hydrologic and morphometric analysis of ofu river sub

ALFA et al: HYDROLOGIC AND MORPHOMETRIC ANALYSIS OF OFU RIVER SUB-BASIN 49

*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1

ABSTRACT: The morphometric characteristics of a river basin are very important factors in watershed hydrology.

The morphometric analysis of the Ofu River sub-basin was carried out in this study to assess its morphologic and

hydrological characteristics as well as its flood potentials based on the morphological characteristics. The study was

carried out using remotely sensed spatial data analysed using Geographical Information Systems (GIS). The

morphometric parameters analysed were the areal, linear, and relief aspects of the sub-basin. The results showed that

Ofu river sub-basin covers a total area of 1604.56 km2 and a perimeter of 556.98 km covering parts of Kogi and

Enugu States in Nigeria. The sub-basin has 3rd order river network based on the Strahler’s classification with a

dendritic drainage pattern and moderate drainage texture. The values of bifurcation ratio, drainage density,

circularity ratio, elongation ratio, form factor, stream frequency and drainage intensity indicate that the sub-basin is

elongated and would produce a flatter peak of direct runoff for a longer duration implying that the sub-basin is

morphometrically less susceptible to flood and that any flood flow that may emanate from it would be easy to

manage.

KEYWORDS: Delineation, GIS, Morphometric analysis, Ofu river sub-basin, Remote sensing.

[Received December 31, 2017; Revised July 01, 2018; Accepted October 01, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

Morphometric analysis of a river basin refers to the

measurement and mathematical evaluation of the surface,

shape and dimension of its landform (Agarwal, 1998; Obi et

al., 2002; Kulkarni, 2015). The morphometric characteristics

of a river basin are very important factors in watershed

hydrology. They reflect the hydrological behaviour of the

river basin and are useful in evaluating the hydrologic

response of the basin. There are relationships between river

basin morphometric parameters and flood potential. For

instance, higher drainage density indicates faster runoff and a

more significant degree of channel abrasion for a given

quantity of rainfall (Withanage et al., 2014). Rivers and

fluvial processes are the most dominant geomorphic systems

of earth’s surface responsible for morphometric changes in

drainage basin or the watershed (Horton, 1945). Sapkale

(2013), in buttressing this stated that the geological nature of

basin and its landform generally controls the river, influence

the channel slope and reveals possibilities of erosion and

depositions of the river.

Quantitative morphometric analysis of a river basin

facilitates an understanding of the drainage characteristics

and development, surface runoff generation, infiltration

capacity of the ground as well as groundwater potential

(Ibrampurkar, 2012; Raj and Azeez, 2012).

The systematic description of the geometry of a river

basin and its stream channel requires the measurement of

linear aspects of the drainage network, areal aspects of the

drainage basin, and relief or gradient aspects of the channel

network and contributing ground slopes (Strahler, 1964;

Withanage et al., 2014). Various researchers across the world

have carried out morphometric analysis of various river

basins in different continents of the world. Waikar and

Nilawar (2014) carried out morphometric analysis for the

drainage basin in Charthana, located in Parbhani district of

Maharashtra state in India, extracting linear, areal and relief

aspects of the basin characteristics. The parameters estimated

include stream length, bifurcation ratio, drainage density,

stream frequency, texture ratio, elongation ratio, circularity

ratio and form factor ratio amongst others. Similarly, Raj and

Azeez (2012) carried out morphometric analysis for

Barathapuzha River in Southern India. GIS and remote

sensing tools were used to study the morphometric

characteristics of the basin. They also determined the linear,

areal and relief aspects of the watershed characteristics. They

noted that the Barathapuzha River, the second longest river in

the state of Kerala was a seventh order river formed by

several lower order streams resulting to a dentritic flow

pattern. Similarly, Withanage et al. (2014) carried out

morphometric analysis of the Gal Oya River Basin in Sri

Lanka to assess its hydrological characteristics and flood

potentials based on the morphological characteristics. They

Hydrologic and Morphometric Analysis of Ofu

River Sub-Basin using Remote Sensing and

Geographic Information System M. I. Alfa1*, M. A. Ajibike2, D. B. Adie2, O. J. Mudiare3 1Department of Civil Engineering, University of Jos, Jos, Nigeria.

2Department of Water Resources & Environmental Engineering, Ahmadu Bello University, Zaria, Nigeria. 3Department of Agricultural & Bioresource Engineering, Ahmadu Bello University, Zaria, Nigeria.

mailto:[email protected]

50 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019


utilized spatial data obtained from Geographical Information

Systems (GIS) to estimate the linear, areal and relief aspects

of the basin characteristics. They noted that the Gal Oya

River was a 6th order river network following the Strahler’s

classification with a dendritic drainage pattern and moderate

drainage texture. Martins and Gadiga (2015) also carried out

morphometric analysis of upper Yedzaram catchment of

Mubi in Adamawa State, Nigeria using Geographic

Information System (GIS). The study focused on the

hydrological and geometrical analysis with emphasis on the

linear and areal morphometric characteristics of the

catchment.

Morphometric analysis of Ofu River sub-basin became

necessary to form a basis for the detailed assessment of the

flood hazard, vulnerability and risk within the catchment.

This will also provide a sound basis for the management of

the watershed for optimum development of the resources

within it. The morphometric analysis of the Ofu River sub-

basin was carried out in this study to assess its morphologic

and hydrological characteristics as well as its flood potentials

based on the morphological characteristics.

II. MATERIALS AND METHODS

A. The Study Area

Ofu River sub-basin lies between latitudes 6o 46ˈ 48.38ˈˈ

N and 7o 38ˈ 31.2ˈˈ N and longitudes 6o 42ˈ 43.56ˈˈ E and 7o

20ˈ 54.6ˈˈ E covering parts of Dekina, Ofu, Igalamela/Odolu,

Idah and Ibaji Local Government Areas in Kogi State and

Uzo-Uwani Local Government Area in Enugu State, Nigeria

(Fig. 1), within the humid tropical rain forest of Nigeria. It

falls within the Lower Benue River Basin Development

Authority in North Central Nigeria. Rainfall within the

catchment is concentrated in one season lasting from

April/May to September/October. The main river within the

sub-basin (Ofu) is perennial and parallel in pattern to Imabolo

and Okura rivers which are close to the study area. It took its

root from Ojofu, in Dekina Local Government area in Kogi

State flowing in the eastward direction with a catchment area

amounting to about 1,604 km2 most of which is covered by

dense forest. Okura River joined Imabolo River in Egabada

(Kogi State) and further flow southwards before joining the

Ofu River and the ‘three-in-one’ river empties into the

famous Anambra River in Anambra State (Gideon et al.,

2013).

B. Delineation of Ofu River Watershed

The delineation of Ofu River Catchment was carried out

using the Shuttle Radar Topographic Mission Digital

Elevation Model (SRTM-DEM) version 3 and the drainage

network extracted from the River map of Africa. The pre-

processing was done using ArcHydro extension in ArcGIS

10.2.2 while the actual delineation was done using HEC-

GeoHMS extension in ArcGIS 10.2.2 with the DEM and

drainage network as input.

C. Estimation of Morphometric Parameters

Areal characteristics such as basin area, perimeter,

longest flow path and main stream length were extracted from

the attribute tables of the sub-basin and the main river in

ArcGIS while the other parameters were estimated using the

respective equations developed previously as shown in Tables

1-3.

III. RESULTS AND DISCUSSION

The boundaries of Ofu River catchment delineated in this

study using remote sensing and GIS is shown in Fig.2. The

figure shows the basic areal characteristics of the catchment.

Fig. 1: Map of Study Area Source: Adapted from the

Administrative Map of Nigeria, LOC (n.d); www.nationsonline.org

Fig. 2: Areal Characteristics of Ofu River Catchment.


http://www.nationsonline.org/



Table 1: Methods used for Estimation of Areal Morphometric Parameters.

Parameter Symbol Formula Reference

Area A GIS Analysis - Perimeter P GIS Analysis -

Basin Length Lb GIS Analysis Schumm (1956)

Longest Flow Path Lfp

GIS Analysis -

Main Stream Length SL GIS Analysis -

Basin Centroid Longest Flow Path Lcfp

GIS Analysis -

Elongation ratio Re Re = 2√(A/п)/Lb Schumm (1956)

Circularity ratio Rc R

c = 4пA)/P

2

Miller (1953)

Form factor Ff F

f = A/L

b

2

Horton (1932)

Compactness coefficient Cc C

c = 0.282038P/A

0.5

Horton (1945)

Shape Factor Bs B

s = L

b

2

/A Horton (1932)

Stream frequency F F = ΣNu/A Horton (1945)

Drainage Density Dd D

d = ΣL

u/A Horton (1932; 1945)

Drainage Texture Dt D

t = ΣN

u/P Horton (1945)

Drainage Intensity Id I

d = F/D

d Faniran (1968)

Constant of Channel Maintenance Cm C

m = 1/D

d Strahler (1952)

Length of Overland Flow Lo L

o = 1/2D

d Langbein & Leopold (1964)

Channel Sinuosity Sc S

c = ΣL

u/L

fp Le Roux (1992)

Time of Concentration Tc 𝑇𝑐 = 0.000323𝐿𝑓𝑝

0.77𝑆−0.385 Kirpich (1940)

Time to Recession N 𝑁 = 0.84𝐴0.2 Mustafa & Yusuf, 2012

Table 2: Methods used for Estimation of Linear Morphometric Parameters.


Stream order U GIS Analysis Strahler (1964)

Stream Number Nu GIS Analysis Horton (1945)

Stream Length Lu GIS Analysis Horton (1945)

Mean Stream Length Num

Lum

= Lu

/ Nu

Strahler (1964)

Bifurcation Ratio Rb R

b

= Nu

/Nu+1

Schumm (1956)

Stream Length Ratio RL R

L

= Lu

/ Lu-1

Horton (1945)

Table 3: Methods used for Estimation of Relief Morphometric Parameters.


Basin Relief H H = Z-z Strahler (1957)

Relief Ratio Rh R

h = H/Lb Schumm (1956)

Relative Relief Rhp

Rhp

= H*100/P Melton (1957)

Ruggedness Number RN R

N=D

d×(H/1000) Patton and Baker (1976)

Basin Slope S GIS Analysis -

A. Areal Characteristics of Ofu River Catchment

The areal characteristics of the catchment estimated in

this study are presented in Table 4. The results show that Ofu

River catchment covers a total area of 1,604.56 km2 and is

bounded by a perimeter of 556.98 km. 41.89 % of this area

falls in Dekina LGA, 24.4 % in Ofu LGA, 19.72 % in

Igalamela/Odolu LGA, 0.23 % in Idah LGA and 13.30 % in

Ibaji LGA all in Kogi State while 0.42 % falls in Uzo-Uwani

LGA in Enugu State.

In addition, the percentage of each LGA land mass

drained by Ofu River are 27.02 %, 23.48 %, 14.06 %, 9.25 %,

14.04 % and 0.80 % for Dekina, Ofu, Igalamela/Odolu, Idah,

Ibaji and Uzo-Uwani LGAs respectively. Schumm’s basin

length of Ofu River catchment is 100.93 km. the longest flow

path is 159.14 km while the length of main stream (Ofu

River) is 121.37 km. The basin’s centroid longest flow path is

89.32 km.




Table 5: Morphologic Characteristics of Ofu River Catchment (Linear Aspects)

Stream Order

(U)

Stream

Number (Nu)

Stream Length

(Lu)

Mean Stream Length

(Lum)

Bifurcation Ratio

(Rb)

Stream Length Ratio

(RL)

1 20 98.76 4.94 1.25

2 16 101.17 6.32 5.33 1.02

3 3 41.47 13.82 0.41

ΣNu = 39 ΣLu =241.40 - Av. Rb = 3.29 Av. RL = 0.72

Table 4: Morphometric Characteristics of Ofu River Catchment (Areal

Aspects).

Parameters Symbol Unit Value

Basic Parameters

Area A km2 1604.56

Perimeter P km 556.98 Basin Length Lb km 100.93

Longest Flow Path Lfp km 159.14

Main Stream Length SL km 121.37 Basin Centroid Longest Flow Path Lcfp km 89.32

Derived Parameters

Elongation ratio Re - 0.45 Circularity ratio Rc - 0.07

Form factor Ff - 0.16

Compactness coefficient Cc - 3.92 Shape Factor Bs - 6.35

Stream frequency F km-2 0.11

Drainage Density Dd km/ Km2 0.26

Drainage Texture T km-1 0.31

Drainage Intensity Id km-1 0.42

Constant of Channel Maintenance Cm km2/km 3.90 Length of Overland Flow Lo km 1.95

Channel Sinuosity Sc - 2.59

Time of Concentration Tc Hrs 6.17 Time from peak to Recession N Days 3.68

The results further show that the catchment has an

elongation ratio of 0.45, circularity ratio of 0.07, form factor

of 0.16, compactness coefficient of 3.92 and a shape factor of

6.35. More so, the stream frequency of the catchment is 0.11

km-1 while the drainage density is 0.26 km/km2. The drainage

texture is 0.31 km-1, the drainage intensity 0.42 km-1, while

the constant of channel maintenance is 3.90 km2/km. Finally,

the length of overland flow is 1.95 km, and the channel

sinuosity is 2.59 while the time of concentration and time

from peak to recession were 6.17 hours and 3.68 days

respectively implying that while it will take a drop of water

6.17 hours to flow from the remotest part of the catchment to

get to the outlet, it will take approximately four days for flood

water to recede after peak.

The low value of Drainage density (Dd) of 0.29 km/km2

indicates that the catchment has highly permeable subsoil and

thick vegetative cover. In addition, the low Circularity ratio

(Rc) of 0.07 obtained also indicates that as the catchment is

almost elongated in shape, it has a low discharge rate of

runoff and highly permeable subsoil conditions. More so, the

low elongation ratio (Re) of 0.45 and Form factor (Ff) of 0.16

confirm that the basin is elongated and thus the basin has a

flatter peak with a longer duration.

The lower values of Stream frequency (Fs) and Drainage

intensity (Id) values further confirm that the surface runoff is

not quickly removed from the river basin. The results reveal

that the basin is well capable of absorbing water into the soil

and recharging groundwater while reducing the risk of

flooding. If such floods happen, they could be managed easily

from this type of elongated Catchments than from circular

basins. The results of the areal morphologic characteristics

show that Ofu river catchment is inherently and

morphometrically capable of reducing the flood risk but

sustainable management plans should be made in advance to

cope with the potential floods that can occur due to high

rainfalls as has been the case with the low lying flood plains

for years.

B. Linear Morphometric Characteristics of Ofu River

Catchment

The analyzed drainage network of the Ofu river

catchment is presented in Fig. 3 while the linear aspects of

the morphometric analysis conducted for the river network

are given in Table 5.

A total of 39 streams are found in Ofu River catchment.

These streams are linked up to the 3rd order spreading over an

area of 1,604.56 km² (Fig. 3). There are a total of 20, 16 and

3 streams of orders 1, 2 and 3, respectively with stream

lengths 98.76 km, 101.17 km and 41.47 km in respective

orders. This small number of streams indicates mature

topography in the catchment (Zaidi, 2011). The mean stream

lengths for order 1, 2 and 3 were, respectively 4.94 km, 6.32

km and 13.82 km. A plot of the respective logarithm of

stream number (Nu), stream length (Lu) and mean stream

length (Lum) versus stream order are presented in Figs.4, 5

and 6.

There was a decrease in stream length (Fig. 5),

respectively with increasing order which agrees with Horton

(1945). The mean stream length (Lum) on the other hand

showed an increase with increasing order (Fig. 6) as

explained by Strahler (1964). These trends agree with those

of previous studies carried out on other similar catchments

(Withanage et al., 2014; Waikar et al., 2014).

Dendritic drainage pattern can be observed in Ofu River

basin (Fig. 3) which is probably the most common drainage

pattern identified in Nigerian river basins and the world at

large. This is a randomly developed, tree-like pattern

composed of branching tributaries and a main stream,

characteristic of essentially flat-lying and/or relatively

homogeneous rocks and impervious soils (Zernitz, 1932).

.




Fig.5: Logarithm of Stream Length (Lu) versus Stream Order (U).

Fig. 6: Logarithm of Mean Stream Length (Lum) versus Stream

Order (U).

Fig. 4: Logarithm of Stream Number (Nu) versus Stream Order (U).

This pattern develops on rocks of uniform resistance which

indicate a complete lack of structural control (Withanage et

al., 2014). It is more likely to be found on nearly horizontal

sedimentary rocks or on areas of massive igneous rocks and

sometimes on complex metamorphosed rocks (Garde, 2006).

Ofu River shares similar geological characteristics with

Ankpa which according to Imasuen et al. (2011) falls within

the Anambra Basin whose genesis has been linked with the

development of the Niger Delta Miogeosyncline and the

opening of the Benue Trough. According to them, the Benue

Trough is underlain by the rocks of Anambra Sedimentary

Basin consisting of the Ajali and Mamu formations.

Furthermore, the bifurcation ratios were 1.25 and 5.33

while the average bifurcation ratio was 3.29. According to

Horton (1945), bifurcation ratio is an index of reliefs and

dissections. The bifurcation ratios were not the same from

one order to the next which according to Strahler, (1964) and

Withanage et al. (2014) is attributable to the geological and

lithological development of the drainage basin. Strahler

(1964) and Nag (1998) stated that lower values of bifurcation

ratios are characteristics of watersheds which have suffered

less structural disturbances. The higher bifurcation ratio of

5.33 obtained for order 2 streams in this present study

indicates that strong structural disturbances have occurred in

the basin when the underlying geological structure underwent

transformations.

In addition to the forgoing, Chorley et al. (1957) noted

that bifurcation ratio could be an index of flood risk level. He

Fig. 3: Strahler’s Stream Order of Ofu River Basin.




Fig. 7: Digital Elevation Model (DEM) of Ofu River Catchment.

stated that the lower the bifurcation ratio, the higher the risk

of flooding, particularly of parts and not the entire basin. This

explains why the flooding within the Ofu River catchments

affects only a part of the basin amongst other factors. The

values of bifurcation ratio (Rb) obtained in this study (1.25

and 5.33), the high average of 3.29 together with the

elongated shape of Ofu River basin would result in a lower

and extended peak flow, which will reduce the risk of

flooding within the basin.

C. Relief Morphologic Characteristics of Ofu River

Catchment

The Digital Elevation Model (DEM) of Ofu River

catchment is shown in Fig.7 while the relief characteristics of

the catchment are presented in Table 6.

The highest and lowest elevations of Ofu River basin are

extracted from the DEM (Fig. 7) were 436 and 11 m above

mean sea level (m asl.), respectively. The Basin relief (H),

Relief ratio (Rh) and Relative relief (Rhp) are 425 m, 0.0042

and 0.0008, respectively while the Ruggedness number and

Basin slope are respectively 0.109 and 0.19. The Relief ratio

according to Schumm (1956) is equal to the tangent of the

angle formed by two planes intersecting at the mouth of the

basin. It is also a measure of the overall steepness of a river

basin which is an indicator of the intensity of erosion process

operating on the slope of the basin.

The Rh value of 0.0042 obtained for Ofu River basin

reveals that the basin is morphometrically less susceptible to

severe erosion. From the reconnaissance survey conducted, it

was observed that the catchment is not affected by serious

erosion characteristic of a major part of Kogi East Senatorial

district. The relief ratio (Rhp) is an important morphometric

variable used for the overall assessment of morphological

characteristics of terrain.

V. CONCLUSION

A quantitative morphometric analysis using remotely

sensed data and GIS has been demonstrated to be a fast,

convenient and effective method of studying the

characteristics of a river basin. Ofu River catchment has a

dendritic drainage pattern showing a 3rdorder stream network

and a total of 39 streams. The high values of bifurcation ratio

reveal that a lower and extended peak flow would result from

the basin which will reduce the risk of flooding. The low

drainage density indicates that the basin has highly permeable

sub-soil and thick vegetative cover. This is further buttressed

by the low circularity ratio, elongation ratio and form factor.

As the basin is elongated in shape, it has a low discharge rate

and highly permeable sub soil conditions. The low values of

stream frequency and drainage intensity further confirm that

the surface runoff is not quickly removed from the basin.

Morphometrically, the basin is well capable of absorbing

water into the soil and recharging groundwater while

reducing the risk of flooding and possibly increasing the risk

of ground water flooding as it is in some parts of the

catchment. If such flood will emerge, it could be managed

easily from this type of elongated basins than from circular

basins by adopting suitable precautionary measures. Although

the studied Ofu river basin is not morphometrically

susceptible to flood, sustainable management plans should be

made in advance to cope with the potential floods that can

occur due to high rainfalls.

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http://www.nationsonline.org/oneworld/map/nigeria-administrative-map.htm

https://www.loc.gov/item/2010592721/



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powder. Oil extraction from the powder seed was carried out using Sohxlet extraction method. The experiment was

designed using Box-Behnken Design approach on three levels, three factors which generated 17 experimental runs.

Independent factors considered were extraction time (X1), solvent volume (X2) and sample weight (X3). The

accuracy of the regression model obtained from the optimization software was determined using the co-efficient of

determination (R2). Results showed the highest oil yield of 17.878% (w/w) was obtained at solvent volume of 200

ml, sample weight of 50 g and extraction time of 55 min, respectively. However, response surface methodology

predicted an oil yield of 17.826% (w/w), while the artificial neural network predicted 17.875% (w/w) at the same

variables condition. The predicted values were validated in triplicate, and an average of 17.46% (w/w) and 17.72%

(w/w) were obtained for RSM and ANN, respectively. The predicted values obtained were well within the range

predicted. The coefficient of determination, which determines the model accuracy, was obtained to be 0.8454 for

RSM and 0.8712 for ANN. Physicochemical analysis of the oil showed the oil is highly unsaturated with high

saponification value and high iodine value. The study concluded that Dacryodes edulis seeds are found to be rich in

oil and the oil can be applicable in industries as raw materials for products formation.

KEYWORDS: Dacryodes edulis seeds, response surface, artificial neural network, optimization, extraction, physicochemical

properties.

[Received April 16, 2018; Revised September 06, 2018; Accepted September 19, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

The use of oil in Industries for production of cosmetic,

biofuel, bio lubricant and other products has become greatly

increase, which has necessitated the needs to search for

alternative source through biomass (Agricultural oilseeds). To

meet up with the needs of the incessant increase in the

demand for oil by both domestic and industries have resulted

in search for using underutilized seeds as sources of oil to

supplement the already current traditional sources of oil

(Ugbogu et al., 2014). In some nation, specifically Nigeria,

different oil crops exist from the largely used and highly-

utilized to under-utilized seed oils that have not been

investigated for their potential uses.

Dacryodes edulis, an annual fruit known as African plum

or African pear or Safou seed is one of the under-utilized seed

oil. It is an indigenous fruit tree in the humid low lands and

plateau regions of West, Central African and Gulf of Guinea

countries. Usually, the trees are grown around homesteads

and flowering always takes place from January to April, with

fruiting season between May and October (Nwosuagwu et al.,

2009). The pear is locally called ’Ube’ among the Igbos in

South eastern part of Nigeria belongs to the family of

Burseraceae and genus Dacryodes (Ogunsuyi, 2015). It has

the qualities of butter apart from the pulp outlook which

contains 48% oil; the overall plantation can produce 7-8

tonnes of oil per hectare.

Generally, the extraction of oil from the seeds can be

achieved via various methods such as mechanical, (Joglekar

and May, 1987; Haidar and Pakshirajah, 2007; Schinas et al.,

2009) pressurized solvent extraction (Mcginely, 1991),

soxhlet extraction (Meher et al., 2006), ultrasonic extraction

(Ramos et al., 2009; Rodríguez et al., 2012), Aqueous

Enzymatic Oil Extraction (AEOE) (Perez-Serradilla et al.,

2002; Pan et al., 2002), stirring and shaking extraction (Kim

et al., 2004) to mention but few. These methods have been

reported used for extraction of vegetable oils and other plant

essential components, each with intrinsic advantages and

shortcomings (Umer et al., 2011). Mechanical pressing is the

oldest and easiest method used widely, but, the oil produced

always with low value. Meanwhile, (Betiku and Adepoju,

Oil Extraction from Butter Fruit (Dacryodes Edulis)

Seeds and its Optimization via Response Surface

and Artificial Neural Network T. F. Adepoju1*, I. O. Esu1, O. A. Olu-Arotiowa2, E. Blessed1

1Chemical/Petrochemical Engineering, Department, Akwa-Ibom, State University, Ikot Akpaden, Nigeria. 2Chemical Engineering, Ladoke Akintola University of Technology, Ogbomosho, Nigeria.

ADEPOJU et al: OIL EXTRACTION FROM BUTTER FRUIT SEEDS AND ITS OPTIMIZATION 57

*(corresponding author) [email protected], [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1

2013) reported the use of supercritical CO2 extraction; the oil

yield obtained was higher than what was obtained from using

solvent extraction and of high purity, but the high operating

and investment costs make this method not suitable to be

used. Solvent extraction has various advantages including

high yield, less turbidity, environmentally friendly and cost

effective (Adepoju et al., 2013; Betiku et al.,2012), which

was why solvent extraction of oil from Jatropha curcus was

carried out by (Kian et al., 2011), while (Umer et al., 2011)

studied the solvent extraction of oil from Moringa oleifera.

Betiku et al. (2012) extracted oil from sorrel seed using

solvent extraction while solvent extraction of oil from

Chrysophyllum albidium oilseeds and its quality

characterization was carried out by (Adepoju et al., 2013). In

another study, Betiku et al. (2012) worked on solvent

extraction of oil from Beniseed (Sesamum indicum) oilseeds.

This work therefore employed the possibility of using

Dacryodes edulis seed for oil production. For modelling and

optimization, response surface methodology (RSM) and

artificial neural network (ANN) were employed so as to

generate the number of experimental runs, determine the

predicted yields, compare the error values, and analyse the

various variable factors responsible for optimum production

of oil so as to increase the process efficiency. Lastly, the

properties of oil were evaluated with a view to determining

its suitability as edible or non-edible oil.


A. Materials

The Dacryodes edulis seeds used in this work was

collected from Ikot Abasi Village in Eket Local Government

of Akwa Ibom State, Nigeria. The seed was washed with

clean water to remove dirt, and open with a sharp stainless

knife to remove the seed from the pulp. The seeds were cut

into small pieces and sundried for 5 days. Finally, the cleaned

seeds were grinded into powder with a Corona grinder. All

the chemicals used in this study are of analytical grades.

B. Methods

1) Experimental design

To optimize the oil extraction from Dacryodes edulis

seeds powder, three level-three factors were considered. Box-

Behnken Design (BBDRSM) was employed which generated

17 experimental runs used to study the effects of selected

factors on oil yield. Table 1 showed the selected factors

which are solvent volume (X1), sample weight (X2) and the

extraction time (X3) and their levels. These factors were also

used for ANN Modeling and optimization. For the coefficient

of the quadratic model of the response fitting, multiple

regressions model was adopted using design expert software

10 version 15.5 (Stat Inc., Tulsa, OK, USA) and Neural

Power _21356. Regression analysis and test of significance

are the computationally intensive process that is best carried

out via statistical software; hence the quality of the fitted

model was evaluated using test of significance and regression

analysis of variance (ANOVA) via Eq. 1. To compare the

results of the model chosen and validate the coefficient of

determination of the experimental result, artificial neural

network (ANN) was incorporated.

𝑅𝐹 = 𝜏0 + ∑ 𝜏𝑖𝑋𝑖

𝑘

𝑖=1

+ ∑ 𝜏𝑖𝑖𝑋𝑖2

𝑘

𝑖=1

+ ∑ 𝜏𝑖𝑗𝑋𝑖𝑋𝑗

𝑘

𝑖<𝑗

+ 𝑒 (1)

where, RF is the response (oil yield), 𝜏0 is the intercept term,

𝜏𝑖, 𝜏𝑖𝑖, 𝜏𝑖𝑗 are the coefficient terms for linear (𝑋𝑖), quadratic

(𝑋𝑖2) and interaction (𝑋𝑖𝑋𝑗), 𝑋𝑖 is the selected factors, 𝑖= 1, 2,

3. Table 1: Factors and their Levels for Box - Behnken Design. Variable Symbol Coded factor levels

-1 0 +1

SV (ml) X1 180 200 220

SW (g) X2 40 50 60

ET (min) X3 50 55 60

SV = Solvent volume, SW = Sample weight, ET= Extraction time

2) Description of oil extraction procedure

Based on the experimental design by Box Behken

Design, seventeen experimental runs were generated and

were carried out. Soxhlet extractor was used for the

extraction process; the powdered sample was weighed and

placed in the extractor through the muslin cloth. N-hexane

was used as organic solvent for extraction. Three level three

factors were considered, the excess n-hexane was recovered

using rotary evaporator, and the yield of the oil was obtained

using Eq. (2).

𝑂𝑖𝑙 𝑦𝑖𝑒𝑙𝑑 (%) =𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑜𝑖𝑙

𝑤𝑒𝑖𝑔ℎ𝑡 𝐷𝑎𝑐𝑟𝑦𝑜𝑑𝑒𝑠 𝑒𝑑𝑢𝑙𝑖𝑠 𝑝𝑜𝑤𝑑𝑒𝑟 𝑢𝑠𝑒𝑑 (2)

3) Physicochemical analysis of the extracted Dacryodes

edulis seed oil

The properties of the oil were evaluated using standard

of AOAC (1997), official methods of analysis and Wij’s

iodine method as described below:

0.52 g of oil sample was dissolved in 10 ml of

cyclohexane. 20 ml of Wij’s solution was added, the stopper

flask was allowed to stand for 30 min in the dark at room

temperature, and 20 ml of 10% potassium iodide solution was

added. The resulting mixture was then titrated with 0.1 M

Na2S2O3 using starch as indicator. Iodine value was calculated

using equation 3.

𝐼𝑜𝑑𝑖𝑛𝑒 𝑉𝑎𝑙𝑢𝑒 = [𝜌𝑜−𝜌] 𝑋 𝑀𝑋12.69

0.26 (3)

where M = concentration of sodium thiosulphate used;

𝜌𝑜 = volume of sodium thiosulphate used as blank; 𝜌 =

volume of sodium thiosulphate used for determination.

4) Variable interactive effects

To study the effects of independent variables on oil yield,

three factors were taking into consideration (Table 1). The

interactive effects of the variables on the oil yield were

considered by allowing for the linear (X1, X2, X3), the

interaction (X1X2, X1X3, X2X3) and the quadratic (X12, X2

2,



Table 3: Test of Significance for All Regression Coefficient Term.

Source Sum of

squares

df Mean

Square

F-

value

p-value

X1 18.23 1 18.23 12.45 0.01617

X2 13.10 1 13.10 13.89 0.0391 X3 16.67 1 16.67 8.96 0.0613

X1X2 12.65 1 12.65 11.76 0.0437

X1X3 3.82 1 3.82 10.13 0.04600 X2X3 4.03 1 4.03 1.20 0.3101

X12 1.49 1 1.49 10.44 0.05277

X22 0.038 1 0.038 0.011 0.9186

X32 14.63 1 14.63 4.35 0.0755

Table 4: Analysis of variance (ANOVA) of regression equation.

Source Sum of

squares

df Mean

Square

F-

value

p-

value

Model 175.16 9 19.46 12.48 0.0122

Residual 23.55 7 3.36

Lack of fit 21.08 3 7.03 11.37 0.199 Pure error 2.47 4 0.62

Correction for

total sum 98.71 16

R2RSM: 84.54% R2

ANN: 87.12%

Table 2: Box-Behnken Experimental Design for Three Independent

Factors.

Std.

run

X1 X2 X3 Oil

yield

%(w/w)

Predicted Residual

RSM ANN RSM ANN

1 1 1 0 13.1102 13.0282 13.129 1.69 0.019236

2 0 0 0 17.8780 17.826 17.875 6.47 0.0030479 3 0 1 1 13.5602 13.5082 12.476 0.40 1.0838

4 0 -1 1 12.6760 12.624 12.476 -0.55 0.19955

5 1 -1 0 9.6400 9.588 9.7187 -1.77 0.078717 6 0 1 -1 8.8878 8.8358 8.9299 -1.85 0.042103

7 -1 0 -1 9.0790 9.027 9.0722 -0.16 0.0067995

8 0 0 0 12.1744 12.1224 12.476 0.55 0.30205 9 0 0 0 9.9718 9.9198 9.958 -2.25 0.013816

10 -1 0 1 11.4024 11.3504 12.476 -8.34 1.074

11 0 0 0 9.4003 9.3483 9.3893 -1.69 0.011029 12 -1 1 0 12.5876 12.5356 12.476 2.25 0.11115

13 1 0 1 8.1188 8.0668 8.5722 -3.29 0.4534

14 1 0 -1 9.2843 9.2323 8.7767 -0.40 0.50758 15 -1 -1 0 14.1445 14.0925 14.151 1.85 0.0062827

16 0 -1 1 11.3265 11.2745 11.305 0.16 0.021387

17 0 0 -1 10.0145 9.9625 10.034 -1.40 0.019628

X32) on the response. The variable interactive effects also lead

to the formation of regression equation (Eq. 1) and explained

vividly how the contour and three-dimensional plots are

obtained.

C. Optimization of Dacryodes edulis Seed Oil Extraction

The important part of any regression analysis is to

determine whether or not the standard assumptions of the

simple linear regression model are satisfied. The relationship

between the response variable (oil yield) and selected

variables (X1; X2; X3) are assumed to be in form of linear,

interactions and quadratic (Eq. 1). To check the model

accuracy and model estimation capabilities, the coefficient of

determination (R2) was determined by estimating these

parameters using Eqns. (4). Their values were used together

to juxtapose the Box Behnken design and genetic algorithm

models by comparing the evaluated values for the models.

𝑅2 = 1 − ∑(∅𝑖,𝑐𝑎𝑙−∅𝑖,𝑒𝑥𝑝)2

(∅𝑎𝑣𝑔,𝑒𝑥𝑝−∅𝑖,𝑒𝑥𝑝)2𝑛𝑖=1 (4)

where ∅𝑖,𝑒𝑥𝑝 is the experimental value, ∅𝑖,𝑐𝑎𝑙 is the

calculated value and ∅𝑎𝑣𝑔,𝑒𝑥𝑝 is the average experimental

value.

IV. RESULTS AND DISCUSSION

D. Optimization of oil extraction

Table 2 depicts the 17 experimental generated, the oil

yield results obtained together with the predicted oil yield and

the residual values. It was observed that the lowest yield

obtained was 8.1188% (w/w) and the predicted values for

RSM and ANN couple with genetic algorithms were 8.0668%

(w/w) and 8.5722% (w/w), respectively. Meanwhile, the

highest yield obtained was 17.8780% (w/w), while the

predicted values for RSM and ANN were 17.726% and

17.876% (w/w), respectively. The predicted values were

validated in triplicate, and an average of 17.46 % (w/w) and

17.72% (w/w) were obtained for RSM and ANN,

respectively.

Table 3 showed the results of test of significance for all

coefficient of regression. The F-values of X1, X2, X1X2 and

X1X3, implies the significant model terms. Values of "Prob >

F" less than 0.0500 indicate model terms are significant.

Table 4 showed the results of the Analysis of Variance

(ANOVA). The analysis of variance is important to test

significance and suitability of the model and to determine

whether the variation from the model is significant when

compared to the variation due to residual error at 95%

confidence level. The “Lack of Fit” compares the residual

error to the pure error from simulated design points. The lack

of fit F-value of 11.37 with p-value 0.199 implies

insignificant lack of fit relative to pure error.

The mathematical expression of the relationship

between oil yield and the variable factors is given by the

model equation 4. All negative values have reduction impact

on the yield while positive values have ability to increase the

yield (Table 5).

OY (%) = +12.48 – 1.01X1 + 1.28X2 – 1.44X3 – 1.78X1 X2

– 0.98X1X3 – 1.00X2X3 – 0.59X12 + 0.095X2

2 – 1.861X32

To test the fit of the model equation, the regression model

was established using R2 as a measure of how much

variability in the observed response values can be explained

by the experimental factors and their interactions (Sudamalla

et al., 2012). The R2 value is always between 0 and 100%

(Haider and Pakshirajah, 2007; Schinas et al.,

2009). However, to create a good-fit model, it was

recommended that R2 should not be less than 80% (Joglekar

and May 1987). The results in Table 4 indicated an R2 value

of 84.54% for RSM and 87.12% for ANN, which leaves only

15.46% and 12.87% of the variability, not explains by oil

yield, this indicates that an unexplainable total variation could

be caused by other factors, which were not included in the

model. Figure 1 shows the relationship between the predicted

plots (RSM and ANN) and the actual experimental oil yield.

A graphical drawing depicts a functional relation

between two or three variables by means of a curve or surface

containing only those points, whose coordinates satisfy



Table 5: Regression Coefficients and Significance of Response

Surface Quadratic

Factor Coefficient

estimate

df Standard

error

95%

CI

Low

95%

CI

High

VIF

Intercept 12.48 1 0.82 10.54 14.42

X1 -1.01 1 0.65 -2.55 0.52 1.00

X2 1.28 1 0.65 -0.25 2.81 1.00 X3 -1.44 1 0.65 -2.98 0.090 1.00

X1X2 -1.78 1 0.92 -3.95 0.39 1.00

X1X3 -0.98 1 0.92 -3.15 1.19 1.00 X2X3 -1.00 1 0.92 -3.17 1.17 1.00

X12 -0.59 1 0.89 -2.71 1.52 1.01

X22 0.095 1 0.89 -2.02 2.21 1.01

X32 -1.86 1 0.89 -3.98 0.25 1.01

Design-Expert® SoftwareFactor Coding: Actual% OY

Design Points17.878

8.1188

X1 = A: SV (ml)X2 = C: ET (min)

Actual FactorB: APSW (g) = 50

180 190 200 210 220

50

52

54

56

58

60% OY

SV (ml)

ET

(m

in)

8

9

10

11

12

125


Design points above predicted valueDesign points below predicted value17.878

8.1188

X1 = A: SV (ml)X2 = C: ET (min)

Actual FactorB: APSW (g) = 50

50

52

54

56

58

60

180

190

200

210

220

6

8

10

12

14

16

18

% O

Y

SV (ml) ET (min)

Fig. 2(a)

the relationship between the response and the experimental

levels of each variable on the one side, and the type of

interactions between the test variables, on the other, which

allows for deducing the optimum conditions. The interaction

effects of solvent volume (SV), sample weight (SW) and

extraction time (ET) on the oil yield were studied using the

contour plots and 3D surface plots of RSM (Figure 2 (a-d)).

From the plots, it was observed that the oil yield increased

with decreases in ET and SV while keeping SW constant at

zero level. The curvature nature of the surface plots in

Figures 2 (b-e) depict mutual interactions between ET and SV

Figures 2 (b-e) depict mutual interactions between ET

and SV on oil yield. It was observed that an increased in SW

and SV favoured the high yield of the oil, while low SV and

low SW reduced the oil yield. Figures 2 (c-f) showed the

interaction between the SW and ET on the yield of oil. It was

also observed that the high SW with low ET produced the

highest oil yield. Further increase in ET reduced the yield of

the oil.

The RSM and ANN plots of contours and the 3 D’s showed

that the highest oil yield was obtained at high SW, low ET

and low SV (Figures 2(b-e & c-f)).

RSM ANN

Figure 1: Actual yield Vs. Predicted values.




17.878

8.1188

X1 = A: SV (ml)X2 = B: APSW (g)

Actual FactorC: ET (min) = 51.3609

40

45

50

55

60

180

190

200

210

220

8

10

12

14

16

18

% O

Y

SV (ml)APSW (g)

12.07612.076


17.878

8.1188

X1 = A: SV (ml)X2 = B: APSW (g)

Actual FactorC: ET (min) = 51.3609

180 190 200 210 220

40

45

50

55

60% OY

SV (ml)

AP

SW

(g

)

10

12

14

Prediction 12.076

Fig. 2(b)


Design Points17.878

8.1188

X1 = B: APSW (g)X2 = C: ET (min)

Actual FactorA: SV (ml) = 180

40 45 50 55 60

50

52

54

56

58

60% OY

APSW (g)

ET

(m

in)

8

10

12

14

16

Prediction 12.076


Design points above predicted valueDesign points below predicted value17.878

8.1188

X1 = B: APSW (g)X2 = C: ET (min)

Actual FactorA: SV (ml) = 180

50

52

54

56

58

60

40

45

50

55

60

6

8

10

12

14

16

18

% O

Y

APSW (g)ET (min)

12.07612.076

Fig. 2(c)

Fig. 2(e)

Fig. 2(d)



Table 6: Physiochemical Properties of oil.

Parameters Values

Physical properties

Absorbance @660oC 2.032

Moisture content (%) 0.04549 Specific gravity 0.9217

Mean Molecular mass 434.008

Viscosity @34.2oC (N.s/m2) 1.282

Chemical Properties

Free Fatty Acid 13.036

Acid Value (mg KOH/g oil) 27.072 Saponification Value (mg KOH/g oil) 129.03

Iodine Value (g I2/100g oil) 78.09

Peroxide Value (meq O2/kg oil) 37.60 Higher Heating Value (MJ/kg) 42.968

Other Properties

Cetane number 71.0299

E. Physiochemical Properties of African Pear Oil (APO)

Table 6 showed the results of the physicochemical

properties of the extracted oil obtained using (AOAC, 1997)

standard methods. The oil obtained was liquid, brownish in

colour with the moisture content of 0.04549% and specific

gravity of 0.9217. The high acid value of 27.072

corresponding to high FFA of 13.036 obtained in this study

indicated the good resistance of the oil to hydrolysis.

Peroxide value measures the content of hydroperoxides in the

oil (Mcginely, 1991) and its high value (37.60 meq.

O2/kg) indicates high resistance to oxidation.

High saponification value of 129.03 mg KOH/g with a

high iodine value of 78.09 gI2/100 g indicated a low

concentration of triglycerides and the oil contained a

substantial level of unsaturation. The high heating value of

42.968 MJ/kg takes into account the latent heat of

vaporization of water in the combustion products. Fuel

properties such as Cetane number, a measure of the fuel’s

ignition delay and combustion quality, and its fuel standard is

a minimum of 40 (Meher et al., 2006; Ramos et al., 2008).

The high value of 71.03 obtained in this study showed the oil

has high fuel potential.

V. CONCLUSION

Dacryodes edulis seeds oil extraction showed the highest

oil yield of 17.878% (w/w) at solvent volume of 200 ml,

sample weight of 50 g and extraction time of 55 min,

respectively. However, response surface methodology

predicted an oil yield of 17.826 % (w/w), while the artificial

neural network predicted 17.875 % (w/w) at the same

variables condition. The predicted values were validated in

triplicate, and an average of 17.46 % (w/w) and 17.72%

(w/w) were obtained for RSM and ANN, respectively. The

predicted values obtained were well within the range

predicted. The coefficient of determination, which determines

the model accuracy, was obtained to be 0.8454 for RSM and

0.8712 for ANN. Physicochemical analysis of the oil showed

the oil is highly unsaturated with high saponification value

and high iodine value.

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http://www.rainwaterharvesting.org/methods/methods.htm

OHIAMBE et al: ASSESSING THE SURFACE RAINWATER HARVESTING POTENTIAL FOR ABUJA, NIGERIA 63


ABSTRACT: This study aimed at assessing the surface rainwater harvesting potential in Abuja as a means of

mitigating the problem of water scarcity. Surface rainwater harvesting potential for the year 2046 was assessed using

Geographical Information System (GIS) and Spatial Multi-criteria Evaluation (MCE). The criteria considered were

annual rainfall, land use/land cover (LULC), slope and soil. The spatial MCE was used to estimate the extent of

surface rainwater harvesting and rank the potential. Analytical Hierarchy Process (AHP) was employed to determine

the priority weights of the criteria which gave; rainfall 55.9%, LULC 26.3%, slope 12.2% and soil 5.7%. A potential

map for surface rainwater harvesting was produced showing moderate, good and excellent with the percentages of

Abuja 10.7, 34.4 and 54.9% respectively. After considering an increased rainfall from (1170 mm-1470 mm) in 2016

to (1230 mm-1910 mm) in 2046, expansion in built-up areas, bare surfaces due to urbanisation and population

growth, the result showed that Abuja will have a minimum of 5.8 billion litres of water harvestable from rainfall per

year which is about 14.8% increase compared to the estimated harvestable quantity for 2016. Therefore, the potential

for surface rainwater harvesting in 2046 is significantly greater than it was in 2016.

KEYWORDS: Surface Rainwater Harvesting Potential, Water Scarcity, Analytical Hierarchy Process, Multi-Criteria

Evaluation.

[Received May 14, 2018; Revised September 07, 2018; Accepted September 27, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

Water is an important resource in every area of life, it is

essential for all aspects of life ranging from agriculture to

commerce, manufacturing and several types of energy

including electrical energy. The existence of humans, animals

and plants is solely dependent on water (Pandey et al., 2003;

Rutherford, 2000). As important as water is, it cannot be

manufactured yet it can be polluted, recycled, desalinated or

treated (Eletta et al., 2018). Even though water is never lost,

different parts of the world are experiencing water scarcity as

a major environmental problem (Mahmoud and Alazba,

2014).

Water scarcity is an inequality of supply in response to

demand for water with respect to existing institutional

arrangements and prices; where demand is excessively high

compared to available water supply; especially if the supply

potential is difficult or expensive to tap (Stratfor, 2018; Food

and Agriculture Organisation, 2010; Kisakye et al., 2018).

Water scarcity can be caused by artificial and natural causes.

The artificial causes are basically human activities and

behavior while natural causes include geographical terrain

and climate (Eletta et al., 2018; Stratfor, 2018). In Nigeria

water scarcity problem is also prominent especially in the

ASAL regions which are situated in the northern part of the

country. However, the water scarcity issue in Abuja is unique

because Abuja is not classified as an ASAL region. In fact,

Abuja actually experiences an average annual rainfall of

about 1100 mm-1600 mm and its temperatures are not as high

as the ASAL regions. But, the population growth in Abuja

has been very rapid within a short period. The population

grew from 107,069 in 1991 to 2,238,800 in 2011 which is

only 20 years and has grown even more to 3,564,100 in 2016.

Urbanization has led to a lateral expansion of the cities which

is leading to a higher demand for water, strain on the existing

water sources and distribution systems. In recent times, both

urban and rural areas in Abuja have suffered from water

scarcity, this is because the rate at which the available water

is consumed is significantly greater than the rate at which the

tapped sources are replenished.

During the Pan-African Conference on Water in Addis

Ababa, 2003, and at the African MDGs on Hunger meeting in

2004, rainwater harvesting was identified as an important

way of meeting the African Water Vision of minimizing

water scarcity and reducing poverty (Maimbo et al., 2005). In

Abuja, since the problem of water scarcity is as a result of an

increase in population and expansion of the cities and towns,

rainwater harvesting would be ideal as it will provide water

close to where it is needed. Rainwater harvesting is the

systematic concentration, collection and storage of rainwater

Assessing the Surface Rainwater Harvesting

Potential for Abuja, Nigeria: A Short-term

Projection E. Ohiambe1*, P. G. Home1, A. O. Coker2, J. Sang1

1Pan African University of Basic Science, Technology and Innovation, Jomo Kenyatta University of

Agriculture & Technology, Nairobi, Kenya. 2Department of Civil Engineering, University of Ibadan, Ibadan, Nigeria.



*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1

Figure 1: Location of Abuja in Nigeria (inset), River Niger and Benue and the rainfall grids in Abuja.

and surface runoff for different uses by linking the collection

area or runoff catchment area with the storage facility or

runoff receiving area (Mbilinyi et al., 2005). Rainwater

harvesting is not a new concept, it is an ancient practice

which can be traced back thousands of years BC. Harvested

rainwater was used for many purposes, including drinking

(both for animals and humans alike), domestics, agricultural,

prevention of environmental issues like minimize risk of

drought ASAL areas, flooding, erosion (Intergovernmental

Panel on Climate Change, 2007). It was also used as a means

for groundwater recharge (Rainwater Harvesting, 2006;

Rutherford, 2000). Rainwater harvesting is being encouraged

and promoted in many countries including China, Brazil,

Australia and India.

In New Delhi and Chennai, India, it is mandatory to have

a rainwater harvesting plan for a building plan to be

approved. Rainwater can be harvested through several

mediums, all of which can be summed into three major

categories; roof tops, surface and in-situ rainwater harvesting

(Gould and Nissen-Peterson, 1999; Maimbo et al., 2005).

Surface rainwater harvesting provides natural soft water

which can serve all non-potable water usages. It involves the

collection of runoff from open surfaces such as roads, home

compounds, hillsides, rocks, open pasture lands, bare grounds

(Gould, 1992; Pacey and Cullis, 1989). It may also include

collecting runoff from water courses and gullies. It is an

intervention that could be implemented almost anywhere and

by anyone; however, it would be better implemented by

governmental bodies so that it can be done in large scales to

collect more water from strategic locations. To harvest

rainwater the climatic conditions of a place should be studied

and understood (Gould and Nissen-Peterson, 1999).

The present climatic condition of Abuja is such that

rainwater harvesting can be implemented effectively.

However, climate change might affect rainfall in Abuja either

positively or negatively. Climate change is a change in the

statistical distribution of weather patterns usually over a

short-term period of at least 30 years (Australian Academy of

Science, 2018). The Global climate change estimates show a

variation in weather patterns but most of the estimates concur

that some areas will have increased precipitation while others

will experience a drought (Kisakye et al., 2018). A short-term

projection of the climate change in Abuja will help to

estimate if the change will affect RWH potential positively or

negatively.

Therefore, the objective of this research was to assess the

surface rainwater harvesting potential in Abuja by

considering the short-term (at least 30 years), in which

significant change in climate and land use/land cover could

occur. The aim is to inform decision makers of an additional

source of water to minimize water scarcity and ultimately

balance the existing imbalance between supply and demand

of water in Abuja. This can be done by assessing and

highlighting potential sites for surface RWH. The selection of

potential areas depends on several factors including climate,

hydrology, topography, soils, socioeconomic criteria even

agronomy as highlighted. Mahmoud and Alazba (2014) citing

Kahinda et al. (2008). Several studies have used different

parameters. Mahmoud and Alazba (2014) used soil texture,

elevation, land use/land cover, slope, rainfall surplus and

potential runoff coefficient to identify in-situ rainwater

harvesting potential in Al-Baha, Saudi Arabia. Kahinda et al.

(2008) used soil texture, soil depth, rainfall, land cover

ecological importance to produce suitability maps for in-field

and ex-field rainwater harvesting.

Multi-Criteria Evaluation (MCE) plays a significant role

in life-problems, at some point almost every organization

from private to public sector are involved in the evaluation of

alternatives in decision making especially with conflicting

criteria (Udezo, 2017). Analytical Hierarchical Process

(AHP) is a MCE tool introduced by Saaty (1980). It is one of

the GIS databased MCE which sums and transforms spatial

data to a result decision (Mahmoud and Alazba, 2014). AHP

is the major decision-making tool employed in this study.

Weighted overlay tool is also another relevant for the

selection of potential sites for surface RWH. The overlay

process produces maps with ranks from 1-5 where 1 is the

lowest and 5 is the highest rank. However, some researchers

have classified these ranks using terms like unsuitable,

suitable, low, high, medium, moderate, poor, excellent

(Mahmoud and Alazba, 2014; Kahinda et al., 2008; Maimbo

et al., 2005).


A. Study Area

Abuja is located in the North Central zone, at the center

of Nigeria just north of the confluence of the Niger and

Benue River with a total land area of 7,315 km2. Abuja, also

known as Federal Capital Territory (FCT) has six local



government areas; Abaji, Bwari, Gwagwalada, Kwali, Kuje

and Abuja Municipal as shown in (Figure 1). Abuja lies

between the range of 300-760 m above sea level, the highest

part of Abuja is in the northeast where there are major peaks

some above 760 m. Abuja has three distinct weather

conditions per annum; a warm, rainy season, a hot dry season

and a short period of harmattan between the rainy and dry

season. The rainy season begins in April till October, with

temperatures reaching about 28-30 C in the day and

temperatures range around 22-23 C at night, the total annual

rainfall is about 1100 mm to 1600 mm making it a potentially

good region for rainwater harvesting. During the dry season,

daytime temperatures can increase to 40 C and night

temperatures sometimes drop to 12 C (Cyblug, 2016).

B. Assessing the RWH Potential of Abuja

The criteria necessary in assessing the potential of RWH

are; rainfall data, land use maps, elevation maps, soil maps

(Maimbo et al., 2005; Mahmoud and Alazba, 2014). To

assess the surface RWH potential in the study area, the

following activities were carried out;

1) Rainfall forecast

The rainfall data is a relevant component in estimating

the rainwater harvesting potential for Abuja, however, in

order to estimate the rainwater harvesting potential for the

range of years 2046-2065, there must be a forecast of the

climatic conditions expected at that time. In this study, the

rainfall forecasted data was directly collected from the World

Bank Climate Change Portal (WBCCP) where the forecasting

had already been done. With the data, a spatial representation

of the rainfall was done on GIS using the Interpolated

Distance Weighted (IDW) which according to Mahmoud and

Alazba (2014) is a suitable method for the spatial

representation of rainfall. The extent was set to fit the study

area and the rainfall grids shown in Figure 1.

2) Slope data

The Shuttle Radar Topography Mission (SRTM) 30m

DEM of the study area was obtained from United State

Geological Survey/National Aeronautics and Space

Administration/Shuttle Radar Topography Mission

(USGS/NASA SRTM). The slope ranges were reclassified

into four (0-5, 5.1-10, 10.1-19 and 19.1-71.9) like

Mahmoud and Alazba (2014) giving a view of the flat,

moderate, steep and hilly regions in the study area using their

rise in degrees. This data is assumed to remain constant and

so was not be projected.

3) Land use/Land cover data

In this study the Landsat imagery was used to create the

land use/land cover (LULC) map for the study area. The

spatial resolution 30m of Landsat imagery is adequate for

vegetative analysis particularly, to identify vegetative cover

(Jonathan et al., 2017). Two scenes of Landsat images from

the Landsat7 and Landsat8 were acquired for the LULC of

the years 2001 and 2016 respectively. These were all

obtained online from the data archive of Global Land Cover

Facility (GLCF) under the United States Geological Survey

(USGS). The images acquired for the use of this study were

cloud free. The land use/land cover maps for the years 2001

and 2016 were created using the maximum likelihood

algorithm for supervised image classification on ERDAS

Imagine 2014 after forming a false color composite with

bands 4, 3 and 2 which are the infrared, red and blue bands

respectively. The image classification gave nine different

classes which helped to assess the changes in land use over

15 years (2001-2016).

4) Land use/land cover projection

LULC is an important component of the study of

rainwater harvesting as stated by Maimob et al. (2005) and

especially for this study because surface rainwater harvesting

technologies are dependent on the different land use and land

cover classifications. In this study, the LULC of the years

2001 and 2016 was used to aid the projection of the LULC

for the year 2046. After creating the LULC maps for 2001

and 2016, the Markov model on IDIRISI change was adopted

to produce the LULC for 2046 and the area occupied by each

LULC was calculated using the area calculator on IDIRISI.

Markov model is a reliable tool for simulating LULC change

in situations where changes and processes in the LULC prove

to be complex to describe (Logsdon, 1996).

A Markov process is one in which the later state of a

system can be defined simply by the immediately preceding

state. This is done by creating a transition probability matrix

for LULC change from one time to the next time. It shows the

characteristics of the change as well as serves as the

foundation for projecting to a future time-period (Dongjie et

al., 2008; Zhang et al., 2011; Huang et al., 2008; Muller and

Middleton, 1994). Markov model gives a simple

methodology with which a dynamic system can be dissected

and explained. Several researchers like Zhang et al. (2011)

and Jianping et al. (2005) have attested to the efficiency of

the Markov model.

5) Soil data

The soil map for Abuja was obtained from Harmonised

World Soil (HWS) database. There exist five soil types in

Abuja which are loam, sand, loamy sand, sandy clay and

sandy loam as stated by Kogbe (1978). The composite runoff

coefficient for different soil types in relations to slope and

land use was calculated using the information for runoff

coefficient given by Mohamed et al. (2014).

Composite runoff coefficient is given as;

𝐶 =𝐶1𝐴1+ 𝐶2𝐴2+⋯ 𝐶𝑛𝐴𝑛

𝐴𝑡𝑜𝑡𝑎𝑙 (1)

where: C is the composite runoff coefficient

C1 to Cn are the corresponding runoff coefficients for

different landuses, soil type or slope

A1 to An are corresponding areas of different landuses,

soil types or slopes

Atotal is the sum of the areas considered from A1 to An

(Odot Hydraulics Manual)




6) Application of the analytical hierarchical process

(AHP)

The Analytical Hierarchy Process (AHP) developed by

Saaty (1980) is a method used for analyzing and supporting

decisions in which several competing objectives are involved

with multiple available alternatives. The technique was used

on the basis of three principles: decomposition thereby

forming a hierarchy of decision, comparative judgment and

combination of priorities (Saaty, 1980).

The AHP and weighted overlay for assessing the surface

RWH potential was done using Saaty’s pairwise comparison

scale. The hierarchy is the final goal which is to determine

the potential for surface RWH. The next stage in the

hierarchy is the criteria needed to determine the potential. For

this study, the criteria used are rainfall, soil, slope and LULC.

The ranking in this stage helps to reclassify each of the

criteria maps into their different ranks. The advantage of this

hierarchical decomposition is simply to clearly understand the

decisions as well as results to be obtained, the criteria to be

used and the alternatives present (Decision Lens, 2015).

C. Determining Priorities Weight for each Criteria

The rainfall, LULC, slope and soil as determinant criteria

for rainwater harvesting potential are of different importance.

The second step in the AHP process is to determine the

relative weight of each criteria. This is called relative weight

because the derived criteria priorities are measured with

respect to each other.

1) Pairwise comparison for surface RWH

This is the comparison between the criteria used for the

analysis. Table 1 shows the pairwise comparison matrix of

the criteria for surface RWH. The weight of each criterion is

obtained using the normalized matrix generated from Table 1.

The average value of each row in the normalized matrix is the

weight.

The second stage is the calculation for the weight of each

criterion used in the pairwise comparison. It is obtained by

summing up the values in each column, a normalized matrix

is formed by dividing each value in the pairwise comparison

matrix by the total of its column as shown in Table 2.

2) Consistency

Once judgment is made and the criterion weights

obtained, it is important to verify the consistency of the

judgment made. This is illustrated below.

a) Start with the matrix showing the judgment

comparisons and derived weights which is presented in

Table 1.

b) Use the weights as factors (priority) for each column.

c) Multiply each value in the first column of the pairwise

comparison matrix in Table 1 by the first criterion

weight (i.e., 1 x 0.0565 = 0.0565; 3 x 0.0565 = 0.1694;

5 x 0.0565 = 0.2823; 7 x 0.0565 = 0.3952) multiply

each value in the second column with the second

weight; continue this process for all the columns of the

comparison matrix (in our case, we have four

columns).

d) Add the values in each row to obtain a set of values

called the weighted sum

e) Divide the values of the weighted sum vector (obtained

in the previous step) by the corresponding weight of

each criterion. Calculate the average of the values from

the previous step; this value is called λmax.

λmax = (4.0290 + 4.0203 +…4.2109)/4 = 4.1057.

f) Then we calculate the consistency index (CI) as

follows:

CI= (λmax - n) / (n-1) (2)

Where n is the number of compared elements (in

this example n =4).

Consistency index is therefore,

CI= (λmax - n) / (n-1) = (4.1057-4) / (4-1) = 0.0352

g) Now, the Consistency Ratio can be calculated thus:

CR = CI/RI (3)

CR = 0.0352/0.9 = 0.0396

where the Random Index (RI) is 0.89 for n=4

given by Saaty (1980) and Mahmoud & Alazba

(2014).

Since this value (0.0396) for the proportion of

inconsistency CR is less than 0.10, we can assume that our

judgments matrix is reasonably consistent, so we may

continue the process of decision-making using AHP

(Mahmoud and Alazba, 2014).

3) Weighted Overlay Process

The Weighted Overlay Process (WOP) allows the

implementation of several steps in the general overlay

analysis process all in one tool. It combines the following

steps:

a) It reclassifies values in all input raster layers

(rainfall, LULC, slope, soil) into a common

evaluation scale of suitability or preference.

b) It multiplies the values of the cells in each input

raster file by the raster’s weight of importance.

c) It then sums the resulting values of each cell to

produce the final raster file which is the suitability

raster file (Udezo, 2017).

Assuming Point A in the study area of the four criteria

maps used in the AHP example above have a ranking of 5 in

all four maps, (i.e., the rain class as 5, LULC class 5, slope

class 5 and soil class also 5) the overlay result would show

Table 1: Pairwise judgment matrix and weights.

Surface RWH Soil class Slope class LULC class Rain class

Soil class 1 0.33 0.2 0.14

Slope class 3 1 0.33 0.2

LULC class 5 3 1 0.33

Rain class 7 5 3 1

Column addition 16 9.33 4.53 1.67

Table 2: Normalized Matrix.

Surface

RWH

Soil

class

Slope

class

LULC

class

Rain

class

Weight

Soil class 0.0625 0.0354 0.0442 0.0838 0.0565

Slope class 0.1875 0.1072 0.0728 0.1198 0.1218

LULC class 0.3125 0.3215 0.2208 0.1976 0.2631

Rain class 0.4375 0.5359 0.6623 0.5988 0.5586



that exact point to have a suitability of 5 (i.e., soil – 5 x

0.0565 = 0.2823… rain – 5 x 0.5586 = 2.7931). The final

potentiality value is the sum of the resulting values for all

criteria, in our example the suitability of Point A is 5.

The spatial distribution of the suitability map which

shows the surface RWH potential was done using spatial

Multi-criteria evaluation (MCE) to rank. The identification of

suitable sites was considered as a multi-objective and multi-

criteria problem (Mahmoud and Alazba, 2014). The quantity

of rainwater harvestable is given by the formula;

Qa = Ra x A x C (4)

where Qa is the annual harvestable rainwater, Ra is the

annual rainfall, A is the Area and C is the runoff coefficient

(Maimbo et al., 2005).


A. Slope Map

The slope map generated using ArcGIS is presented in

Figure 2. The distribution of the slope for the study area

ranged from 0 – 71.86. This means there are areas with

steepness as low as 0 and hilly areas with steepness as high

as 71.86. Areas with steep slopes would allow for easy flow

of water along the path while water would stagnate around

areas with gentle slopes.

The slope maps were classified from 0 – 5, 5 – 10,

10 – 19 and 19 – 72 (Figure 2). The slope of the area

explains how rapidly water will move during the event of

rains, example areas above 5 will generate runoff quickly

which will increase the potential for surface RWH compared

to areas with slopes less than 5 which will result in the

increase of stagnated water (Mahmoud and Alazba, 2014).

B. Soil Map

The soil data for Abuja collected from Harmonised

World Soil (HWS) database showed five soil textural classes

which are clay loam, sand, loamy sand, sandy clay and a

predominant sandy loam as shown in Figure 3. The soil

textures with a higher percentage of sand allows infiltration

therefore has less runoff, while soil textures which limit

infiltration will lead to more runoff.

C. Forecasted Rainfall

The 2046 rainfall map in Figure 4 was created with the

forecasted rainfall data collected from World Bank Climate

Change Portal (WBCCP) for 2046 and the 2016 rainfall map

was created using satellite data from Tropical Rainfall

Measuring Mission (TRMM). They highlight the changes in

the precipitation between 2016 and 2046. In 2046, according

to (WBCCP), the minimum rainfall in Abuja would be about

1225 mm/year and the maximum would be 1908 mm/year.

The rainfall map for 2016 according to the rainfall satellite

data from Tropical Rainfall Measuring Mission (TRMM)

showed the minimum rainfall to be 1170 mm/year and the

maximum was 1470 mm/year.

The forecasted rainfall map in Figure 4 shows 5 different

ranges of the total annual rainfall for 2046 in Abuja. This

shows a more precise spatial view of the rainfall interpolation

in the study area (Maimbo et al., 2005). The global climate

change has made it widely accepted that changes in climate

will lead to intensified drought in some areas while others

would experience excessive rainfall which could lead to

Figure 2: Slope Map for identifying surface RWH potential.

Figure 3: Soil Texture for Abuja.




Figure 4: Abuja Rainfall maps for 2016 and 2046 respectively.

floods (Kisakye, 2018). From Figure 4, it is obvious that in

total there would most likely be an increase of the annual

rainfall in Abuja up till 2046 and beyond which will affect the

surface RWH potential positively.

D. Land use/land cover Map

The LULC map for 2046 signified distinct changes in the

areas occupied by each LULC class as shown in Figure 5 and

Table 3.

The areas occupied by each LULC class differ in size

from one year to another, some continuously increasing like

built-up areas, some decreasing and others varying from one

year to another as illustrated in Table 2. However, for classes

like built-up areas which were seen to be continuously

increasing, the explanation is obvious considering that the

population is increasing massively as a result of birth rate and

urbanization. The forested areas decreased between the years

2001 and 2016 due to deforestation problem in Nigeria and

Abuja specifically (Adeniyi et al., 2014; Mongaby.com 2018)

and so that decrease was reflected in the 2046 projection. The

LULC classes for 2046 is shown in Figure 5, having 9 classes

as the other years with which, it was predicted.

A. Surface rainwater harvesting Potential for 2046

The suitable sites for surface RWH are shown in Figure

6. Three categories were obtained in the surface RWH

potential map, moderate potential, good potential and

excellent potential. These categories were based on

reclassification of each criterion map, the weight of each

criterion and the weighted overlay of the criteria maps with a

minimum ranking of 3.1 and maximum of 5 after the overlay

operation. This means that every area in Abuja has at least

moderate potential (i.e. 3.1 of 5) for surface RWH. The

difference in RWH potential was based on the criteria

considered, rainfall, soil texture, slope and the LULC in the

areas. Some areas had less rainfall with 0 slope, sandy soil

texture and maybe wetlands. The area enclosed by the

moderate potential region was 781.6 km2, the area enclosed

by the sites with good potential was 2513.9 km2 while the

sites with excellent potential enclosed the largest area of

Figure 5: Projected LULC map for Abuja. Figure 6: Surface RWH Suitability Map for 2046.



about 4019.5 km2.

The spatial distribution showed minimum ranking to be

3.1 and maximum 5, this means that the entire study area was

above the average ranking for RWH potential. These areas

were classified as moderate, good and excellent adopting the

classification done by Mahmoud and Alazba (2014). The

percentage area enclosed by each class were estimated to be

about 10.7%, 34.4 and 54.9% respectively; making the whole

of Abuja 100% potentially viable for surface RWH. The

composite runoff coefficients for the suitable, more suitable

and most suitable sites were estimated to be 0.53, 0.62 and

0.72 respectively.

Therefore, quantifying the potential of surface rainwater

harvesting in terms of harvestable rainwater gave 5,840,287

m3 at minimum rainfall and at maximum rainfall 9,247,121

m3. This water can be harvested and used for several

purposes. This quantity shows that Abuja will be harvesting

about 14.8% more at minimum rainfall in 2046 than the

5,087,765 m3 it would have harvested in 2016. Although

every area in Abuja was found to have potential for RWH, a

larger part of Abuja was found to have an excellent potential.

IV. CONCLUSION

Identification of suitable sites for surface rainwater

harvesting is an important step towards minimizing water

scarcity in Abuja, Nigeria. Surface rainwater can be used to

provide water for all non-potable water needs very close to

where it is needed, which will reduce the stress on

distribution systems and stop the over exploitation of existing

and tapped water sources. The study showed within the years

2016 to 2046, the maximum annual rainfall of the state will

increase from 1470 mm to about 1908 mm due to climate

change.

The result showed that from 2016 to 2046, the rainwater

harvesting potential will increase by about 14.8%. Despite the

results of the potential Abuja has for RWH, some other

factors like environmental, socioeconomical and quality

factors need to be carefully considered to improve the

usefulness of these research findings. It is therefore

recommended that further study be carried out on the

environmental impact of RWH and the quality of rainwater in

Abuja.

V. ACKNOWLEDGMENT

The authors acknowledge both the African Union

Commission and Pan African University, Institute for Basic

Science Technology and Innovation (PAUSTI) for their

financial support to the first author towards the completion of

this research.

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ODETOYE et al: PYROLYSIS AND CHARACTERIZATION OF JATROPHA CURCAS SHELL AND SEED COAT 71


ABSTRACT: The utilization of dedicated energy crops and agricultural residues for producing biofuels and bio-oil in

a range of energy conversion technology is attracting more research interests. Pyrolysis is one of such important

thermochemical method for converting lignocellulosic biomass into biofuels. This work investigates the pyrolysis of

residues from a dedicated energy crop, jatropha of Nigerian origin using intermediate pyrolysis. Pyrolysis of

Jatropha biomass residues [Jatropha fruit shells (JFS) and Jatropha seed coat (JSC)] was carried out in a tubular

fixed bed reactor at a temperature of 450oC, using intermediate pyrolysis method. Bio-oils were obtained and

subsequently characterised for their physico-chemical properties. The yields of the resulting bio-oil, biochar and gas

were determined. The compositions of the bio-oils obtained were also determined by gas-chromatography mass

spectrometry (GC-MS) and carbon, hydrogen, nitrogen, sulphur (CHNS) elemental analysis. The main constituents

of the bio-oils obtained from JFS and JSC were acetic acid, guaiacol, 2,6-dimethoxyphenol and phenol. The

empirical formula of the obtained JFS and JSC bio-oils were found to be CH1.77 O0.28 N0.04 and CH2.03 O0.47 N0.04

respectively. The bio-oil samples that were produced from JSC and JFS of Nigerian origin were found suitable for

bio-oil production. Valuable compounds found in the bio-oils indicated potential industrial applications.

KEYWORDS: Jatropha shell, pyrolysis, biomass waste, biofuel, bio-products.

[Received June 29, 2018; Revised September 10, 2018; Accepted October 23, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

The utilization of biomass as alternative renewable

energy source to meet growing energy needs and to reduce

carbon emission, has attracted global attention in recent times

due to its economic potential and environmental concerns

(Titiloye et al., 2013; Odetoye et al., 2014; Aysu et al., 2016;

Thapa et al., 2018). Biomass is an important source of

energy especially in the developing countries (Akinrinola et

al, 2014).

Jatropha curcas is a widely cultivated plant for energy

purpose as it has been regarded as one of the most suitable

feedstocks for biodiesel production (Pambudi et al, 2017).

Extensive studies have been done on the production of

biodiesel from jatropha oil (Ajala et al., 2015; Thapa et al.,

2018), therefore several researches have been extended

towards the utilization of biomass residues generated from

Jatropha fruits and seeds (Biradar et al., 2014; Adinurani,

2015; Kaewpengkrow, 2017; Patel, 2018).

In Nigeria, jatropha has been listed as one of the

potential feedstocks considered for biofuel production and

diversification of the monolithic petroleum-based economy

by the Government (PPRA, 2010, Ohimain, 2013). More so,

jatropha grows locally in Nigeria and the oil yields of up to

53% had been reported for jatropha of Nigerian origin

(Aransiola et al., 2012; Somorin et al., 2017). Subsequently,

large scale cultivation of jatropha has been recently embarked

on by the Nigerian Government to encourage the industrial

application of the seed oil for biodiesel production (Lateef et

al., 2014). Jatropha seed coat and the fruit shell are wastes

generated during the processing of jatropha oil that can be

converted to bio-oil as value added product (Patel et al.,

2018).

One of the effective technologies for converting such

biomass wastes to bio-oil is by pyrolysis, a method which

involves thermal decomposition of the lignocelluosic biomass

waste in the absence of air at high temperatures of about 400 oC (Aysu et al., 2016; Patel et al., 2018). Two main types of

pyrolysis technology widely practiced had been the slow and

fast pyrolysis (Yang et al., 2014; Abu Bakar and Titiloye,

2013). The classification was based on the variation in

heating rate, residence time and the product distribution

(char, bio-oil, gas). Fast pyrolysis involves rapid cooling of

the short-residence-time-heated finely ground biomass to

room temperature so as to obtain higher yield of the liquid

products. Slow pyrolysis which is characterised by longer

residence time, produces higher yield of char. Intermediate

pyrolysis is a recently emerged pyrolysis technology which

offers the opportunity of process integration as extended

involvement of char in the pyrolysis process seems to

Pyrolysis and Characterization of Jatropha Curcas

Shell and Seed Coat T. E. Odetoye1,2*, M.S. Abu Bakar1,3, J. O. Titiloye1,4

1European Bioenergy Research Institute, CEAC, Aston University, Birmingham, B4 7ET, United Kingdom. 2Department of Chemical Engineering, University of Ilorin, PMB 1515, Ilorin, Nigeria.

3Faculty of Integrated Technologies, Universiti Brunei Darussalam, Jalan Tungku Link, Gadong, BE1410,

Negara Brunei Darussalam. 4Chemical & Environmental Engineering, College of Engineering, Swansea University, SA1 8EN, United Kingdom.



improve the bio-oil quality. This is a technology that has

recently been patented by Aston University, the designer of a

Pyroformer, an intermediate pyrolysis reactor (Yang et al.,

2014).

Although several works have been done on pyrolysis of

Jatropha of various origins (Sing et al., 2008; Manurung et

al., 2009; Murata et al., 2011; Wever et al., 2012), there is

dearth of report about bio-oil production from Jatropha

wastes of Nigerian origin. This study investigates the

suitability of the biomass residues of Jatropha of Nigerian

origin for the production of bio-oil via intermediate pyrolysis.

The intermediate pyrolysis method on a fixed bed reactor was

chosen over fast pyrolysis method because the method is

relatively more affordable for growing economies.

II. MATERIALS AND METHOD

A. Materials preparation

The jatropha fruit shell (JFS) and jatropha seed coat

(JSC) residues were obtained from the matured jatropha fruits

collected at Ilorin, Kwara State, Nigeria. 5 kg of the residues

were sundried for five days and ground using Fritsch blade

heavy-duty cutting mill (USA) fitted with a 2 mm particle

size screen and characterized according to standard methods

as reported in another work (Odetoye et al., 2018).

B. Pyrolysis

The intermediate pyrolysis experimental set up

was as shown in Figure 1. The experiments were carried out

on a bench scale fixed – bed vertical tubular reactor at

reaction temperature of 450 oC. The internal diameter and

height of the quart glass reactor was about 8 cm and 35 cm,

respectively. The reactor was filled with 90 g of JFS or JSC

as required. A Carbolite vertical split furnace was used as a

source of heating while the reactor temperature and pressure

were monitored by AALBORG model DFM digital monitor.

Nitrogen gas flow into the reactor was maintained at a flow

rate of 50 cm3/min. The heating rate of the reactor was 25 oC/min while the residence time was 25 minutes. The primary

condenser was cooled with dry ice to enable the collection of

condensable bio-oil in the oil pot while the non-condensable

gases were scrubbed with isopropanol before sending a

stream of the gases to the GC-MS HP Series 5890 for

analysis. The remaining gases were vented through the fume

cupboard.

The bio-oil yield was obtained considering the oil

entrapped in the glass wares, condensers, by weighing each

part of the glassware apparatus before and after each

pyrolysis experiment since the pyrolysis procedures included

setting up and running the experiment with a good

consideration of mass balance. The mass of the bio-oil,

biogas and biochar produced were accounted for by

measuring the mass of each component of the apparatus

(reactor tube, connecting tubes, and oil pots) before and after

each pyrolysis experiment. The biogas was also accounted for

by difference (Abu Bakar and Titiloye, 2013).

C. Characterization of bio-oil

The bio-oils obtained were characterized to determine the

quality and composition. The following characteristics were

determined: acid number, pH value, density and water

content determinations. Acid number, pH value, density and

water contents were carried out using apparatuses based on

standard methods. The acid number of the oil was determined

using Mettler Toledo acid number analyser G20 Compact

Titrator, which was based on the standard method ASTM

D664-04 (ASTM, 2011) for the determination of acid number

in motor oil while the pH values of the bio-oils were

determined using the Sartorius pH meter model PB-11.

Mettler Toledo PortableLab Densimeter was used to

determine the density of the bio-oil. The water content of the

bio-oil was determined with Karl –Fischer volumetric

titration using a Metrohm 758 KFD Titrino water content

analyser that was based on the standard ASTM method

D1744 (ASTM,2011). The heating values of the bio-oil

samples as well as the elemental analyses of the samples were

carried out by MEDAC Ltd. Surrey, U.K. using standard

method on biomass characterization with Carlo-Erba 1108

elemental analyser. Metals and inorganic components were

also determined using a PerkinElmer Optima 7300DV

Induced Coupled Plasma (ICP) Emission Spectrometer.

The composition of the bio-oils produced were

determined using the Hewlett Packard 5890 Series II Plus

Gas Chromatograph incorporated with a Hewlett Packard

5972 mass selective detector. Helium was used as the carrier

gas with a DB 1706 non-polar capillary column. The initial

oven temperature was 40 °C and ramped up to 290 °C at a

rate of 3 °C/min. The injection temperature was held at 310

°C with a volume of 5µl. The dilution solvent used was

ethanol and the dilution rate was 1:5. Identification of

compounds in the spectral and chromatograph data was done

with the aid of NIST mass spectra database.

1 = primary reactor, 2 = secondary reactor, 3 = dry ice condenser, 4 = oil pot

1, 5 = secondary condenser, 6 = scrubber

Figure 1: Experimental set up for intermediate pyrolysis experiment


A. Characterization of the bio-oils produced

The relatively semi-homogenous bio-oil obtained clearly

separates into aqueous and organic phases when stored. The

properties of the bio-oils obtained from Jatropha seed coat

and Jatropha fruit shells are as shown in Table 1.



Figure 3: GC-MS chromatogram for Jatropha fruit shell.

Figure 2: Jatropha residue bio-oils from (a) JSC and (b) JFS.

The bio oil samples obtained from the JFS and JSC biomass

residues were dark brown in colour as shown in Figure 2.

The pH values of 5.3 and 5.8 of the Jatropha waste bio-

oils obtained for JFS and JSC are relatively higher than the

value of 3.3 obtained in literature for JSC (Manurung et al.,

2009). Higher pH values (as the values approach 7, being

neutral) are desirable for bio-oils since acidity can wear out

the engine components when the bio-oil is used as fuel.

Sulphur contents are desirably low in both JSC and JFS bio-

oils indicating that the formation of sulphur dioxide is at

lower risk (Tsai et al, 2018).

The higher heating value (HHV) of the Jatropha fruit

shell bio-oil (29.84 MJ/kg) is relatively higher than that

obtained for Jatropha seed coat (25.24 MJ/kg). However, the

heating values of both bio-oil samples prepared were

comparable to the value of 25.63 MJ/kg (Jourabchi et al.,

2016), 30 MJ/kg (Das et al., 2015) available in literature for

jatropha seed cake bio-oil.

Carbon contents were found to be desirably relatively

higher in JFS (62.4%) compared to JSC bio-oil (52.6%) while

the oxygen content was lower in JFS. The chlorine and the

sulphur contents were desirably low in both bio-oil samples.

Hence, there is a lower risk of sulphur dioxide formation

which can lead to environmental pollution (Tsai et al, 2018).

B. Composition of the Bio-oil Produced

Analysis of the bio-oil samples indicated the presence of

a vast number of complex mixtures of compounds which

include alkenes, phenols, carboxylic acids and their

derivatives. The GC-MS chromatograms for JFS and JSC

pyrolysis oils were as shown in Figures 3 and 4. The most

prominent peaks identified, corresponding chemical names,

retention time, chemical formulae, molecular weight and %

peak area measured are summarised in Tables 2 and 3.

Table1: Some physicochemical characteristics properties of the prepared Jatropha waste bio-oils.

Properties Jatropha Seed Coat

(This study)

Jatropha Fruit shell

(This study)

Jatropha Seed Coat

(Manurung et al., 2009)

Jatropha Seedshell cake

Kim et al., 2013)

pH 5.2 5.8 3.3

Density (g/cm3) 1.006 1.008

Water content (wt %) 18.47 21.76 23.3 Elemental composition (wt %)

C 52.6 62.4 65.6 65.8

H 8.89 9.19 9.5 8.92 N 2.29 2.73 0.9 5.62

O 33.04 23.14 nd 18.8

S 0.25 0.26 nd 0.19 Cl 2.93 2.31 nd

HHV(MJ/kg) 25.24 29.84 39

Empirical Formula CH2.03O0.47N0.04 CH1.77O0.28N0.04 H/C molar ratio 2.0 1.8 1.63

O/C molar ratio 0.47 0.28 0.11



The main identified components of the Jatropha seed

coat include dimethoxyphenol, guiacol and acetic acid while

the main identified components of the fruit shells are acetic

acid, 2-cyclopenten-1-one, phenol, guaiacol and 2,6-

dimethoxyphenol as shown in Figures 5, 6 and 7. These

compounds are characteristic components of bio-oil that are

candidates for biorefinery. They are useful precursor for

the synthesis of industrial products and can be used as fuels

chemicals and food bioproducts after refining (Demiral et

al, 2012). Guaiacol is useful for medicinal purposes, 2,6-

dimethoxyphenol has been recognized as a volatile flavor

component (Bridgwater et al., 2008) found in soy sauce,

wine and smoke.

Lignin which is a phenolic bio-polymer (Das et

al.,2015) was responsible for the phenolics and aromatics

constituents in the bio-oils. The presence of acetic acid, an

organic acid, undesirably contributes to low pH values in

bio-oils. Such relatively high content of acetic acid

indicates the need for upgrading procedure to be performed

on the oil prior to applications as fuel in engines (Odetoye et

al, 2014).

Figure 4: GC-MS chromatogram for Jatropha seed coat.

Table 2: Most prominent identified compounds of Jatropha Fruit Shell.

Peak

ID

RT

(min)

Compound Name Area

%

1 9.184 Acetic Acid 6.9

2 10.242 Hydroxyacetone 1.05

3 10.794 Toluene 1.12 4 11.518 Pyridine 1.79

5 15.059 Ethylbenzene 0.35

6 15.45 p-Xylene 0.44 7 16.462 Cyclohexanone 0.75

8 16.922 m-Xylene 0.23

9 20.659 2-Cyclopenten-1-one, 2-methyl- 2.89

10 21.452 2-Furyl Methyl Ketone 0.61

11 22.199 Mesitylene 0.24 12 25.545 3-Methyl-2-Cyclopentenone 0.66

13 25.717 3-Methyl-2-Cyclopentenone 3.04

14 26.718 3-Picoline 0.58 15 27.304 2,4-dimethyl-2-oxazoline-4-methanol

Maple lactone /2-hydroxy-3-methyl-2

2.11

16 28.776 Cyclopenten-1-one 4.64 17 30.351 Phenol 3.67

18 31.374 Guaiacol 2.83

19 32.869 2-Methylphenol 2.44 20 33.375 3-Ethyl-2-hydroxy-2-cyclopenten-1-

one

1.17

21 34.697 p-Cresol 1.95 22 36.996 2,4-Dimethylphenol 2.31

23 39.043 4-Ethylphenol 0.37

24 40.02 Decane 0.47 25 40.653 4-Ethylguaiacol 1.07

26 45.574 2,6-Dimethoxyphenol 2.63

27 60.141 4-Allyl-2,6-dimethoxyphenol 0.46

Table 3: Peak assignment for Jatropha seed coat bio-oil.

Peak ID RT

(min)

Compound Name Area %

1 6.771 2-butanone 1.33

2 9.105 Acetic Acid 14.68

3 10.796 Toluene 0.69 4 11.612 Pyridine 0.52

5 13.302 Hydroxyacetone 2.43

6 14.383 Cyclopentanone 1.66 7 14.498 1-hydroxy-2-butanone 1.74

8 17.602 2-Cyclopenten-1-one 2.86

9 19.913 2-Furanmethanol 3.25 10 20.66 2-Cyclopenten-1-one, 2-methyl- 2.06

11 21.454 2-Furyl Methyl Ketone 0.73

12 25.719 3-Methyl-2-Cyclopentenone 2.5 13 26.214 Tetrahydro-2-furanmethanol 1.13

14 28.778 cyclopenten-1-one 3.6

15 30.341 Phenol 4.31 16 31.365 Guaiacol 12.14

17 32.871 2-Methylphenol 2.53

18 33.377 3-Ethyl-2-hydroxy-2-cyclopenten-1-one

0.76

19 34.687 m-Cresol 3.52

20 36.573 Isocreosol / 5-methylguaiacol 3.12 21 38.746 2,4-Dimethylphenol 1.17

22 38.918 4-Ethylphenol 0.83 23 40.137 Dianhydromannitol 0.91

24 40.655 4-Ethylguaiacol 5.06

25 45.576 2,6-Dimethoxyphenol 6.04 26 49.163 Isoeugenol 2.57

27 49.611 1,2,4-Trimethoxy-benzene 2.13

28 52.75 1,2,3-trimethoxy-5-methylbenzene 1.97 29

55.9

2,4-hexadienedioic acid, 3,4-

diethyl-, dimethyl ester, (EZ)- 0.73

30 60.143 4-Allyl-2,6-dimethoxyphenol 0.72



Figure 5: Main chemical constituents of Jatropha bio-oils.

0 2 4 6 8 10 12 14 16

Acetic Acid

Hydroxyacetone

Toluene

Pyridine

2-Cyclopenten-1-one, 2-methyl-

3-Methyl-2-Cyclopentenone

2,4-dimethyl-2-oxazoline-4-methanol

2-hydroxy-3-methyl-2-cyclopenten-1-one

Phenol

Guaiacol

2-Methylphenol

p-Cresol

m-cresol

2,4-Dimethylphenol

2,6-Dimethoxyphenol

Isoeugenol

JSC

JFS

Area %

Figure 6: Main ketones constituents of Jatropha bio-oils.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Hydroxyacetone

Cyclohexanone

2-Cyclopenten-1-one

2-Furyl Methyl Ketone

3-Methyl-2-Cyclopentenone

2-hydroxy-3-methyl-2-cyclopenten-1-one

2-Cyclopenten-1-one

2-Furyl Methyl Ketone

3-Ethyl-2-hydroxy-2-cyclopenten-1-one

JSC

JFS

Area %



Figure 7: Phenols and its derivatives in Jatropha bio-oils

0

2

4

6

8

10

12

14

JFS

JSC

V. CONCLUSION

Jatropha wastes (seed coat and fruit shell) of Nigerian

origin, have been found suitable for use as renewable energy

feedstock with potential for bio-oil production. The

characteristics of the bio-oils produced were found to be

similar to those reported in literature. The presence of

valuable compounds such as phenolic compounds suggests

useful potential for industrial applications. Jatropha fruit shell

(JFS) and Jatropha seed coat (JSC) bio-oils need to be

upgraded before they can be utilized as a fuel substitute

particularly in engines as they consist of various complex

organic compounds with varying composition. This work has

provided database on some properties of Jatropha residues

bio-oils of Nigerian origin, that are applicable for bio-energy,

bio-refinery, waste management and vegetable oil industries.

VI. ACKNOWLEDGEMENT

The authors are thankful for the financial support

obtained from European Bioenergy Research Institute/School

of Engineering and Applied Sciences, Aston University,

Birmingham, UK.

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ABSTRACT: Recent catastrophic events, involving the accidental loading of structures caused either intentionally for

example aircraft crashes on structures, blast loadings, or unintentionally due to object impact, gas explosions etc, has

changed our view from something connected to the stage of war to a much more domestic scene. This makes it

imperative to study the response of structural elements under such accidental loading conditions in an attempt to

assess structures vulnerability and characteristic performance. The study presented in this paper investigates the

response of steel beams under impact loads by using the energy principles in assessing the capacity of the steel beam

to absorb impact energy in deflecting before fracture ensues. In addition, the point at which the ductile material is

considered to have failed was also examined, in an attempt to give safety recommendations to steel structures under

impact. This study also looks at the evaluation of dynamic loads, different impact scenarios, behaviour of steel

material at high strain rates (i.e. dynamic increase factor DIF) as well as influence of joint rotation on failure. The

findings from this study show that the maximum strain energy beyond which the beam is considered to have failed is

largely influenced by joint rotation.

KEYWORDS: Structural behaviour, Impact scenario, High strain rate, Joint rotation and Dynamic load.

[Received April 26, 2018; Revised August 06, 2018; Accepted September 04, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

Impact loads are dynamic in nature. They are generally

of great magnitudes and usually of very short duration with a

time rise of typically less than a second, so that it is the

response of structures to such loading which produces large

inelastic deformations leading to failure, which is of

particular interest to engineers (Johnson, 1972). In studying

the dynamics of impact, ‘the critical factor is not the stress

distribution in the elastic range but the capacity of the

structure to absorb energy without collapse and that the proof

resilience of a ductile continuous structure is insignificant in

comparison with energy that can be absorbed in the elastic-

plastic range’ (Baker, 1948).

An understanding of this concept of energy absorption by

structural elements will enable structural engineers to predict

likely responses of structures subject to impact loading, thus

facilitating their design to sufficiently withstand the effect of

impact load, ensuring the safety of personnel and valuables

(Corbett et al. 1996). Generally, structures having low

frequencies when loaded very rapidly, fails in a sudden brittle

manner as the structure does not have sufficient time to react

to rapid low period (less than 0.05 s) high frequency loads; in

this scenario the localized effects are considered more

dominant (Wessman and Rose 1942).

However, where the period of impact loading is high

(e.g. < 2 s) and the frequency of loading is low, the structure

is able to respond in a ductile manner before brittle fracture.

This study is however, limited to a low frequency high period

impact loading of a steel beam from an impactor generated

missile. The aim here is to investigate the deformation (i.e.

the strain energy absorption capacity) of the steel beam in

absorption of impact energy before brittle fracture ensues and

the influence joint rotation has on failure in other to give

safety recommendations that will guard against such failure.

For this study, the strain energy model developed by Mugah

et al. (1994) was adopted and the results validated using

ANSYS nonlinear finite element package.

II. ANALYSIS PROCEDURE

For this study the impact loads were as a result of

concrete cubes of specific weights dropped from the

following heights: a 500 kg concrete cube dropped from a

height of 15m; a 1 tonne concrete cube dropped from a height

of 20 m and a 2 tonne concrete cube dropped from the highest

point of 25m The concrete cubes used for this study had a

self-weight of 25 kN per cubic meter (Mosley et al 2007).

The steel beam which was 30 m long was impacted at the

following positions; at the quarter span and mid-spans as this

is where the main connections for the beam are located.

Although it is not possible to predict the actual size of

impactors in actual impact situations, for this study however,

the following sizes of impactors were selected and dropped

from the above respective heights.

Design Recommendation for Steel Beams Subject to

Impact Load to Prevent Brittle Fracture

Ohunene Hafsa Aliyu*

Department of Building, Federal University Birnin Kebbi, PMB 1157, Kebbi State, Nigeria.

ALIYU: DESIGN RECOMMENDATION FOR STEEL BEAMS SUBJECT TO IMPACT LOAD 79

*(corresponding author) [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1

Figure 1: The size of impactors dropped onto the steel beam at different

positions from different heights.

The velocity of impact was evaluated using the technique

suggested by Jones (1993). In his views, the velocity of

impact resulting from dropped weights can be evaluated

using the principles of conservation of energy which is

normally derived from the following principle.

𝐾. 𝐸 𝑔𝑎𝑖𝑛𝑒𝑑 = 𝑃. 𝐸 𝑙𝑜𝑠𝑡 𝑖. 𝑒. Mgh = 1

2M𝑣2 (1)

Figure 2: The portal frame roof (rafter beam) as datum level.

III. THE ANALYTICAL MODELLING

A. Structural Response Due to Impact Loading

Since the response of a structure to dynamic (impact)

load depends as much on the dynamic properties of the

structure as well as on the force-time history of the applied

loading, in establishing the principles for predicting these

structural responses, a number of simplifications have been

made to facilitate the analysis procedure which includes the

following: idealization of the structure to an equivalent single

degree of freedom system, the force-time and resistance

functions where possible are expressed in simple

mathematical forms, idealization of the deformation

characteristics in terms of an elasto-plastic resistance function

B. Single Degree of Freedom (SDOF) System

The simplest representation of discrete transient

problems is by means of a single degree of freedom system.

Although, only a small number of structures respond in this

manner because structures ideally have distributed masses

and stiffness characteristics but, in such situations, the actual

structure is replaced by an equivalent single degree of

freedom system where the structural elements are idealized in

terms of equivalent concentrated mass, load and resistance

displacement function. The response of the actual structure

will then be obtained by use of transformation factors which

offers a comparable system for analysis. The equation of

motion for the equivalent single degree of freedom system is

formed using the actual system properties given as:

𝑀𝑒�̈� + 𝐾𝑒𝑥 = 𝐹𝑒(𝑡) (2)

Figure 3: Single degree of freedom system.

C. Effective Mass

Effective mass (𝑀𝑒) is used to ensure a balance of

kinetic energy between the equivalent and actual system. The

ratio of these masses however, gives the mass factor (𝐾𝑚 )

𝐾𝑚 = 𝑀𝑒

𝑀𝑡⁄ (3)

In their full deformation mode, the assumed deflected

shape is taken to be the same as that resulting from the static

application of the dynamic loads. For this study where the

stress wave travel time 𝑡𝑐 is much less than the duration of

impact 𝑡𝑖 the deflected shape during impact is approximated

from the first mode shape. Therefore, (𝑀𝑒) is given as:

𝑀𝑒=𝑘𝜔2⁄ or 𝑀𝑒 = 𝑘 ⌊𝑇𝑛

2𝜋⁄ ⌋2 (4)

D. Effective Load

The effective load as used in the expression in

equation (1) is obtained by equating work done by actual

system in deflecting to the assumed deflected shape, to the

work done by the equivalent system. The load factor 𝐾𝐿 is

given as the ratio of equivalent load to actual load and can be

based on either the elastic or plastic deformation shape.

𝐾𝐿 =𝐹𝑒

𝐹𝑡⁄ (5)

E. Effective Resistance

The resistance of an element is the materials internal

force (strength), tending to restore the element to its unloaded

equilibrium position. The equivalent stiffness and maximum

resistance are defined in terms of the actual load distribution,

such that 𝐾𝑅 equals the load factor 𝑘𝐿.

𝐾𝑅 = 𝑅𝑚𝑒

𝑅𝑚⁄ = 𝑘𝐿 (6)

𝐾𝑅 = 𝐾𝑒

𝐾⁄ = 𝑘𝐿 (7)

F. Natural Period of Vibration

The natural period (𝑇𝑛) of the equivalent system is given

by (Mughal et al. 1994):

𝑇𝑛 = 2𝜋√𝑀𝑒𝐾𝐸

⁄ = 2𝜋√𝐾𝑀𝑀𝑡

𝑘𝐿𝐾⁄ = √𝐾𝐿𝑀𝑀𝑡

𝐾⁄ (8)

𝐾𝐿𝑀 is the load-mass factor = 𝐾𝑀

𝐾𝐿⁄ (9)



The maximum response of the equivalent system to dynamic

load (i.e. excitation force) is usually measured in terms of

displacement, velocity, and acceleration.

G. Material Behaviour at High Strain Rates

Impact loading according to Johnson (1972) tends to

produce strain rates in the range of 102/𝑠𝑒𝑐. Some materials

are however strain rate sensitive; a condition where the

materials stress versus strain relationship is highly dependent

on the rate of loading. Wei et al. (1992) however suggests

that because mild steel materials are highly strain rate

sensitive, their effect needs to be accounted for under impact

situations which according to Li et al. (2005) is best

addressed through the use of a dynamic increase factor (DIF).

This is the ratio between the unconfined dynamic uniaxial

compression strength and its corresponding quasi static value.

H. Dynamic Properties of Steel under High Strain Rates

Scholars such as (Johnson 1972 and Mughal et al. 1994)

are of the opinion that materials tend to behave differently

under dynamic loading situations than their more familiar

behaviour under static loading. Mughal et al. (1994), further

went on to say that this variation in behaviour represents the

increase in strength observed in these materials over their

characteristic value which can be accounted for in design by

basing the dynamic capacity of structural members on their

dynamic properties which as mentioned earlier can be

obtained by applying a DIF to the static strength value i.e.

𝑓𝑦𝑑𝑛 = 𝐷𝐼𝐹𝑓𝑠𝑡𝑎𝑡; 𝜎𝐷

𝜎𝑆⁄ = DIF (10)

where: 𝑓𝑦𝑑𝑛= Allowable dynamic strength; 𝑓𝑠𝑡𝑎𝑡=

Allowable static strength.

Johnson (1972) has tried to explain this phenomenon of

strength increase above their characteristic value by saying

that a delay in time usually exists between the time of load

application and the onset of plastic flow in low carbon steels

which is particularly important when considering the impact

loading of mild steels beams.

I. Ductility Requirement

The term ductility according to the United States

Department of Defence in “The effects of nuclear weapons”,

(1964) can be described as the ability of a structure or its

component members to absorb energy in the inelastic range

without fracture, implying that the more ductile a structure or

its components are, the more its resistance to failure. In

simple terms however, ductility can be viewed in terms of

displacement. In considering the example a single degree of

freedom system with a clearly defined yield point, the

displacement ductility (𝜇), can be expressed as the ratio of

displacement at first yield to maximum displacement.

where: 𝜇 =𝑋𝑚

𝑋𝑒⁄ is the allowable ductility and

𝜇′ =12 is the maximum ductility (Mughal et al. 1994)

In design it is essential to ensure that the ductility supply

be greater than the ductility demand. Where ductility supply

is the maximum ductility that the structure can sustain

without collapse implying that it is only a structural property

independent of the impact load. Ductility demand on the

other hand is the maximum ductility that the structure

experiences during impact and as such a function of both load

and structure.

Figure 4: Idealized Resistance displacement curve for an elastic-

plastic SDOF system (adapted from Mughal et al. 1994).

J. Analysis Method

The method adopted for this study was based on the

energy and momentum balance solution which is an

analytical approach. According to Mughal et al. (1994) this

procedure should ideally give the upper bound estimate of the

structural response. It involves establishing the displacement,

𝑋𝑚 at which the available strain energy of the system equals

the Kinetic Energy of the system after impact(𝐾𝐸′). The

upper limit estimate of 𝐾𝐸′ was however, determined by

assuming that the resisting spring back force (𝑅𝑥), did not act

during impact and that the coefficient of restitution ‘e’ was

zero which characterised the impact situation as a completely

inelastic collision between two solid bodies namely a missile

with velocity 𝑉𝑆 and mass 𝑀𝑚 striking a beam of mass 𝑀𝑒

which originally was at rest. The kinetic energy of the system

after the completely inelastic impact is derived from the

expression

𝐾𝐸′= 𝑀𝑚

2𝑉𝑆2

2(𝑀𝑚+𝑀𝑒) (13)

Since the coefficient of restitution was assumed to be

zero and given the fact that an elasto-plastic response was

assumed. The maximum displacement 𝑋𝑚 at which the

available strain energy equalled the kinetic energy was

derived from the expression.

𝑋𝑚=𝐾𝐸′

𝐾(𝑋𝑒−𝑋𝑜)+

𝑋𝑒+𝑋𝑜

2..14 𝑋𝑚 >

𝑋𝑒

𝜇 =𝐾𝐸′

𝑅𝑚(𝑋𝑒−𝑋𝑜) +

𝑋𝑜

2𝑋𝑒+ 1

2⁄ (15)

Available strain energy capacity of beam was obtained

by equating the internal strain energy (U) to the external work

done by the impactor.

(16)

The maximum allowable displacement 𝑋𝑚 is obtained from

the allowable ductility ratio given by 𝜇 where 𝜇 =𝑋𝑚

𝑋𝑒



Figure 5: Resistance displacement function with associated structural

response with effect of other loads. Adapted from Mughal et al (1994:

53).

Where: 𝑋𝑜 = displacement due to other loads; 𝑋𝑒= yield

displacement; 𝑋𝑚= maximum combined displacement; 𝑅𝑚 =

yield resistance; 𝐾 = elastic spring constant; Μ = ductility

ratio. However, adequacy of the beam under the impact load

was checked by ensuring that the strain energy (𝑆𝐸) utilized

in resisting the impact loading was not greater than half the

available strain energy at failure(𝑆𝐸𝑓). Conversely, according

to Mughal et al. (1994) when the strain energy is analytically

defined then the strain energy should not exceed 0.5𝑆𝐸𝑓.

IV.MODEL SIMULATION

A. Plastic Deformation

For large plastic deformations to be acceptable, the

stability of the structure under investigation must be assured.

With this type of deformation, the behaviour of the beam is

most likely to change from bending to centenary actions.

(This is a curve that an idealized hanging chain of cable

assumes, when fixed at its ends) (Yin, Y. Z and Wang, Y.C,

2004). For this behaviour to be modelled properly, both

linear and bilinear material properties have been specified as

nonlinearities in steel members could be both geometric as

well as material making them very important when high

levels of deformation are being investigated.

B. Modelling of the Beam Using Ansys

Ansys (finite element analysis software) is generally

applicable to a wide variety of engineering problems. In the

numerical simulation of the beam, a Beam 4 element has been

used with an encastre boundary condition specified. A total

number of 30 finite element mesh was used.

C. Beam 4

This element is a uniaxial element having tension,

compression, torsion and bending capabilities with stress

stiffening and large deflection capabilities also included and

has six degrees of freedom at each node (Ansys library, 10.0).

D. Material Model

For small deflections, it can be assumed that the

geometric effects are small and as such can be neglected but

with large deformations, this needs to be specified. In

analysing the beam to determine its plastic deformation

capacity the following material properties have been

specified.

Linear Isotropic and

Bilinear Isotropic

This is to ensure that the beam is properly modelled in

both the elastic and the plastic range. The values of the

material properties adopted are:

Modulus of elasticity 2.1 x 1011 𝑁 𝑚2⁄

Passion ratio 0.3

Yield stress 4.10 x 108 𝑁 𝑚2⁄

Tangent modulus of elasticity 0

Figure 6: Idealized elasto-plastic stress strain curve adapted

for Johnson, (1972).

where:

𝐸𝑇 = tangent modulus

𝐸𝑡 = elastic modulus

E. Analysis Type

Transient dynamic analysis technique has been used to

determine the displacement response of the beam under time

varying load. For this analysis, a triangular pulse has been

assumed with a rise time of about half the impact duration

which has been taken as 2 s.

Figure 7: Triangular pulse shape with equal rise and decay times.



Although, it can be argued that true dynamic loads would

probably be characterised by a load–unload cycle of less than

a second, this is not a hard and fast rule. The structure under

investigation has a low natural frequency and hence a high

period of loading therefore should respond well by deflecting

when subjected to impact load which also has high loading

periods.


For structures in general, the integrity of design must be

guaranteed over its service life, therefore there is a need to

ensure that the structure is safe under normal and accidental

loading situations.

A. Evaluation of Displacement from Drop Test using Hand

Calculation

A 2-tonne, 1-tonne, and a 500 kg concrete cube were

dropped from heights of 25 m, 20 m and 15 m respectively,

unto a 533 x 210 UB 92 mild steel beam with a span of 30 m

at both the quarter-span and mid-span positions respectively.

The results obtained are as shown in the graph below.

The graph shows that the displacement at mid span of

1.98 m coincides with the maximum allowable deflection (see

Figure 9) while the displacement 1.6 m at quarter span (See

Figure 10) exceeds the maximum allowed (1.55 m). Implying

that in considering the effects other loads have on the

allowable ductility, the strain energy available for resisting

the impact loading is significantly reduced. This option of

considering the effects other loadings have on the available

ductility ratio which in turn affects the available strain energy

of the beam should be considered especially where the risk of

collapse or failure is extremely severe. The deflections as

shown in Figures 9 and 10 will however be limited by

rotation capacities of the member which ensure the deflection

sustained is not too excessive.

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

0 15m/500kg 20m/1000kg 25m/2000kg

d

e

f

l

e

c

t

i

o

n

Height of drop / Mass of impactorFigure 9: A graph of actual versus allowable displacement considering the effects of other loads for mid-span

deflection.

Actual Deflection Allowable Deflection

0

0.3

0.6

0.9

1.2

1.5

1.8

0 15m/500kg 20m/1000kg 25m/2000kg

d

e

f

l

e

c

t

i

o

n

Height of drop/Mass of impactor

Mid Span Deflection Quarter Span Deflection

Figure 8: A combined graph of the mid-span and the quarter-span deflection versus the drop heights.



Figure 10: A graph of actual versus allowable displacement considering

the effects of other loads for mid-span deflection.

B. Ansys Model Simulation (Transient Analysis)

A transient analysis simulation was carried to validate

the results obtained from the hand calculation using the

energy momentum balance analytical approach. The transient

analysis simulation showed that the deflection sustained at

mid span due to the 2-tonne impactor load dropped from a

height of 25 m was 1.962 m at a stress level of 358 N/𝑚𝑚2

(see Figure 11).

While the quarter span deflection due to the 2-tonne

impactor load dropped from a height of 25 m gave a value of

1.301 m at a stress level of 460 N/𝑚𝑚2 (see figure 12). The

safe rotation capacity beyond which the beam is considered to

have failed is 20, which corresponds to a deflection of 0.25

m. This implies that for the mid-span and quarter-span

deflection of 1.98 m and 1.301 m respectively, the beam is

considered to have failed.

C. Comparison of Results

Comparing the results from the hand calculation to the

Ansys model shows that, the static deflection, from the hand

calculation with a value of 0.047 m compares closely to the

Ansys result of 0.0426 m (see Figure 13). Similarly, for the

dynamic deflection, the maximum value of 1.984 m at mid

span as well as the quarter span deflection of 1.6 m (see

Figure 9 and 10) due to the 2000 kg (2tonne) from the hand

calculation compared closely with those from the Ansys

simulation of 1.984 m and 1.301 m (see Figure 11 and 12).

V. CONCLUSION

A 30 m long mild steel beam was subjected to drop

weights (impact loading) from heights of 15 m, 20 m, and 25

m respectively. The deflection sustained was evaluated using

the energy method by Mughal et al. (1994) and validated

using the Ansys transient analysis which was performed to

simulate the beams response to the impact loading. As the

results for the hand calculation matched those from the Ansys

model, it was concluded that the presence of other static loads

significantly reduced the beam’s stiffness thus reducing the

Figure 11: Ansys model for midspan span deflection.

Figure 13: Static deflection.

Figure 12: Ansys model for quarter-span deflection.



capacity of structural elements in absorbing impact energy by

deflecting. Also, the maximum allowable deflection for safety

depending on structures classification should be controlled by

rotation capacity.

VI. RECOMMENDATION

For the safe design of steel structures, it is important to

identify the modes of failure that is the weak links in a

structure. This is because a structure can only be as strong as

its weakest link. For steel structures this will mostly be the

connections and welded joints. It is therefore recommended

that these weak link positions are designed to develop their

full strength. Implying that the ductility capacity of

connections and welded joints are crucial in ensuring the

safety of steel structures under impact loads as unanticipated

accidental loadings will ultimately have to be accommodated

by the connections.

To further ensure safety of design, it is recommended

that the ductility supply of the connection must at least be

20% greater than the ductility demand on it so that brittle

failure does not occur.

REFERENCES

Alves, M. and Jones, N. (2002). Impact Failure of

Beams Using Damage Mechanics Part II Application, 27(8):

863-890.

Arias, A.; JA. Rodriguez-Martinez, and A. Rusknek.

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steel plates subject to cylindrical conical and hemispherical

non-deformable projectiles. Eng. Fract. Mech. , 6(75): 1635-

56.

Baker, J. F. (1948). The design of war time structures.

The Civil Engineer in war, Inst of Civil Engrs, 3: 30-52.

B∅rvik, T.; O. S. Hopperstad, M. Langseht, and K. A.

Malo. (2003). Effect of Target Thickness in Blunt Projectile

Penetration of Weldox 460E Steel Plates. Int. J. Impact Eng.,

4(28): 413-464.

B∅rvik, T.; L. Olovsson, A. G. Hanssen, K. P.

Dharmasena, H. Hansson, and H. N. G. Wadley. (2011). A discrete particle approach to simulate the combined effect

of blast and sand impact loading of steel plates. Journal of the

Mechanics and Physics of solids, 59(5): 940-958.

Chen, X. and Li, Q. M. (2003). Plugging and

perforation of ductile circular plates struct by a blunt

projectile. Int. J. Impact Eng. , 5(28): 513-536.

Corbett, G. G.; S. R. Reid and W. Johnson. (1996).

The impact loading of plates by free flying projectiles: A

review. Int. J. Impact Eng., 2/18: 141-230.

Dey, S.; T. B∅rvik, O. S. Hopperstad, J. R. Leinum,

and M. Langseht. (2004). The effect of target strenght on the

perforation of steel plates uing three different nose shapes.

Int. J. Impact Eng., 30: 1005-1038.

Gardner, L. and Nethercot, A. D. (2005). Designers’

guide to EN 1993-1-1: eurocode3: design of steel structures:

general rules and rules for buildings. Thomas Telford

Publishing, London.

Gulvanessian, H. and Holichy, M. (1996). Designers

Handbook to Eurocode 1 Part: 7 Basics of design. Thomas

Telford Publishing, London.

Janiszewski, J.; M. Grazka, D. E. Tria, Z. Surma, and

B. Fikus. (2015). Laboratory Investigations on Perforation of

30PM Steel Plates. Problems of Mechatronics Armament,

Aviation, and Safety Engineering, 2(24): 19-40.

Johnson, W. (1972). Impact strength of materials.

Edward Arnold Publishers, London.

Jones, N. (1984). In structural impact and crash

worthiness. In Davies, G.A.O (ed) Elsevier Applied Science,

1: 45-47.

Li, Q. M.; S. R. Reid, H. M. Wen and A. R. Telford.

(2005). Local Impact Effects of Hard Missile on Concrete

Targets. International Journal of Impact Engineering, 32:

224-284.

Mughal, M. A.; S. J. Smith and A. C. Roberts. (1994). Design Guide for Structures Subject to Impulse and

Impactive Loads.

Shen, W. Q. and Jones, N. (1993). Dynamic response

and failure of fully clamped circular plates under impulsive

loading. Int. J. Impact Eng., 13 (2): 259-278.

Shen, W. Q. and Jones, N. (1993). Dynamic Plastic

Response and Failure of Clamped Beam Struck Transversely

by a Mass. Int. J. Solids Structures Vol. 30 (12): 1631-1648.

Takanshi, K.; K. Morita, T. Suzuki and T. Ishil.

(2000). Design Scheme of Steel Connections for Preventing

Brittle Fracture. 12 WCEE

United States Department of Defense. (1964). The

Effects of Nuclear Weapons. Revised Edition Reprinted

February 1964, America: United States Atomic Energy

Commission.

Voyiadjis, G. Z.; B. Deliktas, and N. A. Palazotlo.

(2009). Thermodynamically consistent coupled viscoplastic

damage model for perforation and penetration in metal matrix

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Wessman, H. E. and Rose, W. A. (1942). Aerial

Bombardment Protection. John Wiley and Sons, Inc. New

York.

ABDULLAHI: NUMERICAL ANALYSIS OF STRUCTURES OF REVOLUTION USING UNIVERSAL MATRICES 85


ABSTRACT: Stress and displacement analysis of structures of revolution under axisymmetric loading is of

considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which

simplifies the analysis and reduces the computational work. The axisymmetric triangular element is commonly used

for modeling these cases. This paper proposes a method of generating stiffness matrix for the axisymmetric

triangular element using universal matrices instead of numerical integration. The computation time of the proposed

method was compared against the Gaussian numerical integration. The CPU time ratio for the 3-node element was

1:1.56, 1:1.79, and 1:1.89 for the proposed method against 1-point, 3-points, and 4-points Gaussian numerical

integration respectively. The accuracy of the proposed method was 0.012% against the exact integration method.

The 1-point, 3-points, and 4-points Gaussian numerical integration have an error of 0.059%, 0.001%, and 0.0006%

respectively. Nodal displacements from this method were compared against the results of some commercially

available finite element packages. The proposed method has a deviation of 0.44% from the theoretical values, while

ABAQUS, ANSYS, and Optistruct has a deviation of 1.26%, 1.29%, and 1.44% respectively using the default

number of integration points provided by the packages.

KEYWORDS: Stiffness matrix; explicit formulation; closed-form; universal matrix; axisymmetric triangular elements.

[Received April 26, 2018; Revised August 10, 2018; Accepted September 19, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110

I. INTRODUCTION

In Finite Element Analysis, some cases of 3D problems

associated with the structures of revolution (SOR) can be

reduced to a 2D problem by using axisymmetric elements,

which simplifies the analysis and reduces computational work

(Cui and Xu, 2013). These structures are generated by

rotating a cross-section about an axis, as shown in

Figure 1. The cross-section can be of any 2D shape; the

resulting structure is said to be axisymmetric (O. C.

Zienkiewicz et al., 2014). These structures are paramount in

engineering applications due to their ease of manufacture and

optimality in strength-weight ratio, by hollowing the structure

it can further be used as a container. Axles, bottles, cans,

cups, nails, piles, pipes, tanks, vessels, and wheels are all

examples of structures of revolution. In the transportation of

fluids at different atmospheric conditions such structures are

widely used (Gill, 1970).

For an axisymmetric structure to be defined as an

axisymmetric problem, it is imperative that the boundary and

loading conditions be rotationally symmetric, with these two

conditions, the mechanical response of the structure is

regarded as axisymmetric and the displacement, strains, and

stress are not affected by the circumferential position (O. C.

Zienkiewicz et al., 2014).

Figure 1: Axisymmetric cylinder.

The finite element technique predicts deformation and its

intensity on a given structure, this is achieved by dividing the

structure into a network of elements called mesh, the

elements are non-complex shapes for which the finite element

code can evaluate the stiffness matrix (Chandrupatla and

Belegundu, 2001; Pachpor et al., 2011). The nodes, which are

the points at which the elements are connected are used to

determine the unknown field variables such as displacement

or temperature. Element stiffness matrices are further

combined into a global stiffness matrix for the whole model

Numerical Analysis of Structures of Revolution

using Universal Matrices Approach

Hamza Sulayman Abdullahi*

Department of Mechanical Engineering, Bayero University, Kano, 700241, Nigeria.




and then solved for the unknowns. Elements can either have a

constant, linear or cubic strains within the element

(Zienkiewicz et al., 2005). The first archival-journal on the

axisymmetric finite element using solid elements was applied

to a rocket nozzle problem presented by Wilson (1965).

Shape functions are used to describe the elements

behavior between element nodes (Huttton, 2004). The

coefficients in the interpolation polynomial denote the shape

function, which is written for each individual node of a finite

element and its magnitude is 1 at that node and 0 for all other

nodes in that element. The local coordinate system x and y

can be converted into another coordinate system that allows

for specifying a point within the element by a dimensionless

number whose magnitude never exceeds unity called natural

coordinate system (Huttton, 2004).

Numerical Integration has been widely applied in finite

element analysis mainly due to its simplicity. It provides an

approximate solution of the exact integration. Researchers

over the past few decades have been studying and developing

better approximation than the conventional numerical

integration. An alternate method was presented by

Subramanian (Subramanian and Bose, 1982) for plane

triangular elements which result in a closed-form solution i.e.

same as exact integration. Another method for computing

stiffness matrix that results in closed-form solution and

reduction in computational effort for quad elements was

presented by Zhou and Vecchio (2006). McCaslin et al.

(2012) considers isoparametric and subparametric higher

order tetrahedral element and proposed yet another closed-

form approach. Symbolic computation was used to reduce

computation time by 50% for exact integration (Videla et al.,

2008). An alternate midpoint quadrature was suggested by

Jeyakarthikeyan et al. (2017) to enhance the stiffness matrix

of quad elements. For axisymmetric triangular element under

axisymmetric loading, using a closed-form approach is

possible only when the radius of the element is much larger

than the element thickness (Subramanian and Bose, 1982;

Jeyakarthikeyan et al., 2015).

Familiarity with the stiffness matrix is essential to

understanding the stiffness method. A stiffness matrix K is

a matrix such it relates the local forces F on an element

with the displacement u on the nodes as F K u ,

the stiffness matrix indicates the defiance of the element to

axial, bending, shear, or torsional deformation (Zienkiewicz

et al., 2005). In fluid flow and heat transfer analyses, the

stiffness matrix represents the resistance of the element to

change when subjected to motion or temperature gradient

(O.C. Zienkiewicz et al., 2014). Element stiffness matrices

are always symmetric and positive for definitive structural

problems, the diagonal coefficients are always positive and

relatively large when compared to the off-diagonal values in

the same row, it is banded and singular (Zienkiewicz et al.,

2005).

The objective of this paper is to generate stiffness matrix

for the axisymmetric triangular element using universal

matrices instead of numerical integration. First, the

foundation of finite element formulation and the development

of universal matrices is described. The accuracy and

computation time of the proposed method was analyzed.

Lastly, a linear-static finite element study of a cylinder

subjected to internal pressure was carried out, the result from

three commercially available packages was compared against

the results of the proposed method.

II. SYSTEM MODELLING The axisymmetric triangular elements have 2 degrees of

freedoms (u, v) per node which is represented by the nodal

displacements. For the purpose of illustration in this paper,

the three-node axisymmetric triangular element will be used,

it is usually referred to as Constant Strain Triangle (CST) as

the strain is constant along its sides. The radius of the element

is approximated as

3

1

1

3ix x (1)

where x is the radial coordinate of the element nodes.

The strain-displacement equation gives

x

y

xy

u

x

v

y

u v

y x

u

x

(2)

where , ,x y are the three normal strains and xy is

the shear strain. The subscripts ,x y and denotes the radial,

axial and tangential directions. The field variable

(displacements) are denoted by u and v . The shape

functions for the CST are

*

1

*

2

*

3

,

,

1

N

N

N

(3)

Where ξ and η are interpolating terms with values

ranging from 0 to 1. For a 3-node CST element with the

isoparametric formulation, the geometry ( x and y ) and field

variable ( u and v ) are of the same order.

1 1 2 2 3 3

1 1 2 2 3 3

* * *

1 1 2 2 3 3

* * *

1 1 2 2 3 3

u N u N u N u

v N v N v N v

x N x N x N x

y N y N y N y

(4)

The Jacobian matrix for the transformation is given by

[ ]

x y

Jx y



Figure 2: Axisymmetric problem formulation (Chandrupatla and Belegundu, 2001).

The strain-displacement equation becomes

1

2P g

(5)

where

23 13

23 13

23 13 23 13

0 0 0

0 0 0

0

20 0 0 0

y y

x x

P x x y y

x

,

ij i j

ij i jy

x x x

y y

,

T u v u vg u

and is the

area of the triangular element.

The internal energy of the element is given by

11

0 0

(2 )2

TtU D d d

where 2t x and [ ]D is

the elasticity matrix for axisymmetric problems.

Substituting the strain-displacement equation we have

11

0 02

TxU g G g d d

Where T

G P D P a 5 x 5 matrix of constants,

we can also express [g]T as:

0 0

0 0 0

T T T

T

g u v N

N NN

NN N

Which yields

11

0 0

1

2

T T

T

xU u v N G N u v d d

U u v K u v

Where the stiffness matrix [K] is given by

11

0 0

TxK N G N d d

(6)

The universal matrices are denoted by [A], [B], [C], [E],

[H] and [J], they are the result of integration over the shape

functions of the field variable (Abdullahi, 2015).

11

0 0

1 0 11

0 0 02

1 0 1

TdN dNA d d

d d

11

0 0

0 1 11

0 0 02

0 1 1

TdN dNB d d

d d

11

0 0

0 0 01

0 1 12

0 1 1

TdN dNC d d

d d

11

0 0

2 1 11

1 2 124

1 1 2

TE N N d d

11

0 0

1 0 11

1 0 16

1 0 1

T dNH N d d

d

11

0 0

0 1 11

0 1 16

0 1 1

T dNJ N d d

d

Substituting the universal matrices into equation (6), the

element stiffness matrix of the 3-noded constant strain

triangle (CST) can be written as:

T

X YxK

Y Z

(7)

where

11 12 22 25 15 55

13 23 53 14 54 24

33 43 44

T T T

T

T

X G A G B B G C G J J G H H G E

Y G A G B G H G B G J G C

Z G A G B B G C

ijG are the terms of the G matrix.

An algorithm was developed to explicitly compute the

stiffness matrix terms and save it in memory for retrieval,

these explicit equations will be used instead of evaluating the

integrals or matrix multiplication when solving the problem,

therefore the stiffness matrix becomes a simple algebraic

computation and reduces the computation time.




An axisymmetric problem (Figure 2) which consists of a

cylinder subjected to internal pressure was used to assess the

capability of the method presented in this paper. The cylinder

has an internal diameter of 80mm and an external diameter of

120mm subjected to internal pressure of 2MPa, the Young

modulus of the cylinder wall material is 200Gpa with a

Poisson ratio of 0.3.

The axisymmetric problem depicted in Figure 2 was

modeled using three finite element packages; ABAQUS,

ANSYS, and Optistruct. Modeling procedure for each

package is explained in the following subsections. The

material of the cylinder wall has a Young Modulus of 200

GPA and Poisson Ratio of 0.3.

A linear-static analysis was employed using

Abaqus/Standard (ABAQUS, 2015). The part was set to be a

deformable axisymmetric shell, an isotropic elastic property

was defined. A general static step was created. A three-node

linear stress/displacement element without twist (CAX3) was

used to mesh the model, the model consists of 2 elements and

4 nodes. Fixed boundary conditions were employed on the

outer radius nodes while the inner nodes are only allowed to

move in a radial direction. The inner radius edge was

subjected to a uniform pressure of 2Mpa.

A static analysis using Plane182 element was employed,

the element is a four-node rectangular element that was

further degenerated to a triangular element by merging the

last two nodes (ANSYS, 2013). The axisymmetric option was

selected along with full integration and pure displacement.

An isotropic elastic property was defined. Uniform pressure

of 2MPa was resolved into forces and applied on the inner

radius nodes.

Axisymmetric triangular element CTAXI was used to

define the problem, all the nodes were placed on the x-z plane

with x as the radius. The pressure was applied using

PLOADX1, which is a bulk unsupported card for static

pressure load on axisymmetric elements. Material and

property were defined as MAT1 and PAXI cards respectively.

A linear static load step with two set of constraints for the

inner and outer radius was defined.


A. Accuracy and Computation Time

In non-axisymmetric triangular elements, the Universal

Matrix Method (UMM) gives the exact solution

(Subramanian and Bose, 1982). Due to the approximation of

the radius of the element shown in equation (1) the proposed

method gives another approximation. Therefore, the need for

determining the deviation of UMM and numerical integration

from the exact integration becomes paramount.

To assess the computational efficiency of the proposed

method, we consider the cylinder in Figure 2 and compute the

stiffness matrices using the universal matrices and Gaussian

numerical integration for the 3-node (CST) and the 6-node

(LST) axisymmetric triangular elements. The CPU time is

taken for 10,000 elements. The numerical integration was

coded as explicit equations this is aimed at providing a

common ground for the execution time comparison.

The test was carried out on a desktop computer with

Intel® Core™ CPU i5-6400 (2.70 GHz) and 16GB of RAM

running on a 64-Bit Windows operating system for all the

steps to ensure a fair comparison. For each of the elements a

problem is solved using the methods and then the stiffness

matrix generated is compared and the error is estimated using

the expression presented by Videla et al. (2008) as follows

, 1

100| |

nT

ij ij

i j

T

ij

K K

eK

(8)

where T

ijK the stiffness matrix is terms using exact

integration and ijK is the stiffness matrix term using UMM

or Gaussian numerical integration. The CPU time ratio for

element 1 with radius x = 46.67mm is shown in Table 1.

Table 1: Computation time ratio for 10,000 elements. Elements Method CPU time ratio

CST

Current Work 1.00

NI 1 point 1.56

NI 3 points 1.79

NI 4 points 1.89

LST

Current Work 1.00

NI 1 point 5.64

NI 3 points 12.84

NI 4 points 16.69

NI 7 points 28.12

The CPU time ratio for the 3-node CST element was

1.00 for UMM while Gaussian numerical integration has

1.56, 1.79 and 1.89 for 1-point, 3-points, and 4-points

integration respectively. The computation time increases with

an increase in the number of points due to re-computation

loop for each point and then taking the weighted sum. While

UMM uses only one computation loop. Similarly, for the 6-

node LST element, the CPU time ratio was 1.00 for the

universal matrix method and 5.64, 12.84, 16.69 and 28.12 for

1-point, 3-points, 4-points, and 7-points Gaussian numerical

integration.

Figure 2 shows the percentage error for UMM and

Gaussian numerical integration with 1, 3 and 4 points against

the exact integration. CST elements with radius x =

46.67mm and 53.33mm were used for the cylinder problem

shown in Figure 2. The result indicated that UMM has a

better approximation (0.012% error) than the 1-point

numerical integration (0.059%) which is the most commonly

used by commercial packages. However, by increasing the

number of integration points to 3 and 4 the error drastically

decreases to 0.001% and 0.0006% respectively. This clearly

shows that when using a 3-node constant strain triangle, a

minimum of 3 points is required in the commercial finite

element packages.

Figure 44 shows the percentage error for UMM and

Gaussian numerical integration with 1, 3, 4 and 7 points

against exact integration. Six-node linear strain triangle



Figure 2: Percentage Error for CST using UMM and Numerical

Integration.

Figure 4: Percentage Error for LST using UMM and Numerical

Integration.

(LST) elements with radius x = 46.67mm and 53.33mm

were used for the cylinder problem shown in Figure 2. Three

mid-nodes are added to the CST to create the LST. The result

indicated that UMM has a better approximation (1.873%

error) than the 1-point numerical integration (27.1%).

However, by increasing the number of integration points to 3,

4 and 7 the error drastically decreases to 0.43%, 0.032%, and

0.00015% respectively. This clearly shows that when using a

6-node linear strain triangle, a minimum of 3 points is

required in the commercial finite element packages.

B. Nodal Displacement

The axisymmetric problem illustrated in Figure 2 was

solved using the explicit equations generated. To further

understand the computational accuracy of the proposed

method, the nodal displacements from the current work,

ABAQUS, ANSYS, and Optistruct was compared against the

theoretical values obtained using exact integration. The result

for node 1 of element 1 is shown in Figure 5.

The universal matrix method has a deviation of 0.44%

from the theoretical values, while ABAQUS, ANSYS, and

Optistruct has a deviation of 1.26%, 1.29%, and 1.44%

respectively using the default number of integration points

provided by the packages. A similar trend was observed on

node 2 as shown in Figure . The deviation of the current work

from the theoretical values on the second node displacement

is 0.54%, while ABAQUS, ANSYS, and Optistruct have a

deviation of 1.62%, 1.64%, and 1.84% respectively using the

default number of integration points provided by the

packages. These deviations shown by the commercial

packages considered in this study is highly associated with

fewer integration points for the numerical integration of the

shape functions.

ABAQUS uses 1-point integration for the 3-node linear

axisymmetric triangular element (CAX3). The 6-node

quadratic axisymmetric triangular element (CAX6) and the 4-

node bilinear axisymmetric quadrilateral element (CAX4) are

recommended by ABAQUS because of the number of

integration points (ABAQUS, 2015). The CAX6 uses 3

integration points while the CAX4 has the option for full (4-

point) and reduced (1-point) integration. ANSYS and

Optistruct both use 1-point integration for the Plane182 and

CTAXI elements. ANSYS recommends using the 4-node

version of Plane182 without degeneration (ANSYS, 2013).

Figure 5: Displacement of node 1.

Figure 6: Displacement of Node 2.




V. CONCLUSION

A method of generating stiffness matrix for triangular

axisymmetric elements was presented, the method utilizes

universal matrices generated by integrating the shape

functions once and saved for retrieval in memory.

Furthermore, a set of explicit equations were generated for

each term of the stiffness matrix to improve the

computational efficiency. Unlike other closed-form

approaches to finite elements, the stiffness matrix

computation method presented in the current work results in

yet another approximation, due to the element radius

estimation.

However, the method shows a better approximation to

the theoretical baseline, with better acceptable percentage

error and lower computation time. The proposed method has

a deviation of 0.44% and 0.54%, while the commercial finite

element packages considered in this work have deviations up

to 1.44% with the default number of integration points.

Increasing the number of the integration points decreases the

error significantly and increases the computation time.

Therefore, careful consideration should be given when

choosing the element and the number of points to find a

balance between accuracy and computation time.

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