training requirements are not always

directly linked to the scheme type and

size, but are more likely to be linked to the

number of beneficiaries and existing skill

levels.

The scheme types are also limited in the

variety of infrastructure options. These were

limited to:

■ pump-based schemes with only sprinklers

and draglines, and

■ gravity schemes that include sprinklers

and draglines, drip irrigation and short

furrow flood irrigation options.

The impact of these limited selections for

this study on the design, costs and results are

as follows:

■ The analysis is biased towards draglines

and sprinklers.

■ Results are limited to the cost associated

with these pre-selected options.

■ Annual O&M costs are calculated only

on the actual infrastructure.

■ A large portion of the O&M costs are

attributed to the electrical costs of the

pumping equipment.

■ O&M costs allow for water charges of

67 cents per cubic metre of water.

■ Kama Furrow, Wolf River and

Ncambedlana have formalised their

union as the Water Users Association,

with an associated management cost of

R250 per hectare per annum.

Financial evaluation

The gross margin analysis was based on

one hectare under irrigation, planted with a

mixture of field crops and vegetables. The crop

types were green mealies, potatoes, tomatoes,

carrots, maize and dry beans (summer crops)

and cabbage (winter crop). The costs for each

crop type excluded management, but included

indicative market selling prices and transport

to markets. The crop types were chosen to

provide a fair representation of crops and a

profitability that could realistically be achieved.

The hectare would be fully planted with the

six summer crops, but only 30% of the area

would be used for cabbages in winter. The

gross margin was calculated for each LOS con-

sidering the overall yield difference between a

commercial and smallholder irrigator. In terms

of efficiency of production, the evaluation

is based on smallholder irrigators achieving

production levels of 60% of the commercial

yields, as would be expected from the regional

Figure 1 Scheme schematics

Existing bulk gravity main

New bulk gravity main

Existing main

Existing Sandile Dam

Schematic for Kama Furrow

51 ha(Refurbishment of existing sprinkler

infrastructure)

Existing reservoir

End of existing pipeline

Schematic for Tamboekiesvlei

New drip infield infrastructure

33.89 ha

New distribution main

New dam

Existing Sandile Dam Existing Mthatha Dam

12 ha

Existing reservoir

Existing booster pump station (to be rehabilitated)

Rehabilitated sprinkler system

New sprinkler system

Existing bulk gravity main

New pump station

Schematic for Wolf River

Schematic for Mantusini

Mngazi River

New rising mains

New sprinkler infrastructure

New pump stations 3

0 h

a

Schematic for Ncambedlana

12 ha

Mthatha River

Existing Mthatha dam

New elevated tank

No infield infrasructure

85 ha

New rising main

Rehabilitated sprinkler system

7.41 ha11.8 ha

Schematic for Kruisfontein

Existing Klaas se Dam

Existing Dan se Dam

Existing Frank se Dam

New canal

New distribution

main

New infield infrastructure


Computerised Enterprise Budgets (COMBUD)

published by the Department of Agriculture.

Additional key elements of the evaluation were:

■ The financial analysis includes the DWA

Bulk Water subsidy of R 10 000 per

hectare with a maximum of R 50 000 per

eligible farmer.

■ The analysis does not make provision for

the replacement of infrastructure.

■ The tax rate used for the financial evalu-

ation is 15%.

■ Infrastructure loans will be at an interest

rate of 8%.

■ It is assumed that farmers will require loans

for 100% of their operational costs during

the first two years and that thereafter they

will reduce their requirements to 50%.

SUMMARY OF FINDINGS

Summarising the costs of the interventions

of each of the schemes allows us to evaluate

the type of system applied and whether there

are similarities between the schemes. Table 3

shows the characteristics of the different

types of schemes evaluated in this study.

Capital costs

For each scheme, a design was created for the

commercial and smallholder levels. A sum-

mary of the associated development capital

costs are presented in Table 4. Table 4 shows

that the initial capital costs are likely to be

linked to the type of scheme. A ‘rehabilitated’

scheme is likely to cost less than any other

type of scheme; a new ‘pumped’ scheme

costs more than a rehabilitated scheme; and

a new ‘gravity’ scheme is the most expensive.

Operation and maintenance costs

From the capital costs developed for each

scheme, the associated O&M costs have

been calculated and presented in Table 5.

The actual cost per hectare of the schemes,

based on the annual O&M costs, reveals

four distinct groups. These are: Wolf River

and Kruisfontein, Mantusini, Wolf River and

Kamma Furrow, and Ncambedlana. Table 5

shows that gravity schemes are likely to have

lower O&M costs than pumped schemes.

However, a gravity scheme with significant

infrastructure would have higher O&M

costs, making it similar to a smaller pumped

scheme. A pumped-to-storage scheme has

higher O&M costs than any other scheme.

The costs given in Table 5 include:

■ O&M: These include the annual mainte-

nance costs of the proposed infrastruc-

ture; and operational costs, including

water charges, water user association

charges and electrical operational costs.

No additional allowances have been made

for increases in electricity costs.

Table 3 Scheme characteristics

Scheme Area (ha) Type Source

Kamma Furrow, extension of pipeline 50.9 Gravity with bulk supply Bulk pipeline

Wolf River, section in Zanyokwe 25 Rehabilitation pumped Bulk pipeline

Ncambedlana 85 Pumped to storage Run of river

Tamboekiesvlei 33.84 Gravity with bulk supply Dam

Mantusini 30 Pumped to infield Run of river

Kruisfontein 19.21 Rehabilitation gravity Dam

Table 4 Summary of capital costs

SchemeArea(ha)

Commercial LOS Smallholder LOS

Variation in cost

Capital cost Capital cost

R x 106 R/ha R x 106 R/ha

Kamma Furrow, extension of pipeline 50.90 8.34 163 874 6.97 136 886 16%

Wolf River, section in Zanyokwe 25.00 1.08 44 027 1.06 42 433 4%

Ncambedlana 85.00 10.78 126 877 9.24 108 704 14%

Tamboekiesvlei 33.84 5.28 155 888 3.50 103 488 34%

Mantusini 30.00 2.40 80 089 2.17 72 352 10%

Kruisfontein 19.21 0.64 33 397 0.45 23 485 30%

Table 5 Summary of O&M costs

SchemeArea(ha)


Variation of O&M

costs

Variation of annual

cost of water

O&M (R/ha)

Annual cost of water

(R/m3)

O&M (R/ha)

Annual cost of water

(R/m3)

Kamma Furrow, extension of pipeline

50.90 2 503 0.29 2 344 0.38 6% –34%

Wolf River, section in Zanyokwe

25.00 2 527 0.30 2 156 0.36 15% –22%

Ncambedlana 85.00 11 734 1.60 7 553 1.47 36% 8%

Tamboekiesvlei 33.84 635 0.08 442 0.08 30% 1%

Mantusini 30.00 2 811 0.64 2 209 0.72 21% –12%

Kruisfontein 19.21 213 0.03 150 0.03 30% 0%

Table 6 Summary of costs for commercial under-utilised LOS

SchemeArea (ha)

Capital costO&M (R/ha)

Annual cost of water (R/m3)R x 106 R/ha

Kamma Furrow, extension of pipeline 50.90 8.34 163 874 2 479 0.41

Wolf River, section in Zanyokwe 25.00 1.08 43 303 2 425 0.41

Ncambedlana 85.00 10.78 217 855 10 409 2.03

Tamboekiesvlei 33.84 5.28 155 888 618 0.11

Mantusini 30.00 2.40 80 088 2 418 0.79

Kruisfontein 19.21 0.64 33 396 199 0.04


■ Annual cost of water: The value shows

the annual O&M cost of water used on

the scheme. The cost does not allow for

capital repayment. The cost of operating

the scheme in R/m3 was based on level

of consumption. The lower the cost per

cubic metre, the greater the value to the

user, because it will cost less to use the

same amount of water.

Variation of costs

It is important to determine the impact of the

variation between the two LOS designs on

capital, O&M and water costs. To illustrate this

variation between the costs, the percentage

variation of the commercial LOS to the small-

holder irrigator LOS is shown in Tables 4 and 5.

Zero percent indicates that there is no

variation; a positive percentage that the

commercial LOS has a higher value than the

smallholder irrigator LOS; and a negative per-

centage that the commercial LOS has a lower

value than the smallholder irrigator LOS.

The capital cost has a variation range

of costs between 4% and 34%, with the

average about 18%. The increased costs are

not proportional to the increased volume

of water used, which was expected due to

economies of scale. For example, the infra-

structure required to deliver 30% more water

would not need to cost 30% more.

Commercial under-utilised

level of supply

Tables 4 and 5 compare the commercial and

smallholder LOSs, and show how they affect

the initial capital and on-going operational

costs. The impacts on the smallholder irriga-

tor caused by over-designing the scheme are

revealed, not by simply comparing the com-

mercial and smallholder irrigator costs, but by

considering the full scenario of the commercial

under-utilised LOS. Commercial under-use

occurs when a smallholder irrigator is placed on

a commercially designed scheme, but still oper-

ates like a smallholder. To evaluate the impacts

of this, the costs for the commercial designed

scheme and the water use of the smallholder

LOS need to be compared. Table 6 summarises

the costs associated with this option.

The costs in Table 6 for the commercial

under-utilised LOS projects provide the

best information for comparison with the

smallholder irrigator’s costs. The commercial

under-utilised LOS and the commercial LOS

have been compared to the smallholder LOS

in Figure 2.

Figure 2 shows that the capital and O&M

costs of the commercial under-utilised LOS is

on average 18% more expensive than a correctly

sized scheme. If the capital costs do not need

Figure 2: Percentage comparison of commercial, commercial under-utilised against smallholder irrigators

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25

15

10

0

5

–5

–10

–15

–20

–25

–30

–35

–40

Scheme

Kamma Furrow Wolf River Ncambedlana Tamboekiesvlei Mantusini Kruisfontein

Captital cost O&M – Commercial O&M – Commercial under-utilised

Annual cost of water – Commercial Annual cost of water – Commercial under-utilised

16%

6% 5% 5%

–34%

–22%

2%

15%

11% 11%

14%

36%

27% 27%

8%

34%

30% 29% 29%

1%

10%

21%

9%9%

–12%

30% 30%

25% 25%

0%

Figure 3 O&M cost of scheme vs scheme area for all three LOSs

O&

M c

ost

(R

1 0

00

/ha)

14

0 2010 30 40 6050 70 80 90

Area (ha)

Commercial LOS – pumped

Smallholder LOS – gravity

Small holder LOS – pumped

Commercial under-utilised LOS – pumped

Commercial LOS – gravity

Commercial under-utilised LOS – gravity

12

10

4

6

8

0

2


to be repaid, it may not have the initial negative

impact that it would have if the farmers needed

to fund the construction themselves. However,

the O&M costs of the larger capacity system

affect the farmers on an on-going basis. They

are between 5% and 29% higher than if the

system were designed for the smallholder LOS

only, and farmers must pay these higher costs

each year, which affects their financial viability.

A commercial farmer would be produc-

ing a higher yield crop than a smallholder

irrigator on the same system, and unlike the

smallholder, would recoup the additional costs.

The variation in O&M costs for the three LOSs

is depicted in Figure 3. It would be expected

that the larger schemes would benefit from

economies of scale and that the annual O&M

cost per hectare would decrease as the scheme

size increased. Figure 3 indicates that the char-

acteristics of the selected schemes for the study

outweigh the economies of scale and have a

greater effect on the annual O&M.

The O&M costs for the commercial LOS

are higher and generally vary from 5% to

34% compared to the other LOSs. A further,

distinct variation occurs between the gravity

and pumped schemes: the pumped system

has higher O&M costs, which are largely

attributable to electricity charges.

The higher annual O&M cost per cubic

metre for the commercial under-utilised LOS

is shown in Figure 4. While the O&M cost

per cubic metre for the commercial LOS and

smallholder LOS are roughly the same, the

commercial under-utilised LOS has signifi-

cantly higher annual O&M cost per cubic

metre – between 5% and 29% – than the

commercial and smallholder LOSs.

Financial evaluation

Table 7 presents the results of a financial

evaluation for each scheme and LOS. The

return on investment presented in Table 7

has been calculated at year 5 when the initial

infrastructure capital debt repayments have

reduced and normal working capital require-

ments account for the lending needs of the

farmers. The full calculations show the same

return on investment from year 5 until year 19

(not presented here). The return on invest-

ment was calculated using the net benefit

after financing divided by the initial capital

outlay. The cash surplus is the net benefit after

financing divided by the irrigable area.

The results of the financial evaluation

show that a commercially operated farm pro-

vides the best net present value (NPV) and

cash surplus. The higher NPV is expected,

since commercial farmers will have higher

returns from their crops. The smallholder

irrigator has the second best NPV for each of

the schemes, except for Ncambedlana, which

provided the best NPV. ‘Commercial under-

utilised’ ranks third in each category.

For normal investment purposes, a nega-

tive NPV would indicate that a project is not

viable in its current form and should be either

abandoned or revised to determine a suitable

strategy for achieving a positive return.

CONCLUSIONS

The higher water use associated with the

commercial LOS results in infrastructure

with greater capacity, but with higher

construction costs and higher annual O&M

costs. The infrastructure for the smallholder

LOS has been reduced to suit its lower needs,

reducing its capital and O&M costs.

The evaluation of the two LOSs has

shown that the capital cost for the com-

mercial LOS is approximately 18% higher

than for the smallholder LOS, and the O&M

costs are 6% to 36% higher. The initial capital

cost may, in some cases, be grant-funded

Table 7 Financial evaluation of each scheme and LOS

Scheme LOSNPV (R)

Net return on investment in year five

Annual cash surplus (R/ha)

Kama Furrow

Commercial –4 391 249 4.06% 17 762

Smallholder –4 794 580 2.41% 8 823

Commercial under-utilised –6 306 129 1.94% 8 98

Wolf River

Commercial 3 265 699 35.34% 20 422

Smallholder 1 685 013 21.69% 12 078

Commercial under-utilised 1 615 857 20.61% 11 909

Ncambedlana

Commercial –8 316 079 1.28% 7 260

Smallholder –1 125 785 2.72% 4 999


Tamboekiesvlei

Commercial –243 546 8.03% 22 251

Smallholder –250 038 7.21% 13 258


Mantusini

Commercial 2 244 703 16.13% 20 352

Smallholder 820 951 10.73% 12 224

Commercial under-utilised 555 314 9.58% 12 079

Kruisfontein

Commercial 4 227 572 68.39% 23 034

Smallholder 2 604 644 58.27% 13 801

Commercial under-utilised 2 426 184 40.85% 13 759

Figure 4 Annual O&M cost of water vs scheme area

Co

st o

f w

ate

r (R

/m3)

2.5

0 2010 30 40 6050 70 80 90

Area (ha)

Commercial LOS – pumped

Smallholder LOS – gravity

Small holder LOS – pumped

Commercial under-utilised LOS – pumped

Commercial LOS – gravity

Commercial under-utilised LOS – gravity

2.0

1.5

0.5

1.0

0


by the government, but the on-going O&M

costs will be funded by the farmer. If farmers

are producing the yields associated with the

different LOSs, they will have no additional

financial burden, as the infrastructure has

been sized to suit that LOS.

The evaluation, even though based on

limited specific projects, provides a general

estimate of possible costs associated with

each scheme type and LOS. As the calcu-

lated costs depend on each scheme’s indi-

vidual requirements and location, they will

not be applicable to every similar scheme.

The schemes that were investigated can be

grouped into five general scheme types:

■ Gravity schemes that need rehabilitation,

where the bulk supply is in place and no

augmentation or rehabilitation is required

(e.g. Kruisfontein)

■ Rehabilitated schemes where water is

supplied from a nearby bulk pipeline and

pumped directly to the lands (e.g. Wolf

River)

■ Run-of-river schemes where water is

abstracted and pumped directly to the

lands (e.g. Mantusini)

■ Run-of-river schemes where water is

abstracted and pumped to storage (e.g.

Ncambedlana)

■ Gravity schemes where bulk supplies

need to be installed (e.g. Tamboekiesvlei

and Kama Furrow)

A summary of the indicative costs of the

different scheme categories is provided in

Table 8.

A a new irrigation system may have been

designed for a commercial LOS because the

designer either had not taken into account

the irrigator type or had expected that the

smallholder irrigator would attain a commer-

cial LOS. If the smallholder irrigator attains

a commercial LOS, they would receive a ben-

efit because the system would cater for the

higher LOS they require. If the irrigator has

neither the desire, necessary skills, mainte-

nance support, sufficient training, access to

credit, nor links to markets needed to attain

a commercial LOS, they would continue to

operate at a smallholder LOS, but with the

additional challenges associated with the

cost of water, due to the over-designed sys-

tem. Where the smallholder irrigator is never

going to achieve a commercial LOS, they will

find they must use a system that is optimised

to neither their skills nor their water needs.

A comparison between the commercial

under-utilised LOS and the smallholder LOS

has shown that the capital cost for commer-

cial under-utilised LOS is 2% to 34% higher,

and the O&M costs 5% to 29% higher, than

for the smallholder LOS. The O&M variation

is higher with the same water use, indicating

that the costs of maintaining the higher cost

infrastructure and of operating higher capa-

city pumps have a significant impact on the

smallholder irrigator.

The smallholder irrigator on a com-

mercial LOS scheme is therefore at a definite

disadvantage to a smallholder irrigator on a

smallholder LOS scheme. Even if the initial

capital costs are grant-funded by govern-

ment, the irrigator must pay higher annual

O&M costs. The higher O&M costs will

directly affect the farmers’ margins and how

much they will profit from the venture. It

could also affect the farmers’ sustainability;

they would need to consolidate land and

manage larger areas to generate greater

profits to overcome their higher O&M costs.

Failure rates of these farmers would also

probably be higher.

A further indication of the cost effective-

ness of the smallholder LOS is illustrated in

the annual O&M costs per cubic metre of

water used. This figure is significant – the

commercial LOS and smallholder LOS have

similar values, showing that their design and

water use are being optimised. The O&M

costs of the commercial under-utilised LOS

are significantly higher, ranging between

5% and 29%. The higher values indicate that

smallholder irrigators using less water on a

commercial LOS are not operating optimally

and their water use is not as cost-effective as

that on the correctly designed schemes.

The financial evaluation provides further

evidence that a commercial scheme offers

little benefit for a smallholder irrigator. The

smallholder irrigator will achieve lower

returns and faces additional risk due to high

debt. Table 8 shows that the commercial

under-utilised LOS provides the lowest NPV,

net return on investment and annual cash

surplus. A summary of the indicative finan-

cial return of the different scheme categories

is provided in Table 9.

RECOMMENDATIONS

To appropriately apply the information

provided by the study, the individual

Table 8 Indicative cost on irrigation schemes

Scheme type


Capital cost(R/ha)

O&M(R/ha)

Annual cost of water (R/m3)

Capital cost(R/ha)

O&M(R/ha)

Annual cost of water (R/m3)

Pumped – rehabilitation 44 027 2 527 0.30 42 433 2 156 0.36

Run of river – pumped to field 80 089 2 811 0.64 72 352 2 209 0.72

Run of river – pumped to storage 126 877 11 734 1.60 108 704 7 553 1.47

Gravity with bulk supply 163 874 to 155 888 2 503 to 635 0.29 to 0.08 136 886 to 103 488 2 344 to 442 0.38 to 0.08

Gravity – rehabilitation 33 397 213 0.03 23 485 150 0.03

Table 9 Financial evaluation of each scheme type

Scheme type


NPV (R)

Net return on investment (%)


NPV (R)

Net return on investment (%)


Gravity – rehabilitation 4 227 572 68.39% 23 034 2 604 644 58.27% 13 801

Pumped – rehabilitation 3 265 699 35.34% 20 422 1 685 013 21.69% 12 078

Run of river – pumped to field 2 244 703 16.13% 20 352 820 951 10.73% 12 224

Run of river – pumped to storage –8 316 079 1.28% 7 260 –1 125 785 2.72% 4 999

Gravity with bulk supply –243 546 to –4 391 249 8.03% to 4.06% 22 251 to 17 762 –250 038 to – 4 794 580 7.21% to 2.41% 13 258 to 8 823


circumstances of each scheme and the farm-

ers involved in it must be understood.

Business farmers are likely to require the

commercial LOS. They are willing to accept

higher risk, have financing to cover the

higher inputs and have market access to sell

their larger amount of produce.

Smallholder farmers will require a design

based on the smallholder LOS, as this is most

suited to a more risk-averse farming style

where inputs are reduced and reliance on out-

side assistance is not an important component.

Understanding the farmer types and the

appropriate LOS allows the results from the

evaluated schemes to be correctly correlated.

The farmer types, anticipated LOS and associ-

ated costs have been incorporated in Table 10.

The design of any scheme must involve

consultation with the end users to determine

their main objectives and ability to manage

risk. Once these have been determined, the

scheme can be designed for an appropriate

LOS and the associated costs can be evalu-

ated. When approaching a new project for

which the farmer type and scheme type have

been determined, Table 10 can be used to

provide a starting point for the anticipated

LOS and associated costs. Site-specific

design and economic calculations will then

need to be completed for the proposed

scheme to determine its capital costs and

financial viability.

REFERENCES

Arcus Gibb 2004a. Eastern Cape Resource-poor Farmers

Irrigation Scheme Feasibility Study: Kama Furrow

final report. Report No PWMA12/000/00/1807,

Pretoria: Department of Water Affairs and Forestry.

Arcus Gibb 2004b. Eastern Cape Resource-poor Farmers

Irrigation Scheme Feasibility Study: Kruisfontein final

report. Report No PWMA12/000/00/1107, Pretoria:

Department of Water Affairs and Forestry.

Arcus Gibb 2004c. Eastern Cape Resource-poor Farmers

Irrigation Scheme Feasibility Study: Mantusini final



Arcus Gibb 2004d. Eastern Cape Resource-

poor Farmers Irrigation Scheme Feasibility

Study: Ncambedlana final report. Report No

PWMA12/000/00/2007, Pretoria: Department of

Water Affairs and Forestry.

Arcus Gibb 2004e. Eastern Cape Resource-poor Farmers

Irrigation Scheme Feasibility Study: Tamboekiesvlei

final report. Report No PWMA12/000/00/1007,

Pretoria: Department of Water Affairs and Forestry.

Arcus Gibb 2004f. Eastern Cape Resource-poor Farmers

Irrigation Scheme Feasibility Study: Wolf River final



Arcus Gibb 2005. RESIS – The Limpopo programme for

the revitalisation of smallholder irrigation schemes:

A description and critique. Report No 5 of WRC

Project K5/1464/4, East London: Arcus Gibb.

Backeberg, G R 2004. Research management of water

economics in agriculture – An open agenda.

Agrekon, 43(3): 357–374.

Bennie, A T P 1993. Besproeiingswater

Bestuursprogram (BEWAB): Hersiene weergawe.

[Irrigation Water Management Programme, revised

version]. Bloemfontein: University of the Orange

Free State, Department of Soil Science.

Chaminuka, P, Senyolo, G M, Makhura M N & Belete,

A 2008. A factor analysis of access to and use of

service infrastructure amongst emerging farmers in

South Africa. Agrekon, 47(3): 365–378.

Crosby, C T & Crosby, C P 1999. SAPWAT – A comput-

er program for establishing irrigation requirements

and scheduling strategies in South Africa. WRC

Report No. 624/1199, Report to the Water Research

Commission, Pretoria: MSS Consulting Engineers.

Crosby, C T, De Lange, M, Stimie, C M & Van der

Stoep, I 2000. A review of planning and design

procedures applicable to small-scale farmer irriga-

tion projects. WRC Report No 578/2/00, Report to

the Water Research Commission, Pretoria: MSS

Consulting Engineers.

Denison, J D 2005. A comparative analysis of South

African and international irrigation revitalisa-

tion approaches. Report No 10, WRC Project No

K5/1463/4, Pretoria: Water Research Commission.

Denison, J D 2006. Data base on smallholder irrigation

schemes in South Africa. WRC Project No K5/1463/4,

Pretoria: Water Research Commission.

Denison, J D & Manona, S 2006. Principles, approaches

and guidelines for the participatory revitalisation

of smallholder irrigation schemes. Vol 1: A rough

guide for irrigation development practitioners. WRC

Report No TT 308/07, Pretoria: Water Research

Commission.

Doorenbos, J & Pruitt, W O 1977. Guidelines for

Predicting Crop Water Requirements. FAO Irrigation

and Drainage Paper No 24, Rome: Food and

Agriculture Organization of the United Nations.


2004. Policy on the Financial Assistance to Resource-

poor Irrigation Farmers. Pretoria: DWAF.

Fan, S & Zhang, X 2004. Infrastructure and regional

economic development in China. China Economic

Review, 15: 203–214.

Inocencio, A, Kikuchi, M, Tonosaki, M, Maruyama,

A, Merrey, D, Sally, H & De Jong, I 2007. Costs and

performance of irrigation projects: A comparison of

sub-Saharan Africa and other developing regions.

IWMI Research Report No 109, Colombo, Sri Lanka:

International Water Management Institute.

Kamara, A B 2004. The impact of market access on

input use and agricultural productivity: Evidence

from Machakos District, Kenya. Agrekon, 43(2):

202–216.

Nieuwoudt, L & Groenewald, J 2003. The Challenge of

Change: Agriculture, Land and the South African

Economy. Scottsville: University of Natal Press,

265–282.

Perret, S R & Stevens, J B 2003. Analysing the low

adoption of water conservation technologies by

smallholder farmers in southern Africa. Working

Paper No 2003-01, Pretoria: University of Pretoria:

Department of Agricultural Economics, Extension

and Rural Development.

Van Averbeke, W & Mohamed, S S 2005. Smallholder

farming styles and development policy in South

Africa: The case of Dzindi Irrigation Scheme.

Pretoria: Tshwane University of Technology,

Department of Crop Science, Centre for Organic and

Smallholder Agriculture.

Van Averbeke, W & Mohamed, S S 2007. Smallholder

irrigation schemes in South Africa: Past, present and

future. Pretoria: Tshwane University of Technology,

Department of Crop Science, Centre for Organic and

Smallholder Agriculture.

Table 10 Anticipated cost of irrigation schemes according to farmer type

Farmer type LOS Cost

Scheme type

Gravity – in-field

rehabilitation

Pumped – rehabilitation

Run of river – pumped

to field

Run of river – pumped to storage

Gravity with bulk supply

Commercial (business) farmer

Commercial

Capital cost (R/ha) 33 397 44 027 80 089 126 877 163 874–155 888

O&M (R/ha) 213 2 527 2 811 11 734 2 503–634

Annual cost of water (R/m3) 0.03 0.30 0.64 1.60 0.29–0.08

Smallholder farmer

Smallholder

Capital cost (R x 103/ha) 23 485 42 433 72 352 108 704 136 86–103 488

O&M (R/ha) 150 2 156 2 209 7 553 2 344–441

Annual cost of water (R/m3) 0.03 0.36 0.72 1.47 0.38–0.08


TECHNICAL PAPER



DR PETRA GAYLARD holds a PhD in Chemistry

and an MSc in Statistics from the University of

the Witwatersrand. This publication arises from

the research report for her MSc in Statistics.

Contact details:

School of Statistics and Actuarial Science

University of the Witwatersrand

Private Bag 3, Wits, 2052

South Africa

T: +27 11 486 4836

F: +27 86 671 9895


PROF YUNUS BALLIM holds BSc (Civil Eng), MSc

and PhD degrees from the University of the

Witwatersrand (Wits). Between 1983 and 1989 he

worked in the construction and precast concrete

industries. He has been at Wits since 1989,

starting as a Research Fellow in the Department

of Civil Engineering and currently holds a

personal professorship. He was the head of the

School of Civil and Environmental Engineering from 2001 to 2005. In 2006 he

was appointed as the DVC for academic aff airs at Wits. He is a Fellow of SAICE.

Contact details:

School of Civil & Environmental Engineering



South Africa

T: +27 11 717 1121

F: +27 11 717 1129


PROF PAUL FATTI is Emeritus Professor of

Statistics at the University of the Witwatersrand

and acts as consultant in Statistics and

Operations Research to a broad range of

industries. He holds a PhD in Mathematical

Statistics from the University of the

Witwatersrand and an MSc in Statistics and

Operational Research from Imperial College,

London. He spent most of his professional career at the University of the

Witwatersrand, including 18 years as Professor of Statistics. His other

employment includes the Chamber of Mines Research Laboratories, the

Institute of Operational Research in London and the CSIR.

Contact details:

School of Statistics and Actuarial Science



South Africa

T: +27 11 880 6957

F: +27 11 788 9943


Keywords: concrete; shrinkage, model prediction, dataset

INTRODUCTION

Shrinkage is an important property of

concrete as it influences the durability,

aesthetics and long-term serviceability of the

concrete, as well as its load-bearing capacity

(Addis & Owens 2005). Thus, the accurate

prediction of shrinkage is important in

the design stage of any concrete structure

(American Concrete Institute 2008). Most

existing shrinkage prediction models do not

take into account the effect of concrete raw

materials, such as different supplementary

cementitious materials and aggregate types.

Furthermore, these models were generally

developed using data derived from non-

South African concretes and thus do not take

into account the effects of local materials,

which may differ substantially from those

used elsewhere.

This paper presents a hierarchical,

non-linear model for predicting the drying

shrinkage of concrete intended for structural

use. Using historical data for shrinkage of

South African concretes, the model was

developed by firstly identifying the most

appropriate nonlinear shrinkage-time growth

curve for individual shrinkage profiles.

Secondly, the parameters of this growth

curve model were fitted to each measured

shrinkage profile individually, in terms of

suitable known covariates (independent

variables), namely, the composition of the

concrete, its other engineering properties, as

well as shrinkage test conditions. The model,

referred to as the WITS model, is therefore

intended to account for the raw materials

used to make the concrete, the composition

of the concrete (expressed through both

the mixture design and the measured

engineering properties of the hardened

concrete), and lastly, the environmental

conditions of exposure when shrinkage

occurred. With reference to the database

of measured shrinkage on South African

concretes that was gathered for this project,

the WITS model was compared to several

shrinkage models that are already in use in

the concrete industry.

The importance of the study is two-fold:

This is the first comprehensive model to

bring together laboratory data on the shrink-

age of concrete generated in South Africa

over a span of around 30 years, identifying

the covariates which are the most important

contributors to both the magnitude and

rate of concrete shrinkage. Secondly, the

concept of hierarchical nonlinear model-

ling (Davidian & Giltinan 1995), as briefly

outlined above, has been applied for the first

time to the modelling of concrete shrink-

age. This approach could prove useful to

other researchers seeking to model concrete

shrinkage and related time-dependent prop-

erties such as creep. Within the limitations

of the study, particularly the use of historical

data, the model provides a starting point

for further, statistically designed, tests and

assessments to more fully explore the effects

of the key variables.

DESCRIPTION OF THE MODEL

A detailed description of the data used in the

study, its limitations and the mathematical

A model for the drying shrinkage of South African concretes

P C Gaylard, Y Ballim, L P Fatti

This paper presents a model for the drying shrinkage of South African concretes, developed from laboratory data generated over the last 30 years. The model, referred to as the WITS model, is aimed at identifying the material variables that are the most important predictors of both the magnitude and rate of concrete shrinkage. In comparison with several shrinkage models already in use in the South African concrete industry, namely the SANS 10100-1, ACI 209R-92, RILEM B3, CEB MC90-99 and GL2000 models, the WITS model exhibited the best performance across a range of goodness-of-fit criteria. The ACI 209R-92 model and the RILEM B3 model showed reasonably good prediction. However, since the B3 model could be used to predict just over two-thirds of the data set, it was thus arguably the best alternative to the WITS model for the South African data set. The SANS 10100-1 model performed poorly in its predictive ability at early drying times. This may indicate that its 30-year predictions are more suited to the South African data set than its six-month predictions.


Figure 1 Summary of the WITS model for concrete shrinkage

ln(γ) = 3.04

+ Cement type factor (choose one cement type):

–0.01 CEM III A GGBS

0 CEM I, CEM II A-D, CEM II A-L, CEM II A-M(L), CEM II A-S, CEM II A-V, CEM II B-M(V/L), CEM II B-S, CEM II B-V, CEM III A GGCS and CEM III A GGFS

0.19 CEM V A

+ Stone type factor (choose one stone type):

0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite

0.01 Quartzite

0.05 Tillite

0.34 Granite

+ Sand type factor ( choose one sand type unless given proportions indicate otherwise):

–2.58 River Vaal (0 to 20%)

–0.44 Wits Quartzite

–0.40 Shale

–0.36 Granite

–0.12 Natural

–0.03 Andesite

0 Cape Flats, Dolomite, Ecca Grit, Pretoria Quartzite, Quartzite (0 to 80%), River (0 to 25%), Tillite (0 to 80%)

0.02 Klipheuwel Pit

0.50 Dolerite

+ 0.16 * ln(cement content in kg/m3)

+ 0.08 * Aggregate/Binder mass ratio

– 0.62 * ln(2*Volume to surface area ratio in mm)

– 0.08 * Temperature

ln(β) = 9.76


–0.29 CEM III A GGBS


0.79 CEM V A


–0.32 Tillite

0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite, Quartzite

0.33 Granite


–0.64 Wits Quartzite

–0.49 Shale

–0.42 Natural

–0.36 Granite

–0.35 River Vaal (0 to 20%)


0.04 Andesite

0.43 Klipheuwel Pit

1.22 Dolerite

+ 0.01 * ln (cement content in kg/m3)

– 0.05 * Aggregate / Binder mass ratio

– 1.76 * ln(2*Volume to surface area ratio in mm)

– 0.26 * Temperature in ºC

α = –2245.19


–3.85 CEM V A


8.63 CEM III A GGBS


–43.02 Granite

0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite

211.75 Tillite

302.21 Quartzite



99.54 Andesite

134.27 Dolerite

139.92 Klipheuwel Pit

170.57 Natural

201.75 Granite

260.15 Wits Quartzite

321.77 Shale

43.08 River Vaal (0 to 20%)

+ 55.71 * ln (cement content in kg/m3)

+ 2.54 * Water content in kg/m3

– 0.05 * Stone content in kg/m3

+ 25.35 * Aggregate/Binder mass ratio

+ 173.17 * ln(2*Volume to surface area ratio in mm)

+ 44.34 * Temperature in ºC

Mean shrinkage strain in the cross-section: εsh(t – t0) = α(1 – e–β(t–t0))γ

Ranges covered by the model:

Cement content: 112–536 kg/m3

Water content: 160–225 kg/m3

Aggregate/Binder ratio: 3.18–8.74

Stone content: 900–1400 kg/m3

2*Volume to surface area ratio: 16.5–75.0

Temperature: 21–25ºC

Humidity: 43–72%

For combinations of cement, stone and sand covered by the model, see Table 1.

Abbreviations:

GGBS Ground Granulated Blast-furnace Slag

GGCS Ground Granulated Corex Slag

GGFS Ground Granulated Ferro-manganese Slag


development of the model is given in an

associated publication (Gaylard et al 2012). A

key limitation of the data set must be noted

here, which is that the individual studies

making up the data set were not necessarily

carried out with the development of a model

for shrinkage as the main aim. This has

two consequences. Firstly, not all important

factors affecting shrinkage were varied over

sufficiently wide ranges. In fact, some factors

were kept constant because they were known

to have a significant effect on shrinkage,

most notably the levels of environmental

temperature and humidity maintained

during the shrinkage tests. Secondly, not all

data required for this study was recorded in

some of the studies making up the data set.

High levels of missing data led to certain

potentially useful covariates (for example

the 28-day compressive strength and elastic

modulus of the concrete) being excluded

for consideration as part of the model.

However, a model can still be developed with

these limitations in mind, and can then be

enhanced by further, designed, experiments

to include such factors.

The form of the growth curve model

selected is given by

εsh(t – t0) = α(1 – e–β(t–t0))γ (1)

where εsh(t – t0) is the mean shrinkage strain

in the cross-section (in microstrain) at dry-

ing time t – t0 (in days) (where t is the age

of the concrete and is the age at first drying

in days), α represents the ultimate shrinkage

(when (t – t0) is very large), β represents the

rate of shrinkage development with time and

γ is a growth curve shape parameter which

does not have a direct physical interpreta-

tion. The parameters α, β and γ in turn

depend on known properties of the concrete,

namely its composition, its other engineering

properties and the shrinkage test conditions.

The types and combinations of cement,

stone and sand covered by the WITS model

are given in Table 1. These are limited to the

data which was available for the derivation of

the model. The model parameters are given

in Figure 1.

The operation of the model therefore

requires that the user has to calculate

the appropriate values of α, β and γ from

Figure 1. These values are then substituted

into Equation 1 to produce a shrinkage-time

relationship for the particular concrete under

consideration.

To give an indication of the fit of the

model to the raw data, the two shrinkage

profiles with predicted values of α closest to

the observed asymptote (long-term shrink-

age), as well as the two shrinkage profiles

with predicted values of α furthest from the

Table 1 Types, levels and combinations of cement, stone and sand covered by the WITS model

Stone type

Cement type

CE

M I

CE

M I

I A

-D

CE

M I

I A

-L

CE

M I

I A

-M(L

)

CE

M I

I A

-S

CE

M I

I A

-V

CE

M I

I B

-M (

V/L

)

CE

M I

I B

-S

CE

M I

I B

-V

CE

M I

II

A CE

M V

A

Andesite √ √ √ √ √ √ √ √ √

Dolerite √ √ √ √ √ √ √ √

Dolomite √ √ √

Granite √ √ √ √

Greywacke √ √ √ √

Pretoria Quartzite √

Quartzite √

Shale √

Tillite √ √ √ √

Wits Quartzite √ √

Sand type

Cement type

CE

M I

CE

M I

I A

-D

CE

M I

I A

-L

CE

M I

I A

-M(L

)

CE

M I

I A

-S

CE

M I

I A

-V

CE

M I

I B

-M (

V/L

)

CE

M I

I B

-S

CE

M I

I B

-V

CE

M I

II

A CE

M V

A

Andesite √

Cape Flats √ √ √

Dolerite √ √ √ √

Dolomite √ √ √ √ √ √ √

Ecca grit √

Granite √ √ √ √ √ √ √ √

Klipheuwel pit √ √

Natural √ √ √ √


Quartzite (up to 80%*) √

River (up to 25%*) √ √

River Vaal (up to 20%*) √ √ √ √

Shale √

Tillite (up to 80%*) √ √ √ √


* indicates maximum proportion of sand type in total sand content

Sand Type

Stone Type

An

de

site

Do

leri

te

Do

lom

ite

Gra

nit

e

Gre

y-w

ack

e

Pre

tori

a

Qu

art

zit

e

Qu

art

zit

e

Sh

ale

Til

lite

Wit

s Q

ua

rtz

ite

Andesite √

Cape Flats √

Dolerite √

Dolomite √ √

Ecca grit √

Granite √ √

Klipheuwel pit √

Natural √ √


Quartzite √

River √

River Vaal √ √ √ √ √ √ √ √

Shale √

Tillite √



observed asymptote, from the experiments

in the data set, are shown in Figure 2. The

American Concrete Institute (2008) notes

that the variability of shrinkage test mea-

surements prevents models from matching

measured data closely, and it is thus unreal-

istic to expect results from shrinkage predic-

tion models to be within less than 20% of the

test data. In this case, the two predicted pro-

files exhibiting the largest deviations from

the raw data (Figure 2 (c) and (d)) show the

last data points having deviations of 16.2%

and 22.9%, respectively, which indicates that

the model lies in the range of acceptable

prediction.

The covariates (independent variables)

which have the most significant effect on the

parameters α, β and γ are listed in descend-

ing order in Table 2.

With reference to Table 2, we first con-

sider the material parameters that influence

the dependent variable α, which represents

the ultimate shrinkage. The different sand

types feature very strongly in the model,

with three sand types (granite, natural and

Wits Quartzite) making the largest contri-

bution to high values of α. All seven sand

types which were found to be significant had

positive coefficients relative to the reference

sand type, dolomite, which is considered to

be the sand type showing the lowest shrink-

age of the aggregates covered by this study

(Alexander 1998). This is not an unexpected

result, since a number of researchers have

shown the strong influence of aggregate

type on concrete shrinkage (Roper 1959;

Alexander 1998; Ballim 2000). Such research

indicates that this effect is due to the shrink-

age of the aggregate itself, the stiffness of the

aggregate and the surface characteristics of

the aggregate in modifying the aggregate-

cement paste interface in concrete.

The next most important parameter

influencing the variable α was the environ-

mental temperature. As expected, a higher

temperature leads to a higher ultimate

Table 2 The ranking of the significant terms for each of the three parameters α, β and γ for the

WITS model

α ln(β) ln(γ)

Sand Granite (+)*

Sand Natural (+)

Sand Wits Quartzite) (+)

Temperature (+)

Sand Klipheuwel Pit (+)

Aggregate/Binder Ratio (+)

ln(2*Volume to Surface Area)(+)

Sand Shale (+)

Stone Tillite (+)

Stone Quartzite (+)

Water Content (+)

Sand River Vaal (+)

Sand Andesite (+)

ln(2*Volume to Surface Area) (–)

Temperature (–)

Sand Dolerite (+)

Sand Natural (–)

Sand Klipheuwel pit (+)

Sand Wits Quartzite (–)

Sand Granite (–)

Cement CEM III A GGBS (–)

Cement CEM V A (+)

Stone Content (–)

Stone Granite (+)

Sand Shale (–)

Sand River Vaal (–)

ln(2*Volume to Surface Area) (–)

Aggregate/Binder Ratio (+)

Sand Granite (–)

Sand Wits Quartzite (–)

Temperature (–)

Stone Granite (+)

Sand Dolerite (+)

Stone Content (–)

Sand Shale (–)

* The sign of the coefficient is indicated.

Figure 2 Mean (solid line) and 95% confidence interval (dashed line) predictions for the two shrinkage profiles with predicted values of α ((a) and (b))

closest to the observed asymptote and ((c) and (d)) furthest from the observed asymptote

Sh

rin

ka

ge

(mic

rost

rain

)700

600

500

400

300

200

100

01 000100101

Time (days

WITS#0225(a)

Sh

rin

ka

ge

(mic

rost

rain

)

700

600

500

400

300

200

100

01 000100101

Time (days

WITS#0228(b)

Sh

rin

ka

ge

(mic

rost

rain

)

700

600

500

400

300

200

100

01 000100101

Time (days

WITS#0214(c)

Sh

rin

ka

ge

(mic

rost

rain

)

700

600

500

400

300

200

100

01 000100101

Time (days

WITS#0032(d)


shrinkage. The effect of the aggregate-binder

ratio may be understood in terms of the

restraining effect of the aggregate volume

(Alexander & Mindess 2005). The specimen

size effect (as represented by the ratio of

the volume to the surface area of the speci-

men) is unexpected: the positive sign of the

coefficient suggests that specimens with a

lower surface area available for moisture

loss, relative to their volume, are expected to

reach higher levels of ultimate shrinkage. It

must be noted that this variable was subject

to some multi-collinearity (mostly with sand

type dolerite and temperature) and thus the

meaning of the magnitude and sign of the

coefficient should not be over-interpreted

(Gaylard et al 2012). This is certainly an

aspect requiring further investigation.

The two stone types which were found

to have a significant effect on α had positive

coefficients relative to the reference stone

type, andesite. Given the range of stone

types for which sufficient data was available,

andesite stone concretes showed the lowest

shrinkage, and andesite was therefore used

as the reference stone. Finally, the water

content of the concrete also plays a role in

influencing ultimate shrinkage. As expected,

increasing the water content of the concrete

mix increases the ultimate shrinkage.

Much less is known about the factors

which influence the rate of shrinkage.

However, the significant terms in the regres-

sion equation for ln(β), which represents the

rate of shrinkage development with time,

may be interpreted as follows: As expected,

the specimen size effect is the strongest con-

tributor to the rate of shrinkage development

with time – specimens with a higher surface

area available for moisture loss, relative to

their volume, lose moisture more rapidly.

The rate of shrinkage decreases with increas-

ing temperature. This is unexpected, but is

likely to be linked to the very narrow range

of temperatures covered by this study (21–

25ºC) as a result of the near-constant labora-

tory conditions under which the shrinkage

experiments were carried out. Sand type

plays an important role in determining the

rate of shrinkage. In contrast to the findings

for the ultimate shrinkage, here the signs of

coefficients for the different sand types are

both positive and negative. A few cement

types have an effect on the rate of shrinkage.

Cements with high levels (36–65%) of GGBS

(i.e. CEM III A) appeared to slow the rate of

shrinkage. The effect was not statistically

significant for comparable concretes contain-

ing Corex or Ferro-manganese slag. Cements

containing both GGBS (18-30%) and fly

ash (18–30%) (i.e. CEM V A) appeared to

increase the rate of shrinkage. Increasing

stone content decreases the rate of shrinkage,

Figure 3 An illustration of the effects of the different model parameters, α, β and γ, in modifying

the rate and magnitude of predicted concrete shrinkage development by the WITS model

Sh

rin

ka

ge

(mic

rost

rain

)

700

600

500

400

300

200

100

01 000100101

Drying time (days)

α = 450, β = 0.02, γ = 0.40 α = 450, β = 0.02, γ = 0.90

α = 450, β = 0.02, γ = 0.65

α = 650, β = 0.02, γ = 0.65

α = 650, β = 0.03, γ = 0.65

α = 650, β = 0.01, γ = 0.65

α = 250, β = 0.02, γ = 0.65

Table 3 Covariates included in the published models as well as the WITS model

Covariates

Model

AC

I 2

09

R-9

2

RIL

EM

B

3

CE

BM

C9

0-9

9

GL

20

00

SA

NS

1

01

00

-1

Eu

ro-

cod

e 2

WIT

S

Concrete raw materials and composition:

Cement type * √ √ √ √ √

Cement content √ * √

Water content √ √ √

Water / cement mass ratio *

Air content √

Sand type √

Stone type √

Stone content √

Sand / total aggregate mass ratio √

Aggregate / cement mass ratio *

Aggregate / binder mass ratio √

Testing conditions:

Curing method * √ *

Age at first drying √ √ *

Specimen shape √

Specimen volume to surface area ratio √ √ √ √ √

Specimen ratio of cross-sectional area to exposed perimeter √ √

Temperature * * √

Humidity √ √ √ √ √ √

Concrete properties:

28-day compressive strength √ √ √ √

28-day elastic modulus √

Slump √

The symbol √ denotes that the covariate is required for model prediction calculations, while the symbol * denotes that the covariate is only required to assess the applicability of the model


presumably due to the restraining effect of

the aggregate. One stone type, granite, was

found to increase the rate of shrinkage rela-

tive to the reference stone type, andesite.

The growth curve shape parameter ln(γ)

itself is difficult to interpret in the context

of the growth curve equation, and thus its

interpretation in terms of the significant

covariates is even more difficult and was not

attempted.

By way of illustration, Figure 3 shows a

range of shrinkage profiles that are obtained

with the model proposed here, using values

of α, β and γ that lie within the range of

values for the data set used in developing

the model. Figure 3 shows the effects of

the different model parameters in varying

both the rate and magnitude of shrinkage

development.

COMPARISON OF THE WITS MODEL

TO OTHER PUBLISHED MODELS

FOR CONCRETE SHRINKAGE

In the published literature, the most thorough

model comparisons have been based on the

RILEM data bank, a collection of 490 con-

crete shrinkage profiles mainly from North

American and European research groups

(Bažant & Li 2008). The RILEM B3 model

was developed on an older version of the

current RILEM data bank (Bažant & Baweja

1996; Bažant 2000). In this study, model

comparisons were based on the local data set,

which may be considered as a smaller, South

African, version of the RILEM data bank.

Five published models were used as

comparisons to the WITS model developed

in this study:

■ The ACI 209R-92 model developed by the

American Concrete Institute (1982)

■ The RILEM B3 model developed by

Bažant and co-workers (Bažant & Baweja

1996; Bažant 2000)

Table 4 Ranges of applicability for the published models as well as the WITS model

Constraints

Model

ACI209R-92

RILEMB3

CEBMC90-99

GL2000 SANS 10100-1 Eurocode 2 WITS

Concrete raw materials and composition:

Cement type Type I and III Type I, II and III see Table 1

Cement content 279–446 kg/m3 160–720 kg/m3 112–536 kg/m3

Water content 150–230 kg/m3 160–225 kg/m3

Water / cement mass ratio 0.35–0.85

Aggregate / cement mass ratio 2.5–13.5

Aggregate / binder mass ratio 3.18–8.74

Sand type see Table 1

Stone type see Table 1

Stone content 900–1400 kg/m3

Testing conditions:

Curing method and timemoist: ≥ 1 day

or steam: 1–3 days

moist: ≥ 1 day or steam

moist ≤ 14 daysmoist: ≥ 1 day

or steam

Specimen volume to surface area ratio1.2*exp

(–0.00472*V/S) ≥ 0.2

16.5–75.0

Specimen ratio of cross-sectional area to exposed perimeter

Temperature 21.2–25.2ºC 10–30ºC 21–25ºC

Humidity 40–100% 40–100% 40–100% 20–100% 20–100% 20–100% 43–72%

Concrete properties:

28-day (cylinder) compressive strength 17–70 MPa 15–120 MPa 16–82 MPa 20–90 MPa

Figure 4 The percentage of the data set which could be predicted by each of the models

Pre

dic

tio

n m

od

el

WITS (data used for model)

WITS (data not used for model)

WITS (all data)

ACI 209

RILEM B3

CEB MC90-99

GL2000

Eurocode 2

SANS 10100-1

Percentage of data set predicted by model

100806040200


■ The CEB MC90-99 model developed by

the Comité European du Beton (1999)

■ The GL2000 model developed by Gardner

and Lockman (2001)

■ The SANS 10100-1 model adopted by the

South African Bureau of Standards (2000)

■ The Eurocode 2 (EN 1992-1-1) model

adopted by the European Committe for

Standardization (2003).

The covariates (other than drying time) used

in each of these models are given in Table 3

and the ranges of applicability of each model

are summarised in Table 4. The ranges of

applicability of the WITS model given in

Table 4 are equivalent to the ranges of the

data used in fitting the model. However, the

actual ranges of applicability could well be

wider.

A predicted shrinkage profile was cal-

culated for each model, including the WITS

model, for each qualifying experiment in the

data set (in terms of the range of applicabil-

ity of each model – see Table 4), and the

goodness-of-fit of these predictions to the

actual data was assessed. Since the WITS

model was also derived from this data set, its

assessments were divided into two groups,

namely the experiments used to derive the

model, and the experiments which qualified

to be predicted by the model but which were

not used to derive the model as a result of

poor quality data, for example shrinkage

profiles which had not reached any indication

of their long-term shrinkage value by the time

measurements ceased. Combined goodness-

of-fit statistics for the two groups are also

Figure 5 Illustration of the fit of the models to six experiments in the data set. The experiments illustrated in (a) to (d) were part of the data set used

to derive the WITS model, while the experiments illustrated in (e) and (f) were not

700

600

500

400

300

200

100

01 000100101

WITS

#0115

(a)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

ACI 209 RILEM B3 CEB MC90-99

GL2000 SANS 10100-1Eurocode 2

700

600

500

400

300

200

100

01 000100101

WITS

#0117

(b)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

ACI 209 RILEM B3 CEB MC90-99

GL2000 SANS 10100-1Eurocode 2

700

600

500

400

300

200

100

01 000100101

WITS

#0181

(c)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

RILEM B3 CEB MC90-99

GL2000 SANS 10100-1

Eurocode 2

700

600

500

400

300

200

100

01 000100101

WITS

#0082

(d)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

ACI 209 RILEM B3

GL2000 SANS 10100-1

Eurocode 2

700

600

500

400

300

200

100

01 000100101

WITS

#0007

(e)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

ACI 209 RILEM B3

GL2000 SANS 10100-1

Eurocode 2

700

600

500

400

300

200

100

01 000100101

WITS

#0024

(f)

Sh

rin

ka

ge

(mic

rost

rain

)

Time (days)

ACI 209 RILEM B3

GL2000 SANS 10100-1

Eurocode 2


presented. The ACI 209R-92, RILEM B3, CEB

MC90-99 and GL2000 models were imple-

mented according to the model specifications

given in the American Concrete Institute

Committee 209’s guide for modelling and

calculating shrinkage and creep in hardened

concrete (American Concrete Institute 2008).

In the ACI 209R-92 model, the air content was

set at the standard value of 6%, making the air

content factor equal to one, since data on this

variable was not available. For the RILEM B3,

CEB MC90-99, GL2000 models, 28-day cube

compressive strengths were converted to the

corresponding cylinder strengths using the

conversion table given in the British Standard

Common Rules for Buildings and Civil

Engineering Structures (British Standards

Institution 2004). The effective section thick-

nesses of most of the specimens used in the

study were smaller than the minimum value

of 100 mm presented in the Eurocode 2 model

(European Committee for Standardization

2003). The values given in the standard were

thus extrapolated to the required effective

section thickness to determine the required

value of the coefficient kh:

kh = 1.2 – 0.00225h0 + 0.0000025h20

(R2 = 0.999)

where h0 is the effective section thickness.

The SANS 10100-1 model was implemented

according to the South African Bureau of

Standards SANS 10100-1 standard (2000) for

the prediction of shrinkage in concrete. The

effective section thicknesses of the speci-

mens used in this study were smaller than

the minimum value of 150 mm presented in

the SANS 10100-1 model. The values given

in the standard were thus extrapolated to

the required effective section thickness (and

interpolated to the required relative humid-

ity) by applying separate quadratic models

(for the six-month and 30-year shrinkage)

fitted to the shrinkage data read from the

nomograph at relative humidities of 40, 50,

60, 70 and 80% and effective section thick-

nesses of 150, 300 and 600 mm:

6-month shrinkage (microstrain)

= 314.0 + 1.035H – 1.025u + 0.003494Hu

– 0.02962H2 + 0.0007302u2 (R2 = 0.994) (2)

30-year shrinkage (microstrain)

= 395.6 + 6.231H – 0.6173u + 0.003239Hu

– 0.09595H2 + 0.0002922u2 (R2 = 0.994) (3)

where H is the humidity in % and u is the

effective section thickness in mm.

After correction for the water content of

the concrete, the predicted six-month and

30-year shrinkage values were used to deter-

mine the time-shift factor, α, in the hyper-

bolic growth curve (Gilbert 1988; Ballim

1999) used to determine the shrinkage at

other drying times:

εsh(t – t0) = t

α + t ∙ εsh(30 years) (4)

where

α = 183 days ∙ εsh(30 years) – εsh(6 months)

εsh(6 months) (5)

Firstly the proportion of the data set which

could be predicted by a particular model

was determined. This analysis is presented

in Figure 4. As a result of its minimalist

input requirements, the SANS 10100-1

model could be used to predict all the

experiments in the data set. The WITS

model had the next highest proportion of

experiments which could be predicted (87%).

Those experiments which did not qualify,

failed to do so mostly because they used

aggregate types which were not included in

the derivation of the model or because of the

poor quality of the shrinkage data, some-

times showing significant but unexplained

deviations from the characteristic shrinkage

development curve. Of this 87%, just over

three-quarters of the data had been used

in the development of the model, while the

rest (47 experiments) had been excluded

from model development because the data

was insufficient to allow a realistic predic-

tion of the ultimate shrinkage, but these

experiments still qualified for prediction by

the model. This latter set can thus not be

regarded as a true validation data set since

it comprises poor quality data compared to

the overall data set. In the discussions which

follow, reference to the WITS model includes

consideration of all three subsets of data

unless specifically indicated otherwise. The

other models were able to predict lower pro-

portions of the data set due to a combination

of missing data and experiments not meeting

the qualifying criteria.

The fit of the various models to six

shrinkage profiles is illustrated in Figure 5.

The illustrated profiles were randomly

selected from the 57 experiments to which

five or all six of the models could be fit-

ted. While the selection of the experiments

was random, some effort was made to

select experiments which spanned the range

of shrinkage profiles in both magnitude

and rate of shrinkage development. The

full database containing the concrete

details and shrinkage results for the 290

experiments used in this study is available at

www.cnci.org.za for download at no cost.

It is clear from Figure 5 that the WITS

model performed well, which was to be

expected since the model was derived from

the data. The SANS 10100-1 and GL2000

models tended to under- and over-predict,

respectively. No particular trend regarding

the performance of the other models is

immediately obvious from an inspection of

the results in Figure 5.

Many goodness-of-fit measures have been

used by different researchers in the develop-

ment of models for concrete shrinkage. The

American Concrete Institute (2008) is of the

opinion that “the statistical indicators avail-

able are not adequate to uniquely distinguish

Table 5 Parameters of the linear relationship between the actual and predicted shrinkage values

for the models

Model nAdjusted

R2

Slope(95% confidence

interval)

Intercept(95% confidence

interval)

WITS (data used for model development)

2 603 0.920.97

(0.96–0.99)18

(15–21)

WITS (data NOT used for model development)

483 0.870.89

(0.86–0.92)19

(11–27)

WITS (all data) 3 086 0.910.96

(0.95–0.97)18

(15–21)

ACI 209R-92 850 0.710.96

(0.92–1.0)53

(42–64)

RILEM B3 2 581 0.670.73

(0.71–0.75)17

(10–23)

CEB MC90-99 868 0.760.62

(0.59–0.64)–6

(–16–4)

GL2000 3 005 0.530.52

(0.50–0.54)39

(31–46)

SANS 10100-1 3 376 0.591.08

(1.05–1.11)118

(113–123)

Eurocode 2 2 903 0.540.69

(0.66–0.71)34

(27–42)


Figure 6 Plots of the actual vs predicted shrinkage values for the models

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

800

800

800

800

800

800

800

800

800

600

600

600

600

600

600

600

600

600

400

400

400

400

400

400

400

400

400

200

200

200

200

200

200

200

200

200

0

0

0

0

0

0

0

0

0

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

800

800

800

800

800

800

800

800

800

200

200

200

200

200

200

200

200

200

0

0

0

0

0

0

0

0

0

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Predicted shrinkage (microstrain)









600

600

600

600

600

600

600

600

600

400

400

400

400

400

400

400

400

400


WITS (all data)

CEB MC90-99

GL2000

Eurocode 2


ACI 209R-92

RILEM B3

SANS 10100-1

The line of equality is shown in red


Figure 7 Plots of the actual vs predicted shrinkage values, on a log scale, for the models

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

100

100

100

100

100

100

100

100

100

10

10

10

10

10

10

10

10

10

0

0

0

0

0

0

0

0

0

1 000

1 000

1 000

1 000

1 000

1 00010

10

10

10

10

10

10

10

10

1

1

1

1

1

1

1

1

1

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)










100

100

100

100

100

100

100

100

100


WITS (all data)

CEB MC90-99

GL2000

Eurocode 2


ACI 209R-92

RILEM B3

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

Ac

tua

l sh

rin

ka

ge

(mic

rost

rain

)A

ctu

al

shri

nk

ag

e (m

icro

stra

in)

SANS 10100-1

The line of equality is shown in red


between models”. Given this concern, it was

thought best to use a broad range of these

measures, both graphical and numerical,

to assess the relative performance of the

different models. Where possible, a critical

assessment of these measures from a statisti-

cal point of view is also given.

Plots of the actual versus predicted

shrinkage values are shown in Figure 6.

The points from an ideal model would lie

entirely on the line of equality. Bažant et al

(Bažant & Baweja 1995; Bažant 2000) recom-

mend focusing on the longer drying times,

where predictions are most important, since

such plots are typically dominated by data

gathered at short drying times. For most

concrete engineering projects, designers are

more concerned with long-term shrinkage.

However, this is not to say that early-age

shrinkage is unimportant. For example,

prediction of early-age shrinkage would be

very important in post-tensioned, prestressed

concrete structures. The results in Figure 6

show that the WITS model, particularly at

longer drying times, remained closest to the

line of equality, thus indicating the best fit to

the data. The adjusted R2, as well as the slope

and intercept, of the fitted lines to the plots

are given in Table 5. A good model would

have a slope close to 1 and an intercept close

to 0, as well as a high adjusted R2 value.

The WITS model exhibited the least scatter

(highest R2) and the slope closest to 1, while

its intercept was the third closest to zero of

all the models. This is to be expected, since

a large proportion of the data was used to

develop the WITS model.

Nevertheless, it is interesting to note

that the international models generally

over-predict the shrinkage of South African

concretes. This may be related to the fact

that South African concretes are generally

made with crushed aggregates, resulting in

a higher water demand than many northern

hemisphere concretes where natural gravels

are more commonly used as aggregates. On

balance of the three regression criteria, the

CEB MC90-99 and ACI 209R-92 models

performed the next best. The over-prediction

by the RILEM B3, ACI 209R-92, CEB MC90-

99, Eurocode 2 and GL2000 models, as well

as the under-prediction by the SANS 10100-1

model, was evident from both the plots and

the regression statistics.

Plots of the actual versus predicted

shrinkage values on a log scale are also

useful since they illustrate the relative

errors, which should decrease as shrinkage

strain increases as a consequence of the

homoscedasticity of errors (Bažant & Baweja

1995; Bažant 2000). These plots, and the

parameters of their fitted lines, are shown in

Figure 7 and Table 6 respectively. The WITS

model was again closest to the unity line and

exhibited the least scatter, indicating it to

be the best model when viewed according to

these criteria. The RILEM B3 model exhib-

ited more scatter of the data around the line

of equality (i.e. greater positive and negative

residuals) at longer drying times than the

WITS model, while the performance of the

other models was worse.

In the above analysis of the results, all the

concretes were allocated the same weight-

ing. Of course, this unreasonably weights

the older, lower-strength concretes, which

exhibit higher levels of shrinkage strain at a

given drying time. To correct for this, plots

of actual versus predicted shrinkage values

were both multiplied by:

fc28,i

fc28,av

where fc28,i is the 28-day compressive

strength for the experiment and fc28,av is

the average 28-day compressive strength for

the data set (Bažant & Baweja 1995; Bažant

2000). This effectively normalised shrinkage

according to compressive strength. However,

this analysis did not change the conclusion

that the WITS model performed the best,

while the RILEM B3 and ACI 209R-92 mod-

els exhibited the next best performance.

Plots of the differences between mea-

sured and predicted shrinkage (residuals)

against Log10(time) are shown in Figure 8.

These residuals should not fan out (indicat-

ing increased deviation of a model from the

raw data at longer drying times – where

prediction is more important) or show any

other obvious pattern or trend (McDonald &

Roper 1993, Al-Manaseer & Lam 2005). The

over- and under-prediction of the different

models, as discussed previously, can clearly

be seen in these plots. The mean residuals

for the WITS model were the closest to zero

and the most consistent across the different

intervals of drying time, whereas the abso-

lute values of the mean residuals of the other

models tended to increase with drying time.

The ACI 209R-92 and RILEM B3 models

exhibited the next best performance on this

criterion.

A MORE DETAILED ANALYSIS

OF VARIATION

In order to further assess the suitability

of the proposed WITS model, a range of

numerical goodness-of-fit summary statistics

were determined. Bažant’s coefficient of

variation, ωBP (Bažant & Baweja 1995; Bažant

2000, Al-Manaseer & Lam 2005) for all the

data, as well as that calculated separately

for three time intervals (on a log10 scale)

spanned by the shrinkage profiles, for the

different models is shown in Table 7. The

WITS model exhibited the lowest coefficient

of variation overall, as well as across all three

intervals of drying time, followed by the ACI

209R-92 model. The coefficient of variation

of the WITS model, calculated on the South

African data set from which the model was

derived, was found to be 27%. This compares

favourably to the 34% coefficient of variation

for the RILEM B3 model calculated on the

RILEM database, from which it was derived

(Bažant 2000). This said, it should be noted

that the RILEM model was developed on a

Table 6 Parameters of the linear relationship between the actual and predicted shrinkage values,

on a log scale, for the models

Model nAdjusted

R2

Slope(95% confidence

interval)

Intercept(95% confidence

interval)

WITS (data used for model development)

2 603 0.860.96

(0.94–0.97)0.11

(0.08–0.14)

WITS (data NOT used for model development)

483 0.840.76

(0.73–0.79)0.55

(0.48–0.62)

WITS (all data) 3 086 0.850.93

(0.91–0.94)0.18

(0.15–0.22)

ACI 209R-92 850 0.670.70

(0.67–0.74)0.76

(0.67–0.84)

RILEM B3 2 579 0.681.06

(1.03–1.09)–0.29

(–0.36––0.22)

CEB MC90-99 868 0.671.33

(1.27–1.39)–1.1

(–1.3––0.96)

GL2000 3 005 0.591.04

(1.01–1.07)–0.35

(–0.43––0.28)

SANS 10100-1 3 374 0.710.54

(0.53–0.55)1.31

(1.28–1.33)

Eurocode 2 2 906 0.620.85

(0.82–0.87)0.24

(0.18–0.30)


Figure 8 Plots of the residuals vs log10 (time) for the models

700

700

700

700

700

700

700

700

700

100

100

100

100

100

100

100

100

100

–300

–300

–300

–300

–300

–300

–300

–300

–300

–700

–700

–700

–700

–700

–700

–700

–700

–700

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

10

10

10

10

10

10

10

10

10

1

1

1

1

1

1

1

1

1

Re

sid

ua

lsR

esi

du

als

Re

sid

ua

lsR

esi

du

als

Re

sid

ua

ls

Re

sid

ua

lsR

esi

du

als

Re

sid

ua

lsR

esi

du

als

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

Drying time (days)

100

100

100

100

100

100

100

100

100


WITS (all data)

CEB MC90-99

GL2000

Eurocode 2


ACI 209R-92

RILEM B3

SANS10100-1

–100

–100

–100

–100

–100

–100

–100

–100

–100

–500

–500

–500

–500

–500

–500

–500

–500

–500

500

500

500

500

500

500

500

500

500

300

300

300

300

300

300

300

300

300


Table 7 Summary of the numerical goodness-of-fit statistics calculated for the models

Model

WITS(data used for model

development)

WITS(data NOT

used for model development)

WITS(all data)

ACI209R-92

RILEMB3

CEBMC90-99

GL2000SANS

10100-1Eurocode

2

Bažant’s coefficient of variation

ωBP (overall) (%) 25 35 27 49 84 84 130 76 73

ωBP (1-9 days) (%) 37 45 39 70 76 133 136 105 100

ωBP (10-99 days) (%) 21 25 22 36 49 59 87 75 57

ωBP (100-999 days) (%) 13 20 13 33 40 71 67 48 40

CEB coefficient of variation

VCEB (overall) (%) 22 32 23 43 54 83 95 63 62

VCEB (0-10 days) (%) 37 45 39 68 75 126 135 104 98

VCEB (11-100 days) (%) 21 25 21 36 49 58 86 74 57

VCEB (101-365 days) (%) 13 20 14 33 36 57 58 53 36

VCEB (366-730 days) (%) 13 13 18 50 79 87 22 49

VCEB (731-1095 days) (%) 15 15 54 77 93 5 52

CEB mean square error

FCEB (overall) (%) 35 34 34 38 141 174 212 53 126

FCEB (0-10 days) (%) 70 45 66 55 293 356 426 84 247

FCEB (11-100 days) (%) 24 30 25 38 76 89 135 66 99

FCEB (101-365 days) (%) 15 24 17 33 45 65 85 45 48

FCEB (366-730 days) (%) 13 13 16 55 83 91 17 54

FCEB (731-1095 days) (%) 14 14 55 80 94 10 55

CEB mean relative deviation

MCEB (overall) 0.99 1.01 0.99 0.96 1.25 1.40 1.41 0.76 1.23

MCEB (0-10 days) 1.04 0.91 1.02 0.89 1.47 1.76 1.75 0.42 1.28

MCEB (11-100 days) 0.98 1.05 0.99 0.98 1.20 1.30 1.37 0.60 1.25

MCEB (101-365 days) 1.01 1.05 1.02 0.97 1.14 1.25 1.22 0.77 1.07

MCEB (366-730 days) 0.97 0.97 1.01 1.23 1.34 1.35 0.97 1.21

MCEB (731-1095 days) 0.94 0.94 1.23 1.33 1.37 1.02 1.23

Gardner mean residuals

3-9.9 days 10 16 11 49 -36 -94 -89 84 -37

10-31.5 days 16 -3 12 35 -56 -120 -137 140 -82

31.6-99 days 18 -33 10 38 -79 -107 -163 181 -78

100-315 days -3 -23 -6 72 -60 -196 -144 188 -18

316-999 days 26 53 27 7 -159 -263 -282 50 -130

Gardner root mean square of residuals

3-9.9 days 32 39 33 70 64 108 116 97 90

10-31.5 days 48 44 47 81 97 137 180 156 127

31.6-99 days 54 61 55 114 127 140 222 202 137

100-315 days 54 79 59 149 145 219 236 222 144

316-999 days 50 144 54 143 184 272 317 116 180

Gardner coefficient of variation

ωG (overall) (%) 17 27 18 36 49 71 83 60 51


larger database with a possibly greater varia-

tion in concrete types.

In the calculation of the CEB-FIP coef-

ficient of variation, mean square error and

mean relative deviation (Al-Manaseer &

Lam 2005), all the data is pooled and then

grouped into six intervals of drying time:

0-10 days, 11-100 days, 101-365 days, 366-730

days, 731-1095 days and above 1 095 days.

The disadvantage of these three measures

is that the data is immediately grouped into

drying time intervals, which means that,

although time intervals are weighted equally,

different experiments are not weighted

equally in the calculation of the overall

mean statistics. Bažant’s approach, described

above, does not suffer this weakness and

satisfies both these objectives. The use of the

mean of the shrinkage values for a given time

period rather than the grand mean of all the

shrinkage values in the calculation of the

CEB coefficient of variation results in large

values of the coefficient of variation for short

drying time intervals and vice versa. This

in turn means that the calculated value of

the overall coefficient of variation is unduly

influenced by the short drying time data.

With respect to both the Bažant and CEB

coefficients of variation, it should also be

noted that, for the WITS model at least, the

model fit was obtained by minimising the

variance, not by minimising the coefficient

of variance. The use of the relative errors

in the calculation of the CEB mean square

error is prone to over-emphasise the errors

in low shrinkage values, which are relatively

less important, and vice versa. The CEB

mean relative deviation is a useful statistic

as it identifies the magnitude and direction

of bias in the predicted values. The results

from all the above calculations are given in

Table 7. Results for only five time intervals

are shown, since there was no data at drying

times longer than 1 095 days in the data set

used in this study. The WITS model exhib-

ited the lowest overall CEB coefficient of

variation, followed by the ACI 209R-92 and

RILEM B3 models. Over the different time

intervals, the WITS model had the lowest

coefficient of variation, except for the longest

drying time interval (731-1 095 days) where it

was superseded by the SANS 10100-1model.

It appeared that the SANS 10100-1model

is a good predictor of shrinkage at longer

drying times, but under-predicts at shorter

drying times, perhaps due to poor prediction

of the six-month shrinkage, as illustrated in

Figure 5, and also in Figure 9 for an experi-

ment which includes data at very long drying

times. The over-emphasis of the CEB mean

square error statistics for low shrinkage

values (and vice versa), as discussed above,

can clearly be seen (Table 7). The WITS

model, closely followed by the ACI 209R-92

and SANS 10100-1 models, performed better

than the other models on this measure. The

CEB mean relative deviation statistics are

shown in Table 7, which illustrate the magni-

tude and direction of the bias in the different

models (discussed previously), as a function

of drying time. The WITS model showed the

least bias across all time intervals, closely

followed by the ACI 209R-92 model. The

narrowing difference between the actual and

predicted values of the SANS 10100-1 model

with increasing drying time is shown clearly

here, again indicating that the longer-term

(30-year) predictions of this model are more

in line with the measured data than the

shorter-term (six-month) predictions.

In the method used by Gardner (2004),

the observations are grouped into half-log

decades (starting at a drying time of three

days). Within each time interval, the average

and the root mean square (RMS) values of the

differences between the actual and predicted

values (residuals) are calculated. The trend of

the average residual with time shows whether

there is over- or under-estimation (bias) with

time by the model, while the trend of the

RMS values with time shows if the deviation

of the model increases with time. Next, the

RMS values are simply averaged. The average

RMS values are then normalised by dividing

by the average of the average shrinkage values

(for the different time intervals) to produce

a measure analogous to a coefficient of

variation. This formula given by Gardner is,

however, incorrect, since the mean squares,

not RMS values, should be averaged. In this

study, the corrected formula for the Gardner

coefficient of variation, ωG, was applied. As in

the case for the overall CEB statistical indica-

tor, ωG also suffers from the disadvantage

that the data is immediately grouped into

drying time intervals, which means that,

although time intervals are weighted equally,

experiments are not weighted equally in the

calculation of this overall mean statistic.

Figure 9 Illustration of the fit of the models to an experiment with data at long drying times

700

Sh

rin

ka

ge

(mic

rost

rain

)

600

500

400

300

200

100

01 000100101

Drying time (days)

WITS

#0177 RILEM B3 CEB MC90-99GL2000

SANS 10100-1Eurocode 2

Figure 10 Comparison of the goodness-of-fit measures for the different concrete shrinkage models

WITS (all data)



ACI 209

RILEM B3

SANS 10100-1

Eurocode 2

CEB MC90-99

GL2000

ωBP (%)

V(CEB) (%)

F(CEB)M(CEB)

1.00

0.80

0.60

0.40

0.20

0

ωG (%)


The Gardner average residuals and the root

mean squares of the residuals for the dif-

ferent time periods for all the models are

given in Table 7. The WITS model had the

lowest mean residuals, followed by the ACI

209R-92 model. The bias towards over- or

under-prediction by the other models can

clearly be seen. The Gardner coefficient of

variation also identified the WITS model as

the best model according to this criterion,

as did the root mean squares of the residuals

for the different drying time intervals. The

latter statistic showed that the deviations of

all the models increased with time, with the

exception of the WITS model (over all drying

times) and the SANS 10100-1 model (at long

drying times).

The discussion above has shown that

there is no single goodness-of-fit statistic

which can adequately capture all aspects of

the performance of a model for the shrink-

age of concrete. In order to summarise the

information contained in the different overall

numerical goodness-of-fit measures discussed

above, their calculated values for the different

models are represented in Figure 10 by means

of a radar chart. This plot showed that,

across all the goodness-of-fit measures, the

WITS model performed the best. This was

perhaps to be expected, since the model was

derived largely from this data. However, even

the performance of the model on the data

which was not used in the development of the

model was excellent, although, as was men-

tioned earlier, this small data set should not

be regarded as a true validation data set. The

ACI 209R-92 model exhibited the second-best

performance, but here it must be noted that

this model could be used to predict only 36%

of the data set. The third best performance

across the goodness-of-fit indicators was

shown by the RILEM B3, SANS 10100-1 and

Eurocode 2 models indicating that these are

arguably the best alternative models to the

WITS model for the South African data set.

The SANS 10100-1 model performed poorly

relative to the other models, but as discussed

above, its predictive ability at longer drying

times was better than that at shorter drying

times. This may indicate that its 30-year pre-

dictions are more suited to the South African

data set than its six-month predictions, i.e.

that the time development of shrinkage of the

model may need to be adjusted relative to the

British Standard from which the model was

directly taken.

CONCLUSIONS

The WITS model presented in this paper

represents a first attempt at applying the

concept of hierarchical nonlinear modelling

to the prediction of shrinkage for South

African concretes. Furthermore, this is

the first time that a shrinkage model has

been derived from a gathering of test data

on the shrinkage of concretes which had

been generated by a range of South African

laboratories over a span of 30 years. The

proposed model identifies the material and

environmental covariates that are the most

important contributors to both the magni-

tude and rate of concrete shrinkage. Based

on a range of reliability and goodness-of-fit

measures, the WITS model was found to

perform better than a number of local and

international models on the basis of the mag-

nitude and rate of prediction at both early

and late drying times. The coefficients pro-

posed for the model have yet to be confirmed

through further testing with a wider range of

material and environmental variables. This

will require further, statistically designed,

shrinkage tests that are aimed at exploring

the effect of key variables more fully. This

approach could also prove useful to future

research seeking to model concrete shrink-

age and related time-dependent properties

such as creep.

ACKNOWLEDGEMENTS

The provision of data and helpful com-

ments by Prof Mark Alexander and Dr

Hans Beushausen (Department of Civil

Engineering, University of Cape Town, Cape

Town, South Africa) are gratefully acknowl-

edged. The authors are also grateful to the

Cement and Concrete Institute for their data

and logistical support and, together with

Eskom, for their financial support to our

research programme.

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– Part 1: General Rules and Rules for Buildings.

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Performance. Updated Knowledge of the CEB/FIP

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Switzerland: Federation Internationale du Beton,

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Gardner, N J & Lockman, M J 2001. Design provisions

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TECHNICAL PAPER


Vol 55 No 1, April 2013, Pages 60–71, Paper 813 Part 1

DR MAHONGO DITHINDE (Visitor) holds a PhD in

Civil Engineering from the Stellenbosch

University, an MSc in Foundation Engineering

from the University of Birmingham (UK), and

BEng in Civil Engineering from the University of

Botswana. He works as a Senior Lecturer at the

University of Botswana. His specialisation and

research interests are in the broad area of

geotechnical reliability-based design. In addition to academic work, he is also

a geotechnical partner for Mattra International where he is active in

consultancy work in the fi eld of geotechnical engineering.

Contact details:



Private Bag X1

Matieland

7602

South Africa


University of Botswana

Private Bag UB 0061

Gaberone

Botswana

T: +267 355 4297

F: +267 395 2309


PROF JOHAN RETIEF (Fellow of SAICE) has, since

his retirement as Professor in Structural

Engineering, maintained involvement at the

Stellenbosch University, supervising graduate

students in the fi eld of risk and reliability in civil

engineering. He is involved in various standards

committees, serving as the South African

representative to ISO TC98 (basis of structural

design and actions on structures). He holds a BSc (cum laude) and a DSc from

the University of Pretoria, a DIC from Imperial College London, and an MPhil

from London University. Following a career at the Atomic Energy

Corporation, he joined Stellenbosch University in 1990.

Contact details:



Private Bag X1

Matieland

Stellenbosch

7602

T: +27 21 808 4442

F: +27 21 808 4947


Key words: pile foundation design, southern African practice, pile load tests,

model factor, statistical characterisation

INTRODUCTION

Geotechnical design is performed under a

considerable degree of uncertainty. The two

main sources of this uncertainty include:

(i) Soil parameter uncertainty and (ii) cal-

culation model uncertainty. Soil parameter

uncertainty arises from the variability

exhibited by properties of geotechnical mate-

rials from one location to the other, even

within seemingly homogeneous profiles.

Geotechnical parameter prediction uncer-

tainties are attributed to inherent spatial

variability, measurement noise/random

errors, systematic measurements errors, and

statistical uncertainties. Conversely, model

uncertainty emanates from imperfections of

analytical models for predicting engineer-

ing behaviour. Mathematical modelling

of any physical process generally requires

simplifications to create a useable model.

Inevitably, the resulting models are simpli-

fications of complex real-world phenomena.

Consequently there is uncertainty in the

model prediction even if the model inputs

are known with certainty.

For pile foundations, previous studies (e.g.

Ronold & Bjerager1992; Phoon & Kulhawy

2005) have demonstrated that calculation

model uncertainty is the predominant com-

ponent. One of the fundamental objectives

of reliability-based design is to quantify and

systematically incorporate the uncertainties

in the design process. The current state of

the art in the quantification of model uncer-

tainty associated with a given pile design

model entails determining the ratio of the

measured capacity to theoretical capacity.

Accordingly, in this paper a series of pile per-

formance predictions by the static formula

are compared with measured performances.

To capture the distinct soil types for the

geologic region of southern Africa, as well as

the local pile design and construction experi-

ence base, pile load tests and associated

geotechnical data from the southern African

geologic environment are used.

In reliability analysis and modelling, both

materials properties and calculation model

uncertainties are incorporated into a perfor-

mance function representing the limit state

design function in terms of basic variables

which express design variables (loads, mate-

rial properties, geometry) as probabilistic

variables. The objective of this paper is to

present detailed statistical characterisation

of model uncertainty for pile foundations.

The analysis is an extension of the model

uncertainty characterisation reported by

Dithinde et al (2011). The purpose of the

characterisation is to relate southern African

pile foundation design practice to reliability-

based design as it has been developed and

Pile design practice in southern Africa Part I: Resistance statistics

M Dithinde, J V Retief

The paper presents resistance statistics required for reliability assessment and calibration of limit state design procedures for pile design reflecting southern African practice. The first step of such a development is to determine the levels of reliability implicitly provided for in present design procedures based on working stress design. Such an assessment is presented in an accompanying paper (please turn to page 72). The statistics are presented in terms of a model factor M representing the ratio of pile resistance interpreted from pile load tests to its prediction based on the static pile formula. A dataset of 174 cases serves as sample set for the statistical analysis. The statistical characterisation comprises outliers detection and correction of erroneous values, using the corrected data to compute the sample moments (mean, standard deviation, skewness and kurtosis) needed in reliability analysis. The analyses demonstrate that driven piles depict higher variability compared to bored piles, irrespective of materials type. In addition to the above statistics, reliability analysis requires the theoretical probability distribution for the random variable under consideration. Accordingly it is demonstrated that the lognormal distribution is a valid theoretical model for the model factor. Another key basis for reliability theory is the notion of randomness of the basic variables. To verify that the variation in the model factor is not explainable by deterministic variations in the database, an investigation of correlation of the model factor with underlying pile design parameters is carried out. It is shown that such correlation is generally weak.


standardised for geotechnical and structural

design. The derived statistics constitute the

backbone of all subsequent pile foundations

limit state design initiatives in southern

Africa. Specific usage of the derived statistics

include: assessment of reliability indices

embodied in the current southern African

pile design practice, as presented in the

accompanying paper (Retief & Dithinde

2013 – please turn to page 72); derivation of

the characteristic model factor for pile foun-

dations design in conjunction with SANS

10160-5 (2011); and reliability calibration of

resistance factors. The following topics are

presented subsequently:

■ The geotechnical background to the

dataset is briefly reviewed, including the

basis and application for classification

into homogeneous datasets and the for-

mal definition of the model factor M to

represent model uncertainty.

■ An assessment and detection of outliers

and correction of erroneous samples,

considering the sensitivity of reliability

analysis to even a limited number of such

values in a dataset.

■ Using the corrected data and conven-

tional statistical methods to compute

the sample moments: mean, standard

deviation, skewness and kurtosis for the

respective datasets.

■ Verification of randomness of the dataset

through investigation of any system-

atic dependence on the relevant design

variables.

■ Determination of the appropriate prob-

ability distribution to represent model

uncertainty provides the final step in

characterising model factor statistics.

PILE LOAD TEST DATABASE

Although this paper primarily considers the

statistical characteristics of southern African

pile model uncertainty, as based on the data-

base of model factors reported by Dithinde

et al (2011), with additional background

provided by Dithinde (2007), it is also neces-

sary to appreciate the geotechnical basis and

integrity of the dataset. This section presents

an extract of the way in which the dataset

has been compiled and a formal definition of

a model factor (M).

The database of static pile load tests

reported by Dithinde et al (2011) include

information on the associated geotechnical

data, such as soil profiles, field and labora-

tory test results. A comprehensive range of

soil conditions, pile geometry and resistance

is incorporated in the dataset, to provide

extensive representation of southern African

pile construction practice. Although the pile

load test reports were collected from various

piling companies in South Africa, a signifi-

cant number of pile tests were performed

in countries such as Botswana, Lesotho,

Mozambique, Zambia, Swaziland and

Tanzania. The main pile types in the data-

base include Franki (expanded base) piles,

Auger piles, and Continuous Flight Auger

(CFA) piles. In addition, there are a few cases

of steel piles and slump cast piles. The steel

piles are mainly H-piles, with one case where

a steel tubular pile was used.

The collected pile load test data was

carefully studied in order to evaluate its

suitability for inclusion in the current

study. For each load test, emphasis was

placed on the completeness of the required

information, including test pile size (length

and diameter), proper record of the load-

deflection data, and availability of subsur-

face exploration data for the site. Only cases

where sufficient soil data was available

for the prediction of pile resistance were

included in the database.

The pile load tests were used to deter-

mine the measured pile resistance, while the

geotechnical data was used to compute the

predicted resistance. The measured resis-

tances from the respective load-settlement

curves were interpreted on the basis of

Davisson’s offset criterion (Davison 1972).

However, for working piles, Chin’s extrapola-

tion (Chin 1970) was carried out prior to the

application of the Davisson’s offset criterion.

The predicted resistance was based on the

classic static formula which is essentially the

generic theoretical pile design model based

on the principles of soil mechanics. The

soil data that was obtained from the survey,

and used for the predicted resistance, was

mainly in the form of borehole log descrip-

tions and standard penetration (SPT) results.

Soil design parameters were selected on the

basis of common southern African practice

(Dithinde 2007).

Model factor statistics

The primary output of the database of pile

load tests reported by Dithinde et al (2011)

consists of the interpreted pile resistance (Qi)

and the predicted pile resistance (Qp) from

which a set of observations of the Model

Factor (M) as given by Equation [1] can be

obtained:

M = Qi

Qp

(1)

where:

Qi = pile capacity interpreted from a

load test, to represent the measured

capacity;

Qp = pile capacity generally predicted using

limit equilibrium models, and

M = model factor.

Each case of pile test included in the dataset

is consequently treated as a sample of the set

of n cases under consideration. In Dithinde

et al (2011) the complete set of 174 cases was

further classified in terms of four theoretical

principal pile design classes based on both

soil type and installation method. These

fundamental sets of classes include:

(i) driven piles in non-cohesive soil (D-NC)

with 29 cases, (ii) bored piles in non-cohesive

soil (B-NC) with 33 cases, (iii) driven piles

in cohesive soils (D-C) with 59 cases, and

(iv) bored piles in cohesive soils (B-C) with

53 cases. In this paper, the principle four data

sets are now combined into various practical

pile design classes considered in design codes

such as SANS 10169-5 (2011) and EN 1997-1

(2004). The additional classification schemes

include:

■ Classification based on pile installation

method irrespective of soil type. This is

the classification adopted in EN 1997-1

(2004) and it yields: 87 cases of driven

piles (D) and 83 cases of bored piles (B).

■ Classification based on soil type. This

classification system is supported by the

general practice where a higher factor of

safety is applied to pile capacity in clay

as compared to sand. This combination

results in 58 cases in non-cohesive soil

(NC) and 112 cases in cohesive soil (C).

■ All pile cases as a single data set irrespec-

tive of pile installation method and soil

type. This is the practical consideration

presented in SANS 10160-5 (2011) where

a single partial factor is given for all com-

pressive piles. The scheme yields 174 pile

cases (ALL).

DETECTION OF DATA OUTLIERS

The presence of outliers may greatly

influence any calculated statistics, lead-

ing to biased results. For instance, they

may increase the variability of a sample

and decrease the sensitivity of subsequent

statistical tests (McBean & Rovers 1998).

Therefore prior to further numerical treat-

ment of samples and application of statistical

techniques for assessing the parameters of

the population, it is absolutely imperative to

identify extreme values and correct errone-

ous ones.

The statistical detection and treatment

of outliers in the principal four sets were

reported by Dithinde et al (2011). The meth-

ods used include (i) load-settlement curves,

(ii) sample z-scores, (iii) box plots, and (iv)

scatter plots. The results for cases with outli-

ers are reproduced in Figure 1. Inspection

of Figure 1(a) reveals two potential outliers

(i.e. cases 27 and 54). The curves for these

two cases depict different behaviour from


Figure 1(a) Load-settlement curves method

1.6

1.6

1.6

1.6

Q /

Qi

Q /

Qi

Q /

Qi

Q /

Qi

1.2

1.2

1.2

1.2

0.8

0.8

0.8

0.8

0.4

0.4

0.4

0.4

0

0

0

0

30

30

30

30

25

25

25

25

20

20

20

20

15

15

15

15

10

10

10

10

5

5

5

5

0

0

0

0

Settlement, s (mm)

Settlement, s (mm)

Settlement, s (mm)

Settlement, s (mm)

Case 27

Driven piles in non-cohesive soilsN = 29

Case 54

Driven piles in cohesive soilsN = 59

Bored piles in non-cohesive soilsN = 33

Bored piles in cohesive soilsN = 53

Figure 1(b) Box plot methods

Box Plot of B-CSpreadsheet1 10v*174c

Box Plot of B-NCSpreadsheet1 10v*174c

M

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Median = 1.1154

25%–75% = (0.9615, 1.3202)

Non-Outlier range = (0.5436, 1.7478)

Extremes

Outliers

M

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Median = 1.9911

25%–75% = (0.7953, 1.1481)

Non-Outlier range = (0.4894, 1.5241)

Extremes

Outliers

#53#156


the rest of the curves (case 27 with a soft

initial response and case 54 with a large

normalised capacity). Visual inspection of

Figure 1(b) for outliers shows one data point

marked as outlier for B-NC and B-C data

sets. The tagged data points correspond to

pile cases number 53 and 156. However, it

should be noted that the box plot method for

identifying outliers has shortcomings, par-

ticularly for small sample sizes as is the case

here. Accordingly the identified cases will

have to be corroborated by other methods.

Examination of Figure 1(c) shows two data

points with z-score values at a considerable

distance from the rest of the data points.

These data points belong to B-NC (case 53)

and B-C (case 156) with z-scores of 3.13

and 2.95 respectively. Although the z-score

for case 156 is less than the criterion limit

value of 3, and therefore technically is not an

outlier, it is sufficiently close to the limit to

require further scrutiny. The results of the

scatter plots of pile capacity (Qi) versus the

predicted capacity (Qp) revealed the same

outliers detected by the other methods.

Aggregate of outliers

A total of five observations were detected

as potential outliers, namely cases 27, 53,

54, 55 and 156. However, it is not proper to

automatically delete a data point once it has

been identified as an outlier through statisti-

cal methods (Robinson et al 2005). Since an

outlier may still represent a true observation,

it should only be rejected on the basis of

evidence of improper sampling or error.

Accordingly the five data points identified as

outliers were carefully examined by double-

checking the processes of determination

of interpreted capacities and computation

of predicted capacities. This entailed going

back to the original data (pile testing records

and derivation of soil design parameters) and

checking for recording and computational

errors. Following this procedure the correc-

tions were as follows:

■ Cases 53, 54 and 55: Examination of

records for these cases showed that an

uncommon pile installation practice was

employed. The steel piles were installed

in predrilled holes and then grouted. The

strength of the grout surrounding the

piles contributed to the high resistance

and hence the higher interpreted capaci-

ties. Since the installation procedure

for these piles deviates from the normal

practice, they represent a different

population. These were the only piles in

the database constructed in this rather

unusual method. These data points were

therefore regarded as genuine outliers and

were deleted from the data set.

■ Case 27: There was no obvious physical

explanation for the behaviour of pile case

27. The depicted behaviour is attributed

to extreme values of the hyperbolic

parameters representing the non-linear

behaviour of the test results. Since piles

in terms of pile type, size and soils condi-

tions (i.e. cases 28 and 29) did not show

similar characteristics, it was concluded

that an error was made during the execu-

tion of the pile test. Accordingly this pile

case was regarded as having incomplete

information, and was therefore deleted.

■ Case 156: Again there was no obvious

physical explanation for the behaviour of

this pile case. Furthermore, the location

of this data point on the scatter plot of

Qi versus Qp fits the general trend for

the dataset. Therefore no correction was

justified for this pile case.

In summary, four outliers were removed and

one retained, bringing the dataset to n = 170

cases in total and for the respective subsets

nD-NC = 28; nB-NC = 30; nD-C = 59; nB-C = 53.

SCATTER PLOTS OF QI VS QP

Scatter plots of Qi versus Qp can serve as a

multivariate approach to outlier detection.

However they are presented here to provide

an indication of whether the variance of

the data set is constant or varies with the

dependent variable (i.e. homoscedasticity).

The ensuing scatter plots are presented in

Figure 2. Visual inspection of the scatter

plots seems to suggest variation in the degree

of scatter increases with values of Qp. In this

regard, it is evident that there is reduced

scatter at smaller values of Qp. However, due

to the small sample size, the case for large

values of Qp is not sufficiently clear to make

any firm conclusion. Furthermore, Figure 2

gives the impression that the variance of

the points around the fitted line increases

linearly, thereby suggesting that the standard

deviation increases with the square root

of the values of Qp. This explains why the

scatter tends to flatten off for large values of

Qp. The foregoing assumption implies that

weighted regression analysis must be used

to establish the relationship between Qi and

Qp. Such regression analysis was applied in

this study (Figure 2) with the regression line

forced to pass through the origin. In this

case, the slope of the regression line is an

estimate of the model factor M.

SUMMARY STATISTICS

Following the outlier detection and removal

process, the descriptive statistics for M

consisting of mean (mM), standard deviation

(sM), skewness and kurtosis are presented

in Table 1. The sample descriptive statistics

were computed using conventional statistical

analysis approach. These are quantities used

to describe the salient features of the sample

and are required for calculations, statisti-

cal testing, and inferring the population

parameters.

The sample mean mM indicates the aver-

age ratio of Qi to Qp, with mM > 1 indicating

a conservative bias of Qi exceeding Qp. This

is generally the case, with a positive bias

of between 1.04 and 1.17 shown in Table 1,

except for the B-NC case where Qi is on

average slightly less than Qp with mM = 0.98,

which is slightly un-conservative. The

general conservative bias reflected by mM is,

however, small in comparison to the disper-

sion of M as reflected by the sample standard

deviation sM for which values range from

0.23 to 0.36; the dispersion is also presented

Figure 1(c) Z-score method

Figures 1(a)–(c) Outlier detection results (after Dithinde et al 2011)

Z-s

core

3

4

1

2

0

–1

–3

–2

M

0 1 2 3

D-NC B-NC D-C B-C


in normalised form as the coefficient of

variation VM = sM/mM.

The combined effect of values of mM

close to 1 and the relatively large values

of sM or VM indicate large probabilities of

realisations of M in the un-conservative

range M < 1. The lower tail of the distribu-

tion of M derived from the dataset and M

statistics is therefore of specific interest

for application of the results in reliability

assessment.

A comparison of the standard deviations

or coefficient of variations for the respective

cases indicates small differences. However,

there seems to be a distinct trend that is

influenced by the pile installation method

(i.e. driven or bored). In this regard, driven

piles depict higher variability compared to

bored piles, irrespective of soil type. This

Table 1 Summary of statistics for M

M nMean

mM

Confidence -75%

mM; -0.75

Std. Dev.sM

Upper CI SD 75%sM; +0.75

COV Skewness Kurtosis

D-NC 28 1.11 1.03 0.36 0.40 0.33 0.35 –1.15

B-NC 30 0.98 0.93 0.23 0.26 0.24 0.14 –0.19

D-C 59 1.17 1.12 0.3 0.32 0.26 –0.01 –0.74

B-C 53 1.15 1.10 0.28 0.30 0.25 0.36 0.49

D 87 1.15 1.11 0.32 0.34 0.28 0.1 –0.95

B 83 1.09 1.05 0.28 0.30 0.25 0.41 0.47

NC 58 1.04 1.00 0.30 0.32 0.29 0.55 –0.37

C 112 1.16 1.13 0.29 0.30 0.25 0.15 –0.29

ALL 170 1.1 1.07 0.31 0.32 0.28 0.24 –0.75

Figure 2 Scatter plots of Qi versus Qp

Qi

(kN

)Q

i (k

N)

Qi

(kN

)

Qi

(kN

)Q

i (k

N)

8 000

8 000

15 000

14 000

6 000

6 000

10 000

10 000

4 000

4 000

5 000

6 000

2 000

2 000

2 000

0

0

0

0

(a) All driven piles

(c) All piles in non-cohesive soil

(e) All piles

(b) All bored piles

(d) All piles in cohesive soil

0

0

0

0

2 000

2 000

5 000

2 000

4 000

4 000

10 000

4 000

6 000

6 000 6 000

8 000

8 000

15 000

14 000

Qp (kN)

Qp (kN)

Qp (kN)

Qp (kN)

Qp (kN)

12 000

8 000

4 000

14 000

10 000

6 000

2 000

0

12 000

8 000

4 000

8 000 10 000 12 000

0 2 000 4 000 6 000 14 0008 000 10 000 12 000

Qi = 1.0685Qp Qi = 1.1018Qp

Qi = 1.1189QpQi = 0.9901Qp

Qi = 1.0886Qp


implies that the densification of the soil sur-

rounding the pile emanating from the pile

driving process is not well captured in the

selection of the soil design parameters. Even

the bias for the driven piles dataset is rela-

tively higher, thereby reiterating the notion

that current practice is conservative in

selecting design parameters for driven piles.

Furthermore, the variability in non-cohesive

materials is higher than that in cohesive

materials. This is attributed to the fact that

in cohesive materials the un-drained shear

strength derived from the SPT measurement

is directly used in the computation of pile

capacity, while in non-cohesive materials,

the angle of friction obtained from the SPT

measurement is not directly used. Instead,

the key pile design parameters in the form

of bearing capacity factor (Nq), earth pres-

sure coefficient (ks) and pile-soil interface

friction (δ) are obtained from the derived

angle of friction on the basis of empirical

correlation, thus introducing some additional

uncertainties.

Skewness provides an indication of the

symmetry of the dataset. The skewness

represented in Table 1 is generally positive,

indicating a shift towards the upper tail

(conservative) of the values for M. There is,

however, no consistent trend amongst the

values for the respective datasets. The value

of 0.24 for the combined dataset (ALL)

could therefore be taken as indicative of the

general trend. As a guideline it should be

noted that the skewness of the symmetrical

normal distribution is 0; for a lognormal

distribution it is dependent on the distribu-

tion parameters, with a value of 0.83 based

on the parameter values for the combined

dataset.

Values of kurtosis indicate the peakedness

of the data, with a positive value indicating a

high peak, and a negative value indicating a

flat distribution of the data. Negative values

generally listed in Table 1 indicate flat dis-

tribution of the data, particularly for driven

piles. Since these characteristics can only be

captured by advanced probability distribu-

tions not generally considered in reliability

modelling, kurtosis is not further considered.

In order to provide for uncertainties in

parameter estimation, Table 1 also presents

the confidence limits of the mean and stan-

dard deviation at a confidence level of 0.75;

this is the confidence level recommended by

EN1990:2002 for parameter estimation for

reliability models with vague information

on prior distributions. The lower confidence

limit of the mean (mM; -0.75) and the upper

confidence limit of the standard deviation

(sM; +0.75) is used to present conserva-

tive estimates of the range of parameter

estimates.

CORRELATION WITH PILE

DESIGN PARAMETERS

Although the mean and standard deviation

values presented in Table 1 provide a useful

data summary, they combine data in ways

that mask information on trends in the data.

If there is a strong correlation between M

and some pile design parameters (pile length,

pile diameter and soil properties), then part

of its total variability presented in Table 1

is explained by these design parameters.

The presence of correlation between M and

deterministic variations in the database

would indicate that:

■ The classical static formula method does

not fully take the effects of the parameter

into account.

■ The assumption that M is a random vari-

able is not valid.

Reliability-based design is based on the

assumption of randomness of the basic

variables. Since the model factor is among the

variables that serve as input into reliability

analysis of pile foundations, it is critical to

verify that it is indeed a random variable.

This was partially verified by investigating

the presence or absence of correlation with

various pile design parameters. The measure

of the degree of association between variables

is the correlation coefficient. The basic

and most widely used type of correlation

coefficient is Pearson r, also known as

linear or product-moment correlations.

The correlation can be negative or positive.

When it is positive, the dependent variable

tends to increase as the independent variable

increases; when it is negative, the dependent

variable tends to decrease as the independent

variable increases. The numerical value of

r lies between the limits -1 and +1. A high

absolute value of r indicates a high degree

of association, whereas a small absolute

value indicates a small degree of association.

When the absolute value is 1, the relationship

is said to be perfect and when it is zero,

the variables are independent. For the

numerical correlation values in-between the

limits a critical question is, “When is the

numerical value of the correlation coefficient

considered significant?” Several authors

in various fields have suggested guidelines

for the interpretation of the correlation

coefficient. For the purposes of this study an

interpretation by Franzblau (1958) is adopted

as follows:

■ Range of r: 0 to ±0.2 – indicates no or

negligible correlation

■ Range r: ±0.2 to ±0.4 – indicates a low

degree of correlation

■ Range r: ±0.4 to ±0.6 – indicates a moder-

ate degree of correlation

■ Range r: ±0.6 to ±0.8 – indicates a

marked degree of correlation

■ Range r: ±0.8 to ±1 – indicates a high

correlation

The statistical significance of the correlation

is determined through hypothesis testing

and presented in terms of a p-value. In this

regard, the null hypothesis is that there is no

correlation between M and the given design

parameter (indicative of statistical independ-

ence). A small p-value (p < 0.05) indicates

that the null hypothesis is not valid and

should be rejected. Values for the correlation

between M and the respective pile design

parameters with the associated p-values are

listed in Table 2. The results indicate that

R < 0.4 for all the pile design parameters and

therefore the degree of correlation is low.

The associated p-values are generally much

greater than 0.05, confirming that the cor-

relation between the model factor and the

various pile design parameters is statistically

insignificant. Therefore, variations in the

model factor are at least not explainable by

systematic variations in the key pile design

parameters, and a random variable model

appears reasonable.

For visual appreciation of the correlation

results in Table 2, some of scatter plots of M

versus pile design parameters are shown in

Figure 3.

Table 2 Correlation with pile design parameters

Design parameter

Case

Spearman rank correlation

R p-value

Pile length

D 0.11 0.29

B 0.11 0.31

NC –0.25 0.05

C 0.17 0.07

ALL 0.02 0.75

Shaft diameter

D 0.01 0.92

B 0.12 0.26

NC 0.13 0.34

C –0.02 0.82

ALL 0.05 0.53

Base diameter

D –0.16 0.15

B 0.05 0.63

NC 0.00 1.00

C –0.06 0.51

ALL –0.03 0.67

φ-base NC 0.19 0.16

φ-shaft NC 0.19 0.16

Cu-base C –0.002 0.98

Cu-shaft C –0.21 0.02


PROBABILISTIC MODEL FOR

THE MODEL FACTOR

The theory of reliability is based on the

general principle that the basic variables

(actions, material properties and geometric

data) are considered as random variables

having appropriate types of distribution. One

of the key objectives of the statistical data

analysis is to determine the most appropriate

theoretical distribution function for the basic

variable. This is the governing probability

distribution for the random process under

consideration and therefore extends beyond

the available sample (i.e. the distribution of

the entire population). Once the probability

distribution function is known, inferences

based on the known statistical properties of

the distribution can be made.

For reliability calibration and associated

studies, the most commonly applied distribu-

tions to describe actions, materials properties

and geometric data are the normal and log-

normal distributions (Holický 2009; Allen et

al 2005). Accordingly, for the current analysis

only the normal and lognormal distribution

fit to the data are considered. The fit is inves-

tigated through (i) a cumulative distribution

function (CDF) plotted using a standard

normal variate with z as the vertical axis, and

(ii) direct distribution fitting to the data.

The cumulative distribution function

is the most common tool for statistical

characterisation of random variables used in

reliability calibration (e.g. Allen et al 2005).

In the context of the current analysis, the

CDF is a function that represents the prob-

ability that a value of M less than or equal to

a specified value will occur. This probability

can be transformed to the standard normal

variable (or variate), z, and plotted against

M values (on x-axis) for each data point.

This plotting approach is essentially the

equivalent of plotting the bias values and

their associated probability values on normal

probability paper. An important property

of a CDF plotted in this manner is that

normally distributed data plot as a straight

line, while lognormally distributed data on

the other hand will plot as a curve. The fol-

lowing steps were used to create the standard

normal variate plot of the CDF:

■ The capacity model factor values in a

given data set were sorted in a descending

order, then the probability associated

with each value in the cumulative distri-

bution was calculated as i/(n +1).

■ For the probability value calculated in

Step 1 associated with each ranked capac-

ity model factor value, z was computed in

Excel as: z = NORMSINV(i/(n +1)) where

i is the rank of each data point as sorted,

and n is the total number of points in the

data set.

■ Once the values of z have been calculated,

z versus model factor (X) was plotted for

each data set.

The ensuing plots are presented in Figure 4(a)

from which it can be seen that the CDF for

the five data sets plot more as curves than

straight lines, thereby implying that the data

follow a lognormal distribution. A further

characterisation entailing fitting predicted

normal and lognormal distributions to the

CDF of the data sets is carried out. These

theoretical distributions are also shown in

Figure 4(a). Both distributions seem to fit

the data reasonably well. However, with the

exception of the bored piles data set, the

lognormal distribution has a better fit to the

lower tail of the data, which is important for

reliability analysis and design.

Figure 3 Correlation with some of the pile design parameters

MM

MM

2.2

2.0

2.2

2.2

0

24

200

0

5

28

300

400

10

32

400

800

15

34

500

1200

35

42

900

L

Phi shaft

Shaft diameter (mm)

Cu-base

2.0 2.0

2.0

1.8

1.8

1.8

1.8

1.6

1.6

1.6

1.6

1.4

1.4

1.4

1.4

1.2

1.2

1.2

1.2

1.0

1.0

1.0

1.0

0.8

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

All piles cases

Phi shaft

All piles cases

Cu-base

20

36

600

1600

25

38

700

2000

30

40

800 1 000

26 30

L:M: r = 0.0245, p = 0.7512 Shaft diameter:M: r = 0.0486, p = 0.5288

Phi shaft:N-C: r = 0.01868, p = 0.1604 Cu-base:C: r = –0.0021, p = 0.9822


To further confirm that the data best

fits a lognormal distribution, z-scores are

plotted as a function of Ln (M). The plots

would follow a straight line if the data in

fact follows the lognormal distribution. The

results are presented in Figure 4(b) from

which it is apparent that all the data sets plot

as a straight line. This therefore confirms

the strong case for a lognormal distribution

assumption for the data.

In Figure 5 the histogram of M for the

respective datasets are compared to normal,

lognormal and general lognormal (also three-

parameter 3P) probability density function

distributions based on the sample moments

listed in Table 1 as distribution parameters.

The graphic comparison indicates the degree

to which the alternative distributions provide

a reasonably smoothed representation of the

M data. At the same time the approximate

nature of the M data is indicated by the

Figure 4(a) CDF plots with normal and lognormal fit

No

rma

l st

an

da

rd v

ari

ab

le,

zN

orm

al

sta

nd

ard

va

ria

ble

, z

No

rma

l st

an

da

rd v

ari

ab

le,

zN

orm

al

sta

nd

ard

va

ria

ble

, z

3

3

2.5

3

0.4

0.4

0.4

0.4

0.4

0.9

0.9

0.9

0.9

0.9

1.4

1.4

1.4

1.4

1.4

1.9

1.9

1.9

1.9

1.9

2.4

2.4

2.4

2.4

2.4

M

M

M

M

M

2

2

2.0

2

1

1

1.0

1

0

0

0

0

–1

–1

–1.0

–1

–2

–2

–2.0

–2

–3

–3

–2.5

–3

(a) Driven piles

(c) Piles in non-cohesive soil

(e) All

(a) Bored piles

(d) Piles in cohesive soil

–1.5

–0.5

1.5

0.5

No

rma

l st

an

da

rd v

ari

ab

le,

z

2.5

2.0

1.0

0

–1.0

–2.0

–2.5

–1.5

–0.5

1.5

0.5

Normal dist fit

Lognormal dist fit

CDF of data


uneven nature of the histogram. The quan-

titative assessment of the difference between

the empirical data frequencies and the

assumed distributions is provided by the chi-

square goodness-of-fit test. In this regard, the

p-value is a measure of the goodness-of-fit,

with larger values indicating a better fit.

In testing the hypothesis that the

distribution of the data is similar to the

selected probability distribution (normal

or lognormal), the hypothesis is rejected if

p < 0.05. The p-values for chi-square testing

are presented in Table 3 from which it is

apparent that such values for all the data sets

are greater than 0.05 and therefore there is

no evidence to reject the null hypothesis of

either normal or lognormal distributions.

However, on the basis of the magnitude of

the p-values, the lognormal distribution

seems to show a better fit compared to

the other two distributions. The general

Figure 4(b) Z-score vs LN(M)

2.0

3 3

3

10

(a) Driven piles


(e) All

(b) Bored piles


Z-s

core

Z-s

core

Z-s

core

Z-s

core

Z-s

core

LN(M)

LN(M) LN(M)

LN(M)

LN(M)

1.5

2 2

2

5

1.0

1 1

1

00.5

0

0 0

0

–0.5

–5

–1.0

–1

–10

–1.5

–1 –1

–2

–15

–2.0

–2 –2

–3

–20

–2.5

–3 –3

–4

–25

–1.0

–1.0 –1.0

–1.0

–1.0

–0.5

–0.5 –0.5

–0.5

–0.5

1.0

1.0 1.0

1.0

1.0

0.5

0.5 0.5

0.5

0.5

0

0 0

0

0


Figure 5 Normal and lognormal distribution fit to the data

(a) Driven piles


(b) Bored piles


f(M

)0.26 0.36

M

0.240.32

0.22

0.280.20

0.24

(e) All

0.18

0.20

0.16

0.16

0.14

0.12

0.12

0.10

0.08

0.080.06

0.040.04

0.02

0 00.6 0.8 1.0 1.2 1.4 1.6 1.8 0.6 1.8 2.00.8 1.0 1.2 1.4 1.6

f(M

)

M

0.36 0.30

0.320.26

0.280.24

0.24

0.22

0.20

0.20

0.16

0.18

0.12

0.16

0.08

0.14

0.04

0.12

0 0

f(M

)

f(M

)

0.6 0.8 1.0 1.2 1.4 1.6

0.28

0.10

0.08

0.06

0.04

0.02

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

M M

f(M

)

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

00.6 0.8 1.0 1.2 1.61.4 1.8 2.0

M

Histogram

Lognormal

Lognormal (3P)

Normal

Note: LN and LN (3) fits coincide


lognormal distribution provides distributions

which are generally intermediate between

the normal and lognormal distributions

(Figure 5), with similar results for the

p-values (Table 3).

On the basis of the results of the two

standard distribution fitting approaches

studied, it can be concluded that the

data fits both the normal and lognormal

distributions, although the ordinary

lognormal distribution has a slight

edge, particularly towards the lower tail

(Figure 5). However, theoretically M

ranges from zero to infinity, resulting in

an asymmetric distribution with a zero

lower bound and an infinite upper bound.

The lognormal probability density function

is often the most suitable theoretical

model for such data, as it is a continuous

distribution with a zero lower bound and

an infinite upper bound. On the basis of

this practical consideration, past studies

(e.g. Phoon 2005; Briaud & Tucker 1988;

Ronold & Bjerager 1992; Titi & Abu-Farsakh

1999; FHWA-H1-98-032 2001; Rahman et

al 2002) have recommended the lognormal

distribution as the most suitable theoretical

model for model uncertainty. Furthermore,

in the Probabilistic Model Code by the Joint

Committee on Structural Safety (JCSS)

(2001), model uncertainty is modelled by

the lognormal distribution. Therefore the

lognormal distribution is considered a valid

probability model for M. Nonetheless, it

should be acknowledged that there could

be some other distributions that can

provide a better fit to the tails. Generally

such advanced and complex distributions

require a large sample size. For a small

sample size, as is the case in this study, such

distributions may only lead to a refinement

of the results, but not a significant

improvement.

CONCLUSIONS

Pile foundation design uncertainties are

captured by the M statistics. The M statistics

constitute the main input into reliability

calibration and associated studies. Since

the M statistics are derived from raw data,

statistical characterisation of such data is

of paramount importance. Accordingly

characterisation of the data collected for

pile foundation reliability studies have been

presented in this paper. The key conclusions

reached are as follows:

■ Based on the mean values for M, the

static formula yields a positive bias of

between 1.04 and 1.17, except for the

B-NC data set where Qi is on average

slightly less than Qp with mM = 0.98,

which is slightly un-conservative.

■ There is a distinct trend that driven

piles depict higher variability compared

to bored piles, irrespective of materials

type. This suggests that the densification

induced by pile driving is not fully cap-

tured by existing procedures for selecting

design parameters.

■ The variability in non-cohesive materials

is higher than that in cohesive materials.

This is attributed to the high degree of

empiricism associated with the selection

of pile design parameters (Nq, ks and δ) in

non-cohesive soils.

■ The values of mM close to 1 and the

relatively large values of sM or VM

indicate large probabilities of realisa-

tions of M in the un-conservative range

M < 1. Therefore the lower tail of the

distribution of M is of specific interest

for application of the results in reliability

assessment.

■ At the customary 5% confidence level,

the chi-square goodness-of-fit test results

indicate that both the normal and log-

normal distributions are valid theoretical

distributions for M. However, when

taking into account other practical con-

siderations, the lognormal distribution

is considered to be the most appropriate

distribution for M.

■ None of the pile design parameters is

significantly correlated with the model

factor. From the probabilistic perspec-

tive, this implies that the variation in

the model factor is not caused by the

variations in the key pile design para-

meters. Therefore it is correct to model

the model factor as a random variable.

REFERENCES

Allen, T M, Nowak, A S & Bathurst, R J 2005.

Calibration to determine load and resistance factors

for geotechnical and structural design. Washington

DC: Transport Research Board.

Briaud, J L & Tucker, L M 1988. Measured and pre-

dicted response of 98 piles. Journal of Geotechnical

Engineering, 114(9): 984–1001.

Chin, F K 1970. Estimation of the ultimate load

of piles not carried to failure. Proceedings, 2nd

Southern Asian Conference on Soil Engineering,

81–90.

Davison, M T 1972. High-capacity piles. Proceedings,

Soil Mechanics Lecture Series on Innovation in

Foundation Construction, Chicago, American

Society of Civil Engineers, Illinois Section,

22 March, 81–112.

Dithinde, M 2007. Characterisation of model uncer-

tainty for reliability-based design of pile foundations.

PhD Thesis, Stellenbosch, South Africa: University

of Stellenbosch.

Dithinde, M, Phoon, K K, De Wet, M & Retief J V

2011. Characterisation of model uncertainty in the

static pile design formula. Journal of Geotechnical

and Geoenvironmental Engineering, ASCE, 137(1):

333–342.

European Committee for Standardization 1997.

EN-1997:2004. Eurocode 7: Geotechnical Design. Part

1: General Rules. Brussels: European Committee for

Standardization (CEN).

FHWA (US Federal Highway Administration) 2001.

Load and Resistance Factor Design (LRFD) for

Highway Bridge Substructures. Publication No

FHWA-HI-98-032, Washington DC: FHWA.

Franzblau, A 1958. A Primer for Statistics for Non-

Statisticians. New York: Harcourt Brace & World.

Holický, M 2009. Reliability Analysis for Structural

Design. Stellenbosch: SUN MeDIA Press.

JCSS (Joint Committee on Structural Safety) PMC 2001.

Probabilistic model code. JCSS Working Materials

[Online] http://www.jcss.ethz.ch (retrieved 1 Feb.

2011).

McBean, E A & Rovers, F A 1998. Statistical Procedures

for Analysis of Environmental Monitory Data and

Risk Assessment. Upper Saddle River, New Jersey:

Prentice-Hall.

Phoon, K K & Kulhawy, F H 2005. Characterisation of

model uncertainty for laterally loaded rigid drilled

shaft. Geotechnique, 55(1): 45–54.

Phoon, K K 2005. Reliability-based design incorporating

model uncertainties. Proceedings, 3rd International

Conference on Geotechnical Engineering combined

with the 9th Yearly Meeting of the Indonesian

Society for Geotechnical Engineering, 191–203.

Rahman, M S, Gabr, M A, Sarica, R Z & Hossan, M S

2002. Load and resistance factors design for analysis/

design of piles axial capacities. North Carolina State

University.

Table 3 Chi-Square goodness-of-fit test results

Pile class

Chi-Squared test p-value

Normal LognormalGeneral Lognormal

(3P)

Driven piles 0.32 0.60 0.43

Bored piles 0.07 0.77 0.20

Piles in non-cohesive soil 0.32 0.81 0.81

Piles in cohesive soil 0.69 0.68 0.70

All piles 0.29 0.62 0.51


Retief, J V & Dithinde, M 2013. Pile design practice in

southern Africa. Part 2: Implicit reliability of exist-

ing practice. Journal of the South African Institution

of Civil Engineering, 55(1): 72–79.

Robinson, R B, Cox, C D & Odom, K 2005. Identifying

outliers in correlated water quality data. Journal of

Environmental Engineering, 131(4): 651–657.

Ronold, K O & Bjerager, P 1992. Model uncertainty

representation in geotechnical reliability Analysis.

Journal of Geotechnical Engineering, ASCE, 118(3):

363–376.

SANS 2011. SANS 10160-5:2011: Basis of Structural

Design and Actions for Buildings and Industrial

Structures. Part 5: Basis for Geotechnical Design

and Actions. Pretoria: South African Bureau of

Standards.

Titi, H H & Abu-Farsakh, M Y 1999. Evaluation of

bearing capacity of piles from cone penetration test

data. Project No. 98-3GT, Baton Rouge: Louisiana

Transportation Research Centre.


INTRODUCTION

The model factor statistics presented in the

accompanying paper (Dithinde & Retief 2013

– please turn to page 60) provide a clear indi-

cation of the need for a systematic treatment

of the variability and uncertainty of design

parameters and procedures in geotechnical

design practice. The principles of reliability-

based design providing the conceptual basis

for such systematic treatment are sufficiently

established to be captured in standardised

procedures such as the International

Standard ISO 2394:1998 (adopted as SANS

2394:2004) and converted into operational

basis of design procedures such as Eurocode

EN 1990:2002. The standardised procedures

are based on limit states design format with

a reliability-based framework to ensure

appropriate performance levels for the load-

bearing capacity and characteristics of the

structure or civil engineering works.

Sufficient advances in the theory of reli-

ability have been made to derive guidelines

for levels of performance as expressed in

terms of reliability representing probability

of failure (Pf) for classes of structures and

facilities. For various reasons, however,

there is insufficient information available to

develop reliability-based procedures purely

on frequentist or statistical probability

models. The most compelling argument for

taking information from existing practice

into account when reliability-based design

procedures are developed comes from the

success of present practice and codes which

primarily rely on experience-based expertise

and judgement.

Capturing the reliability performance

from existing practice which is deemed

to be acceptable, such as presented in the

accompanying paper, is an important source

of information for the development of

standardised design procedures. One of the

possible applications of the information on

existing practice is to obtain an indication of

acceptable levels of reliability, in comparison

to other ways in which target reliability

is established. This is the purpose of the

Pile design practice in southern Africa Part 2: Implicit reliability of existing practice

J V Retief, M Dithinde

Limit state design has become the basis of geotechnical design codes worldwide. With the semi-probabilistic limit state design approach, load and resistance factors of (deterministic) design functions are calibrated on the basis of reliability theory. The calibration is done to obtain procedures that will ensure that a target level of reliability is exceeded under the design conditions within the scope of the design function. This is conventionally expressed in terms of the reliability index (β), which is related to the probability of failure (Pf). Acceptable existing design practice is an important source of information on appropriate levels of reliability. This paper uses the results from a pile load test database to evaluate the reliability levels implied in the current South African pile design approach. The results of the analysis indicate that the reliability index values for ultimate limit state failure of single piles implicit to present design practice vary with the pile class. However, the influence of the probability model applied is more significant. Based on conventional and standardised procedures for reliability analysis, a representative implicit reliability index value βI,Rep 3.5 is obtained, corresponding to a probability of failure Pf = 2.10-4. The values for various sets of pile conditions range from βI = 3.1 (Pf = 1.10-3) to βI = 4.3 (Pf = 1.10-5). This compares well with target levels of reliability for structural and geotechnical performance of βT = 3.0 as set in SANS 10160-1:2011 Part 1 Basis of structural design. These indicative results provide a useful reference base to establish the reliability of existing and therefore acceptable South African pile design practice. It could also be interpreted as indicative of geotechnical design practice in general. The standard SANS 10160-5:2011 Part 5 Basis for geotechnical design and actions provides the framework for future calibration investigations.

TECHNICAL PAPER



PROF JOHAN RETIEF (Fellow of SAICE) has, since

his retirement as Professor in Structural

Engineering, maintained involvement at the

Stellenbosch University, supervising graduate

students in the fi eld of risk and reliability in civil

engineering. He is involved in various standards

committees, serving as the South African

representative to ISO TC98 (basis of structural

design and actions on structures). He holds a BSc (cum laude) and a DSc from

the University of Pretoria, a DIC from Imperial College London, and an MPhil

from London University. Following a career at the Atomic Energy

Corporation, he joined Stellenbosch University in 1990.

Contact details:



Private Bag X1

Matieland

Stellenbosch

7602

T: +27 21 808 4442

F: +27 21 808 4947


DR MAHONGO DITHINDE (Visitor) holds a PhD in

Civil Engineering from the Stellenbosch

University, an MSc in Foundation Engineering

from the University of Birmingham (UK), and

BEng in Civil Engineering from the University of

Botswana. He works as a Senior Lecturer at the

University of Botswana. His specialisation and

research interests are in the broad area of

geotechnical reliability-based design. In addition to academic work, he is also

a geotechnical partner for Mattra International where he is active in

consultancy work in the fi eld of geotechnical engineering.

Contact details:



Private Bag X1

Matieland

7602

South Africa


University of Botswana

Private Bag UB 0061

Gaberone

Botswana

T: +267 355 4297

F: +267 395 2309


Key words: pile foundations, South African practice, geotechnical design,

reliability level


present paper. In the process, representative

probability models for pile resistance are

obtained, that could subsequently be used

for reliability calibration of standard design

procedures.

A brief overview is firstly provided of the

state of limit states design in South Africa –

the standardised way in which the principles

of reliability is formulated and related to

limit states design, including a discussion of

target levels of reliability in general and as

established for South Africa, serves as basis

for comparison of implicit levels of reliability

derived for existing practice. Ultimately

such implicit levels of reliability are derived,

considering alternative probability models

from the results of the accompanying paper,

and determining representative cases and

probability models.

RELIABILITY-BASED GEOTECHNICAL

LIMIT STATES DESIGN

The need of converting the now defunct

Code of Practice for Pile Foundation Design

(SABS 088:1972) to limit states design princi-

ples was recognised by the South African pil-

ing industry as far back as 1993. A concerted

effort was also made by the Geotechnical

Division of the South African Institution

of Civil Engineering (SAICE) to adopt and

apply geotechnical limit state design in

South Africa, as summarised by Day &

Retief (2009). Recent international and local

developments have now added impetus to

the introduction of probabilistic-based limit

state geotechnical design in South Africa.

These include:

i. Increased interest in harmonisation of

technical rules for design of building and

civil engineering works internationally

as is demonstrated for instance by the

activities of the ISSMGE (Orr et al 2002)

and across disciplines, as demonstrated

by the Eurocode set of design standards

(CE 2002).

ii. The international acceptance of semi-

probabilistic limit states as the standard

basis on which the new generation of

geotechnical codes are being developed

today, such as Eurocode EN 1997:2004

Geotechnical design (EN 1997:2004)

and the FHWA Manual for Load and

Resistance Factor Design (LRFD) of

bridge substructures (FHWA 2001).

iii. The publication of the revised South

African Loading Code (SANS 10160:2011

Basis of structural design and actions

for buildings and industrial structures)

providing the reliability framework in

Part 1 Basis of structural design, with

the implication that the subsequent

materials codes will be based on the

same framework. Geotechnical design is

included in this framework with the first

step taken in Part 5 Basis of geotechnical

design and actions as related to buildings

and similar industrial structures.

The main advantage of the derivation of geo-

technical limit states design procedures from

the principles of reliability is that it provides

a rational basis for such practice. In addition

to enhancing the rationality of design for a

specific situation (limit state, failure mode,

construction type, etc) it also improves the

consistency between the various situations

within a single construction (geotechnical,

substructure, superstructure, structural

materials) or extends to the scope of applica-

tion of the design procedures.

Common principles of reliability provide

the rational basis for unification of geo-

technical and structural design. This is an

essential requirement for interrelated but

specialised design procedures, not only since

both elements are shared by individual con-

structions, but also for the purpose of tech-

nical communication between geotechnical

and structural design practitioners.

At the highest level a rational basis for

the underlying models and procedures is the

only way in which international harmonisa-

tion of design practice can be maintained.

The importance of sharing the wealth of

international experience on the basis of

harmonisation is usually appreciated, but

the ability to provide optimally for local

conditions whilst maintaining fundamental

alignment with internationally accepted

procedures is not always achieved or even

attempted.

The theory of reliability, as applied

to determine the performance of civil

engineering works, is sufficiently mature

to formulate standardised procedures

for its application in design practice:

The International Standard General

principles on reliability for structures, ISO

2394:1998, was adopted as a South African

National Standard SANS 2394:2004. The

Joint Committee on Structural Safety

Probabilistic Model Code (JCSS-PMC 2001)

provides more detailed pre-normative reli-

ability procedures and models. A notable

development is the conversion of general

reliability concepts into operational proce-

dures as captured in the Eurocode Standard

EN 1990:2002 Basis of structural design

which provides a common basis for the

set of Eurocodes. SANS 10160-1:2011 and

SANS 10160-5:2011 respectively provide

harmonisation with the Eurocode for the

basis of design and geotechnical design. EN

1990 Annex C Basis of partial factor design

and reliability analysis serves as reference

for standardised reliability practice, with

probabilistic models taken from Annex D

Design assisted by testing in this paper.

A critical element of converting reliability

analysis into design procedures is the estab-

lishment of acceptable levels of reliability.

Some guidance on appropriate levels of reli-

ability is given in SANS 2394:2004 and JCSS-

PMC:2001. Application of appropriate levels

of reliability in South African structural

design is discussed by Retief & Dunaiski

(2009). The implicit levels of reliability of

existing design practice are recognised in

standardised procedures such as SANS

2394:2004, EN 1990:2002 and FHWA HI-98-

032 (FHWA 2001) as a basis for selecting

target levels of reliability.

MOTIVATION AND PURPOSE

OF INVESTIGATION

Given the importance of the reliability

performance of existing practice serving as

starting point for the calibration of more

refined limit states design procedures, the

purpose of this paper is to provide such an

assessment of present pile construction and

design practice in southern Africa. Implicit

reliability serves as baseline for acceptable

practice. Inconsistency in reliability across

the scope of application can be identified,

considering possible remedies and adjust-

ments. Systematic calibration of the provi-

sions of SANS 10160-5:2011 is another pos-

sible application of the results reported here.

The purpose of this paper is to assess the

reliability performance of southern African

pile design practice by exploring the applica-

tion of the database of model uncertainties

of pile resistance as reported by Dithinde et

al (2011) where particulars of pile load tests

and associated geotechnical information,

design parameters and descriptive statistics

are fully reported. Information from this pile

database, together with additional statistical

treatment as reported in the accompany-

ing paper, serves as input to the reliability

assessment reported here. A comprehensive

range of soil conditions, pile geometry and

resistance is incorporated in the database, to

provide extensive representation of southern

African pile construction practice in this

assessment.

RELIABILITY CONCEPTS

The concepts of reliability, as developed

for geotechnical and structural design, are

defined in SANS 2394: 2004. The operational

basis for partial factor design and reliability

analysis as presented in EN 1990:2002 is fol-

lowed here since these guidance procedures

also apply to SANS 10160-1:2011 for the gen-

eral basis of design and SANS 10160-5:2011


specifically for the geotechnical basis of

design.

The reliability-based performance func-

tion for a structure g(X1; … Xj) as a random

function of the random variables (X1; … Xj)

is expressed as a limit state function indica-

ting the state beyond which the structure

no longer satisfies the design performance

requirements, as shown in Equation 1. The

random variables consist of a specified set

of variables representing physical quantities

which characterise actions, and material

properties (including soil properties and geo-

metrical quantities) conventionally defined

as basic variables. The probability of failure

of the structure Pf is given by Equation 2. Pf

can also conveniently be expressed in terms

of the reliability index β and the cumula-

tive normal distribution function Ф or the

inverse normal distribution function Ф-1 as

given by Equation 3.

g(X1, … Xj) = 0 [1]

Pf = P[g(X1, … Xj) < 0] [2]

Pf = Φ(–β) or β = –Φ -1(Pf) [3]

Two distinct formats of reliability-based

design applies, with Equation 1 representing

the probabilistic format. The deterministic

partial factors format for standardised limit

states design is defined in SANS 10160-

1:2011; the application of the partial factors

format to geotechnical limit states design is

defined in SANS 10160-5:2011. Reliability

calibration is the process of determining

appropriate values for the partial factors to

achieve a specified level of reliability for a

given limit state as derived from Equation 1.

Since partial factors design procedures are

expressed in deterministic format with vari-

ous partial factors calibrated on principles

or probabilistic reliability, it is classified as

a semi-probabilistic procedure or Level 1

reliability-based design (EN 1990:2002).

Although the theory of reliability is

firmly rooted in the mathematical theory of

probability and related statistics, its success

as an operational basis for geotechnical and

structural design is directly related to the

simplification and approximation applied to

the representation of the basic variables (Xi)

and solving of the performance function,

Equation 1. The ultimate approximation

comes from the conversion of Equation 1

into a deterministic design function which

employs partial factors that are based on the

theory of reliability (see for example Holický

et al 2007).

The most important level of approxi-

mation is related to the degree to which

sources of variability and uncertainty are

treated comprehensively. On the one hand

it is granted that reliability modelling does

not provide for a vital component of failure,

which derives mainly from phenomena

such as gross human error. Therefore reli-

ability levels are often referred to as notional

reliability. On the other hand reliability

modelling presents a powerful tool for iden-

tification of critical sources of uncertainty,

providing the basis for quality management

measures in defence against gross error.

The most compelling argument for reli-

ability theory to provide for variability and

uncertainty is its modelling and predictive

capability, equivalent to structural mechan-

ics modelling of load bearing behaviour for

structural and geotechnical design.

TARGET LEVEL OF RELIABILITY

Central to the reliability basis of design

procedures is the calibration of partial fac-

tors, which consists of an inverse reliability

analysis process of calculating partial factors

to exceed a given or target level of reliability

(βT) as an initial step. The establishment

of an appropriate level of reliability in

accordance with the design case under

consideration therefore plays a key role in

reliability-based limit states design, or more

specifically the calibration of standardised

design procedures.

Several approaches for setting the target

reliability index are available. A pragmatic

approach which is mostly followed is to apply

a combination of the various methods. The

methods include:

■ Risk-based cost-benefit analysis and

optimisation

■ Failure rates estimated from actual case

histories

■ Value set by regulatory authorities for a

given limit state

■ Range of beta values implied in the cur-

rent design practice.

Risk-based optimisation of reliability

The most rational approach for establish-

ing the target level of reliability is through

cost-benefit analysis and optimisation.

Cost-benefit analysis entails the study of the

variation of the initial cost, maintenance

costs, and the costs of expected failure. It

therefore represents the determination of

reliability in the context of risk optimisa-

tion. The matter of the necessary inclusion

of the loss of human life leads this process

to be highly controversial. However, the

relatively recent development of the concept

of the Life Quality Index (LQI) which relates

human life in neutral terms of marginal

changes in life expectancy and working life

(see for example Rackwitz 2008) should

resolve this controversy. Although the LQI

concept developed rapidly in recent years, no

operational guidelines are available as yet,

particularly for South African conditions.

Reliability levels for

geotechnical design

The target probability of failure for a given

structure can be established on the basis

of failure rates estimated from actual case

histories. For the case of foundations it is

estimated that probability of failure (Pf)

ranges from 0.001 to 0.01 – about one-and-

a-half orders of magnitude below a “mar-

ginally acceptable” level and half an order

of magnitude below an “acceptable” level

according to the FHWA Manual for LRFD

bridge pile design (FHWA 2001). However,

many authors (e.g. Phoon 1995; Baecher

& Christian 2003; Christian 2004) have

cautioned that the probability of failure for

constructed facilities is not solely a function

of the design process uncertainties, as is the

case for the calculated failure probabilities.

Therefore, for comparison with calculated

failure probabilities, the rate of failure from

FHWA (2001) should be adjusted by one

order of magnitude downward (Phoon 1995).

If the suggested adjustments are effected,

the probability of failure for foundations

becomes 0.001 to 0.0001 which corresponds

to target reliability index values (βT) of

between 3.1 and 3.7.

Reliability levels for South

African practice

The target levels of reliability for South

African constructions within the scope of

the revised Loading Code SANS 10160-

1:2011 are discussed by Retief & Dunaiski

(2009). Motivation is provided for maintain-

ing the reference level of βT = 3.0 to be the

same as that applied in SABS 0160:1989

(Milford 1988). The decision was based

mainly on the argument that there was no

evidence or justification for adjusting the

level of reliability for South Africa. The

reference reliability agrees with practice in

countries such as the USA and Canada. It

is consistent with guidance given in SANS

2394:2004 when South African economic

conditions are taken into account.

The most serious challenge to maintain-

ing the reference level of reliability for South

Africa came from the default value of βT =

3.8 applied in Eurocode. It should be noted,

however, that this value is not normative

in Eurocode, but since safety is treated as a

national issue βT can be selected by member

countries. The high value of reliability

applied in Eurocode was also judged to

reflect higher levels of economic develop-

ment, which implies lower relative cost of


construction (or higher affordability) and

consequent higher safety levels obtained in

risk-based optimisation.

A factor which moderates the difference

between South African target reliability and

the Eurocode default value is that in calibra-

tion the reliability is seen as a constraint,

whilst the Eurocode value is often seen as a

target to be attained on average (SAKO 1999).

The implication is that βT = 3.0 as a con-

straint differs less from βT = 3.8 as an average

target than it may appear at first glance.

Another moderating factor is that the

South African reference value applies to a

more restricted reliability class of construc-

tion (RC2, typically buildings up to four

storeys high) which corresponds to the lower

part of the corresponding Eurocode reliabil-

ity class (RC2). For the next South African

reliability class (RC3, typically buildings of

five to fifteen storeys) βT = 3.5 approaches

that of the undifferentiated Eurocode RC2.

Implicit reliability levels

of acceptable practice

Keeping the design methodology compat-

ible with the existing experience base is

consistent with the evolutionary nature of

codes and standards that require changes to

be made cautiously and deliberately (Phoon

1995). In the spirit of a Bayesian approach

towards reliability, proven experience is an

important source of information that can be

combined with other sources of data on vari-

ability and uncertainty in reliability-based

design.

Accordingly this paper investigates

the level of reliability of pile foundations

designed in accordance with the static

formula. This is done by determining the

implicit levels of reliability for the current

working stress design (WSD) methods for

piles by comparing design values to reli-

ability models for pile resistance. Reliability

modelling of pile resistance is based on the

uncertainty of pile resistance, as observed by

the comparison of the interpreted resistance

from pile tests and the predicted value for

an extensive survey of pile tests done across

southern Africa, representing a wide range of

conditions, pile construction practices and

configurations.

CONCEPTS OF RELIABILITY

ANALYSIS AND CALIBRATION

Although reliability calibration and the

analysis of existing practice form two dis-

tinct components of the application of reli-

ability theory in design, they are so closely

related that some concepts of their treatment

in practice can share a common formula-

tion. The common concepts are related to

a specific level of reliability over a defined

range of conditions. The following issues are

relevant to reliability calibration of design

procedure such as partial factor limit states

design; therefore by implication also to reli-

ability assessment of existing practice:

■ The representative level of reliability

is either the target reliability in the case

of calibration, or the implicit reliability in

the case of assessing acceptable existing

practice; conventionally expressed in

terms of a reliability index as βT and βI

respectively. The following alternative

approaches apply to the representative

reliability:

■ An average value is taken across the

range of conditions, although the

value may be significantly exceeded in

some cases – this is the view generally

taken in Eurocode, also associated

with relatively high levels of reliability

(typically βT = 3.8).

■ A lower limit value is taken as a con-

straint, generally to be exceeded – this

view is taken in South Africa, where

the representative value is also rela-

tively low (typically βT = 3.0).

■ Consistency of reliability over the range

of application is an objective to ensure

that significantly different levels do not

occur under different design conditions

or cases; in particular systematically as

a function of classes of applications (for

example construction and/or soil type in

the case of piles) or other design para-

meters. The following effects need to be

considered:

■ Conditions under which the lowest

level of reliability is achieved will

control the measures taken.

■ Systematic exceeding of the repre-

sentative reliability represents

conditions which may be unjustifiably

conservative.

■ Consistency of reliability can be

assessed in terms of the absence of

different levels and the absence of

trends, or at least smooth transi-

tions related to continuous design

parameters.

■ The level of confidence of calibration

or assessment should take into account

that it is at best an approximate process,

due to the predictive nature of design. It

is based on limited information, either for

parametric calibration or assessment of

existing practice such as presented here,

or on the actual conditions in the case of

design of a specific project. Calibration or

assessment should therefore be moder-

ated on the following basis:

■ A limited level of confidence applies

to both the required reliability levels

(target or implied) and measures to

achieve these – all based on acceptable

performance of present practice.

■ Best estimates of reliability is there-

fore generally acceptable, only revert-

ing to conservative modelling when

there is specific justification for such

measures.

It should be noted that calibration back to

existing practice does not imply maintaining

the status quo just in a more complex format!

With calibration, allowance can subsequent-

ly be made for rectifying conditions where

reliability is inconsistent with the (present)

general practice, either insufficient or unjus-

tifiably conservative. Where insufficient reli-

ability derives from uncertainty, as opposed

to variability, appropriate measures can be

considered, such as additional investigation

consisting of gathering of data and improved

modelling.

RELIABILITY MODELLING

OF PILE RESISTANCE

The two predominant classes of uncertainty

for geotechnical design can be distinguished

as (i) uncertainties associated with design

soil properties and (ii) calculation model

uncertainties. With regard to geotechnical

property uncertainties, significant research

has been done to generate statistics on

individual components of soil parameter

uncertainty. Conversely, model statistics are

relatively scarcer. In fact, the lack of model

statistics is considered to be a key impedi-

ment to the development of geotechnical

reliability-based design (Phoon 2005). This

consideration provided the motivation for

the investigation of model uncertainty of pile

resistance as reported in the accompanying

paper and by Dithinde et al (2011).

Model uncertainty, as defined for exam-

ple in ISO 2394:1998, EN 1990:2002 and

JCSS PMC (2001), reflects uncertainties of

the structural mechanics model. Variability

of variables, mainly actions, material proper-

ties and geometry is represented explicitly as

basic variables in the performance function,

as defined in Equation 1. In experimental

determination of model uncertainty, values

of basic variables are determined determin-

istically through testing. The implication is

that model uncertainty represents not only

the effect of the structural mechanics model,

but also of all the sources of uncertainty, and

even variability that is not explicitly captured

in the testing process.

The modelling uncertainty reported in

the accompanying paper not only reflects the

uncertainty of the static pile design formula,

but also the interpretation of site investiga-

tions and conversion of measurements into


material properties. Due to the uncertainty

of material properties and the absence of its

representation as basic variables, the model

factor can be considered to represent a prob-

ability model of pile resistance as predicted

by the static pile formula. The procedure for

using soil properties based on subsurface

data surveys to predict pile resistance as

described by Dithinde (2007) implies that the

uncertainties from soil properties are incor-

porated in the predicted values. The pile

resistance probability model can therefore be

taken from the distributions and summary

statistics presented in the accompanying

paper.

In applying working stress design (WSD)

procedures through the static pile design

function, the emphasis is predominantly

placed on pile resistance. Whilst loads are

treated at nominal un-factored values,

safety is treated by the application of a fac-

tor of safety to pile resistance. The initial

parametric investigation of pile design

practice is therefore based on considering

pile resistance only. The effect of consider-

ing variability of loading is then considered

subsequently.

Pile resistance only

In the definition of model uncertainty given

in the accompanying paper, given here as

Equation 4, the interpreted pile capacity (Qi)

can be taken to represent the probability rep-

resentation of the pile resistance (RRel), and

the predicted capacity (Qp) the deterministic

nominal pile resistance (Rn). RRel can there-

fore be expressed by Equation 5. The static

pile design function is given by Equation 6 in

terms of a factor of safety (FS) and nominal

dead load (Dn) and live load (Ln). From

Equations 5 and 6, the specific performance

function given by Equation 7 can be convert-

ed into a parametric limit state function as

shown in Equation 8. The implicit reliability

index value (βI) can then be obtained from

Equation 9 in terms of the probability model

for M and the factor of safety FS which has a

deterministic value.

M = Qi

Qp

[4]

RRel = M.Rn [5]

Rn

FS = Dn + Ln [6]

g = RRel – (Dn + Ln) [7]

g = M × Rn – Rn

FS = 0 = M –

1

FS [8]

βI = Φ–1[Pf(M < 1

FS)] [9]

Values for βI can be obtained in terms of the

pile classes identified in the accompanying

paper. This is done by applying the reported

statistics as parameter estimates for

probability models for M. Comparison of

βI-values for alternative pile classes provides

an indication of the representativeness and

consistency of implicit reliability across the

range of conditions represented by the M

statistics.

As a point of departure the case of a

single combined pile class (ALL) is used as

a representative case to estimate βI,Rep. This

case is then used to investigate the influence

of the probability distribution on βI-values.

The influence of pile class on βI-estimates is

considered below.

The estimate for βI,Rep is based on the

lognormal distribution as standardised prac-

tice for resistance. Generally an overall factor

of safety of 2.5 is regarded as an acceptable

value for piles and has become a norm in

southern Africa (Byrne & Berry 2008). As

indicated in the accompanying paper, the

normal distribution, which is convention-

ally used as the default first approximation

distribution in reliability analysis, could also

be considered. The mild degree of skew-

ness indicated from the sample statistics

presented in the accompanying paper can

be taken into account by considering the

general lognormal distribution. The results

are summarised in Table 1, where values for

the estimated distribution parameters are

also given.

The value for βI,Rep is clearly sensitive

to the distribution applied to represent M

and therefore needs some interpretation:

The value of βI,Rep = 3.5 as obtained from

the lognormal distribution is taken as an

estimate of acceptable practice in accordance

with standardised reliability procedures. The

value of βI,Rep = 2.3 obtained from the nor-

mal distribution is considered to be too low

to reflect acceptable practice. The low value

of skewness taken into account by the gen-

eral lognormal distribution provides a slight

improvement on this apparently low level of

reliability; this result should be considered as

a lower limit estimate of implicit reliability,

as βI,Low = 2.4.

An indication of the representativeness

of these values of βI across the range of pile

classes is presented in Table 2. The value for

βI,Rep = 3.5 listed in Table 1 for the combined

group (ALL) generally lies in the lower range

of the values obtained for the various pile

classes as listed in Table 2. The value of 3.5

is therefore taken to be in agreement with

the approach of defining target reliability at

a lower constraint value, and is thus ranked

to indicate the mid-range value of implicit

reliability.

The class of piles driven in non-cohesive

soil (D-NC) is ranked at a special-range

due to its low value in comparison to the

representative implicit reliability. The more

general pile class of non-cohesive soil (NC)

is classified to be in the low-range. For all

other pile classes, higher values for βI,Rep are

obtained (Mid+); with significantly higher

values (High) obtained for bored piles in

cohesive soils (B-C), as listed in Table 2.

It is therefore concluded that the values

for βI,Rep and βI,Low obtained from Table 1

provide a reasonable representation of the

Table 1 Representative implicit reliability βI,Rep for alternative probability distributions for

combined pile class (ALL) and FS = 2.5

Distribution parameters Distribution Indicator βI

Mean 1.10 Lognormal Representative 3.52

Standard deviation 0.31 Normal – 2.26

Skewness 0.24 General Lognormal Low 2.45

Table 2 Range of implicit reliability values βI and associated pile classes (FS = 2.5)

Range Pile class Lognormal (βI,Rep)

Special Driven piles in non-cohesive soil (D-NC) 3.1

Low Non-cohesive soil (NC) 3.2

Mid Combined group (ALL) 3.5

Mid +

Driven piles (D) 3.7

Bored piles (B) 3.8

Bored piles in non-cohesive soil (B-NC) 3.75

High

Driven piles in cohesive soil (D-C) 4.1

Cohesive soil (C) 4.2

Bored piles in cohesive soil (B-C) 4.3


implicit reliability of existing practice, but

that the special case of driven piles in non-

cohesive soils (D-NC) should be considered

separately for systematically lower levels of

reliability.

In addition to obtaining a lower limit

estimate of the implicit reliability as based

on the probability distribution, confidence

level estimates of the distribution para-

meters can be applied. For this purpose the

confidence limit estimates presented in the

summary statistics in the accompanying

paper are utilised. A single-sided 75% con-

fidence limit estimate is used, as suggested

by Eurocode EN 1990:2002 for cases where

parameter estimation is based on vague

prior distributions. The lower confidence

limit value is used for the mean and the

upper limit for the standard deviation. The

confidence limit estimates βI,Conf are listed

in Table 3 for the two cases identified above

as representative (ALL) and the special lower

pile class (D-NC). Values are based on the

confidence level distribution parameters,

also listed in Table 3, applied to the lognor-

mal distribution.

Although the confidence limit implicit

reliability listed in Table 3 is reduced for

the representative case of the combined

pile conditions listed in Table 1, the change

from 3.5 to 3.2 is not too significant. For the

special case D-NC the change from 3.3 to 2.2

is, however, indicative of not only the ten-

dency of systematic lower value of implicit

reliability, but also of the poor quality of its

prediction.

The influence of the FS-value selected

in pile design on βI-estimates is shown in

Table 4. For comparison, target levels of reli-

ability (βT) are also listed, as given by SANS

10160-1:2011 for different reliability classes

of building structures. The comparison indi-

cates reasonable agreement between βI,Low

for FS(2.0, 0.5 and 3.0) and βT for reliability

classes (RC1, RC2 and RC3}. The values

for βI,Rep generally exceed that for the cor-

responding βT showing a trend of widening

of the difference for the higher FS values and

reliability classes.

Implicit reliability based on

resistance and loads

Expression of the performance function

given by Equation 1 in terms of probabilistic

models for resistance (R), dead (D) and live

(L) is given in Equation 10.

g(R, D, L) = R – (D + L) [10]

A normalised reliability model for Equation

10 can be obtained for parametric reliability

analysis by representing each basic variable

(X) by the ratio of mean to nominal value

(μX/Xn) and the relationship between the

nominal values (Rn, Dn and Ln) given by

the static pile design function (Equation 6).

Similar to the treatment above, the resis-

tance R is represented by the probability

model for M as given by Equation 5. The

load models reported by Kemp et al (1987)

used for the conversion of structural design

in South Africa from working stress to limit

states design procedures listed in Table 5 can

be used for models of D and L.

Different loading conditions can be

treated parametrically through the ratio

Ln/Dn. A typical range of Ln/Dn ratios is 0.5–

1.5 for concrete structures and 1–2 for steel

structures (Melchers 1999). For foundations

dead load would dominate, tending towards

the lower range of load ratios. Based on this

information, a practical range of Ln/Dn ratio

of 0.5 to 2 was adopted as sufficiently repre-

sentative of structures in general. The special

cases of dead and live loads only are indica-

tive of the outer limits of load conditions. For

this reason the range of analysis was done for

Ln/Dn between 0 and 2; the case for Ln only

was also calculated. Parametric reliability

analysis of Equation 10 was done using

Second Order Reliability Method (SORM)

software provided by Holický (2009).

The results for the representative reli-

ability analysis (βI,Rep) based on the model

for the complete dataset (ALL) are shown in

Figure 1(a); the results for the special case

of driven piles in non-cohesive soil (βI,D-NC)

are shown in Figure 1(b). Separate graphs are

provided for the values of FS (2.0, 2.5 and

3.0). The results for the analysis of the com-

plete version of Equation 10 are labelled as

M,D,L(FS); the off-scale case of live load only

is indicated as an arrow () labelled M,L(FS);

the results from the previous analysis consid-

ering pile resistance only are indicated as the

horizontal line labelled M(FS).

As can be expected, the inclusion of the

effects of loading reduces the level of implicit

reliability. Furthermore, the effects are

dependent on the ratio of live to dead load

(Ln/Dn), with trends similar to that obtained

with load calibration analyses (Holický &

Retief 2005). The lower values of implicit

reliability occur for conditions dominated

by live load, which generally can only be

expected under exceptional conditions for

pile foundations. Over the operational condi-

tions of loading dominated by Dn the values

for βI,Rep compare well with the target reli-

ability index values βT listed for the various

reliability classes listed in Table 4. For the

special case of driven piles in non-cohesive

soils, the values obtained for βI,D-NC are

systematically lower than the corresponding

values for βT.

Table 3 Confidence limit (βI,Conf) values of implicit reliability as based on lognormal distribution

and listed parameters (FS = 2.5)

Combined group (ALL) Driven, non-cohesive (D-NC)

βI,Conf 3.2 2.3

Confidence level distribution parameters

Mean 1.07 1.03

Standard deviation 0.32 0.40

Table 4 Implicit reliability (βI) as function of the selected value for FS, as compared to target

reliability (βT) for reliability classes

FS = 2.0 FS = 2.5 FS = 3.0

Combined group (ALL) (βI,Rep) 2.7 3.5 4.2

Driven, non-cohesive (D-NC) (βI,Low) 2.4 3.1 3.6

SANS 10160-1 Reliability Class RC1 RC2 RC3

Target reliability (βT) 2.5 3.0 3.5

Table 5 Load models for reliability calibration (Kemp et al 1987)

Type of load CodeMean load /

Nominal loadCoefficient of variation

Type of distribution

Dead (permanent) load

ANSI A58 1.05 0.10 Normal

Australian 1.05 0.10 Lognormal

SABS 0160 1.05 0.10 Lognormal

Live (office): lifetime max

ANSI A58 1.0 0.25 Gumbel

Australian 0.7 0.26 Gumbel

SABS 0160 0.96 0.25 Gumbel


DISCUSSION AND CONCLUSIONS

The resistance statistics for pile design

practice in southern Africa, as reported

in the accompanying paper, are applied in

this paper to assess the implicit levels of

reliability of such practice. This is done by

deriving reliability models for pile resistance

by applying the model statistics as parameter

estimates to internationally standardised

probability distributions for geotechnical and

structural resistance. Values for implicit reli-

ability, as expressed by the reliability index

(βI), are determined to obtain a measure of

the representative level of performance of

pile design practice. In addition to obtaining

best estimate values for βI, conservative esti-

mates are also made in terms of more severe

interpretation of parameter estimates or

probability distributions for pile resistance.

Consistency of reliability is also investi-

gated across the range of pile construction

practice.

Implicit levels of reliability are derived for

two reliability performance models:

i. Considering pile resistance only and

neglecting loading as basic variable, in

accordance with design practice reflected

by the working stress design format for

pile design, where a single factor of safety

is applied to pile resistance.

ii. Including reliability models for dead (per-

manent) and live (variable) loads into the

performance function, using the models

on which the implementation and calibra-

tion of limit states design for South Africa

were based.

The two main issues of concern for deter-

mining model statistics and applying these

to reliability models for pile resistance

identified in the accompanying paper are

(i) the probability distribution used, and (ii)

the scope of application as based on dif-

ferentiated classes of pile conditions. It was

found that the different plausible probability

distributions have a more significant influ-

ence on the levels of implied reliability than

differentiation into classes of pile conditions.

The default distribution applied in

reliability analysis is generally the normal

distribution, to represent the basic step from

deterministic design practice to at least pro-

vide for the dispersion of basic variables. The

lognormal distribution function at the same

basic level of approximation has the added

utility of not predicting negative values. This

is particularly relevant when the lower tail

of the distribution is considered, such as for

resistance. However, values for βI vary from a

low value βI,N = 2.3 for the normal distribu-

tion to a relatively high value βI = 3.5 for the

lognormal distribution, in both cases for the

combined set of pile conditions and general

design practice based on FS = 2.5. When

skewness obtained from the model statistics

is taken into account by applying the general

lognormal distribution, βI = 2.4 is obtained.

Selecting the lognormal distribution as

basis to obtain a representative value for the

reliability index βI,Rep = 3.5 is based on con-

sideration of standardised practice for reli-

ability analysis, supported by the marginal

preference obtained from the model statistics

results presented in the accompanying paper.

In accordance with Equation 3 the reliability

index value corresponds with a probability of

failure Pf of 2.10-4.

A lower estimate βI,Low = 2.4 (Pf = 8.10-3)

is based on the general lognormal distribu-

tion. Another lower limit estimate of βI is

based on the 75% confidence limit estimates

of the distribution parameters, obtaining a

value of βI,CL = 3.2 (Pf = 7.10-4).

Comparing the values for βI for the

combined set of pile conditions to the various

pile classes, the following observations can

be made: βI,Rep = 3.5 provides a lower limit

estimate value for βI; values for other pile

classes based on construction method and/or

soil type generally provide higher values. The

exception is the case for driven piles in non-

cohesive soil, where βI,D-NC = 3.1 (Pf = 1.10-4)

is obtained; alternatively for non-cohesive soil

βI,NC = 3.2. When confidence level estimates

are made, it is shown that the confidence limit

value for driven piles in non-cohesive soil is as

low as βI,Conf = 2.2 (Pf = 1.10-2).

Figure 1 Implicit reliability of pile design including loading

Re

lia

bil

ity

ind

ex

Re

lia

bil

ity

ind

ex

4.5 4.5

4.0 4.0

3.5 3.5

3.0 3.0

2.5 2.5

2.0 2.0

1.5 1.5

1.0 1.0

(a) Representative implicit reliability (βI,Rep) (b) Implicit reliability for the special case D-NC (βI,D-NC)

0 00.5 0.51.0 1.01.5 1.52.0 2.0

Ln/Dn Ln/Dn

M,D,L(2.0)

M(2.0)

M,L(2.0)

M,D,L(2.5)

M(2.5)

M,L(2.5)

M,D,L(3.0)

M(3.5)

M,L(3.0)

M,D,L(2.0)

M(2.0)

M,L(2.0)

M,D,L(2.5)

M(2.5)

M,L(2.5)

M,D,L(3.0)

M(3.5)

M,L(3.0)


When loads are also modelled as basic

variables, the values for βI,Rep is somewhat

reduced in the typical range of ratios for live

to dead load to be expected for pile founda-

tions. Values above 3.2 are obtained for live

load less than dead load. The limited reduc-

tion in βI,Rep is indicative of the fact that

reliability is dominated by the influence of

pile resistance reliability. The reduction in βI

values for situations dominated by live load

is indicative of the increasing role of the reli-

ability of live load, which should optimally be

provided for in terms of partial load factors,

rather than being of concern for pile design

reliability as such.

Comparison of values for βI,Rep cor-

responding to commonly adopted values for

factor of safety FS (i.e. 2 – 3) generally shows

good agreement with the target reliability

βT set in SANS 10160-1:2011 for different

reliability classes. The values for implicit

reliability for the three values of FS for dead

load dominating conditions βI,Rep (2.5, 3.2

and 3.7) compares well with target reliability

for the first three reliability classes βT (2.5,

3.0 and 3.5). Nonetheless, the range of βI,Rep

values obtained seem to be on the higher

side for single piles, suggesting that current

practice is conservative.

The reliability assessment of pile design

practice does not only provide insight into

the sufficiency of existing practice, but could

also form the basis for achieving appropri-

ate performance levels through reliability

calibrated procedures. The rational basis

for reliability calibration provided in SANS

10160-1:2011 can be applied in accordance

with geotechnical limit states design proce-

dures presented in SANS 10160-5:2011.

LIST OF NOTATIONS FOR

RELIABILITY INDEX (β)

β Reliability index, as related to prob-

ability of failure given by Equation 3

βT Target level of reliability obtained

through calibration of design

expression

βI Reliability level implicitly achieved

by existing practice, expressed in

terms of the reliability index β

βI,Rep Indicative level of reliability taken

to be representative of the set of

pile conditions under consideration,

usually considering pile design in

general

βI,Low Lower limit estimates of implicit

reliability based either on the selec-

tion of the probability distribution

or the pile class

βI,Conf Reliability index value based on

confidence limit estimates of distri-

bution parameters

βI,D-NC Implicit reliability index value for

the special case of driven piles in

non-cohesive soil

REFERENCES

Baecher, G B & Christian, T 2003. Reliability and Statistics

in Geotechnical Engineering. New York: Wiley.

Byrne, G & Berry, A D 2008. A Guide to Practical

Geotechnical Engineering in Southern Africa,

4th edition. Germiston: Franki Africa (Pty) Ltd.

CE (Commision Européenne) 2002. Guidance Paper

L: Application and Use of Eurocodes. Document

CONSTRUCT 01/483 Rev.1, Brussels: CE.

Christian, J T 2004. Geotechnical engineering reli-

ability: How well do we know what we are doing?

The 39th Terzaghi Lecture. Journal of Geotechnical

Engineering and Geoenvironmental Engineering,

130(10): 985–1003.

Day, P W & Retief, J V 2009. Provision for geotechnical

design in SANS 10160, Chapter 5-1. In: Retief, J V

& Dunaiski, P E (Eds), Background to SANS 10160.

Stellenbosch: SUN MeDIA Press.

Dithinde, M 2007. Characterisation of model uncer-

tainty for reliability-based design of pile foundations.

PhD Thesis, Stellenbosch, South Africa: University

of Stellenbosch.

Dithinde, M, Phoon, K K, De Wet M & Retief, J V 2011.

Characterisation of model uncertainty in the static

pile design formula. Journal of Geotechnical and

Geoenvironmental Engineering, ASCE, 137(1): 333–342.

Dithinde, M & Retief J V 2013. Pile design practice in

southern Africa. Part I: Resistance statistics. SAICE

Journal, 55(1): 60–71.


1990:2002. Eurocode: Basis of Structural Design.

Brussels: European Committee for Standardization

(CEN).


1997:2004. Eurocode 7: Geotechnical Design. Part 1:

General Rules. Brussels: European Committee for

Standardization (CEN).

FHWA (US Federal Highway Administration) 2001.

Load and Resistance Factor Design (LRFD) for

Highway Bridge Substructures. Publication No.

FHWA-HI-98-032, Washington DC: FHWA.

Holický, M & Retief J V 2005. Reliability assessment of

alternative Eurocode and South African load combi-

nation schemes for structural design. SAICE Journal,

47(1): 15–20.

Holický, M 2009. Reliability Analysis for Structural

Design. Stellenbosch: SUN MeDIA Press.

Holický, M, Retief, J V & Dunaiski, P E 2007. The

reliability basis of design for structural resis-

tance. Proceedings, 3rd International Conference

on Structural Engineering, Mechanics and

Computation (SEMC 2007), Cape Town, South

Africa: Millpress, 1735–1740.

JCSS (Joint Committee on Structural Safety) PMC 200).

Probabilistic model code. JCSS Working Materials

[Online] http://www.jcss.ethz.ch (retrieved 1 Feb.

2011).

Kemp, A R, Milford, R V & Laurie, J P A 1987. Proposal

for a comprehensive limit states formulation for

South African structural codes. The Civil Engineer in

South Africa, 29(9): 351–360.

Melchers, R E 1999. Structural Reliability: Analysis and

Prediction. Chichester, New York: Wiley.

Milford, R V 1988. Target safety and SABS 0160 load

factors. The Civil Engineer in South Africa, 30(10):

475–481.

Orr, T L L, Matsui, K & Day, P W 2002. Survey of geo-

technical investigation methods and determination

of parameter values. In: Honjo, Y (Ed), Foundation

Design Codes and Soil Investigation in View of

International Harmonization and Performance-

Based Design. Proceedings, International Workshop

on Foundation Design Codes and Performance-

Based Design, Tokyo, Japan, 10–12 April, Lisse,

Netherlands: AA Balkema.

Phoon, K K 1995. Reliability-based design of founda-

tions for transmission line structures. PhD Thesis,

Ithaca, NY, US: Cornell University.

Phoon, K K 2005. Reliability-based design incor-

porating model uncertainties. Proceedings,

3rd International Conference on Geotechnical

Engineering combined with the 9th Yearly Meeting

of the Indonesian Society for Geotechnical

Engineering, 191–203.

Rackwitz, R 2008. Optimization with a LQI acceptance

criterion, Annexure 5. In: JCSS Risk Assessment in

Engineering – Principles, Systems Representation.

pp 78–79. [Online] http://www.jcss.ethz.ch/publi-

cations/background/Risk_backgroundDoc_LQI_

Optimization.pdf (retrieved on 1 Feb. 2011).

Retief, J V & Dunaiski, P E 2009. The limit states basis

of structural design for SANS 10160-1, Chapter 1-2.

In: Retief, J V & Dunaiski, P E (Eds), Background to

SANS 10160. Stellenbosch: SUN MeDIA.

SABS 1972. SABS 088:1972. Code of Practice for Pile

Foundations. Pretoria: South African Bureau of

Standards.

SAKO (Joint Committee of NKB and INSTA-B)

1999. Basis of Design of Structures. Proposal for

Modification of Partial Safety Factors in Eurocodes.

Oslo, Norway: NKB Committee and Work Reports.

SANS 2004. SANS 2394:2004. General Principles on

Reliability for Structures. Adoption of International

Standard ISO 2394-1998, Pretoria: South African

Bureau of Standards.

SANS 2011a. SANS 10160-1:2011. Basis of Structural


Structures. Part 1: Basis of Structural Design.

Pretoria: South African Bureau of Standards.

SANS 2011b. SANS 10160-5:2011. Basis of Structural


Structures. Part 5: Basis for Geotechnical Design

and Actions. Pretoria: South African Bureau of

Standards.


TECHNICAL PAPER



ASSOC PROF SHAMSAD AHMAD, who holds a

PhD in Civil Engineering from the Indian

Institute of Technology (IIT), Delhi, India, has

been involved in several funded research

projects. He has published over 40 research

papers in refereed journals and conference

proceedings, and has taught many graduate

and undergraduate courses mainly related to

mechanics, structural materials and durability of concrete structures.

Presently he is Associate Professor in the Civil Engineering Department at the

King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.

Contact details:

Civil Engineering Department

King Fahd University of Petroleum & Minerals

PO Box 1403

Dhahran-31261

Saudi Arabia

T: +966 3 860 2572

F: +966 3 860 2879


PROF YASSIN SHAHER SALLAM holds a PhD

(NDT Engineering) from the Rouen University,

Haut Normandie, France. He has published

more than fi fty scientifi c articles and held many

positions, including Engineering Consultant,

Head of Civil Engineering Department,

Vice-Dean, and Dean. Presently he is Professor of

Structural Engineering in the Building Science

and Technology Department of the College of Architecture and Planning,

University of Dammam, Dammam, Saudi Arabia.

Contact details:

Department Building Science & Technology

College of Architecture and Planning

PO Box 2397

University of Dammam-31451

Saudi Arabia

T: +966 3 857 7000 x 3244

F: +966 3 857 8739


ISHAQ ABDUL RAZZAQ AL-HASHMI holds a BS in

Building Engineering from the University of

Dammam, Dammam, Saudi Arabia. Presently he

is working as Assistant Lecturer in the

Department of Building Engineering at the

College of Architecture and Planning, University

of Dammam.

Contact details:

Department of Building Engineering

College of Architecture and Planning

University of Dammam

PO Box 695

Alkhobar-31952

Saudi Arabia


Keywords: Lytag, lightweight aggregate concrete, dosage, mixtures,

optimisation

INTRODUCTION

Lytag is a product used as lightweight

coarse aggregate in producing lightweight

concretes. Fly ash, bentonite and water are

used as raw materials in manufacturing

Lytag. The production of Lytag consists of

mixing fly ash, bentonite and water together

and then pelletising the mixture into spheri-

cal balls. Finally these rounded pellets are

heated on a sinter strand to a temperature of

around 1 300°C. This aggregate, with particle

sizes typically ranging from 0.5 to 12 mm, is

called sintered fly ash lightweight aggregate,

more commonly known as Lytag lightweight

aggregate (EuroLightCon 2000). The

manufacturing of Lytag, using fly ash, has

been frequently reported in literature (Moss

1976; Anon 1978; Buttler 1987). However,

the production of other types of lightweight

aggregate similar to Lytag has also been

reported (Wainwright et al 2002; Boljanac et

al 2007). Lytag is produced on an industrial

scale by Lytag Ltd from its production units

in the United Kingdom, Holland, Poland and

China. Recently, Bulk Material International

(BMI) has signed an agreement with Lytag

Ltd for the marketing of Lytag lightweight

aggregate in the Middle East.

Swamy and Lambert (1981), in their

study on microstructure of Lytag aggregate,

reported that the overall structure of a Lytag

pellet is basically made up of unreacted

cenospheres, which are fused together

at their points of contact and/or are sur-

rounded by a solidified honeycomb type

structure, probably formed when some of

the raw materials became semi-molten and

gases escaped through them. They have

revealed through X-ray spectroscopy that

the major chemical elements from which

Lytag pellets are composed are silica and

alumina, with smaller amounts of calcium,

iron, magnesium and potassium. They found,

furthermore, that an excellent bond forms

between the Lytag pellets and a sand-cement

matrix. The microstructure, chemical

composition, and particle size distribution of

Lytag aggregate are important factors which

affect the performance of Lytag lightweight

aggregate concretes. The microstructure of

Lytag aggregate affects its strength, absorp-

tion and pozzolanic activity. These three

properties of Lytag aggregate jointly have

an influence on the strength of lightweight

concretes (Wasserman & Bentur 1997).

Some of the important physical properties

of Lytag aggregate, typically reported by

EuroLightCon (2000), are as follows: porosity

of particles (40%), particle density (1 400

kg/m3), 30-minutes water absorption (15%),

and 24-hours water absorption (18%). The

particle size distribution of Lytag aggregate is

specified in terms of percentages of different

individual fractions. An individual fraction

means a portion of aggregate belonging to

particles of a specific size range. In their

Optimising dosage of Lytag used as coarse aggregate in lightweight aggregate concretes

S Ahmad, Y S Sallam, I A R Al-Hashmi

Lytag, manufactured first by pelletisation of a mixture of fly ash, bentonite and water, and then by sintering the spherical pellets at about 1 300C, is used as coarse aggregate for producing lightweight plain and structural concrete mixtures. The weight of lightweight concretes is reduced significantly without compromising the structural integrity. The reduced dead load results in significant savings in the cost of foundations and reinforcement, as well as reduction in the sizes of columns, beams and slabs, which in turn reduce the overall volume of concrete and the costs of formwork and scaffolding. This paper reports on the results of an experimental study which consisted of designing, preparing and testing different mixtures of lightweight aggregate concrete considering four dosages of Lytag, used as coarse aggregate. It was found that the density and workability of concrete mixtures significantly decreased with increase in the dosage of Lytag. Concrete mixtures containing Lytag were found to be stronger than normal weight concrete. However, the strength of the lightweight aggregate concrete is found to be maximum at an optimum dosage of the Lytag.


study on properties of Lytag-based concrete

mixtures, EuroLightCon (2000) typically

considered different particle size distribu-

tions made up of the individual fractions, as

follows: 0.5-4 mm, 0.5-6 mm, 4-8 mm, and

6-12 mm. Most of the mixtures studied by

EuroLightCon (2000) were made with 60%

of Lytag belonging to 0.5-6 mm fraction, and

40% of Lytag belonging to 6-12 mm fraction.

Swamy and Lambert (1983) carried out a

study on mix design and properties of con-

crete made from Lytag coarse aggregates and

sand. They considered several initial trial

mixtures with target strengths ranging from

20 to 60 MPa. Based on these trials they

finally recommended three mixtures with

target strengths of 30, 45 and 60 MPa with

a slump in the range of 75 to 100 mm. For

all three these mixtures, they kept effective

water content and Lytag content constant at

175 and 715 kg/m3, respectively, and varied

the cement content (250, 335 and 485 kg/m3),

sand content (715, 645 and 515 kg/m3),

and effective water/cement ratio (0.70, 0.53

and 0.36) respectively for mixtures hav-

ing target strengths of 30, 45 and 60 MPa.

Lytag Ltd (2006) has published the data on

typical mix designs for Lytag concrete. The

comprehensive data on mix designs consists

of the proportioning details of various types

of Lytag concretes, such as: skip mix (Lytag

granular / natural sand), pump mix (Lytag

granular / natural sand), skip mix (Lytag

granular / PFA / natural sand), pump mix

(Lytag granular / PFA / natural sand), skip

mix (Lytag granular / GGBS / natural sand),

pump mix (Lytag granular / GGBS / natural

sand), skip mix (Lytag granular / Lytag fines),

and pump mix (Lytag granular / Lytag fines).

Beattie (2005) reported the development

of mixtures of Lytag self-compacting and

pumpable concretes.

Several researchers have reported the

properties of Lytag concrete (Swamy &

Lambert 1983; Bamforth 1987; Wainwright

& Robery 1997; Bai et al 2004; Zhang 2011).

Lytag concrete mixtures are typically used

where low density concrete is required

with the same structural integrity as that

of normal weight concrete. Structural

lightweight concretes, produced using Lytag

as coarse aggregate and natural sand as fine

aggregate, reduce unit weight by approxi-

mately 25% (oven-dry densities in the order

of 1 750 kg/m3) over the normal weight

concrete and still offer strengths exceeding

60-70 MPa. Reduction in the unit weight

of concrete can lead to considerable cost

savings, as the size and number of concrete

sections, foundations and other structural

members can be reduced. Compared to nor-

mal weight concrete, it has been found that

Lytag concrete is easier to place, and has

better compacting and finishing properties,

enhanced durability, reduced coefficient

of thermal expansion, improved insulating

properties, and better fire resistance.

The work on which this paper is based

was conducted to obtain an optimum

mixture of structural lightweight aggregate

concrete made using Lytag as coarse aggre-

gate and natural sand as fine aggregate.

For this purpose, four mixtures of Lytag

concrete were designed, prepared and tested,

considering different percentages of Lytag

and sand, keeping cement content and water/

cement ratio constant at their typically

selected values. A mixture of normal weight

concrete was also considered in the study

to compare the properties of Lytag concrete

mixtures with the properties of normal

weight concrete.

EXPERIMENTAL PROGRAMME

Materials

Type I cement (ordinary Portland cement)

conforming to ASTM C150-07 was used

in all the mixtures. Lytag aggregate having

a maximum size of 19 mm and conform-

ing to ASTM C-33-4 was used in all four

mixtures of structural lightweight concrete.

The chemical composition and physical

properties of Lytag are presented in Table 1.

The fine aggregate used in this investigation

was dune sand. Specific gravity and water

absorption of sand were measured to be 2.66

and 0.8% respectively. The grading curves

of the Lytag and fine aggregates are shown

in Figure 1. The crushed stone particles,

Table 1 The chemical composition and physical properties of Lytag aggregate

Chemical constituent/physical property Measured value

SiO2 53%

Al2O3 25%

Fe2O3 6%

CaO 4%

MgO 2.9%

Acid soluble sulfate SO3 (≤1.0%) 0.3%

Total sulfate (≤1.0%) 0.4%

Cl– (≤0.03%) 0.01%

Loss on ignition (≤4.0%) 3.1%

Particle density (1 350 kg/m3 ± 150 kg/m3) 1 310 kg/m3

Bulk density (loose) 687 kg/m3

Bulk density (rodded) 733 kg/m3

Water absorption 15%

Specific gravity 1.8

Figure 1 Grading curves of Lytag and fine aggregates

% P

ass

ing

100

Sieve size (mm)

90

80

70

60

50

40

30

20

10

00.05 0.5 505

Lytag aggregate Fine aggregate


with a maximum size of 25 mm, were used

as coarse aggregate for preparing normal

weight concrete. The specific gravity and

water absorption of coarse aggregate were

measured to be 2.65 and 1.65%, respectively.

Potable water from the laboratory tap was

used to prepare and cure the specimens.

Superplasticiser was used in all the mixtures

for achieving adequate workability.

Design of concrete mixtures

Four mixtures of Lytag concrete were

designed, with the following percentage

combinations of Lytag and sand: (i) 45%

Lytag and 55% sand; (ii) 50% Lytag and 50%

sand; (iii) 55% Lytag and 45% sand; and (iv)

60% Lytag and 40% sand. Combined grading

of Lytag and sand was carried out for all four

combinations in accordance with ASTM

C330-4. The combined aggregate grading

curves obtained individually for all four mix-

tures of Lytag concrete are shown in Figures

2 to 5. For all four mixtures, cement content,

micro-silica content, and water/cementitious

materials ratio were kept constant at 400

kg/m3, 40 kg/m3 and 0.36 respectively. The

cement content and water/cement ratio for

the normal weight concrete mixture were

the same as for the Lytag concrete mixtures.

The coarse to fine aggregate ratio for normal

weight concrete was kept as 1.5. For all five

mixtures, the dosage of superplasticiser was

kept as 5 litre/m3.

The design of all the concrete mixtures

was carried out using the absolute volume

method, assuming entrapped air contents

of approximately 2% for Lytag concrete

mixtures and 1% for normal weight con-

crete mixtures. The proportions of all five

mixtures considered under this study are

presented in Table 2.

Specimen preparation and testing

Concrete mixtures were prepared by mixing

the ingredients in accordance with ASTM C

192. Fresh concrete mixtures were tested for

slump, air content and density in accordance

with ASTM C 143, ASTM C 173, and ASTM

C 138, respectively. After testing the fresh

concrete mixtures, casting of cylindrical

specimens was carried out for determining

compressive strengths in accordance with

ASTM C 39 after seven and 28 days of water

curing. Oven-dry and air-dry densities of

the specimens were also determined after 28

days of water curing.

RESULTS AND DISCUSSION

The results of the air content in fresh

concrete mixtures are presented in Table 3.

Normal weight concrete mixture with a

maximum aggregate size of 25 mm has 1.8%

Figure 2 Combined aggregate grading curve (45% Lytag and 55% sand)

% P

ass

ing

100

90

80

70

60

50

40

30

20

10

0

Mix curve

Maximumlimit curve

Minimumlimit curve

0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75

Sieve size (mm)

Fine m

ix

Coarse m

ix


% P

ass

ing

100

90

80

70

60

50

40

30

20

10

0

Mix curve

Maximumlimit curve

Minimumlimit curve

0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75

Sieve size (mm)

Fine m

ix

Coarse m

ix


% P

ass

ing

100

90

80

70

60

50

40

30

20

10

0

Mix curve

Maximumlimit curve

Minimumlimit curve

0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75

Sieve size (mm)

Fine m

ix

Coarse m

ix


% P

ass

ing

100

90

80

70

60

50

40

30

20

10

0

Mix curve

Maximumlimit curve

Minimumlimit curve

0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75

Sieve size (mm)

Fine m

ix

Coarse m

ix


air content against the approximately speci-

fied air content of 1.5% for 25 mm aggregate

size. Lytag concrete mixtures with 19 mm

maximum aggregate size should have air

content of approximately 2%. However, it can

be observed from Table 3 that the air content

for the Lytag mixture with 45% Lytag aggre-

gate is 2% and that air content increases with

increase in the Lytag content.

A plot of slump test results is shown

in Figure 6. It was found that the slump

decreases significantly with increase in the

Lytag content due to the high water absorp-

tion capacity and lower density of Lytag

lightweight aggregate. Compared to normal

weight concrete, the reduction in the slump

was found to be 23% with 45% Lytag, and

62% with 60% Lytag. The average decrease

in the slump is around 15% for every 5%

increase in the Lytag content.

The variation in the density of fresh con-

crete with Lytag content is shown in Figure 7.

As can be seen from Figure 7, the fresh den-

sity of Lytag concrete is reduced by around

12% at a Lytag content of 45%, and the den-

sity decreases with an increase in the Lytag

content to around 21% at a Lytag content of

60%. It can be noted that the reduction in

density is more significant when the Lytag

content was increased from 45 to 50% than

the reduction in the density when the Lytag

content was increased beyond 50%. The

variation in air-dry and oven-dry densities of

the concrete mixtures after 28 days of curing

is shown in Figure 8. As with fresh density,

the reduction in air-dry and oven-dry densi-

ties was also more significant when the Lytag

content was increased from 45 to 50%. The

reduction in air-dry and oven-dry densities is

insignificant when the the Lytag content was

increased beyond 50%. The reductions in

air-dry and oven-dry densities at 50% Lytag

content were found to be around 22% and

26%, respectively. The results of both fresh

and hardened densities indicate that the 50%

dosage of Lytag can be considered as the

optimum dosage for reducing the density of

Lytag concrete.

The variation in 7-day and 28-day

compressive strengths of concrete mixtures

with Lytag content is shown in Figure 9. It

should be noted that the difference between

7-day compressive strength in normal weight

concrete is more than that of Lytag concrete.

Furthermore, the strengths of the Lytag

concrete mixtures are more than that of

normal concrete. However, the strength of

Lytag concrete increases with an increase in

Lytag content only up to 50%, and then the

strength decreases with increase in Lytag

content. Therefore, from a strength point

of view, the optimum dosage of Lytag was

found to be 50%.

Table 2 Mixture proportions for producing 1 m3 of concrete

Ingredient

Normal weight

concrete mixture

Lytag concrete mixtures

45% Lytag55% sand

50% Lytag50% sand

55% Lytag45% sand

60% Lytag40% sand

Cement (kg) 400 400 400 400 400

Micro-silica (kg) – 40 40 40 40

Water (kg) 144 158 158 158 158

Lytag aggregate (kg) – 672 732 791 846

Fine aggregate (kg) 762 822 732 647 564

Stone aggregate (kg) 1 143 – – – --

Admixture (litre) 5 5 5 5 5

Table 3 Air content in fresh concrete mixtures

Mixture Air content (%)

Normal weight concrete 1.8

Lightweight concrete (45% Lytag and 55% sand) 2.0




Figure 6 Slump variation with Lytag content

Slu

mp

(m

m)

140

120

100

80

60

40

20

0

Lytag aggregate (%)

0 45 50 6055

80

100

130

70

50

Figure 7 Variation of fresh density with Lytag content

De

nsi

ty (

kg

/m3)

2 700

Lytag aggregate (%)

0 45 50 60551 500

2 500

2 300

2 100

1 900

1 700

2 492

2 183

2 0481 990 1 968


CONCLUSIONS

Based on the results of the experimental

investigation presented in this paper, the fol-

lowing conclusions may be drawn:

1. All four mixtures of Lytag concrete fulfil

the requirements of lightweight concrete,

as they have dry densities of less than

1 900 kg/m3.

2. At the same water/cement ratio and

cement content, the Lytag concrete mix-

tures have better strength than normal

concrete. However, at the same superplas-

ticiser content the workability of Lytag

concrete mixtures is significantly reduced

due to higher water absorption and lower

density of Lytag aggregate.

3. At 50% Lytag content the reduction in the

dry density is around 25%. Beyond 50% of

Lytag content, the reduction in the den-

sity is insignificant. The strength of Lytag

concrete is found to be maximum at 50%

Lytag content. Therefore, the optimum

dosage of Lytag aggregate can typically be

considered as 50% (by mass).

ACKNOWLEDGEMENT

The authors gratefully acknowledge support

received from the Department of Building

Engineering and Technology, College of

Architecture and Planning, University of

Dammam, Saudi Arabia.

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of lightweight concrete manufactured with fly

ash, furnace bottom ash, and Lytag. Proceedings,

International Workshop on Sustainable Development

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Bamforth, P B 1987. Properties of high-strength light-

weight concrete. Concrete (London), 21(4): 8–9.

Beattie, A 2005. Developments in lightweight self-com-

pacting and pumpable concrete. Concrete (London),

39(2): 24–25.

Boljanac, T, Vlahovic, M, Martinovic, S & Vidojkovic, V

2007. Preparation of lightweight sintered aggregate

based on combustion ash. International Journal

of Ceramics: International Ceramic Review, 56(6):

436–439.

Buttler, F G 1987. The manufacture of aggregate from

pulverised fuel ash by the Lytag process and new

and established uses of the product. Proceedings,

Conference on Environmental Aspects, Special

Products, Mineral Beneficiation, Pretoria, Vol. 3.

EuroLightCon 2000. Properties of Lytag-based concrete

mixtures strength class B15-B55. The European

Union – Brite EuRam III, Project Report-Document

BE96-3942/R6.

Lytag Ltd 2006. Mix designs for Lytag concrete. Technical

Manual, Section 3. Escrick, York, UK: Lytag.

Moss, D W 1976. Lightweight aggregate from fly ash in

the United Kingdom. Precast Concrete, 7(8): 409–411.

Swamy, R N & Lambert, G H 1981. The microstructure

of Lytag aggregate. The International Journal of

Cement Composites and Lightweight Concrete, 3(4):

273–282.

Swamy, R N & Lambert, G H 1983. Mix design and

properties of concrete made from PFA coarse aggre-

gates and sand. The International Journal of Cement

Composites and Lightweight Concrete, 5(4): 263–275.

Wainwright, P J & Robery, P 1997. Structural perfor-

mance of reinforced concrete made with sintered

ash aggregate. In: Goumans, J J J M, Senden, G

J & Van der Sloot, H A (Eds), Waste Materials

in Construction: Putting Theory into Practice,

Amsterdam: Elsevier Science, 411–420.

Wainwright, P J, Cresswell, D J F & Van der Sloot, H A

2002. The production of synthetic aggregate from a

quarry waste using an innovative style rotary kiln.

Waste Management and Research, 20(3): 279–289.

Wasserman, R & Bentur, A 1997. Effect of lightweight fly

ash aggregate microstructure on the strength of con-

cretes. Cement and Concrete Research, 27(4): 525–537.

Zhang, L 2011. Fundamental mechanical properties

of Lytag concrete, Proceedings, 2nd International

Conference on Multimedia Technology (ICMT

2011), Hangzhou, China, 26–28 July, 3972–3974.

Figure 8 Variation of 28-day air-dry and oven-dry denisties with Lytag content

De

nsi

ty (

kg

/m3)

2 500

Lytag aggregate (%)

0 45 50 60551 500

2 300

2 100

1 900

1 700

2 447

1 953.51 900 1 893.5 1 879

1 868.51 815 1 808.5 1 794

Oven dry Air dry

Figure 9 Variation of 7-day and 28-day compressive strengths with Lytag content

Co

mp

ress

ive

stre

ng

th (

MP

a)

40

Lytag aggregate (%)

0 45 50 605522

38

36

26

24 25

28-day 7-day

34

32

30

28

31.5

37.237.7 37.5

36.6

34.1

35.3

33.6

32.1


TECHNICAL PAPER



PROF SW JACOBSZ (Pr Eng, MSAICE) graduated

with an MEng in Geotechnical Engineering from

the University of Pretoria in 1996 and worked for

Jones & Wagener before leaving for the United

Kingdom in 1999 to study towards a PhD in

Geotechnical Engineering at the University of

Cambridge. He returned to Jones & Wagener in

2004 where he worked as geotechnical

engineer before joining the University of Pretoria in 2010 as Associate

Professor in the Department of Civil Engineering. His primary interest is

physical modelling of geotechnical problems in the geotechnical centrifuge.

Contact details:



Pretoria

0002

T: +27 12 420 3124


Keywords: soil nail, centrifuge model, strength mobilisation, sand,

residual andesite

INTRODUCTION

Centrifuge modelling of soil-

nailed retaining walls

Various analytical methods can be used

to assess collapse loads of geotechnical

problems, e.g. plasticity solutions like the

slip-line method or the limit equilibrium

methods which have traditionally been the

most widely used method (Shen et al 1982).

However, limit equilibrium methods require

assumptions regarding the shape of the

failure surface and the distribution of stress

along the failure surface. As these assump-

tions affect the solution of the problem, it

is important that they are realistic. Failure

mechanisms and deformation behaviour of

soil-nailed structures can be back-analysed

from full-scale case studies, which are rare

and costly, or from laboratory model studies.

The non-linear stress-strain properties of

soils require the stress levels in models to be

corrected to that of the full scale to ensure

realistic results. This necessitates the use of a

geotechnical centrifuge.

Shen et al (1982) reported on one of the

first centrifuge model studies conducted to

model a soil nail retaining wall in sand and

compared test results against the predictions

from analytical models. A comprehensive

study of soil-nailed walls in sand was also

carried out by Tei (1993). Zhang et al (2001)

carried out parametric studies of soil nail

retaining structures, experimenting with nail

lengths and spacings, and found that failure

surfaces of nailed surfaces were deeper than

without reinforcement. Shen et al (1982) and

Tei (1993) observed curved failure wedges

(logarithmic spirals, according to Tei et al

1998; see also Bolton & Pang 1982), initiat-

ing from the toe of the retained face and

reported good agreement with critical failure

wedges predicted from limit equilibrium

analysis.

Physically modelling all elements of the

process of constructing a soil nail retained

face in the centrifuge presents many dif-

ficulties. In the available case studies, the

soil nails were pre-installed during model

preparation. Modelling of the excavation

can, however, be achieved relatively easily by

draining a fluid selected to exert a horizontal

pressure approximately equal to that of the

soil once the desired acceleration had been

achieved (e.g. Tei 1993). Other researchers

did not model the excavation process and

simply accelerated the completed model to

the required acceleration (e.g. Shen et al

1982 and Zhang et al 2001). Despite some

obvious discrepancies, both reported the

performance of the model to be comparable

to that of the full-scale situation yielding

realistic results.

The geotechnical centrifuge

The Department of Civil Engineering at the

University of Pretoria, South Africa, has

recently acquired a geotechnical centrifuge

with a capacity of 150 G-ton, meaning that

the centrifuge is capable of accelerating a

payload weighing up to one ton to 150 G.

Geotechnical centrifuges are used to subject

small-scale models of geotechnical situations

to high accelerations. Due to the stress-strain

behaviour of soils being highly non-linear,

it is necessary to increase the stresses in a

model to be analogous to the stress distri-

bution in the full-scale situation. This is

Centrifuge modelling of a soil nail retaining wall

S W Jacobsz

This paper describes a physical model of a soil nail retained excavation face which was tested in the new geotechnical centrifuge at the University of Pretoria. As centrifuge modelling is new in South Africa, a short introduction to this technique is presented. The mobilisation of soil nail forces and their maximum values in response to excavation in the model were compared to measurements recently made in an instrumented 10 m high soil nail retaining structure for the Gautrain system in Pretoria. Results were also compared to predictions made using a simple failure wedge analysis and a database of eleven full-scale instrumented soil nail walls from the literature. The centrifuge model data compared well with both full-scale situations and theoretical analyses. The results suggest that soil nail forces measured in the centrifuge are conservative due to the mobilisation of a portion of the shear strength of the model soil during the acceleration of the centrifuge, leaving less un-mobilised shear strength available to resist loads resulting from the excavation.


achieved using centripetal acceleration. As

such, a model with a scale of 1:50 has to be

accelerated to 50 times earth’s gravity (50 G)

to create the correct stress distribution.

Model dimensions scale linearly and

can be used to derive scaling laws for other

physical properties. Table 1 lists scaling laws

for a number of physical quantities. As an

example, the scaling law for force is derived:

According to Newton’s second law, force

(Fp) in the full-scale situation (the prototype)

can be expressed as Fp = mpap, where mp is

the mass and ap the acceleration of the pro-

totype. Assuming that the body to be scaled

is a cube with density ρ and side length lp

and that it is stationary on the earth’s sur-

face, Newton’s second law can be written as

Fp = ρl3p g (1)

where g is gravitational acceleration.

Newton’s second law for the model is

Fm = mmam (2)

where Fm is force at the model scale, mm the

mass of the model and am the acceleration at

model scale. In order to avoid problems with

different material properties, the same mate-

rial as that occurring in the full-scale situ-

ation is normally used to create the model.

The material density (ρ) therefore remains

the same. The model is N times smaller than

the prototype and is therefore accelerated to

N times earth’s gravitational acceleration to

create the correct stress distribution in the

model. Equation 2 therefore becomes

Fm = ρVmNg (3)

For a cube Equation 3 becomes

Fm = ρæççèlpN

æççè

3

Ng = ρl3

p g

N2 =

Fp

N2

which proves the scaling law for force.

In terms of scaling laws, particularly attrac-

tive is the fact that time-related problems,

e.g. consolidation, may be studied in a

fraction of the time that would be required

for a full-scale trial. Also, stiffnesses (e.g.

the Young’s and shear moduli) do not scale

because stresses and strains do not scale.

This enables the same material from the

full-scale prototype to be used to construct

the model.

Jacobsz & Phalanndwa (2011) described

a case study in which three instrumented

soil nails were installed in a retained face

along a cutting for the Gautrain railway line

in Pretoria. The structure was excavated in

residual andesite which increased in strength

and stiffness with depth. The wall was

10 m high with six rows of nails installed

at vertical spacings of 1.5 m and horizontal

spacings of 2 m, and at a downward angle of

10°. The shotcrete facing was 175 mm thick,

reinforced with two layers of mesh. The

retained face and the locations of the instru-

mented couplings are illustrated in Figure 1.

Axial forces in three of the soil nails were

measured as the excavation in front of the

retained face was deepened.

Although the survival rate of the soil nail

instrumentation was poor, it showed that

the maximum axial forces in the top soil nail

stabilised at approximately 50 kN, approxi-

mately two thirds of the load calculated

using a simple failure wedge analysis. It was

Figure 2 Axial load variation in the top instrumented soil nail (Jacobsz & Phalanndwa 2011)

Ax

ial

loa

d (

kN

)

100

75

50

25

002/26 03/26 04/23 05/21 06/18 07/16 08/13 09/10 10/08 11/05

Date

Figure 1 The full scale soil nail retaining structure modelled in the first centrifuge test

(Jacobsz & Phalanndwa 2011)

Nail horizontal spacing is 2 m

10 m

1.5 m

1.5 m 3 m 6 m 9 mInstrumented couplings

Soil nail length

12 m

12 m

12 m

9 m

9 m

6 m10°

Excavation floor

Table 1 Scaling laws for various physical

properties

Property Scale factor

Model scale

Accelerations

Linear dimensions

Stress

Strain

Density

Mass

Force

Bending moment

Moment of area

Time (consolidation)

Time (dynamic)

Time (creep)

Pore fluid velocity

n

n

1/n

1

1

1

1/n3

1/n2

1/n3

1/n4

1/n2

1/n

1/n

n


found that soil nail loads were not mobilised

gradually, but in distinct load increments.

It appeared that the material behind the

excavation remained stable to a point as

the excavation advanced and, only when a

certain excavation depth was reached, did

the retained soil exert more load on the soil

nails, as it depended on the nails for stability.

Soil nail loads were mobilised in a number of

such load steps as the excavation advanced,

as illustrated in Figure 2.

The aims of the centrifuge model study

were:

■ to measure the load mobilisation in the

soil nails over time during and after

excavation, and

■ to compare the mobilised soil nail loads

in the model with those from the Jacobsz

& Phalanndwa (2011) case study, and with

those calculated from conventional wedge

theory.

CENTRIFUGE MODEL

A centrifuge model was set up to model

the soil nail wall described in the Gautrain

retaining wall case study. The model was

constructed at a scale of 1:50 and was there-

fore tested at an acceleration of 50 G. The

scale factor was chosen taking into account

the dimensions of the model container,

referred to as a strong-box, in relation to the

dimensions of the full-scale situation being

modelled. The model is illustrated diagram-

matically in Figure 3.

The model retaining wall was construct-

ed from a 0.6 mm thick galvanised steel

plate. The calculated bending stiffness (EI) of

the shotcrete facing, assuming an un-cracked

panel, was approximately 9.4 x106 Nm2/m

(assuming a Young’s modulus for concrete

of 20 GPa and 200 GPa for steel). Bending

stiffness scales with the fourth power of the

scale factor. The bending stiffness of the

plate used to model the shotcrete face was

calculated at 3.6 Nm2/m, which was there-

fore approximately 2.4 times stiffer than the

scaled-down retaining wall value.

The model soil nails were made from

5 mm wide brass strips, 0.2 mm thick,

which were bolted to the wall using 2 mm

diameter nuts and bolts. The reason for

using flat metal strips was so that the model

soil nails could easily be instrumented with

strain gauges. For ease of installation during

model preparation, the nails were installed

horizontally.

The purpose of the model was to

investigate the mobilisation of axial

loads along the length of the nails during

excavation, i.e. to simulate normal

operational conditions and not to fail the soil

nail wall. Disregarding the effects of dilation,

the design pull-out capacity of the soil nails,

calculated purely from interface friction

between the nails and the soil, therefore

exceeded the imposed load estimated from

active pressure on the wall by approximately

one third, providing a safety margin. The

pull-out load (Qu) of the flat strip model soil

nails was calculated from σv An tan, where

σv is the vertical stress acting at the depth

of the nail, An the surface area of the nail

(top and bottom) and the interface friction

angle between the sand and the brass strips,

measured in a shear box test at 26°. A total

pull-out force of 1272 kN (full-scale) was

calculated for a column of six nails. The

predicted active pressures to be resisted per

column of nails were 932 kN.

The calculated axial stiffness of the

full-scale nails is approximately 100 MN.

Axial stiffness scales with the square of the

scale factor. The required stiffness of the

model nails was therefore 40 kN. The brass

strips were 2.7 times stiffer than the scaled

requirement. It was, however, not practical to

use narrower strips due to instrumentation

difficulties.

Three model nails were instrumented

with three strain gauges each, connected

in quarter Wheatstone bridge circuits. The

strain gauges were positioned with the first

gauge close to the wall and the second gauge

close to the position where the maximum

tensile force was expected, i.e. where an

active failure wedge is expected to be mobil-

ised (roughly at an angle of 45° + ’/2 with

the horizontal) (e.g. Lazarte et al 2003). The

third gauge was mounted approximately

halfway between the second gauge and the

end of the soil nail (see Figure 3).

The soil used in the model was a fine

alluvial silica sand sourced from a com-

mercial source near Cullinan. It was found

that particles larger than approximately

200 μm were relatively well rounded, but

the finer fraction tended to be more angular

with a description of angular to sub-angular

being appropriate. The grading curve for the

sand is presented in Figure 4. The friction

angle of the sand was measured at 37° using

a conventional shear box. During model

preparation the sand was placed by pluvia-

tion during which a constant drop height

Figure 3 The centrifuge model (not to scale)

Soil nail length

Stain gauges (offset fron retaining wall and gauge number)

200 mm

240 mm

240 mm

240 mm

180 mm

180 mm

15 mm

15 mm

15 mm

75 mm 140 mm

105 mm 195 mm

1 2 3

1 2 3

1

60 mm 125 mm

2 3

Enlarged section showing strain gauge positions

Nail 2

Nail 1

Nail 3

30 mm

Water filled Latex mould

Section

45° + φ'/2 = 64°

0.6 mm thick steel plate

Failure wedge

Nail 1

Nail 2

Nail 3

120 mm

Pot 1 Pot 2 Pot 3 Pot 4 Pot 5

50 mm 50 mm50 mm50 mm20 mm

Displacement transducers (potentiometers


and flow rate were maintained. The sand was

pluviated in layers of about 30 mm thickness,

i.e. the vertical spacing between rows of soil

nails. The placed relative density of the sand

was approximately 55% (1566 kg/m3), i.e. a

medium dense sand. The mass of sand was

determined by weighing the model before

and after placing the sand.

The deepening of the excavation was

modelled using a water-filled Latex rubber

mould in which the water level was reduced

during the test. This method was also used

by Tei (1993) (see also Tei et al 1998). During

the acceleration of the centrifuge to 50 G, the

water level in the rubber mould was main-

tained at the correct level using a standpipe

with a fixed overflow level into which water

was continuously fed. This procedure was

followed because it was expected that during

acceleration of the centrifuge some move-

ment of the system would have occurred,

possibly affecting the water level in the

rubber mould which would disturb the stress

regime. After accelerating to 50 G, the water

supply to the standpipe and rubber mould

was stopped. A solenoid valve was opened to

release the water from the rubber mould to

model the excavation of soil in front of the

retained face. In the first test the water level

was allowed to drop without interruption

from 200 mm to 0 mm depth. In the second

test the water level reduction took place in

steps over 2 000 seconds, and in the final

test over 3 000 seconds. After every step in

water level reduction, some horizontal wall

movement took place, which took some time

to stabilise. The next drop in water level was

only initiated after this wall movement had

stabilised.

During the tests the vertical movement

of the sand surface and the horizontal

movement at the top and mid-height of

the retaining wall were monitored using

potentiometer-based displacement transduc-

ers. The water level in the rubber mould

was monitored using a pressure transducer

mounted near the base of the standpipe. A

number of photos of the model are presented

in Figure 5.

CENTRIFUGE MODEL TEST RESULTS

Surface settlement

Surface settlements were recorded with

potentiometers with a resolution of approxi-

mately 0.001 mm during the lowering of the

water level. During the acceleration of the

centrifuge to 50 G the upper surface of the

sand settled between 1 mm and 2 mm in

response to the stress increase acting on the

model. Once at 50 G, the settlement data was

zeroed so that the surface settlements caused

Figure 4 Sand grading

100

90

80

70

60

50

40

30

20

10

0

Pa

ssin

g (

%)

Particle size (mm)

0.01 0.1 1

Figure 5 Sequence of photos illustrating model preparation

(a) Model soil nail wall (b) Model container before placement of sand and retaining structure

(c) Brass soil nails being placed into position during model preparation

(d) Top view of model

(e) Side view over model surface showing displacement transducers and data acquisition system

(f) Model in position on centrifuge ready for testing

Strain gauge electrical connectionsStrain gauge electrical connections

Model Model soil nailssoil nails

Standpipe with Standpipe with solenoid valve solenoid valve

and pressure and pressure transducertransducer

Model Model retaining wallretaining wall

Model soil nailsModel soil nails

StandpipeStandpipe

Model Model retaining wallretaining wall

Water-filled Water-filled latex mouldlatex mould

Displacement Displacement transducerstransducers

Data acquisition Data acquisition systemsystem

StandpipeStandpipe

Centrifuge Centrifuge modelmodel

Model Model retaining retaining

wallwall

Model Model compartmentcompartment


by the lowering of the water level behind the

retaining wall could be measured. Figure 6

shows the settlement of the soil surface

behind the retaining wall in response to the

lowering of the water level.

A maximum settlement of approximately

1.5 mm occurred immediately (20 mm)

behind the wall and reduced with distance

away from the wall. This translates to 75 mm

at the full scale (1:50).

Horizontal wall movement

Figure 7 presents the horizontal movement

measured at the top and mid-height of the

retaining wall in response to lowering of the

water level, modelling the excavation. The

results of the three tests show good repeat-

ability between tests and illustrate that the

rate of water level reduction did not have a

significant effect on the wall movement.

It can be seen from the figure that as

the water level began to be lowered, wall

movement immediately began to occur at the

top of the wall. When the water level in the

model excavation had dropped to below the

depth of the first row of soil nails (30 mm),

the rate of movement decreased as the nails

began to restrain wall movement. The rate of

wall movement then remained approximately

constant as the excavation advanced.

Little horizontal movement was observed

at the mid-height position on the wall until

the water level had reduced to that height.

Thereafter, horizontal movement occurred at

approximately the same rate as the horizon-

tal movement at the top of the wall.

Once the model excavation had been

emptied completely, a maximum horizontal

movement of about 2.5 mm was observed at

the top of the wall, equating to 125 mm for

the full-scale wall. The wall remained stable

after excavation.

Mobilisation of soil nail forces

The development of axial loads in the soil

nails in response to the deepening excavation

is presented in Figure 8. During acceleration

of the centrifuge to 50 G some settlement of

the model wall relative to the sand occurred

so that the parts of the nails close to the wall

were subjected to a small amount of bending.

This affected the zero offsets of force read-

ings registered by the instrumented nails.

Soil nail readings were therefore zeroed prior

to the water level in the model excavation

being reduced, to give loads mobilised due to

the reduction in the water level only. Loads

prior to zeroing were generally small (less

than 10 N at model scale), except where

bending of the nails occurred. The loads

measured in the model are shown on the

left-hand axis, with full-scale (prototype)

loads on the right-hand axis. The calculated

loads for the model from the wedge analysis

based on friction angles of 30° and 37° are

also shown in Figure 8; the comparison is

discussed later.

The evolving axial load distributions in

the instrumented nails, as the excavation

was deepened, are presented in Figure 9.

Initially, the highest loads were mobilised

immediately behind the wall in response to

active pressure behind the wall, but soon the

location of maximum force migrated back-

wards from the wall as a failure mechanism

began to mobilise.

DISCUSSION

Comparison of model results

with analytical methods

Wedge analysis

The equilibrium of a simple triangular active

failure wedge behind the excavation face was

examined to estimate the development of

axial soil nail forces in response to the deep-

ening excavation (Figure 10). This approach is

commonly used for soil nail design, although

the complexity of the mechanisms varies

(SAICE 1989). For the problem modelled in

the centrifuge, only three forces were consid-

ered: the self-weight of the failure wedge (W),

the resisting force mobilised on the failure

plane (R) and the sum of the individual soil

nail forces (T). For a fully mobilised failure

mechanism the resisting force R would act

at an angle as shown in Figure 10, where

is the soil friction angle. The soil nails were

assumed to carry only axial loads, disregard-

ing any bending or shear stiffness they might

possess. The failure wedge was assumed to

Figure 7 Horizontal wall movement in response to increasing excavation depth

Ho

riz

on

tal

pla

te m

ove

me

nt

(mm

)

2.5

3.0

1.5

2.0

0.5

1.0

0200150100500

Excavation depth (mm)

Test 1 Test 2 Test 3

Movement at the top of the wall

Movement at mid-height

Figure 6 Surface settlement in response to “excavation”

Offset from wall (mm)

0

Mo

de

l su

rfa

ce s

ett

lem

en

t (m

m)

–1.6

–1.4

–1.2

–1.0

0

–0.8

–0.6

–0.4

–0.2

50 100 150 200 250

Fu

ll-s

ca

le s

urf

ace

se

ttle

me

nt

(mm

)

80

70

60

50

30

20

10

0

40

0 11 21 28 37

48 72 136 200

Excavation depth (mm):


mobilise at a slope angle . This slope angle

was varied to find the maximum axial soil

nail force (T). For a horizontal soil surface

and smooth vertical retaining wall, the wedge

analysis provides the same solution as the

active Rankine earth pressure case.

The soil nail loads were calculated for vari-

ous depths of excavation by simply dividing

the total calculated soil nail force (T) by the

number of nails intersecting the failure wedge.

The calculated forces (based on horizontal

soil nails) are plotted with the observed loads

in Figure 8. As no failure wedge intersects soil

nails for excavation depths of up to 30 mm

(1.5 m at prototype scale), zero soil nail force

was assumed up to this depth.

Soil nail forces

Figure 8 illustrates that the loads in the soil

nails initially increased approximately linearly

with increasing excavation depth, but the rate

of increase reduced with further excavation.

The trend in the measured soil nail forces

compares well with the predictions from the

wedge analysis, although the latter generally

tends to underestimate the loads. This is

somewhat in contrast with Shen et al (1982),

Tei et al (1998), Lazarte et al (2003) and

others who stated that average nail forces are

generally smaller than those calculated by

considering full active earth pressures. The

most significant underestimation occurred

on the second soil nail.

During the acceleration of the centrifuge

to 50 G it was attempted to balance the

earth pressures behind the model retaining

wall by maintaining a constant water level

in the rubber mould as described. However,

some vertical and horizontal movements

of the various components of the model

were unavoidable during acceleration. The

imperfect method of balancing the earth

pressures as described, in combination with

the movements that occurred during accel-

eration, resulted in a certain amount of load

mobilising in the soil nails prior to reducing

the water level in the rubber mould to model

excavation. This means that a portion of

the shear strength of the sand was already

mobilised prior to water level being reduced.

Because of zeroing of the soil nail reading

prior to reducing the water level, these loads

were ignored. The various disturbances

would most probably have resulted in the

amount of shear strength mobilisation in the

sand before excavation to be different from

the situation applicable to an actual soil nail

wall, probably resulting in less shear strength

being available to support the excavated face

than what would have been expected. The

implication of this is that the soil friction

angle used in analysing the model should

probably be reduced. When a friction angle Figure 8 Development of soil nail forces with increasing excavation depth

Mo

de

l lo

ad

(N

)

60

200


Fu

ll-s

ca

le l

oa

d (

kN

)

150

50

40

30

20

10

0

125

100

75

50

25

0150100500

Strain 1 Strain 2 Strain 3 Wedge analysis 37° Wedge analysis 30°

(a) Soil nail 1

Mo

de

l lo

ad

(N

)

60

200


Fu

ll-s

ca

le l

oa

d (

kN

)

150

50

40

30

20

10

0

125

100

75

50

25

0150100500


(b) Soil nail 2

Mo

de

l lo

ad

(N

)

60

200


Fu

ll-s

ca

le l

oa

d (

kN

)150

50

40

30

20

10

0

125

100

75

50

25

0150100500


(c) Soil nail 3


of 30° is used instead of 37°, the correlation

between the measured soil nail forces and

those calculated using a wedge analysis

improves (see Figure 8).

A further factor contributing to the

difference between the measured and calcu-

lated loads is the fact that the actual stress

distribution behind the retained face is sig-

nificantly more complex than the simple tri-

angular distribution assumed by active earth

pressure theory (Tei 1993 and Tei et al 1998).

Tei (1993) states that the failure surfaces in

sand would resemble a logarithmic spiral

which would result in failure wedges that are

approximately 10% heavier than the assumed

triangular wedge. Also, Zhang et al (2001)

mentioned that the failure wedge in the pres-

ence of soil nails was deeper than without

reinforcement. The actual mobilised soil nail

forces are controlled by many factors, includ-

ing the flexibility of the facing wall and soil

nails and dilation on the soil-nail interface

(Tei et al 1998).

The magnitude of the scaled-up maximum

observed soil nail forces in the centrifuge

model are put into context by comparison

with normalised soil nail forces measured

at eleven sites presented in Figure 11 (Byrne

et al 1998). Observed maximum tensile nail

forces were normalised by KaHgShSv, where

Ka is the coefficient of active earth pres-

sure, H the wall height, the density of the

retained material and Sh and Sv the respective

horizontal and vertical nail spacing. The

figure shows that the general trend is for soil

nail forces to reduce somewhat with depth,

but very significant scatter occurs, probably

as a result of variations in soil strength and

stiffness between sites which were not taken

into account in the normalisation. The obser-

vations from the centrifuge tests plot well

within the data set presented in the figure.

Figure 10 Simplified wedge analysis used for

the estimation of soil nail forces

W R

T

Failure wedge

Failure plane

α

T

W

R

φ

β

Soil nails

Figure 9 The distribution of soil nail forces along their lengths as excavation depth increases

Mo

de

l lo

ad

(N

)60

300

Strain gauge position (mm)

Pro

toty

pe

loa

d (

kN

)

150

50

40

30

20

10

0

125

100

75

50

25

0150100500

(a) Soil nail 1M

od

el

loa

d (

N)

60


Pro

toty

pe

loa

d (

kN

)

150

50

40

30

20

10

0

125

100

75

50

25

0

(b) Soil nail 2

Mo

de

l lo

ad

(N

)

60


Pro

toty

pe

loa

d (

kN

)

150

50

40

30

20

10

0

125

100

75

50

25

0

(c) Soil nail 3

200 250

300150100500 200 250

250150100500 200

0 11 28 48 72 136 200

0 11 28 48 72 136 200

0 11 28 48 72 136 200


In the Jacobsz & Phalanndwa (2011) case

study, soil nail loads of just less than 50 kN

were measured in the top soil nail when the

system was at equilibrium. These are of the

same order of magnitude, albeit somewhat

lower than scaled loads from the model

(see Figure 8). They are also lower than the

prediction from a wedge analysis. Note that

a wedge analysis predicts soil nail forces that

are 12% higher when nails are installed at

10° compared to horizontal nails. The reason

for the scaled model loads being higher

can be ascribed to the fact that the model

soil profile comprised cohesionless sand in

which some shear strength had already been

mobilised during acceleration of the centri-

fuge, while the profile in the field comprised

residual andesite, possessing significant

cohesive strength, increasing with depth.

A further difference between the model

and the case study is the step-wise way in

which loads were mobilised in the case study

compared to a more gradual increase in load

in the model (compare Figure 2 with Figure

8). The reason for the step-wise load increase

was attributed to the fact that the excavation

could support itself to a certain depth and

then suddenly yielded, mobilising load in the

soil nails. With further excavation, it again

remained stable to a certain depth before

yielding again, applying another step-wise

load increase on the soil nails. The cohesion-

less sand did not possess any strength to

support any depth of excavation, so that axial

load had to be mobilised in the soil nails very

shortly after the water level in the model

excavation began to reduce.

The measured axial force distributions

along the length of the nails shown in

Figure 9 generally agreed with the pattern

typically observed in the field. A soil nail

normally carries a load at the retained face

which increases towards the intersection

with the failure plane and then reduces to

zero at the end of the nail (Lazarte et al

2003). The maximum load was measured

consistently at the second strain gauge on

each nail. They were purposefully installed

close to where the failure wedge was expect-

ed to intersect the soil nails.

Wall and ground movements

The vertical soil settlement behind the wall

amounted to approximately double the

amount of the expected settlement given by

the guideline of H/333 by Lazarte et al (2003)

for fine grained soils. However, the observed

settlement applies to a medium dense sand,

the material used in the model in which

some shear strength had already been mobi-

lised during centrifuge acceleration. The

maximum settlement of the full-scale wall

amounted to only 8 mm, illustrating that,

as expected, the residual andesite behaved

much stiffer than the sand in the model,

settling less. The residual andesite appears to

mobilise its strength at smaller strains than

cohesionless sand.

It is interesting to note that the settle-

ments above the active wedge, potenti-

ometers 1 and 2 (see Figure 3 and Figure

6) settled significantly more than the

potentiometers further away, reflecting the

mobilisation of the failure mechanism. An

active failure wedge is predicted to intersect

the sand surface at an offset of 100 mm

from the retained face. The zone behind the

wall where noticeable settlements occurred,

agrees well with the 140 mm (at model scale)

predicted by Lazarte et al (2003).

The horizontal wall movements are pre-

sented in Figure 7 and were recorded from

the onset of water level reduction until the

model excavation was complete. The largest

portion of horizontal movement took place

during the initial reduction in water level to

the depth of the first row of nails. Thereafter

the rate of movement slowed considerably.

In practice this initial movement would not

have been recorded, because the first shot-

crete panels still had to be constructed. The

horizontal movement that would be recorded

in practice corresponds to that associated

with a drop in water level from 30 mm to

the bottom of the excavation. In the tests

reported here, this movement amounted to

approximately 1 mm, or 50 mm at full scale.

As in the case of the vertical movement

behind the wall, this horizontal wall move-

ment also exceeded the guideline recom-

mended by Lazarte et al (2003) (also H/333,

or 30 mm at full scale). The maximum

horizontal movement observed at the top

of the full-scale wall was 34 mm (Jacobsz

& Phalanndwa 2011). The difference can

be explained due to the model comprising

medium dense sand in which some shear

strength had already been mobilised during

centrifuge acceleration, while the full-scale

Figure 11 Normalised maximum tensile forces measured in soil nail retaining walls (Byrne et al 1998)

Normalised maximum load (T/KaHγShSv)

0.2

Na

il h

ea

d d

ea

pth

/ w

all

he

igh

t

0

0.6

0.4

1.0

0.8

0.20 0.60.4 1.00.8 1.61.2 1.4

Byrne et al (1998) Centrifuge tests

Figure 12 Mode of horizontal deformation of model soil nail wall in centrifuge models

Ground surface

Excavation level

Model soil nail wall


situation comprised stiff residual andesite

mobilising strength at smaller strains.

Following each drop in the water level

in front of the model wall, it took some

time before the horizontal wall movement

stopped. This was also seen in the field,

where some movement continued to occur

for some time after completion of the exca-

vation (Jacobsz & Phalanndwa 2011).

Figure 7 illustrates that the top of the

wall deflected rapidly initially, but when the

water level reached the level of the first row

of soil nails, the rate of horizontal movement

reduced due to the restraining effect of the

soil nails. Virtually no horizontal movement

took place at mid-height initially, indicating

that the upper part of the wall bent above

the excavation level. Once the water level

reached mid-height, horizontal movement

there took place at approximately the same

rate as at the top of the wall, indicating that

the wall translated horizontally with little

further bending. This suggests that horizon-

tal wall deformation occurred as indicated in

Figure 12, with bending taking place at the

excavation level while the upper part of the

wall remains approximately planar.

Comparison between the full-

scale situation and the model

Soil

It is often questioned whether the particle

sizes of material used in a centrifuge model

need to be scaled. For example, could the

fine sand at model-scale therefore hypotheti-

cally behave as a gravel at the full-scale? In

practice it is common with a centrifuge

model to model the actual material occur-

ring in the field, or often, to use the actual

material from the field directly in the model.

The material is then viewed as a continuum

with the same stress-strain properties as

in the field. Whether this assumption is

reasonable depends on the ratio between

the particle size in the model and the size

of significant components in the model,

e.g. particle size versus the dimensions of

model piles, foundations or model soil nails

(Taylor 1995). A method that is often used to

investigate whether unrealistic scale effects

occur is the so-called method of “modelling

of models”. Models are tested at different

scales. If the scaled observations from dif-

ferent scale models are consistent, particle

size effects can be ignored and the material

can be assumed to behave as a continuum

at the accelerations tested. However, when

failure mechanism bounded by shear bands

begin to dominate, the ratios between shear

band widths, particle size and model element

dimensions can become important. In such

instances dilation effects within shear bands

are likely to scale-up unrealistically (Taylor

1995). Milligan & Tei (1998) mentioned

that relative size effects between model soil

nail diameter and particle size may tend to

increase the apparent strength and stiffness

of the model compared to the prototype in

the case of rough nails. This scale effect is

significant where the ratio D/D50 ranges

from 1 to 35 (where D is the nail diameter

and D50 the main particle size), but reduces

at higher values applicable in the field. Due

to the thickness of the brass strips (model

soil nails) relative to the means particle

size, scale effects would be expected in the

model. However, due to the smoothness of

the model nails, dilation effects as described

above should have been limited, although

probably not insignificant.

Soil nails

One important aspect in which the soil nail

retaining wall in the centrifuge differed from

the full-scale situation was that the wall and

soil nails were pre-installed prior to model-

ling of the excavation. Installation of soil

nails during a test would be difficult. Due

to the nails being pre-installed, loads could

mobilise before the excavation depth had

advanced to the depth of a particular row

of nails. Also, installation-induced soil nail

loads and soil stresses could not be modelled.

These are likely to differ from the situation

in the model (Milligan & Tei 1998).

CONCLUSIONS

A physical model, examining an instru-

mented soil nail retaining structure, was

tested successfully in three centrifuge tests.

The test yielded realistic and repeatable

data, comparing well with measurements

made in a full-scale case study in Pretoria

(Jacobsz & Phalanndwa 2011) and with a

database of eleven other case studies (Byrne

et al 1998).

In terms of soil nail forces, the model

showed somewhat higher nail forces

compared to those predicted by a simple

equilibrium analysis and when compared

with the case study discussed. This is likely

to be a consequence more of the shear

strength of the soil being mobilised during

acceleration of the model than what would

be applicable in a full-scale (K0) situation,

resulting in less strength being available to

resist excavation-induced loads than what

would have been expected. Information

from the literature suggests that soil nail

forces from a simple wedge analysis or limit

equilibrium analysis are conservative. The

results of these centrifuge tests suggest

that soil nail forces from centrifuge tests

may be even more conservative, due to the

mobilisation of some soil strength during

centrifuge acceleration.

The axial load distributions measured along

the length of the soil nails compared well with

the known distributions from the literature.

The trend in axial load mobilisation in

the soil nails differed from the full-scale case

study reported. In the model, axial load was

mobilised gradually in response to excava-

tion, while in the full-scale field study a step-

wise mobilisation was observed. The reason

for this is that the soil in the model only pos-

sessed frictional strength, while the residual

andesite in the field had some “cohesive”

strength and a fissured structure, enabling it

to remain stable up to a certain depth.

Although differences between the full

scale situation and a model are unavoid-

able, physical modelling in the geotechnical

centrifuge is a valuable technique to model

complex three-dimensional problems. An

advantage is that a physical event can be

observed and realistic results obtained using

the same materials as in the field.

REFERENCES

Bolton, M D & Pang, P R L 1982. Collapse limit state of

reinforced earth retaining walls. Geotechnique 32(4):

349–367.

Byrne, R J, Cotton, D, Porterfield, J, Wolschlag, C

& Ueblacker, G 1998. Manual for Design and

Construction Monitoring of Soil Nail Walls. Report

No FHWA-SA-96-69R, Washington DC: US Federal

Highway Administration.

Jacobsz, S W & Phalanndwa, T S 2011. Observed axial

loads in soil nails. Proceedings, 15th African Regional

Conference on Soil Mechanics and Geotechnical

Engineering, Maputo, Mozambique, 221–227.

Lazarte, C A, Elias, V, Espinoza, R D and Sabatini, P J

2003. Soil nail walls. Geotechnical Engineering Circular

No. 7, Report No FHWA0-IF-03-017, Washington DC:

US Federal Highway Administration.

Milligan, G W E and Tei, K 1998. The pull-out resis-

tance of model soil nails. Soils and Foundations,

38(2):179–190.

SAICE (South African Institution of Civil Engineering)

1989. Lateral Support in Surface Excavations, Code of

Practice. Johannesburg: SAICE Geotechnical Division.

Shen, C K, Kim, Y S, Bang, S & Mitchell, J F 1982.

Centrifuge modelling of lateral earth support.

Journal of Geotechnical Engineering Division, ASCE,

108(GT9): 1150–1164.

Taylor, R N 1995. Geotechnical Centrifuge Technology.

London: Blackie Academic & Professional.

Tei, K 1993. A study of soil nailing in sand. PhD Thesis,

Oxford: University of Oxford.

Tei, K, Taylor, R N & Milligan, W E 1998. Centrifuge

model tests of nailed soil slopes. Soils and

Foundations, 38(2): 165–177.

Zhang, J, Pu, J, Zhang, M & Qui, T 2001. Model tests

by centrifuge of soil nail reinforcements. Journal of

Testing and Evaluation 29(4): 315–328.


TECHNICAL PAPER



PROF DR SAEED-REZA SABBAGH-YAZDI is

professor in the Civil Engineering Department

of the KN Toosi University of Technology,

Tehran, Iran. He obtained his PhD from the

University of Wales, Swansea, United Kingdom.

He has more than twenty years’ academic and

professional experience in management,

design, computation, hydraulics, structural

engineering, computer simulation of fl uid fl ow and heat transfer, and stress

analysis of hydraulic structures.

Contact details:


KN Toosi University of Technology

Valiasr St Mirdamad Cross

Tehran, Iran

T: +98 21 88 77 9623

F: +98 21 88 77 9476


TAYEBEH AMIRI-SAADATABADI is a PhD student

in the Department of Civil Engineering at the

KN Toosi University of Technology. She obtained

her MSc in hydraulic structures from the

KN Toosi University of Technology and started

her PhD research in 2010. Currently she is

developing software to analyse concrete

structures. Her main research interest is in fi nite

volume numerical methods, cracking and creep.

Contact details:




Tehran, Iran

T: +98 21 88 77 9623

F: +98 21 88 77 9476


PROF DR FALAH M WEGIAN has more than 20

years’ academic experience, including the

research work for his Masters and Doctorate.

Prof Wegian is currently chairman of, and

professor in, the Civil Engineering Department

at the College of Technological Studies, Public

Authority for Applied Education and Training

(PAAET), Kuwait. His wide range of research

interests includes the use of Fiber Optic Bragg Grating Sensors embedded in

concrete structures to evaluate strains and cracks and the performance of

bridge structures. Prof Wegian has published numerous research papers and

has also authored two textbooks on concrete structures.

Contact details:

Chairman: Civil Engineering Department

College of Technological Studies

PAAET, Kuwait

PO Box: 42325

Shuwaikh

70654 Kuwait

T: +965 9 975 2002

F: +965 2 489 0767


Keywords: variable thermal property, mass concrete, Galerkin fi nite volume

solution, unstructured meshes of triangular elements

INTRODUCTION

Gradual setting of concrete layers during

construction of mass concrete structures

may give rise to drastic temperature gra-

dients due to the cement hydration and

heat conduction properties of the concrete.

Cement is a basic ingredient of concrete

which, by the process of hydration, mixes

with aggregates and water and produces

concrete. This process is exothermal and

causes the concrete temperature to rise.

After achieving maximum temperature,

the temperature decreases until it reaches

the ambient temperature. Predicting

the temperature field resulting from

the concrete hydration process during a

particular construction programme is an

important consideration in the design and

construction of mass concrete structures

like concrete dams. However, the thermal

properties of concrete (specific heat and

thermal conductivity) vary according to

the concrete temperature and the degree of

concrete hydration. These changes can be

considered in the thermal analysis of the

mass concrete structures by the adoption of

available empirical relationships.

The finite volume method has been

widely applied to heat transfer and fluid

dynamic problems through relatively

simple discretisation (Vaz Jr et al 2009). In

recent years the finite volume method has

been used for the solution of temperature

analysis, stress-strain computations and

thermal stress solutions of solid mechanical

problems, some of which are listed in the

following review.

For the computation of temperature

fields, an unstructured finite volume node-

centered formulation was implemented,

using an edge-based data structure for

the solution of two-dimensional potential

problems (Lyra et al 2002). Lyra et al used

an edge-based unstructured finite volume

procedure for the thermal analysis of steady

state and transient problems (Lyra et al

2004). Recently, a 2D finite volume method

to solve a heat diffusion equation was devel-

oped to predict the transient temperature

field in an RCC (roller-compacted concrete)

2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings of mass concrete considering contact interface and variations of material properties Part 1: Thermal analysisS Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian

In this research, a new explicit 2D numerical solution is presented to compute the temperature field which is caused due to hydration and thermal conductivity by the Galerkin finite volume method on unstructured meshes of triangular elements. The concrete thermal properties vary, based on the temperature variation and the age of the concrete in the developed model. A novel method for imposing natural boundary conditions is introduced that is suitable for the Galerkin finite volume method solution on unstructured meshes of triangular elements. In addition, the thermal contact is considered at the concrete-rock foundation interface to achieve more realistic simulations in this section. In this work we present the comparison of the thermal analysis numerical results of a plane wall, which had different thermal boundary conditions applied to its edges, with its analytical solution to assess the accuracy and efficiency of the developed model. The applicability of the developed numerical algorithm for thermal analysis is presented by the solution of thermal fields during gradual construction of a typical mass concrete structure.


dam wall during concreting of sequential

layers, taking into consideration the constant

thermal properties during concrete setting

(Sabbagh–Yazdi et al 2007).

The variation in concrete properties

significantly influences the prediction of

the temperature history of mass concrete

structures. Much research has been done to

calculate temperature fields, and different

numerical models have been used in the

various solution methods to simulate the

temperature field in mass concrete structures.

For example, a 2D finite difference method for

predicting the hydration-induced temperature

profile in mass concrete was developed,

considering a sinusoidal function for the sur-

rounding air changes (Ballim 2004).

A 3D finite element solution was pro-

posed for thermal analysis by Kim et al

(2001) who considered the effect of pipe

cooling systems. Ilc et al (2009) also devel-

oped a numerical model for the thermal

analysis of young concrete structures, based

on the finite element method. Considering

the constant thermal properties of con-

crete, the NASIR (Numerical Analyzer for

Scientific and Industrial Requirements)

concrete temperature solver, a 2D finite

volume method solver for heat generation

and transfer equation, was developed to

predict the transient temperature field in an

RCC dam wall during sequential layers of

concrete setting (Sabbagh–Yazdi et al 2001).

The accuracy and efficiency of the proposed

model were assessed by comparing the

numerical results from the analysis with ana-

lytical solutions for problems with constant

concrete properties and various boundary

conditions (Sabbagh–Yazdi et al 2007). In

this research, the variation in the heat con-

duction properties of concrete that occurs

due to changes in concrete temperature and

the ageing process is considered in terms of

the NASIR concrete temperature solver. For

this purpose, a 2D matrix-free Galerkin finite

volume solution is utilised for computing the

temperature fields in mass concrete struc-

tures on unstructured meshes of triangular

elements. In the developed numerical model,

the heat generation and transfer equation is

explicitly solved to compute the temperature

field. For the cases where the boundary

normal vector is parallel to the direction of

the grid in the coordinate system, it is easy to

impose the natural gradient boundary condi-

tion. To overcome the difficulties that may

appear when imposing such a boundary con-

dition at inclined boundaries of unstructured

meshes of triangular elements, a technique is

applied in this work to modify the gradient

flux vectors at the centre of the boundary

elements. This method is adopted for the

implementation of the natural gradient

boundary condition for the solution of heat

generation and transfer equation using the

Galerkin finite volume method.

HEAT GENERATION AND TRANSFER

MATHEMATICAL MODEL

Heat transfer mathematical model

The heat generation and transfer equation

is produced from different thermodynamics

and heat transfer references (Sabbagh–Yazdi

et al 2007).

éêêë

δ

δx

æççèkx

δT

δx

æççè + δ

δy

æççèky

δT

δy

æççèéêêë + Q = ρCT (1)

where k(J/m.h.°C) is the thermal conductivity

of concrete, T(°C) is concrete temperature,

Q(J/m3.h) is the rate of heat generation per

volume, ρ(kg/m3) is the density of con-

crete, and C(J/kg.°C) is the specific heat of

concrete.

The two main boundary conditions at the

external surfaces are:

T = Tair, k.dT

dN = –q (2)

where Tair(°C) and q(w/m2) are the air tem-

perature and the rate of heat exchange.

q = ±qc +qr – qs

qc = hc (Tsurface – Tair), hc = hn + hf,

hn = 6(w/m2.°C), hf = 3.7V(w/m2.°C)

qr = hr(Tsurface – Tair)

qs = γ.IN (3)

where qc, qr and qs are heat flux by convec-

tion, long wave radiation and solar radiation,

respectively; hn, hf and hr are natural, forced

and radiation convection; and γ,IN (w/m2)

and V(m/s) are surface absorption, incident

normal solar radiation and wind speed,

respectively.

In this research, the effects of long wave

radiation and solar radiation in heat flux

have been disregarded and the wind speed

has been supposed to be zero.

Cement hydration heat generation

Cement is a basic ingredient of concrete

which gains its cementitious property after

mixing with water. This chemical reaction

called hydration causes the paste to harden

and gain strength. Because of its significance,

several research efforts into the concrete

heat of hydration field and the appropriate

mathematical models, have already been pre-

sented (Noorzaei et al 2006; Riding 2007).

In general, hydration is a thermo-activated

reaction, and temperature primarily affects

the rate of hydration. Hence, the equivalent

age parameter and maturity function are used

to consider this feature. Through the maturity

function, the effect of concrete temperature

on the rate of hydration is regarded.

Equation 4 is used to calculate the heat of

hydration.

Q(te) = A + E.exp(–b.(te)–n) (4)

where A, E, b, n are variables which are cal-

culated by appropriate fitting of Equation 4

to experimental data, and te(hr) is the

equivalent age.

By adopting the Rastrup maturity func-

tion, the following equation is used to calcu-

late the equivalent age:

H(T) = 20.1(T–Tref), te = ∫H(T)dt (5)

where H(T), T, Tref(°C), are the relative

speeds of hydration reaction, concrete

temperature and reference temperature,

respectively.

Finally, Equation 6 is used to calculate the

rate of concrete hydration (Sabbagh–Yazdi et

al 2007):

Q(te) = n.b.E.(te)–n–1.exp(–b.(te)–n).20.1(T–Tref)

(6)

The hydration process is a long-term reac-

tion, with different hydration products

developing over time as a result of the chem-

ical reaction of water with the cement com-

ponents. Through this process, a skeleton of

hardened cement paste is formed. Due to the

ageing process, therefore, the concrete prop-

erties (thermal and mechanical) may change

during the hydration reaction. The degree of

hydration is equivalent to the amount of heat

liberated at any point during the hydration

stage to the total heat corresponding to the

end hydration. Many different relationships

are presented to calculate the degree of

concrete hydration. One of these models is

the Schindler model, in which the degree of

hydration is calculated by the mixture pro-

portions and the concrete age, as presented

in Equation 7.

αcon(te) = αu.expæççè–

æççèτ

te

æççè

β æççè (7)

where αu(unitless) is the ultimate degree of

hydration, τ is hydration time parameter,

te(hr) is the equivalent age, and β is the

hydration slope parameter. The fit param-

eters (αu, τ, β)are specified according to the

mixture proportions (Schindler 2004).

Using Equation 7, the rate of heat genera-

tion due to the concrete heat of hydration can

be represented by the source terms, heat gen-

eration and transfer equation. In addition, the


variation of concrete thermal properties (such

as specific heat and thermal conductivity)

during the ageing process can be considered

in the computational thermal analysis.

Ageing effects on thermal

properties of concrete

The concrete temperature and degree of con-

crete hydration affect the thermal properties

of the concrete. The relationships below,

which are related to change in the thermal

properties of concrete over time, are used in

the present thermal analysis.

Specific heat

The specific heat of concrete, which is equal

to the required heat for 1°C increase of

concrete temperature per unit mass of the

concrete, depends on the mixture propor-

tions, the degree of hydration, concrete

temperature and the relative humidity of

concrete.

The following equation is used for

changes in the specific heat of concrete over

time, as provided by Van Breugel (1998):

C = 1

ρ (wc.αcon.cref + wc(1– αcon)cc + wa.ca + ww.cw

Cref = 8.4 T + 339 (8)

where C(J/kg.K) is the specific heat of con-

crete; ρ(kg/m3) is the density of concrete;

wc, wa, ww(kg/m3) are the weight of cement,

aggregate and water per unit volume;

cc, ca, cw(J/kg.K) are the specific heat of

cement, aggregate and water respectively;

αcon is the degree of concrete hydration; and

T(°C) is the concrete temperature.

Thermal conductivity

The thermal conductivity of concrete, which

is the concrete’s ability to conduct heat,

represents the amount of heat transition

through a unit thickness of concrete in a

direction normal to a surface area at the unit

time. This parameter is dependent on the

relative humidity, type and amount of aggre-

gate, porosity and the density of the concrete.

Schindler (2002) stated that a higher

degree of hydration decreases the thermal

conductivity of concrete. The following

equation was proposed by Schindler:

k(αcon) = kue(1.33 – 0.33αcon) (9)

where k(w/m.K) is the transient thermal

conductivity, kue(w/m.K) is the ultimate

thermal conductivity of concrete, and αcon is

the degree of concrete hydration.

NUMERICAL SOLUTION

Galerkin finite volume formulations

The heat generation and transfer Equation 5

can be written as:

æççèδ

δxi Fi

Hæççèn

+ æççèα

k Q

æççèn

= æççèδT

δt

æççè (i = 1,2) (10)

where FiH is diffusive flux in i direction.

FiH = αn

δT

δxi , αn =

æççèk

ρC

æççèn

(11)

In each time step, the values of thermal

properties (k, C) are updated considering the

concrete temperature and degree of concrete

hydration. Then the source term (Sn) is

computed for every node (n) of the concrete

body.

By application of the Galerkin weighted

residual method, after multiplying the

residual of Equation 10 by a weight function

(which can be considered as the nodal shape

function of a linear triangular element, φn)

and integrating over a subdomain Ωn (which

Figure 1 Triangular element within the subdomain Ωn

dly n

dlxm = 3m = 2

m = 1

n

n

l = 1

l = 2

l = 3

l = N

Figure 2 Triangular elements of the boundary edge

Heat flux

G


is formed by gathering all the elements shar-

ing node n), the weighted integral form of

Equation 10 is written as Equation 12:

∫Ω

æççèδFi

d

δxi

æççè

φndΩ + ∫Ω

æççèα

k Q

æççèn

φndΩ

= ∫Ω

æççèδT

δt

æççèn

φndΩ (12)

The weak form of Equation 12, after

the omission of zero boundary terms, is

expressed as:

–∫Ω(FiH. φn)dΩ + ∫Ω

æççèα

k Q

æççèn

φndΩ

= ∫Ω

æççèδT

δt

æççèn

φndΩ (13)

The approximate ratio given in Equation 14

can be used to calculate the spatial derivative

term of Equation 13:

∫Ω(FiH. φn)dΩ ≈

1

2 ∑3

k=1(FiH.Δli)k (14)

Here (Δli)k is the i direction component of

the normal vector of edge k of the subdo-

main Ωn which is opposite to its central

node n (Figure 1).

The source term of the Equation 13 can

be approximated as:

∫Ω

æççèα

k Q

æççèn

φndΩ ≈ Ωn

3

æççèα

k Q

æççèn

(15)

Using the forward differencing method,

the discrete form of the transient term of

the governing equations can be written as

follows:

∫Ω

æççèδT

δt

æççèn

φndΩ = æççè

Tnt+Δt – Tn

t

Δt

æççèn

Ωn

3 (16)

The explicit form of the heat generation

and transfer equation for subdomain Ωn is

expressed as Equation 17:

Tnt+Δt = Tn

t + (Δt)tn

éêêë

3

2Ωn ∑N

l=1

æççèFiH.Δli

æççèt

1

+ æççèα

k Q

æççèt

n

éêêë (17)

where Tnt+Δt is temperature of node n at

time t+Δt, and N is the number of edges sur-

rounding the subdomain Ωn (Figure 1).

Computation of heat flux

vector components

The components of the heat flux vector

FiH = αn

δT

δxi must be calculated at the centre

of the elements corresponding to the bound-

ary edges of the subdomain Ωn (Figure 1).

The integration over an element can be

converted to a boundary integral using the

Gauss divergence theorem:

∫ΩE δT

δxi dΩ = o∫1T.dli (18)

where ΩE is the area of a triangular element.

The discrete form of the line integral can be

written as:

o∫1T.dli ≈ 1

ΩE ∑3

m=1(T.Δli)m (19)

where Δli is the component of the mth edge

normal vector of a triangular element which

is perpendicular to the i direction, and T is

the average temperature at the same edge

(Figure 1).

Hence, diffusive flux at each triangular

element for both directions can be calculated

using the following equation:

(FxH) =

æççèαn

δT

δy

æççè @ 1

ΩE ∑

3

m=1

(T.Δly)m

(FyH) =

æççèαn

δT

δx

æççè @ 1

ΩE ∑3

m=1(T.Δlx)m (20)

Boundary conditions

Two types of boundary conditions, known as

essential and natural boundary conditions,

are usually applied in thermal analysis.

The essential and natural boundary condi-

tions are used for certain temperature and

temperature gradient flux at boundaries,

respectively.

Figure 3 Schematic illustration of plane wall

100°C

b

xy

50°C

Q = 7.2E7 (W/m3)

Isola

tion

Isola

tiona

Figure 4 Unstructured meshes of triangular elements for thermal analysis (with 940 nodes and

1 718 elements)

Y (

m)

0.014

0.012

0.010

0.008

0.006

0.004

0.002

0–0.005 0 0.005

X (m)


For the cases where the boundary normal

vector n = (nx,ny) is parallel to the direc-

tion of the grid in the coordinate system,

the given normal gradient due to heat flux

by convection, G, can simply be inserted,

but the computational difficulties arise for

inclined or curved boundaries. To solve this

problem, the computed gradient flux vector

(Equation 20) at the centre of the boundary

elements (hatched elements in Figure 2) at

the end of each computational step may be

modified as Equation 23.

FH = (FxH)i + (Fy

H)j = æççèαn

δT

δx

æççèi + æççèαn

δT

δy

æççèj (21)

(G)normal = æççè

qc

k nx

æççè i + æççè

qc

k ny

æççèj (22)

(Fd)modify = αn

æççèδT

δx +

qc

k nx

æççè i + αn

æççèδT

δy +

qc

k ny

æççèj

(23)

where k is thermal conductivity and qc is

heat flux by convection, which was defined

previously.

Time integration

If the propagation speed of heat is considered

proportional to αn, the critical time step size

solution of the heat generation and transfer

equation can be written as Equation 24:

Δt < M æççèΩn

αn

æççè (24)

where M is a coefficient that is less than

unity.

In order to maintain the stability of the

explicit solution, the minimum time step size

of the computational domain must be used

in the computation of the unsteady prob-

lems. For the steady state cases, the concept

of local time stepping can be used where

every node has a special time step which

reduces the programme execution time.

THERMAL CONTACTS

When two solids, of initially different tem-

peratures, are brought into contact, thermal

coupling must be considered within the

contact analysis. Heat normally flows from

one solid to another one at the interface

between the two solids; this affects the

temperature distribution near the contact

surfaces. A constitutive equation is required

for the determination of heat flux in the

contact zone. In addition, the heat conduc-

tion is dependent on contact pressure in the

contact area. The following equation is often

assumed to be the constitutive equation for

heat flux:

q = h(T2 – T1) (25)

Where T2 is the temperature of the slave

node and T1 is the temperature of the closest

point in the master surface to the slave node.

The heat transfer coefficient (h) depends on

the temperature of the contact surfaces and

the contact pressure. The heat transfer can

be accomplished in three possible ways, i.e.

heat conduction through spots (hs), gas (hg)

and radiation (hr). The following equation is

obtained when one assumes that the above-

mentioned mechanisms act in parallel:

h = hs +hg +hr (26)

In this research, the heat conduction through

gas and radiation has been disregarded and

Equation 27 is used to determine the heat

conduction through the spots in the contact

interface.

hs = hræççè

P

Hv

æççèξ (27)

where P is the contact pressure and coef-

ficients hr, Hv and ξ are the thermal resist-

ance coefficient, Vickers hardness and an

Table 1 Specifications of plane wall

Height b = 1 cm

Thickness a = 1 cm

Thermal conductivity k = 18(w/(m.°C))

Internal heat generation Q0 = 7.2 * 107(w/m3)

Figure 5 Computed temperature contours

Y (

m)

0.014

0.012

0.010

0.008

0.006

0.004

0.002

0–0.005 0 0.005

X (m)

220

60

20018016014012010080

°C T

220

220

200

200

180160

160

140120

100

100

80

80

60

60

Figure 6 Convergence of logarithm of root mean square of temperature

RM

S (

Te

mp

era

ture

)

–7

–6

–5

–4

–3

–2

–1

100 00080 00060 00040 00020 0000

Iteration

0

10 000 30 000 50 000 70 000 90 000


Figure 8 Schematic illustration of a typical mass concrete structure on a natural foundation

4.35

30

.00

15.00

30.00

Foundation

Contact surface

exponent, respectively, which are given as

hr = 1.0, Hv = 3.0 and ξ = 1.5.

The thermal boundary condition is

applied by the following equations for each

node in the contact interface:

T2 = T1 , K.dT

dn + q =0 (28)

where T1 and T2 are the temperature of

solids 1 and 2, respectively, and dT

dn and q

are the thermal conductivity, normal tem-

perature gradient and heat flux, respectively

(Wriggers 2002).

VERIFICATION AND APPLICATION

Verification test

In this section, the solution for a steady

state problem with inclined boundary is

presented. Using the developed solver, the

time stepping limit of the formulation is

utilised to maintain the stability of itera-

tive computation from the assumed initial

condition towards the steady state condition.

Furthermore, use of the local time stepping

method speeds up the computation towards

equilibrium. Consider a plane wall with

specifications as presented in Table 1.

The boundary at y = 0,b of the domain

is assumed to be insulated. The boundary

at x = 0 is maintained at T0 = 50°C, and the

boundary at x = a is exposed to ambient

temperature Tc = 100°C (Figure 3). The film

coefficient is hc = 200(w/m2°C). The assump-

tion of an insulated boundary condition at

y = 0,b of the domain results in the 1D heat

flowing along the x direction. In this case,

the analytical temperature field is given as

Equation 29 (Reddy et al 2000).

T(x) = 50 + 5x

a +200

æççè1.9 – x

a

æççèx

a (29)

where x(m) is the distance from the edge,

which is held at a constant temperature of

50°C, and a(m) is the dimension of the plate.

Unstructured meshes of triangular ele-

ments are shown in Figure 4, and computed

temperature contours are illustrated in

Figure 5.

Using the Dell Vostro 1500 with an Intel

Core 2 Duo T7100 CPU with 1.8 GHz, 2 GB

main memory, the CPU time measured 44.6

seconds.

The root mean square of the computed

temperature during iterations, which is cal-

culated by Equation 30, is shown in Figure 6.

In Figure 7 the temperature changes along

the x direction are compared with the ana-

lytical results. The good correlation between

the computed results and the analytical solu-

tion is promising.

RMS = Logæççè

∑Ni=1(Ti

t+Δt – Tit)2

N

æççè (30)

Application case

In this section, the developed algorithm is

utilised to analyse the transient temperature

field during the gradual construction of a

typical mass concrete structure. The dam

is 30 m high, while the base and crest are

30 m and 4.35 m wide, respectively. The left

and right slopes are 0.1:1, 0.8:1 respectively

(Figure 8). Layer thickness at every concreting

is 0.5 m, and the interval between consecutive

concrete placing lasts 48 hours. The portion

of the dam foundation that is considered for

thermal analysis is shown in Figure 8.

The far field boundary of the foundation

is treated as a zero gradient boundary condi-

tion, and the Newman thermal boundary

condition is used for the external surfaces of

the dam wall and ground surface (Figure 8).

Figure 7 Comparison of computed temperature with analytical solution (along the x-axis)

RM

S (

Te

mp

era

ture

)0

50

100

150

200

250

0.010.0080.0060.0040.0020

Distance (m)

Theory Computational

Error Max = 0.96Error Average = 0.36


The use of unstructured meshes of

triangular elements for the geometric

modelling of the foundation media (Figure

9) facilitates simulation of the geo-structure

layers with irregular formation and material

variation. Likewise, application of structured

meshes of triangular elements for the dam

wall (Figure 9) provides the development

of concrete media in the vertical direction

(proportional to the construction stage and

concrete layer). The sinusoidal function is

utilised for air temperature changes.

The thermal properties and mixture pro-

portions of concrete are presented in Tables

2 and 3. The specific heat of materials, which

is needed to calculate the specific heat of

concrete, is presented in Table 4.

As mentioned, thermal properties of

concrete vary with the ageing process. In

the present analysis, the relationships as

presented above are used for the simulation

of the changes in the thermal properties of

concrete over time. The thermal properties

of the mass concrete structure are summa-

rised in Table 2.

Using the presented relationships, the

thermal properties of concrete can be deter-

mined according to concrete ageing over

time, as shown in Figures 10 and 11. Having

the transient changes of the thermal proper-

ties, these properties are assigned to each

node considering the temperature and age of

every concrete layer during thermal analysis.

The simulation results for the various stages

of gradual construction of a typical mass

concrete dam are presented in terms of the

transient temperature contour in Figure 12

(see page 102).

CONCLUSION

A 2D matrix-free Galerkin finite volume

solution is presented to compute the tran-

sient temperature field, considering the vari-

able thermal properties on the developing

linear triangular elements due to the heat of

hydration and thermal conduction through

boundary surfaces during gradual concret-

ing of concrete structures. The represented

explicit solution is a computationally effi-

cient algorithm which can achieve results of

time-dependent heat generation and transfer

problems with considerably low computa-

tional effort and CPU time consumption.

However, for the steady state problems, the

time stepping of the formulation may be uti-

lised for iterative stable computation towards

equilibrium, and using the local time step-

ping method, the programme execution time

can be reduced.

Due to the hydration progress of con-

crete and the ageing process, the thermal

properties of concrete vary over time. In

the present transient thermal analysis of

the concrete media, the proposed relation-

ships by previous researchers, as mentioned

above, are used for the simulation of the

transient changes in the thermal properties

of concrete according to concrete tempera-

ture and the degree of concrete hydration.

The method presented in this research

resolves the problem of imposing a normal

temperature gradient at the inclined bound-

aries of unstructured meshes of triangular

elements. In the developed algorithm, the

temperature gradient boundary condition is

applied by the modification of the gradient

flux vector at the centre of the boundary

elements.

In addition, the geometry of the dam

wall and foundation is not considered

integrated anymore, so the thermal contact

is considered at concrete-rock foundation

interface to achieve more realistic simula-

tions in this part. In this work we present

the comparison of the thermal analysis

numerical results of a plane wall, where

different thermal boundary conditions are

imposed at its edges, with its analytical

solution to assess the accuracy and efficien-

cy of the developed model. The computed

Figure 9 The triangular elements of a typical RCC dam wall

Y (

m)

20

30

0

10

–20

–10

–30

X (m)

20 300 10 40–10 50

Table 2 Thermal properties of concrete

Material property Value

Concrete

Coefficient of thermal expansion Variable (asymptote value = 10–5/°C)

Specific heat Variable (asymptote value = 827 J/kg.°C)

Thermal conductivity Variable (asymptote value = 10 326 J/m.h.°C)

FoundationThermal conductivity 9 360 J/m.h.°C

Thermal diffusivity 0.0038 m2/s

Table 3 Mixture proportions of concrete in a

unit volume

Material Value (kg/m3)

Cement 150

Aggregate 1 936

Water 163

Table 4 Specific heat of materials

MaterialSpecific heat

(J/kg°C)

Cement 1 000

Aggregate 800

Water 2 080


results presented promising correlation with

the analytical solution. In order to present

the applicability of the developed solver to

simulate real-world problems, the developed

model was used for transient thermal analy-

sis of a typical mass concrete structure on

a natural foundation in which the concrete

media were gradually developed via sequen-

tial setting of fresh concrete layers.

The concrete temperature module of

the NASIR Galerkin finite volume solver

can be applied as a useful modelling means

for the prediction of transient temperature

profiles during the desired sequential setting

construction programme of a mass concrete

structure, considering variations in thermal

properties.

NOTATION SECTION

k : Thermal conductivity of concrete

kuc : Ultimate thermal conductivity of

concrete

C : Specific heat of concrete

ρ : Density of concrete

Sn : Source term

te : Equivalent age of concrete

T : Concrete temperature

Tref : Reference temperature

Tsurface : Concrete surface temperature

Tair : The air temperature

Tnt+Δt : Temperature of node n at t + Δt

time

T : Average temperature of edge

Q : Heat of hydration

Q : Rate of heat generation per

volume

Q0 : Internal heat generation

αcon : Degree of concrete hydration

αu : Ultimate degree of hydration

A,E,b,n : Fit parameters

τ : Hydration time parameter

β : Hydration slope parameter

q : Rate of heat exchange

qc : Heat flux by convection

qr : Heat flux by long wave radiation

qs : Heat flux by solar radiation

hn : Natural convection

hf : Forced convection

hr : Radiation convection

γ : Surface absorption

IN : Incident Normal Solar Radiation

V : Wind speed

Ω : Subdomain

Δli : Normal component of boundary

edge at the i direction for the

subdomain Ω

N : Number of control volume out-

side faces

n→ : Normal vector of the boundary

edges

ΩE : Area of the triangular element

Δl : Edge of triangular element

FiH : Diffusive flux in i direction.

G : Given normal temperature

gradient

Δt : Time step size for heat generation

and transfer equation

M : Coefficient that can be consid-

ered less than unity

wc,wa,ww : Weight of cement, aggregate and

water, respectively

cc,ca,cw : Specific heat of cement, aggregate

and water, respectively

hc : Film coefficient

x : Distance

a : Dimension of plate

REFERENCES

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al

con

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cti

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y (J

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.°C

)13 000

12 500

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11 500

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1086420

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(f) Temperature field at 120 days (construction height = 30 m)(e) Temperature field at 100 days (construction height = 25 m)

(b) Temperature field at 40 days (construction height = 10 m)

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2019

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T°C

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1718

1919

20

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21

22

2324

25

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m)

X (m)

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–30

–20

0

–10

–10 403020100

20

50

30

2524

15

1716

1918

2120

2322

T°C

15

16

1718

18

19

1920

21

21

22

2324

25

26

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

30

2625

1615

1817

2019

2221

2423

T°C

1515

15

16

18

19

192021

23

23

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m)

X (m)

10

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–20

0

–10

–10 403020100

20

50

2322

15

1716

1918

2120

T°C

15

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15

15

16

17

19

1920

21

22

22

2324

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m)

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0

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–10 403020100

20

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TECHNICAL PAPER



PROF DR SAEED-REZA SABBAGH-YAZDI is

associate professor in the Civil Engineering

Department of the KN Toosi University of

Technology, Tehran, Iran. He obtained his PhD

from the University of Wales, Swansea, United

Kingdom. He has more than twenty years’

academic and professional experience in

management, design, computation, hydraulics,

structural engineering, computer simulation of fl uid fl ow and heat transfer,

and stress analysis of hydraulic structures.

Contact details:




Tehran, Iran

T: +98 21 88 77 9623

F: +98 21 88 77 9476


TAYEBEH AMIRI-SAADATABADI is a PhD student

in the Department of Civil Engineering at the

KN Toosi University of Technology. She obtained

her MSc in hydraulic structures from the

KN Toosi University of Technology and started

her PhD research in 2010. Currently she is

developing software to analyse concrete

structures. Her main research interest is in fi nite

volume numerical methods, cracking and creep.

Contact details:




Tehran, Iran

T: +98 21 88 77 9623

F: +98 21 88 77 9476


PROF DR FALAH M WEGIAN has more than 20

years’ academic experience, including the

research work for his Masters and Doctorate.

Prof Wegian is currently chairman of, and

associate professor in, the Civil Engineering

Department at the College of Technological

Studies, Public Authority for Applied Education

and Training (PAAET), Kuwait. His wide range of

research interests includes the use of Fiber Optic Bragg Grating Sensors

embedded in concrete structures to evaluate strains and cracks and the

performance of bridge structures. Prof Wegian has published numerous

research papers and has also authored two textbooks on concrete structures.

Contact details:

Chairman: Civil Engineering Department

College of Technological Studies

PAAET, Kuwait

PO Box: 42325

Shuwaikh

70654 Kuwait

T: +965 9 975 2002

F: +965 2 489 0767


Keywords: variable mechanical property, mass concrete, Galerkin fi nite

volume solution, unstructured meshes of triangular elements

INTRODUCTION

The volume changes in concrete that take

place during the hydration process and cool-

ing phase will cause tensile stress develop-

ment. The external and internal constraints

often exist simultaneously and will limit the

thermal strains corresponding to the tem-

perature changes. Therefore, critical thermal

stresses may appear in the concrete members.

The concrete has a relatively low tensile

strength (compared to other building materi-

als) and is susceptible to cracking. Therefore,

if thermal stresses exceed the tensile strength

of concrete, they could cause visible crack-

ing in the concrete members. Hence, mass

concrete structures such as concrete dams,

nuclear reactor containments and bridges may

be subject to thermal cracking due to thermal

stresses. Thermal cracking can influence the

durability and serviceability of concrete dams,

and should therefore be studied in detail.

Calculating the temperature and stress

distribution is one of the most important

considerations in solid mechanics. These

phenomena have therefore been modelled by

various numerical techniques, such as the

finite difference method (FDM), the finite

element method (FEM), the finite volume

method (FVM), etc. Traditionally, solid body

problems were addressed by the FEM. The

FDM has, however, become one of the most

popular methods in the area of computa-

tional fluid mechanics, and recently some

problems in continuum mechanics have been

solved successfully by FVM (Demirdžić et

al 1993). The FDM is the oldest method and

is based on the application of a local Taylor

expansion to approximate the differential

equations, which are truncated usually after

one or two terms. The number of terms

determine the accuracy of the solution

(the more there are, the more accurate the

2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings of mass concrete considering contact interface and variations of material properties Part 2: Stress AnalysisS Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian

In this research, a 2D matrix-free Galerkin finite volume method on the unstructured meshes of triangular elements is utilised to compute thermal stress fields resulting from the predefined transient temperature distribution in a mass concrete structure (dam wall). In the developed numerical model, the convergence of the force equilibrium equations are achieved via some iterative solutions for each given computed temperature field. Since the mechanical properties of concrete may vary over time due to concrete ageing, the presented numerical model considers the variation of mechanical properties corresponding to the degree of concrete hydration and concrete temperature. In addition, the geometry of the dam wall and foundation is not considered integrated any longer, so the mechanical contact is considered at concrete-rock foundation interface to achieve more realistic simulations of the strain-stress fields in this part. In this work we present the comparison of thermal stress analysis numerical results (of a clamped plane which is exposed to constant temperature) with the results of finite element-based ALGOR software to assess the accuracy and efficiency of the developed model, and prove that the results correlate well. As an application of the developed model for a real-world problem, thermal stress analysis of a mass concrete structure which is gradually constructed on a natural foundation is performed with regard to variable mechanical properties.


solution), but this is a complex matter (Yip

2005). The FDM is suitable for structured

grids associated with regular boundaries, and

is not as accurate for complex geometries

as the FVM is. However, for dealing with

irregular boundaries, the use of unstructured

meshes provides considerable flexibility and

accuracy for modelling projects (Sabbagh–

Yazdi et al 2009).

This is a potential bottleneck of the FDM

when hand ling complex geometries in mul-

tiple dimensions. The issue motivated the use

of an integral form of the governing equations

(PDE), and subsequently the development of

the FEM and FVM (Yip 2005). Both methods

have surpassed the FDM and other numerical

methods, and researchers typically use one of

them for numerical simulations of all types of

physical phenomena. The FEM has become

very popular in structural analysis due to the

great practical value of the results, especially

in cases where deformations are limited to

elastic ones (Demirdžić et al 1993).

The FEM is based on the variational

principle and uses the predefined shape

functions dependent on the topology of

the element, easily extends to higher order

discretisation, produces large block-matrices,

usually with high condition numbers, and

as a consequence relies on direct solvers.

The FVM is usually second-order accurate,

based on the integral form of the governing

equation, uses a segregated solution proce-

dure, where the coupling and non-linearity

are treated in an iterative way, and creates

diagonally dominant matrices well suited for

iterative solvers.

The question here is a trade-off between

the high expense of the direct solver for a

large matrix in FEM or the cheaper iterative

solvers in FVM. The reason for this may be

the fact that the FVM is inherently good at

treating complicated, coupled and non-linear

differential equations, widely present in fluid

flows. By extension, as the mathematical

model becomes more complex, the FVM

should become a more interesting alterna-

tive to the FEM. Another reason to consider

the use of the FVM in structural analysis

is its efficiency. In recent years industrial

computational fluid dynamics has been

dealing with meshes of high order which are

necessary to produce accurate results for

complex mathematical models and full-size

geometries (Jasak et al 2000).

It is well known that the numerical analy-

sis of solids in incompressible limit could

lead to difficulties. For example, fully inte-

grated displacement-based lower-order finite

elements suffer from volumetric locking.

Also, some difficulties are experienced pro-

ducing a stiffness matrix and shape function

in order to increase the convergence rate.

From the results of several benchmark

solutions, the FVM appeared to offer a

number of advantages over equivalent finite

element models. For instance, unlike the

FDM solution, the FVM solution is conserva-

tive, and incompressibility is satisfied exactly

for each control volume of the computational

domain. In principle, because of the local

conservation properties, the FVMs should

be in a good position to solve such problems

effectively. Furthermore, numerical calcula-

tion with meshes consisting of triangular

cells showed excellent agreement with ana-

lytical results (Sabbagh–Yazdi et al 2009).

The presented results show that both local

and global norms of error for the FVM are

similar to the FEM. Using the constant strain

triangles leads to a similar stiffness matrix

and consequently a comparable level of accu-

racy in both the FVM and FEM. It is interest-

ing that the execution time for the FVM is

less than that of the FEM for sufficiently fine

mesh (Ekhteraei–Toussi et al 2007).

As mentioned before, the FVM is a

popular method in thermal analysis, while

the FEM is a conventional technique in

the solid mechanics field. The use of both

methods would inevitably necessitate the

transferring of data. However, the trans-

formation of results between the FVM and

FEM is time-consuming. By using the FVM

for the analysis of solids and temperature,

the time-consuming transfer of data can be

avoided, while the method is also more stable

when simulating complicated problems

(Suvanjumrat et al 2011).

For determining the displacement fields

and elastic stress distribution in structures,

Wheel (1996) introduced an implicit finite

volume method for axisymmetric geometries

using structured meshes. Wenke et al (2003)

presented a finite volume-based discretisation

method for determining displacement, strain

and stress distributions in two-dimensional

structures on unstructured meshes. They

incorporated rotation variables in addition to

the displacement degrees of freedom. Slone

et al (2003) evaluated the dynamic structural

response of solids on unstructured meshes. In

this work, a three-dimensional vertex-based

method with a Newmark implicit scheme was

presented and the neutral frequency was pre-

dicted accurately by employing viscous damp-

ing. Demirdžić et al (2000) extended their

numerical technique for the stress analysis in

isotropic bodies subjected to hygro-thermo-

mechanical loads. In this research, the tem-

perature, stress, displacement and humidity

fields were calculated using the fully implicit

time differencing, whereas the source term

and diffusion fluxes were treated explicitly.

Fainberg et al (1996) performed similar work

for thermo-elastic material.

In one of the numerical research efforts,

ANSYS software was used for 2D and 3D

thermo–structural analyses of roller-com-

pacted concrete (RCC) (Malkawi et al 2003).

Both thermal and mechanical properties of

the concrete were considered constant dur-

ing the analysis. In this research, a 2D finite

element programme was used to simulate

the construction process of a mass concrete

structure. A computer code for thermo-struc-

tural analysis of the mass concrete structures

was also implemented by these researchers.

They predicted the time of crack occur-

rence via the crack index with regard to the

constant mechanical properties of concrete

over time. Noorzaei et al (2006) and Jaafar et

al (2007) implemented a 2D computer code

based on the finite element method for the

thermal analysis of a mass concrete structure.

In this research the thermal properties of

concrete were assumed to be constant during

analysis. Azenha & Faria (2008) proposed a

2D numerical method for the prediction of

temperature and stress distribution consider-

ing the evolution of mechanical properties

during the early ages of concrete.

It should be noted that, as the reactions

proceed, the products of the cement hydration

process gradually grow to form the skeleton of

hardened cement paste as a solid mass which

bears the applied loads. Hence, the mechani-

cal properties of concrete change with respect

to concrete age. This process is known as

concrete ageing and must be considered in

precise thermal stress analysis. Luna & Wu

(2000) predicted the temperature and stress

distribution during RCC dam construction

considering the temperature effect on the

elastic modulus and creep behaviour of con-

crete, but the other concrete properties were

assumed to be constant over time. Cervera et

al (2000) implemented a numerical simula-

tion for construction of the mass concrete

structure with regard to the ageing effects.

In that work the numerical analyses were

performed under different scenarios of dam

construction. Chen et al (2001) developed

the finite element relocating mesh method

for stress analysis of RCC dams during the

construction period. The ageing effects on the

elastic modulus of concrete were considered

by Chen et al.

Another module of NASIR (Numerical

Analyzer for Scientific and Industrial

Requirements) solver, which uses a matrix-

free Galerkin finite volume method on

the unstructured meshes of triangular

elements, was recently introduced for strain-

stress analysis of plane-strain problems

under external loads considering constant

mechanical properties (Sabbagh–Yazdi et

al 2008). In Part I of this two-part paper, a

new explicit 2D numerical solution has been


presented to compute the temperature field

which is caused due to the hydration and

thermal conductivity by the Galerkin finite

volume method on the unstructured meshes

of triangular elements with respect to the

variation of temperature and age of concrete.

In this research, NASIR plane-strain

solver, the finite volume method solver of

Cauchy equations for plane-strain problems,

is developed to predict the strain-stress fields

during multi-layer concrete setting of a mass

concrete structure considering the variations

of mechanical properties. For this purpose,

a strain-stress solver based on the Galerkin

finite volume method for plane-strain prob-

lems is developed for stress analysis during

the various stages of gradual construction of

mass concrete structures. In this modelling

strategy, the convergence of 2D force equilib-

rium equations is achieved via some iterative

matrix-free solutions for a given (previously

computed in Part I of this two-part paper)

temperature field at each stage of the gradual

construction of the mass concrete struc-

ture. The thermal stresses are computed

considering the effect of concrete ageing

on the mechanical properties of concrete.

The variations of mechanical properties are

considered corresponding to the concrete

temperature, the time dependent degree of

hydration and the concrete age.

After the detailed description of the

numerical modelling, the accuracy of the

introduced numerical model is assessed

by comparison of the computed principle

thermal stress contours of a clamped plate

due to a uniform temperature field with the

finite element method solution which has

been reported by Logan (2000). Finally, the

thermal stress solution during the multi-layer

construction of a mass concrete structure on

a natural foundation is performed consider-

ing the variable mechanical properties of

concrete

FORCE EQUILIBRIUM AND STRESS

FIELD MATHEMATICAL MODEL

Force equilibrium equations

It is well known that the Cauchy equa-

tions are the predominant equations of

solid mechanics. The following equation

is attained from the equilibrium equations

which can be used on each body with any

material (Sabbagh–Yazdi et al 2008).

δσx

δx +

δτxy

δy = ρüx

δτxy

δx +

δσy

δy = ρüy (1)

where ρ (kg/m3) is the material’s density and

üi (m/s2) is the acceleration of the body.

Strain-stress relations

The stress field for plane-strain problems is

expressed as:

σx = D11εx + D12εy

σy = D21εx + D22εy

τxy = D33γxy

D = E(1 – ϑ)

(1 + ϑ)(1 – 2ϑ)

éêêêêêë

1 ϑ

1 – ϑ 0

ϑ

1 – ϑ 1 0

0 0 1 – 2ϑ

2(1 – ϑ)

éêêêêêë

(2)

where σx,σy,τxy are the normal stresses in the

x and y directions and shear stress, respec-

tively; εx,εy,γxy are the normal strains in the

x and y directions and shear strain, respec-

tively; and E, ϑ denote the elastic modulus

and Poisson’s Ratio coefficient.

The strain field is expressed as:

εx = δux

δx + εEth

εy = δuy

δy + εEth

εxy = δux

δy +

δuy

δx (3)

where (εEth)n is the external thermal strain of

node n which is calculated from Equation 4:

(εEth)n = αΔT = α(Tt+Δt – Tt)n (4)

where

α(l/°C) : coefficient of thermal expansion

Ttn(°C) : temperature of node n at time (t)

Ageing effects on

mechanical properties

The changes of concrete properties dur-

ing the hydration reaction are called the

concrete ageing. The evolution of elastic

Figure 1 Control volume node n with triangular elements

dx

m = 3

m = 2

m = 1

n

l = 1

l = 2

l = 3

l = N

dy

k

j

i

Ux

Uy

Figure 2 Clamped constraint

v

u

Figure 3 Sliding constraint

v

u

un ut


modulus and strength of concrete must

be considered for a precise thermal stress

analysis.

Elastic modulus

The elastic modulus is defined as the

ratio between the constrained strains and

stresses. The elastic modulus of concrete

relates to the hydrated cement paste of

concrete, which is able to support the

applied loads. The hydrated cement paste

of concrete grows with time and causes

considerable increase of the concrete

elastic modulus. Equation 5 may be used

for the evolution of the concrete elastic

modulus over time (Noorzaei et al 2006).

Ec(t) = Ec.eatb , Ec = 4 750 f ’c (5)

where Ec(MPa) is the elastic modulus of

concrete at time (t), Ec(MPa) is the ultimate

elastic modulus of concrete, t(day) is the

equivalent age of concrete, f ’c is the char-

acteristic cylinder strength of concrete,

and a, b are the fit parameters which were

determined for one mass concrete structure

as follows: a = –0.5, b = –0.63.

Poisson’s Ratio

The Poisson’s Ratio coefficient is required

for stress modelling in multi-dimensional

structures. This coefficient is defined as

the ratio of transverse strain to longitu-

dinal strain under uniform axial stress.

De Schutter & Taerwe (1996) presented

a model to calculate the variation in the

Poisson’s Ratio of concrete over time based

on the degree of concrete hydration.

ϑ(αcon) = 0.18sinπαcon

2 + 0.5e–10αcon (6)

where ϑ(αcon) is the Poisson’s Ratio of con-

crete at the degree of hydration (αcon).

Coefficient of thermal expansion

Coefficient of thermal expansion is one of

the most important parameters of thermal

stress analysis. The mixture proportions,

type of aggregate, degree of saturation and

concrete age are the effective parameters

on the coefficient of thermal expansion

of concrete. The coefficient of thermal

expansion is dependent on the coefficient

of thermal expansion of the concrete com-

ponents. Since the aggregate content of

concrete is relatively high, the coefficient

of thermal expansion of the aggregate has

the greatest effect on the coefficient of

thermal expansion of concrete.

The Loukili model expresses the evolu-

tion of the coefficient of thermal expan-

sion of concrete over time (Equation 7).

According to this relationship, the

coefficient of thermal expansion of con-

crete decreases over time and converges to

10–5(1/°C).

α(t) = 77e

0.75–t

2.5 + 10 (7)

where α(10–6/°C) is the coefficient of thermal

expansion of concrete, and t(hr) is the equi-

valent age of concrete (Loukili et al 2000).

NUMERICAL SOLUTION

Galerkin finite volume formulations

The compact form of Cauchy equations can

be expressed as:

æççèδσij

δxi

æççè = æççèρ

δ2ui

δt2

æççèn (i = 1,2) (8)

For j = 1,2 the stress vector can be defined

as F→

i = σi1i + σi2j = F1i + F2j where ui(m) is

displacement in the i direction.

By application of the Galerkin weighted

residual method, after multiplying the residual

of the above equation by a weight function

(which can be considered as the nodal shape

function of a linear triangular element φn)

and integrating over a subdomain Ω (which is

formed by gathering all the elements sharing

node n), the weak form of Equation 8, after

omitting zero boundary terms, is expressed as:

∫Ωφn.( .FiS)n = ∫Ωφn.

æççèρδ2ui

δt2

æççèn dΩ (9)

The first term on the right-hand side of

Equation 9 can be written as Equation 10:

∫Ωφn.( .FiS)n = [φn.nFi

S]Γ – ∫Ω(FiS. φn)dΩ

→ ∫Ωφn.( .FiS)dΩ = –∫Ω(Fi

S. φn)dΩ (10)

The approximate relationship given in

Equation 11 can be used to calculate the

spatial derivative term of Equation (10):

∫Ω(FiS. φn)ndΩ ≈

1

2 ∑3

m=1(FiS.Δli)m (11)

Here (Δli)m is the i direction component of

the normal vector of edge m of the subdo-

main Ωn.

The weighting function φ has a value of

unity at the desired node n, and zero at the

other neighbouring nodes k of each triangu-

lar element.

For an equilibrium condition in which

time stepping can be considered as a strat-

egy to perform the iterative computation

until the desired convergence is achieved,

the transient term of the equation can be

expressed as:

ρΩn

3

æççèδ2ui

δt2

æççèn = ρ

æççèui

k+1 – 2uik + ui

k–1

Δt2

æççèn

Ωn

3 (12)

The discrete form of the Cauchy equation for

a node n is written as Equation 13:

(ui)nk+1 = (Δt)n

kéêêë

3

2ρΩn ∑N

i=1

æççèFiS.Δli

æççèk

1

éêêë

+ 2(ui)nk – (ui)n

k–1 , (i = 1,2) (13)

where (ui)nk+1 is the displacement of node n at

k+1 iteration in the i direction (Figure 1).

Computation of stress vector

components

The stress field can be calculated using the

following equations:

σx = ìïíïî

D11

æççèδux

δx + εEth

æççè + D12

æççèδuy

δy + εEth

æççèìïíïî

σx ≈ ìïíïî

1

ΩE ∑3

m=1

æççèD11uxΔy – D12uyΔx

+ εEth(D11 + D12)æççèm

ìïíïî (14)

σy = ìïíïî

D12

æççèδux

δx + εEth

æççè + D11

æççèδuy

δy + εEth

æççèìïíïî

σy ≈ ìïíïî

1

ΩE ∑3

m=1

æççèD12uxΔy – D11uyΔx

+ εEth(D12 + D11)æççèm

ìïíïî (15)

τxy = τyx = ìïíïî

D22

æççèδux

δy +

δuy

δx

æççèìïíïî

τxy = τyx ≈ ìïíïî

1

ΩE ∑3

m=1

æççèD22uyΔy – D22uxΔx

æççèm

ìïíïî (16)

where

εEth : the external thermal strain which is

the average strain of each edge

ΩE : the area of triangular element

n : the external edges number of control

volume

Boundary conditions

The boundary conditions of the force equi-

librium equation are presented as follows:

Clamped constraint

In this boundary condition, not only the

displacement, but also the rotation must be

limited (Figure 2).

ux = 0, uy = 0, θ = 0 (17)

Sliding constraint

This boundary condition provides only the

tangential displacement, and the normal

displacement is prevented (Figure 3).

un = 0, θ = 0 (18)


Iterative computation

The iterative computations are resumed until

the steady state condition and desired con-

vergence are achieved. In order to maintain

the stability of the iterative computations, the

time stepping size must be limited. Using the

local time stepping method can reduce the

run-time required to reach equilibrium. In

order to have the stable explicit solution, the

Courant’s number must be less than unity.

According to the proposed relation

(Sabbagh–Yazdi et al 2008), the time step size

must be limited to the following equations:

Δtn < rn

C (19)

rn = Ωn

Pn , Pn = ∑

k=1Nedge(Δl)k (20)

where Ωn and Pn are the area and perimeter

of the control volume, respectively.

C is the speed of information transition

which is calculated from Equation 21:

C = E

ρ(1 – ϑ2) (21)

Every node has its own time step size.

Using the concept of the local time step-

ping method accelerates the convergence to

the equilibrium condition for steady state

problems.

CONTACT ANALYSIS

Contact mechanics involves the study of

forces transmitted from one solid to another

and the consequent stresses in those solids.

Contact mechanics has widespread applica-

tion in many engineering problems and

no one can disregard its importance. The

general goals of contact analysis are to deter-

mine the contact stresses transmitted across

the contact interfaces of the solids that are

brought into contact. Nowadays computa-

tional mechanics is a useful tool to simulate

contact problems numerically so that one

is able to analyse large-scale problems. One

of the interesting applications of contact

mechanics is the modelling of dam-rock

foundations interface. Interface may not only

affect the mechanical behaviour of the dam

and foundation system, but also the diffusion

properties, such as moisture transmission.

The safety against sliding has to be assessed

for the interface between the dam and the

foundation, especially in dynamic analysis.

In the contact area, the constraint equa-

tions for normal and tangential contact have

to be formulated. Let us assume that two

solids are brought into contact (Figure 4).

In this case, the non-penetration condition

(constraint equation) is given by the follow-

ing equation:

g = [x1 – x2].n ≥ 0 or g = Cu on Γc = Γ1 + Γ2 (22)

where Γc denotes the contact surface; n is

the normal to solid 2; x1,x2 are the deformed

positions of solids 1 and 2, respectively; u is

the displacement matrix; and g = æççègn

gt

æççè is the

Figure 4 Contact forces

Contactor

Target segment

C

i j

time = t

time = t + dt

gt

gn

ft

fn

(a) Before contact (b) Possible normal and tangential gaps

Figure 5 Schematic illustration of plate

clamped at left and subjected to

uniform temperature

50 cm

Free edge

50

cm

Cla

mp

ed c

on

stra

int

A50°C

Fre

e ed

ge

A

Free edge

Table 1 Plate specifications

Plate Specification Value

Length * Height 50 * 50 cm

Elastic modulus 210 GPa

Poisson’s Ratio ϑ = 0.3

Coefficient of thermal expansion

α =1.2E – 5/°C

Temperature difference 50°C

Figure 6 Unstructured meshes of triangular elements for thermal stress analysis (with 940 nodes

and 1 718 elements)

Y (

m)

0.5

0.4

0.3

0.2

0.1

0

X (m)

0 0.1 0.2 0.3 0.4 0.5


relative motion in normal and tangential

direction, respectively.

If the above relationship isn’t exactly

satisfied, we have some penetration in the

contact surface which could be interpreted

as the g function:

g = Cu – Q (23)

In this research, the penalty method is con-

sidered for enforcing a constraint condition

in contact analysis. The stiffness equation of

a constrained problem is determined by min-

imising the total potential energy (Equation

24). As is clear from this, the stiffness matrix

and force vector are modified to incorporate

the impenetrability constraint stiffness.

[K + CTαC]u = R + CTαQ (24)

where α is the penalty number.

The contact force vector is calculated

from the following equation:

æççèfn

ft

æççèCon

= éêêë αn 0

0 αt

éêêë

æççègn

gt

æççè (25)

where fn, ft are the normal and tangential

contact forces, respectively, and αn, αt are

the normal and tangential contact stiffness,

respectively.

One has to distinguish two cases which

are called stick state and slide state in the

tangential direction of the contact surface. In

the first situation (stick state) a point which

is in contact cannot move in the tangential

direction, but in the slide state situation

relative slip between two solids occurs and

friction law is applied to the contact surface.

A slip criterion is used to indicate whether

stick or slip state occurs, which is stated as in

Equation 26:

φ = |τ| – τcrit = ìïíïî

< 0 stick state

= 0 slip state (26)

where |τ| denotes the norm of the tangential

traction and τcrit is determined by the fric-

tion law.

The Coulomb friction law, which is

adequately applicable to common frictional

contact problems, is adopted in this research

as (Mohammadi 2003):

τcrit = μ|σn| (27)

where μ is the friction coefficient and σn

denotes the normal stress. The value of the

friction coefficient for mass concrete on

sound rock is considered to be 0.7 so that the

stick state always occurs (ETL 1110-3-446

1992).

VERIFICATION AND APPLICATION

Verification test

External thermal stresses are induced in

concrete structures because the coefficients of

Figure 7 Maximum principal stress contours computed by developed model (Pa)

Y (

m)

0.5

0.4

0.3

0.2

0.1

0

X (m)

0 0.1 0.2 0.3 0.4 0.5

4.4E+064.4E

+06

8.8E

+06

8.8E+06

1.3E+07

1.3E+07

1.3E+07

1.8E+07

1.8E

+07

2.2E+07

8E+073.1E

+07

3.1E+072.8E+07

4.4E+06

1.3E+078.8E+06

2.2E+071.8E+07

S1

Figure 8 Maximum principal stress contours computed by ALGOR finite element method

software (Logan 2000)

Y (

m)

500

400

300

200

100

0

X (m)

0 100 200 300 400 500

450

350

250

150

50

50 150 250 350 450


thermal expansion of the body and adjacent

structures are different. When the tem-

perature difference between the body and its

adjacent structures is the same, the thermal

strains in the body and its adjacent structures

due to the difference between their coef-

ficients of thermal expansion are different,

which cause thermally induced stress.

A plate specimen is clamped at the left

and is subjected to a uniform temperature

of 50°C as shown in Figure 5 (Logan 2000).

The properties of the material are given in

Table 1.

The unstructured mesh of triangular

elements, as shown in Figure 6, is used to

perform the Galerkin finite volume method

solution. In order to assess the computed

results of the present solver with other

developed methods, the results of the finite

element-based ALGOR commercial software

(presented in the previous literature review)

are used to compare the computed results.

Under a uniform temperature, the thermal

stresses are induced by the restraint bound-

ary conditions. The computational stress

field is the same as the results from the

ALGOR software (Logan 2000), as are shown

in Figures 7 and 8.

Application case

The applicability of the developed solver to

simulate real-world problems is shown in

this section. Using the developed software,

the simulation of a thermally-induced stress

field of a typical mass concrete structure is

performed with regard to the variations of

mechanical properties of the material. The

mechanical properties of the concrete and

foundation are tabulated in Table 2. For more

geometrical details please refer to Part I of

this two-part paper.

Using the presented relationships, the

mechanical properties of concrete can be

determined according to concrete ageing

during analysis. Their variation diagrams

over time are shown in Figures 9–11.

The numerical analysis of a typical

mass concrete structure is performed using

the above-mentioned relationships of the

mechanical properties and the computed

results of both simulations (constant and

variable properties of concrete), as demon-

strated in Figure 12 (see page 112) in terms

of the transient principal stress contours in a

concrete dam wall during the different stages

of construction.

In order to provide a better understand-

ing of the effects of the gradual load impos-

ing technique and to ensure the convergence

of the presented results, the root mean

square of the computed displacements is

shown in Figure 13.

CONCLUSION

Considering the temperature and time-

dependent mechanical properties of concrete

is an essential task for the precise thermal

stress analysis of mass concrete structures.

In this research, a plane-strain matrix-free

Galerkin finite volume method was used

to develop a numerical solver which is able

to predict the temperature-induced stress-

strain fields in mass concrete structures due

to concrete heat of hydration and thermal

conduction between the concrete and sur-

rounding air through the boundary surfaces,

considering the concrete ageing dependent

mechanical properties.

Figure 9 Variation of Poisson’s Ratio with respect to concrete ageing

Po

isso

n's

ra

tio

0.6

0.5

0.4

0.3

0.2

0.1

0

Variable Constant

Time (hour)

120967248240

Figure 10 Variation of coefficient of thermal expansion with respect to time

Co

eff

icie

nt

of

the

rma

l e

xp

an

sio

n (

1/°

C)

0.000070

Variable Constant

Time (hour)

24181260

0.000060

0.000050

0.000040

0.000030

0.000020

0.000010

0

Table 2 Mechanical properties

Material propertyValue

Concrete Foundation

Final elastic modulus 21 GPa 22 GPa

Characteristic cylinder strength 20 MPa …………

Elastic modulus Variable Constant

Poisson’s Ratio Variable (asymptote value = 0.16) 0.3


Building on the computed transient

temperature field from the similar solver in

Part I of this two-part paper, stress analysis

was performed on the same mesh, and

the converged stress–strain fields were

achieved via some iterative solution of

Cauchy equilibrium equations. The time

step of the Cauchy equation formulation

was used for the iterative solution of the

equilibrium equation at each desired time

step of the thermal analysis. The thermal

stresses were computed using the previously

computed displacements and the thermal

strains which had been accumulatively

calculated from the results of performed

thermal analyses between the two sequen-

tial stress-strain computation stages. In

addition, dam wall and foundation geometry

were not considered integrated anymore,

so the mechanical contact was considered

at concrete-rock foundation interface to

achieve more realistic simulations of stain-

stress fields in this area. The accuracy of

the developed model was evaluated by

the comparison of thermal stress analysis

numerical results of a clamped plane, which

was exposed to constant temperature

(constant mechanical properties), with the

results of finite element-based ALGOR

software. The calculated results correlated

well with the finite element results. Then

the applicability of the developed numerical

solver was demonstrated by the simulation

of the transient stress-strain field during

the gradual construction of a concrete dam

wall on a natural foundation. The numerical

computations were performed for a typi-

cal mass concrete structure on a natural

foundation for the variable mechanical

properties. The simulation results showed

that significant tensile stresses may develop

at the concrete surfaces due to the severe

temperature gradient.

The thermal stress module of the NASIR

Galerkin finite volume solver can be used

as a helpful simulation tool to predict the

thermal stresses of the multi-layer construc-

tion programme of a mass concrete struc-

ture considering the variable mechanical

properties.

NOTATION SECTION

bi : Body force

ρ : Material density

üi : Acceleration of body

D : Stiffness matrix

εEth : External thermal strain

α : Coefficient of thermal expansion

Ttn : Temperature of node n at time t

F→

i : Stress vector in the direction

Ω : Subdomain

φ : Test function

(un)it+Δt : Displacement of node n at k itera-

tion number

ΩE : Area of the triangular element

n : External edges number of control

volume

Ωn : Area of the control volume

Pn : Perimeter of the control volume

C : Speed of information transition

Δtn : Virtual time step of node n

Ec : Ultimate elastic modulus of

concrete

t : Equivalent age of concrete

f ’c : The characteristic cylinder

strength of concrete

a,b : Fit parameters

ϑ : Concrete Poisson’s Ratio

αcon : Degree of concrete hydration

Ec(t) : Elastic modulus of concrete at

time (t)

(Δli)m : The i direction component of the

normal vector of edge m of the

subdomain Ωn

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A new approach to determine autogenous shrinkage

Figure 11 Variation of elastic modulus with respect to concrete ageing

Ela

stic

ity

Mo

du

lus

(GP

a)

20

25

10

15

0

5

Variable Constant

Time (day)

24181260


Figure 12 2D distribution of maximum principle stress for different construction heights (MPa) considering variations of mechanical properties

according to the age of each concrete layer

-0.10

0

0

0

0

0

0

0.1

0.1

0.1

0.1

0.2

0.2

0.30.40.6

-0.1

0

0

00

0.1

0.1

0.1

0.2

0.2 0.2

0.3 0.4

0.40.

5

-0.2

0

0

0.2

0.2

0.2

0.4

0.6

0.8

0

0.2

0.4 0.4

0.8

1

1.2

1.4 S1

1.41.210.80.60.40.20

-0.2

(Mpa)

-0.2

0

0

0

0.2

0.2

0.40.6

0.6

0.8

1.21.4

0

0

0.2

0.2

0.20.4

0.4

0.6

0.6

0.81

1.2

1.4

1.6

(f) Stress field at 120 days(e) Stress field at 100 days

(b) Stress field at 40 days

(d) Stress field at 80 days

(a) Stress field at 20 days

(c) Stress field at 60 days

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

30

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

30

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

30

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

30

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

Y (

m)

X (m)

10

–30

–20

0

–10

–10 403020100

20

50

1.81.6

–0.2–0.4

0.20

0.60.4

1.00.8

1.41.2

S1Mpa

1.21.0

0–0.2

0.40.2

0.80.6

S1Mpa1.41.2

–0.2

0.20

0.60.4

1.00.8

S1Mpa

0.60.5

–0.2–0.3

0–0.1

0.20.1

0.40.3

S1Mpa

1.61.4

0–0.2

0.40.2

0.80.6

1.21.0

S1Mpa

0.60.5

–0.2

0–0.1

0.20.1

0.40.3

S1Mpa


of mortar at an early age considering temperature his-

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321–329.

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Figure 13 Convergence of the results for the computed displacements

Lo

g (

RM

S)

–4

–5

–6

–7

–8

–9

0 0.5 1.51.0 2.0 2.5 3.53.0 4.0

Iterations (millions)

X Direction Y Direction


DISCUSSION


Vol 55 No 1, April 2013, Pages 114–116, Discussion Paper 762-1

Publishing particulars of paper under discussionVol 54 No 1, April 2012, Pages 32–42, Paper 762-1

COMMENT

The paper states the following: “A strongly

cemented layer might show signs of car-

bonation, but the strength of the carbonated

material is still adequate for its use and

purpose in the pavement. This could be

described as ‘non-deleterious’ carbonation

(or simply carbonation), whereas when

carbonation causes the properties of the

material to deteriorate to the extent that the

layer cannot fulfil its intended function it is

known as ‘deleterious’ carbonation, in the

context of this set of papers.” (pp 34–35)

Some of the causes for the formation of

weak interlayers listed in the paper are the

following:

■ Detrimental carbonation of chemically

stabilised layer from below or from sides

after construction. (p 38)

■ Some materials perform well in labora-

tory tests, but have a tendency to form

a soft surface or soft base in the field

(Bergh 1979). (p 38)

■ Weakening due to detrimental car-

bonation, dry out and/or wet-dry cycles is

probably the most common cause of sur-

face weake ning of chemically stabilised

layers. (p 39)

■ Note that in chemical soil stabilisation,

carbonation almost invariably weakens

the stabilised material. (p 39)

■ If a chemically stabilised layer has

been badly cured – even allowed to dry

partially only once – the upper layer has

probably been weakened. (p 39)

■ Most weak layers, interlayers, laminations

and/or interfaces can be prevented by

good construction practices. (p 40)

■ In order to prevent the formation of weak

interlayers the specifications specify the

following:

■ Curing of a chemically stabilised layer

for at least seven days is carefully

specified and it is stated that drying

out or wet-dry cycles may be the cause

for rejection if the layer is damaged

thereby (para 3503(h)). (p 40)

■ No priming shall be carried out on a

base which is visibly wet or which is at

moisture content in excess of 50% of

the OMC (para 4104). (p 40)

■ Before priming, the base shall be

broomed and cleaned of all loose

material (para 4105). (p 40)

■ Asphalt shall not be placed if free

water is present on the working

surface or if the moisture content of

the underlying layer, in the opinion

of the engineer, is too high, or if the

moisture content of the upper 50 mm

of the base exceeds 50% of the OMC

(para 4205(b)). (p 40)

■ Before applying a tack coat or asphalt,

the surface shall be broomed and

cleaned of all loose or deleterious

material (para 4205(c)(ii)). (p 40)

■ Before applying a seal, the moisture

content of the upper 50 mm of base

shall be less than 50% of the OMC

(par 4304(d)(i)). (p 40)

■ Additional precautions may be

required when utilising marginal or

substandard materials (Netterberg et al

1989). (p 40) [These additional precau-

tions are not mentioned in the paper.]

The paper concludes that weak layers,

interlayers and laminations have more than

one cause, but most can be prevented simply

by application of known good construction

practices. (p 41)

From these remarks it is clear that the

paper sees the main cause of ‘deleterious’

carbonation as construction-related and

therefore the contractor’s responsibility.

I would like to refer to Dr P Paige-Green’s

TREMTI paper of 2010 to show that, even if

the true cause of ‘detrimental carbonation’

was the carbonation of the surface layer by

the carbon dioxide in the air, that it is still a

water-driven reaction. Allow me two quotes

from Paige-Greene’s 2010 TREMTI paper:

“During the early 1980s a number of prob-

lems related to the loss of stabilisation and

disintegration of stabilised layers in roads

(lime and cement) were reported in South

Africa. This led to many comprehensive

investigations and it was shown without

any doubt that the problems were related

to carbonation of the stabilised materials.

A paper was presented at the TREMTI

conference in Paris in 2005 indicating

that many of the problems in South Africa

that were attributed to carbonation, were

actually caused by ‘water driven reactions’

and were thus material related and not

construction related. This paper assesses

the fundamental principles of each of the

processes and draws conclusions as to their

likelihood and the increasing occurrence of

stabilisation problems. It is concluded that,

although there is indubitable proven field

and laboratory evidence for carbonation of

stabilised layers, there is no solid scientific

evidence for the occurrence of ‘water driven

reactions’ in soil stabilisation in roads.”

“The carbonation reaction depends on

the solubility and diffusion of the compo-

nents. The diffusion is controlled by the

concentration differences and is an inward

diffusion of CO2 gas and carbonate ions

(Lagerblad 2005). The gas diffusion is much

faster than ion diffusion. Thus the rate of

reaction is controlled by the humidity in the

material, i.e. how much liquid fills the con-

nected pore system. In dry material the CO2

can penetrate well, but there is insufficient

water for the reaction to take place. In the

saturated condition, only the carbonate ions

move and carbonation is slow. Typically, the

reaction is most likely and rapid at humidi-

ties of 40 to 70% (Lo & Lee 2002; Ballim &

Basson 2001; Gjerp & Oppsal 1998).”

However, Ballim & Basson also state that no

carbonation takes place when the pores are

completely dry or when they are fully saturated

and that the rate of carbonation also increases

with increasing ambient temperature (Fulton

2002 p 150). Neither of these conditions is

normally found in chemically stabilised layers.

In actual fact, the moisture regime of the stabi-

lised layer is usually closer to 50% of the OMC

as can be seen from the above quotes.

Encyclopaedia Britanica states:

“The atmosphere is made up of a number

of gases of which water vapour is in

many respects the most important. This

importance arises from the fact that water

vapour is the only constituent of air whose

state changes at the temperatures encoun-

tered in the atmosphere. Water substance

occurs as vapour (invisible), as liquid (fog,

cloud and rain droplets) and as a solid (ice

crystals, hail and snowflakes). The subject

Weak interlayers in fl exible and semi-fl exible road pavements: Part 1

F Netterberg, M de Beer


of atmospheric humidity deals only with

water in its vapour state.”

Relative humidity gives the amount of water

vapour present in a volume of air as a per-

centage of the maximum possible amount

of water vapour in that volume at the same

temperature. The relative humidity depends

on the temperature, as well as the water

vapour content.

Wikipedia states the following about the

effect of carbonation on phenolphthalein:

“The acid-base indication abilities of

phenolphthalein also make it useful for

testing for signs of carbonation reactions in

concrete. Concrete has naturally high pH

due to the calcium hydroxide formed when

Portland cement reacts with water. The

pH of the ionic water solution present in

the pores of fresh concrete may be over 14.

Normal carbonation of concrete occurs as

the cement hydration products in concrete

react with carbon dioxide in the atmo-

sphere, and can reduce the pH to 8½ – 9,

although that reaction usually is restricted

to a thin layer at the surface. When a 1%

phenolphthalein solution is applied to

normal concrete it will turn bright pink. If

the concrete has undergone carbonation,

no colour change will be observed.”

Therefore, the carbonation of cement-

stabilised layers cannot take place without a

certain amount of water vapour being present.

Therefore it is a water-driven or water-

activated reaction. However, the pink colour

of the phenolphthalein on the loose powdery

interlayer shows that the cement-stabilised

layer is not carbonated. Furthermore, the

contractor has no permanent control over the

moisture regime in the stabilised layer, which

is specified to be close to 50% OMC and thus

in the active carbonation humidity range.

Therefore the problem is material related.

The fact that performance of the stabi-

lised material on site sometimes differs from

the performance in the laboratory is due to

the fact that laboratory design tests pres-

ently do not simulate specified construction

conditions on site. It is not possible for the

contractor to simulate laboratory conditions

on site during construction. The laboratory

tests should simulate site constraints.

Dr CJ Semelink

[email protected]

RESPONSE FROM AUTHORS

The additional precautions which may be

required when utilising marginal or substan-

dard materials were discussed by Netterberg

et al (1989) referred to in our paper.

Carbonation is inevitable in the long term

as both Portland-type cements and lime are

unstable, both under normal atmospheric

conditions and those in the road and soil.

However, it can be prevented or delayed in

engineering time by means of suitable design,

e.g. a sufficiently high stabiliser content and/

or a high density (used as a proxy for low

permeability to air) and construction precau-

tions, e.g. good stabiliser control, compac-

tion and curing. Obviously, only the latter

aspects are under the contractor’s control

and therefore his responsibility. Most of these

factors are specified and/or regarded as good

engineering practice. The prevention of ‘del-

eterious’ carbonation is thus the responsibility

of both the designer and the contractor.

It is correct that carbonation is most rapid

under conditions of intermediate humidity of

about 40 – 70% and very slow under very dry

or saturated conditions, and in that sense it

does require water, as do many other chemical

reactions. However, it is driven more by the

difference between the partial pressure of

carbon dioxide in the atmosphere, pavement

air or soil air, and that in the stabilised layer

and only requires water vapour or minute

amounts of water as a carrier. During curing

the upper part of the layer is exposed to the

humidity of the atmosphere when it is allowed

to dry, as is often the case. As southern African

conditions are usually warm and at such

intermediate humidities, they are in fact often

at an optimum for carbonation. Moreover, it

has been shown that carbonation is accelerated

by wet-dry cycles, which are worse than doing

nothing (Netterberg et al 1987).

If the upper base dries to 50% of

MAASHO OMC before priming, and to

less than this before sealing, the whole base

will not necessarily remain exactly at this,

but will in time equilibrate to something of

this order – on average about 0.6 OMC in

the base as a whole and 0.75 OMC in the

sub-base (Emery 1992). Whilst published

(Netterberg &Haupt 2003) and unpublished

measurements of suction and humidity show

that the relative humidity in the base as a

whole is mostly over 99%, this varies during

the daily temperature cycle and can be much

lower in the upper base. The combination

of suitable and varying humidities and high

temperatures in the base, but probably

especially the high partial pressures of

CO2 in the underlying layers and roadbed

air – which latter can easily exceed 10 or 20

times that of the atmosphere – constitute

an environment suitable for carbonation in

the medium to long term (e.g. Netterberg

1987, 1991; Sampson et al 1987). In spite of

the apparently unfavourably high average

humidity in the pavement layers, it has been

known since at least 1984 that complete

carbonation of a lime or cement-stabilised

pavement layer from the bottom upwards

can occur (Netterberg 1987, 1991; Sampson

et al 1987; Paige-Green et al 1990).

Contrary to Dr Semmelink’s opinion

then, the conditions in a pavement are actu-

ally conducive to carbonation and, as the

above-mentioned authors have shown, it

does indeed occur and it does also weaken

the layer. However, it does not always lead

to distress or failure of the pavement, and in

this sense only is not always deleterious.

Regarding the phenolphthalein test, it is

important to note that a deep red (or purple)

only indicates a pH of more than about 10 and

that phenolphthalein starts to turn pink at a

pH of about 8.3, is pale pink by 8.5 and a dark

pink or light red by 9. A pink colour therefore

only indicates the presence of very little (prob-

ably less than about 0.2%) lime or cement, and

a deep red more than about 1%, whereas only

a pH of more than about 12.4 can be taken as

indicating the more or less complete absence

of carbonation. This is a very old test, and

Netterberg’s (1984) main contribution was to

use diluted hydrochloric to confirm that the

stabiliser had indeed been added and that it

was therefore carbonation.

A pink – and in some cases even a red

– colour therefore usually indicates either

partial carbonation or that very little stabi-

liser was present in the first place, the acid

test usually providing the answer.These tests

are of course only indicative and qualitative,

and a chemical or mineralogical analysis is

required for confirmation and quantitative

determination of the degree of carbonation.

Whilst it is correct to say that the contrac-

tor has no permanent control over the moisture

regime, it is only specified to be less than 50%

of OMC in the upper 50 mm of the layer before

sealing. Fifty percent of OMC does not equate

to a relative humidity of 50% – in fact it is likely

to be much higher than this, but is dependent

on the material, as well as other factors.

Premature drying out is of course deleterious

in the sense that it both promotes carbonation

and prevents hydration of the cement. In this

case there may be a conflict between the speci-

fication requirement to dry out and the need to

keep it moist to promote proper curing.

However, it is only correct to state that

the problem is material related insofar as the

material properties affect the equilibrium

moisture content, compactability and perme-

ability. It is also only correct to state that

some laboratory design tests (such as UCS)

do not simulate site conditions, as these are

simulated by the wet-dry test (wet-dry cycles

and, effectively, surface carbonation) and the

UCS and PI tests before and after accelerated,

complete carbonation of the whole briquette.

Dr Frank Netterberg Dr Morris de Beer

[email protected] [email protected]


COMMENT

I was very interested to read this useful con-

tribution to the practical aspects of concret-

ing on site, specifically for bored piles. The

information given is very helpful in assessing

the influence of ingressing water into such

pile holes during concreting operations, and I

would like to commend the authors on their

contribution.

It reminds me of a case I dealt with about

30 years ago, on exactly the same problem.

Unfortunately we did not have this paper

to refer to then, because it could have saved

quite some difficulties. The case involved a

series of deep (20 m) bored piles for a very

large cement silo. I was privileged to work

with the late Dr Ross Parry-Davies on the

problem–I as a young and somewhat green

engineer and academic, he as an already

well-experienced and knowledgeable geo-

technical engineer of substantial reputation.

There had been a lot of water ingress

into some of the pile holes before and dur-

ing concreting. While the piling contractor

had taken all the necessary precautions,

there was concern that the water may have

compromised the integrity of the piles.

Consequently, cores were taken through the

full depth of some piles. The appearance

of the cores was remarkably similar to the

photographs given in the cited paper. It was

obvious that water had created lenses in the

concrete at certain points.

The client and his engineer were of

the opinion that the contractor had been

negligent in the piling operation. It was our

contention that all reasonable precautions

had been taken, but that in spite of these, the

ingressing water had caused problems in the

piles – problems that would have been very

difficult to avoid. I recall having to defend

my theory of how the ingressing water had

affected the piles before a very critical and

somewhat caustic senior engineer, which

was certainly intimidating! After consider-

able argument, the client and the engineer

eventually accepted our explanation, and it

was decided to remedy the piles by grouting

of the voids. I am happy to report that the

cement silo has operated quite successfully

for the last 30 years, and continues to do so!

Prof Mark Alexander

[email protected]

The eff ects of placement conditions on the quality of concrete in large-diameter bored piles

G C Fanourakis, P W Day, G R H Grieve

REFERENCES

Emery, S J 1992.The prediction of moisture content

in untreated pavement layersand an application

to design in southern Africa. NTRR, Pretoria:

CSIR, National Institute for Transport and Road

Research.

Netterberg, F 1984. Rapid field test for carbonation of

lime or cement treated materials. NITRR Research

Report RS/2/84, Pretoria: CSIR, National Institute

for Transport and Road Research.

Netterberg, F 1987. Durability of lime and cement

stabilization.NITRR ReportTS/9/87, Pretoria: CSIR,

Revision of July 1987 of TRH 13 Symp.

Netterberg, F 1991. Durability of lime and cement

stabilization. In: Concrete in Pavement Engineering.

Halfway House, South Africa: Portland Cement

Institute.

Netterberg, F, Paige-Green, P, Mehring, K & Von Solms,

C L 1987. Prevention of surface carbonation of lime and

cement stabilized pavement layers by more appropriate

curing techniques. Proceedings, Annual Transportation

Convention (ATC), Pretoria, Paper 4A/X.

Netterberg, F, Van der Vyver, I C & Marais, C P 1989.

Some problems experienced during the construc-

tion of a substandard base course for a very low

volume surfaced road. Proceedings, 5th Conference

on Asphalt Pavements for South Africa, Mbabane,

Session 1X, pp 28–31.

Netterberg, F & Haupt, F J 2003. Diurnal and seasonal

variation of soil suction in five road pavements and

associated pavement response. Proceedings, 13th

Regional Conference for Africa on Geotechnical

Engineering, Marrakech, pp 427–438, Megamix,

Marrakech.

Sampson, L R, Netterberg, F & Poolman, S F 1987. A

full-scale road experiment to evaluate the efficacy

of bituminous membranes for the prevention of

in-service carbonation of lime and cement stabilized

pavement layers. Proceedings, Annual Transportation

Convention (ATC), Paper 4A/IX.

Paige-Green, P, Netterberg, F & Sampson, L R 1990.

The carbonation of chemically stabilised road con-

struction materials: guide to its identification and

treatment. Research Report DPVT 123, Pretoria:

CSIR Division of Roads and Transport Technology.

DISCUSSION


Vol 55 No 1, April 2013, Page 116, Discussion Paper 806

Publishing particulars of paper under discussionVol 54 No 2, October 2012, Pages 86–93, Paper 806

Guidelines for the preparation of papers and technical notes

Authors should comply with the following guidelines when preparing papers for publication in the journal

The Journal of the South African Institution of Civil

Engineering is published biannually in April and October.

Articles submitted for publication are reviewed by a panel

of referees under the guidance of the SAICE Journal

Editorial Panel, a sub-committee of the SAICE Editorial

Panel. When preparing articles for publication, authors

should please take note of the following and comply with

the guidelines as set out:

CLASSIFICATION OF ARTICLES CONSIDERED FOR PUBLICATION

■ Technical papers are well-researched, in-depth, fully

referenced technical articles not exceeding 6 000

words in length (excluding tables and illustrations).

Related papers that deal with ‘softer sciences’ (e.g.

education, social upliftment, etc) are accepted if they

are of a technical nature and of particular interest

to the civil engineering profession. The latter type

of paper will be subject not only to peer-review by

civil engineers, but also to review by non-engineering

specialists in the field covered by the paper.

■ Technical notes are short, fully referenced technical

articles that do not exceed 2 000 words. A typical

technical note will have limited scope often dealing

with a single technical issue of particular importance

to civil engineering. An article incorrectly submitted

as a technical paper can, with the author’s agreement,

be re-categorised by the Panel as a technical note.

Alternatively, on recommendation by the appointed

referees, the Panel may request an author to condense

a technical paper into a technical note.

■ Reviews and case studies are considered for publica-

tion as either technical papers or technical notes on

condition that they are the original work of the author

and will assist the reader with the understanding,

interpreting or applying of the subject under review.

■ Discussion on published articles is welcomed up to

six months after publication. The length of discus-

sion contributions is limited to 1 500 words. Where

appropriate, discussion contributions will be subject

to the normal reviewing process and will be for-

warded to the authors of the original article for reply.

POLICY REGARDING LANGUAGE AND ORIGINALITY OF SUBMITTED ARTICLES

■ Language: Manuscripts should preferably be

presented in English, as the journal is distributed

internationally. Articles submitted in any of the other

official South African languages should be accompa-

nied by an expanded abstract in English.

■ Original work: Papers and technical notes must

be original contributions. Authors must affirm that

submitted material has not been published previously,

is not under consideration for publication elsewhere

and will not be submitted elsewhere while under

consideration by the SAICE Journal Editorial Panel. It

is the responsibility of the authors to ensure that pub-

lication of any paper in the journal will not constitute

a breach of any agreement or the transgression of any

law. The corresponding author should confirm that

all co-authors have read and approved the manuscript

and accept these conditions. Authors are responsible

for obtaining permission to publish experimental data

and other information that may be confidential or

sensitive. Authors are also responsible for obtaining

permission from copyright owners when reproducing

material that had been published elsewhere.

SUBMISSION PROCEDURES AND REQUIRED FORMAT

■ Hard copies: Hard copies should only be submitted

if the author is unable to submit electronically, for

whatever reason. In such a case only one unstapled

copy, together with an electronic copy on CD, should

be posted to the Chief Executive Officer of SAICE,

Private Bag X200, Halfway House, 1685, or delivered

to Building 19, Thornhill Office Park, Bekker Street,

Midrand. Hard copies should be printed on one side

of A4 paper.

■ Electronic submission: Manuscripts should be

e-mailed to the editor at [email protected]. File

sizes should preferably not exceed 3 MB per e-mail

– figures may for example be sent one by one or in

groups not larger than 3 MB. Manuscripts should

not be sent in PDF format as this precludes review-

ing of papers per track changes.

■ Format: Manuscripts should be prepared in MS

Word and presented in double line spacing, single

column layout with 25 mm wide margins. All pages

should bear the authors’ names and be numbered at

the bottom of the page. With the exception of tables

and figures (see below) the document should be

typed in Times New Roman 12 pt font. Contributions

should be accompanied by an abstract of not more

than 200 words and a profile not exceeding 100

words on each of the authors.

■ First page: The first page of the manuscript

should include the title of the paper, the initials

and surnames of the authors, professional status

(if applicable), SAICE affiliation (Member, Fellow,

Visitor, etc), telephone and fax numbers, and e-mail

and postal addresses. The name of the corresponding

author should be underlined. Five keywords should

be suggested. The copy must not contain instructions

to the editor.

■ Figures, tables, photos and illustrations: These

should preferably be submitted in colour, as the jour-

nal is a full-colour publication. Figures, tables, photos

and illustrations, complete with captions, should be

placed on separate pages at the end of the text. Their

positions should be clearly marked in the text as fol-

lows: [Insert figure 1].

Captions for tables should appear above the table.

All other captions should appear below the illustra-

tion (figures, graphs, photos).

Only those figures and photographs essential to

the understanding of the text should be included. All

illustrations should be referred to in the text. Original

prints of photographs are required. Alternatively

photos should be scanned at 300 dpi minimum and

submitted as separate files in JPEG (.jpg) format. Care

should be taken not to damage photos by writing on

the back or using paper clips. Illustrations will not be

returned after publication, unless arrangements are

made.

The final paper will be typeset in a three column

format. Figures and tables should be 52 mm, 115 mm

or 176 mm wide – to fit across one, two or three

columns respectively. The maximum height of any

figure or table should not exceed 250 mm including

the caption.

Tables should be typed in Times New Roman

9 pt font. They should not duplicate information

already given in the text, nor contain material that

would be better presented graphically. Tabular mat-

ter should be as simple as possible, with brief column

headings and a minimum number of columns.

Tables, figures and equations should be num-

bered consecutively and should appear in the text

directly after they have been referred to for the first

time.

Figures should be produced using computer

graphics. They should be submitted as separate files

in JPEG (.jpg) format and not embedded in the text

document. Lettering on figures should be equivalent

to a Times New Roman 9 pt font or slightly larger

(up to 12 pt) if desired. Lettering smaller than 9 pt

is not acceptable. Hand-drafted figures will not be

accepted.

■ Mathematical expressions: Equations should be

presented in a clear form which can be easily read

by non-mathematicians. Symbols should be typed

using the Times New Roman symbol set. Equations

should be in italics. Each equation should appear on a

separate line and be numbered consecutively.

Symbols should preferably be defined in the

text, but if this is not feasible, a list of notations may

be provided for inclusion at the end of the paper.

Symbols should conform to accepted interna-

tional usage. The SI system of units should be used.

Decimal commas may be used, but decimal points

are preferred.

Since mathematical formulae are generally

scanned in during the production process, they

should be set out as they are to appear in the printed

paper.

■ Headings: Sections and paragraphs should not be

numbered. The following hierarchy of headings

should be followed:

HEADING OF MAIN SECTION

Heading of subsection

Heading of sub-subsection

■ References: References should follow the Harvard

system. The format of text citations should be as

follows: ‘Jones (1999) discovered that …’ or ‘recent

results (Brown & Carter 1985; Green et al 1999)

indicated that …’

References cited in the text should be listed in

alphabetical order at the end of the paper. References

by the same author should be in chronological order.

The following are examples of a journal article, a

book and a conference paper:

■ Donald, A W 1954. Pore pressure coefficients.

Géotechnique, 4(4):143–147.

■ Terzaghi, K 1943. Practical soil mechanics. New

York: Wiley.

■ Smith, A W, Black, C & White, A 1999. Factors

affecting the strength of soils. Proceedings, ASCE

Conference on Shear Strength of Soils, Colorado,

pp 503–532.

■ Footnotes, trade names, acronyms, abbreviations:

These should be avoided. If acronyms are used, they

should be defined when they first appear in the text.

Do not use full stops after abbreviations or acronyms.

FINAL ARTICLE ■ Copyright: On acceptance of the paper or technical

note, copyright must be transferred by the author to

the South African Institution of Civil Engineering on

the form that will be provided by the Institution.

■ Photos of authors: The final corrected version of

the paper should be accompanied by recent head and

shoulders colour photographs of the authors.

■ Proofs: First proofs of papers will be sent to authors

in PDF format for verification before publication.

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