Computer Modelling of Landslides

by

Tommi J. Leinala

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Graduate Department of Civil Engineering University of Toronto

O Copyright Tommi Johannes Leinala (1 998)

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Computer Modelling of Landslides Masters of Applied Science 1998 Tommi Johannes Leinala Graduate Department of Civil Engineering University of Toronto

Abstract

Heavy rains, earthquakes, volcanoes and even forestry have an effect on

whether or not a landslide will occur. With increased urban sprawl, construction

often occurs on slopes of minimum stability. This leads to a greater influence of

landslides on both people and property. which in tum leads to a greater desire for

realistic modeling of landslides. The computer model presented in this thesiç is

one such model. It is based on a single semi-rigid block model that will allow

various resistance terms. A demonstration of the computer model and the effects

of the different resistance ternis will be presented using the Aberfan landslide of

October 1966 as a basis.

Acknowlednements

The author would like to thank Professor Adrian Crawford at the University

of Toronto for his thoughts and suggestions for this thesis. Members of the Rock

Group at the University deserve credit for their suggestions and tips for the

cornputer program developed. 1 would also like to thank al1 my family and friends

for their support during the past years.

iii

Table of Contents

List of Tables List of Figures List of Appendices

Chapter One Introduction ? .l Introduction

Chapter Two Background 2.1 Background 2.2 Description of Landslides

2.2.1 Landslide Initiation 2.3 Factors lnfiuencing Landslides

2.3.1 Rainfall 2.3.2 Land use and Slope Morphology 2.3.3 Geological and Topographie Factors 2.3.4 Volcanoes and Earthquakes

2.4 Landslide Models 2.4.1 Physical Modeling 2.4.2 Empirical Modeling 2.4.3 Dynarnic or Continuum Analysis

vi vii viii

1 1

4 4 4 5 6 6 8 9 11 12 13 16 19

2.5 Landslide Risk Assessrnent and Hazard Mapping 24 2.6 Landslide Warning Systerns, Countermeasures

and Prevention 26 2.6.1 Waming Systems 26 2.6.2 Countermeasures 27 2.6.3 Prevention 30

Chapter Three The Computer Model 3.1 The Computer Model 3.2 Driving and Resistance Terms

3.2.1 Basic Principles 3.2.2 Driving Force 3.2.3 Resisting Forces 3.2.4 Earthquake Loading

3.3 Geometric and Material Properties and Options 3.3.1 Geornetric Properties 3.3.2 Material Properties 3.3.3 Modeling Options

3.4 Model Output

Chapter Four Results and Validation 4.1 Introduction to the Aberfan Landslide 4.2 Results of Computer Analysis of the Aberfan

Landslide 4-3 Effect of Variables on the Results

4.3.1 Plastic Flow Model 4.3.2 Friction Flow Model 4.3.3 Voellmy Fluid Flow 4.3.4 Turbulent Flow 4.3.5 Larninar Flow

4.4 Earthquake Loading

Chapter Five Recomrnendations and Conclusions 5.1 Conclusions 5.2 Recommendations

References

Appendices

List of Tables

Chapter Two 2.1 Some Landsiides and Their Effects. 2.2 Manning's Coefficients for vanous forest conditions.

Chapter Three 3.1 Earthquake Data File Format

Chapter Four 4.1 Aberfan Landslide Data (Hutchinson ,1986) 4.2 Resistance Tenn and Material Property Varied

for Initial Run 4.3 Summary of Varied Material Properties and Results 4.4 Earthquake Data Table

Appendix A A l . 1 Plastic Flow Initial Run A l .2 Friction Flow lnitial Run A1.3 Voellmy Flow lnitial Run A1.4 Turbulent Flow lnitial Run A1 -5 Laminar Flow lnitial Run A 2 1 Plastic Flow with Deposition (4.5 kglm) A2.2 Friction Flow with Deposition (4.5 kglm) A23 Voellmy Flow with Deposition (4.5 kglm) A24 Turbulent Flow with Deposition (4.5 kglm) A25 Laminar Flow with Deposition (4.5 kglm) A3.1 Plastic Flow with Deposition (2.25 kglm) A3.2 Friction Flow with De position (2.25 kglm) A3.3 Voellrny Flow with Deposition (2.25 kglm) A3.4 Turbulent Flow with Deposition (2.25 kglm) A3.5 Laminar Flow with Deposition (2.25 kglm) A4.1 Slope Morphology A4.2 Slope Morphology and Consolidation A4.3 Slope Morphology and Consolidation with Deposition A4.3b Initial Starting Velocity (O mls) A 4 . 3 ~ lnitial Starting Velocity (5 mls) A5.1 Friction Flow with Erosion (2.25 kglm) A5.2 Friction Flow with Erosion and Consolidation -

Saturated soi1 height = 0.2m A 5 3 Voellmy Fluid Flow with Erosion (2.25 kglm) A5.4 Friction Flow with Erosion and Consolidation -

Saturated soi1 height = 0.6m

List of Figures

Chapter Two 2.1 Bedding Planes and Failure Surface 2.2 The Angle of Reach and Apparent Friction 2.3 Large Scale Landslide Test Slope 2.4 Hutchinson Sliding Block Model 2.5 Debris flow counterrneasures 2.6 Open Type, Steel Pipe Sabo Dam 2.7 Examples of DifTerent Road Construction

Chapter Three 3.1 Forces Acting on Block 3.2 Flow chart for Solution to Earthquake Loading

Chapter Four 4.1 Aberfan Slope Profile 4.2 Presentation of Different Flow Resistance Terms 4.3a Deposition of 4.5 kgfrn 4.3b Deposition of 2.25 kg/m 4 . 3 ~ Erosion of 2.25 kglm 4.4 Slope Morphology 4.5 Earthquake Acceleration 4.6 Block Motion with Earthquake 4.7 Block Displacement with Time

Appendix B Resistance Term Dialog Box Geometric Properties Dialog Box Material Properties Dialog Box Modelling Options Dialog Box Block Motion Output Screen Graphing Program Output Screen

vii

List of Appendices Appendix A - Results from Cornputer Model Calculations A1 -A24

Appendix 8 - Dialog Boxes and Output Screens from Computer Model B I -85

CHAPTER 1

1.1 Introduction

With increased urban expansion cornes an increasing stress on the

surrounding sub-urban area. Unfortunately, most of the land that remains around

major urban centres has some risk of potential geotechnical or hydrological

problems. Examples of these problerns include development on unstable or

marginally stable dopes or on river flood plains. Also with this increased

development, there is a much larger effect on property and lives when a natural

disaster such as landslides occurs. For the geotechnical engineer to help

rnitigate the effects'of landslides there are a number of issues that must be

investigated.

The main issues are:

1) Identification and recognition of factors that effect slope stability and increase

the potential of slope failures.

2) Use of cornputer models in assessing the effects of landslides.

3) Rewgnizing and mapping of possible landslide prone areas.

4) Combining the three previous issues to provide risk assessments of landslides

towards property and lives.

This thesis focuses on the first two issues, namely 1 and 2 of the preceding k t ,

with references to the other issues were appropriate.

It may be sornewhat obvious that the influencing factors on the mitigation

of landslides must be understood before an accurate and representative

computer model can be developed. To make the computer model generic it must

be able to handle a wide range of material properties and geometrical layouts.

This requirement of flexibility of the computer program is due to the wide range of

Row properties, triggering mechanisms and locations where landslides ocwr.

Flow properties exhibited by landslides range from fluid like motion in debris

flows to rigid flows in rock avalanches or rockslides. As for location. landslides

occur in various material types and conditions varying from snow topped

mountains to underwater mountain ranges. Frorn this viewpoint alone, the ability

of one computer model to properly capture the motion of a landslide is extremely

difficult.

Currently, the majority of landslide models have an ernpirical basis. This

approach is based on the examination of landslide events within the area and

examining the major influences on the slide. Typically, a regression analysis is

perfonned to develop an equation with the major influences as variables. This

approach, al1 though practical, is often tirne consurning to generate. Also, there is

considerable difficulty in transferring a model in one subject area to another

subject area. By developing a computer model based on intrinsic material

properties and various slope conditions, and from a fundamental consideration of

mechanics, it is anticipated that a more generic and more readily applicable

rnodel will be obtained.

With such a model, the engineer can use dope morphology properties or

interna1 material properties to determine run-out distance, velocity, acceleration

and the time duration of the landslide.

In this thesis, the results of the developed computer model are compared

to the Aberfan landslide that occurred on October 1966. The material properties

are well defined and extensive work has been done by Hutchinson (1986) in

presenting the results of some other computer models.

The results of the models developed in this thesis show that the computer

program can give insight into landslide modeling. The Turbulent and Laminar

resistance models do not give the best results due to the velocity dependence of

the resistance. The Plastic resistance terni yields higher velocities then was

observed. The Friction model and the Voellmy model provide reasonable results

with the semi-empirical Voellmy model giving the best results.

With landslide related incidences receiving more attention and becoming

more prevalent, there are certain issues where great progress c m be made.

Future work will involve integrating static dope stability programs and landslide

computer programs to model retrogressive slides, modelling landslide

countermeasures and instrumentation of actual Iandslides. Instrumentation of an

actual landslide would be extremely helpful in determining the mechanisms of

motion.

CHAPTER 2

2.1 Backaround

There is an

increasing demand

that have been put

increasing demand for accurate landslide modeling. This

is due to the use of fringe areas surrounding urban centres

in to use due to the demand of new land for development.

These land developrnents place people and property at risk from landslide

occurrences. Table 2.1 shows some affects of selected landslides on human

populations.

To develop a better understanding of landslides, the factors affecting

landslides must reviewed. Factors that help initiate landslides are logging, road

creation, earthquakes and heavy, intense rainfalls - to name a few. Only after

the main factors affecting landslides have been reviewed should one attempt to

derive empirical or analytical models. This is not only true for landslides but for

any engineering problem.

2.2 Descriptions of Landslides

The term landslide refers to any soil, rock or debris movement down a

slope. Landslides are generally initiated by high rainfalls but are also influenced

by other naturai events such as, earthquakes and volcanoes. Different types of

landslides can be placed into specific categories. Rockslides and rock

avalanches describe landslides that occur mainly in rock. Rock avalanches have

shown remarkable velocities of more than 100 kmlhr (Nisbett and Collins, 1997)

and of being able to fun-up more than 640 m up the opposite slope in a valley

(Evans et al., 1994). Debtis flows refer to a rapidly moving mixture of soil, rocks,

water and other debris. Debris flows are often shallow usually within a few

metres of the surface. Takahashi (1978) states that debns fIows c m move at

surprisingly high speeds and travel hundreds of metres or even kilornetres.

Submarine landslides have generated tsunamis and have moved land areas the

size of Manhattan Island (Nisbett and Collins, 1997).

2.2.1 Landslide Initiation

Typically, landslides are shallow unless failure occurs along a deep

distinct plane. In this case, shallow refers to a few metres in depth. Debris fiows

tend to initiate in hollows where colluvial material has been deposited. As

colluvial material is deposited, the hollow becomes unstable and may fail. The

failure of the dope within the hollow is typically caused by an intense rainfall.

This may be due to the pemeability of the colluvial deposit being lower than the

initial material in the hollow. This would lead to artesian water pressures being

generated leading to reduced effective stress causing a decreased shear

resistance which would lead to a slope failure. Rainfall. pore-water pressures and

topographie influences are discussed in the next sections.

2.3 Factors lnfluencing Landslides

There are numerous factors affecting the initiation and ninout distances

of landslides. These factors include (but are not limited to): land use, rainfall -

both intensity and duration, slope morphology and earthquakes. Sidle et al.

(1985) has a detailed description of land use and the effects of land use on slope

stability. These factors are often interrelated. For example, clear-cut lumber

harvesting affects not only slope morphology but also the effect of rainfall on

slope stability due to decreased evapotranspiration.

2.3.1 Rainfall

Rainfall duration and intensity have a pronounced effect on dope stability. High

rainfall intensities and long duration can raise pore-water pressures substantially

within the slope. This rise in pore-water pressures leads to a reduced effective

stress, which in turn reduces the force resisting sliding. In addition, the driving

force can be increased as the mass of the soi1 increases as it becomes

increasingly saturated with water. As well, once motion is initiated on the slope,

the water can act as a lubricant increasing the run-out distance.

Rainfall intensity and duration have been used on their own to predict

landslide occurrences by both Sidle et al. (1985) and Wilson et al. (1993). (See

section 2.6 for a discussion of Wilson's paper.) Of course, the effects of rainfall

are also related to dope morphology and land use due to changes in

evapotranspiration, issues that are discussed in the next section.

2.3.2 Land use and Slope Morphology

While most factors effecting dope stability are typically not directly

controllable, land use can be influenced. Conversion of land t o m its natural state

to forestry, agriwltural or urban uses can cause a tremendous change in the

stability of slopes. Urban development can lead to signifiant changes in the

morphology of the surrounding area. Vegetation is often removed or replaced,

which affects slope morphology. Construction can cause increased loading of

slopes or unloading of the toe of the slopes and will lead to an increased

likelihood of slope failures.

Sidle et al. (1985) notes that conversion of land from forests to pastures

results in substantially higher slope movements within the pastures. Eigenbrod

and Kaluza (1997) note that shallow slope failures occurred after forest clearing

in Northern Ontario. The cause of these slope failures is due to a decrease in

evapotranspiration and decaying of the root system. Decreased

evapotranspiration results in a higher water table within the soi1 that leads to

reduced slope stability. Forests also effect the depth of frost penetration. Frost

penetrates deeper into the soi1 once the forest cover is removed. This increased

frost penetration leads to slower thawing and higher water tables present. It is

also interesting to note that the slopes obtain peak instability afier forest removal

in about 6 years (Sidle et al., 1985). This time delay is due to the decomposition

of the root system left behind during lumber harvesting.

Forest harvesting also leads to a change in dope morphology. By

performing back calculations, one can calculate the effect of different vegetation

types on landslides. The relationship between vegetation type and landslide

movements can then be used to determine the resistance to fiow. Examples of

this method include using Manning's equation in calculating resistance ternis or

specifying changes in the contact friction angle along the base of the landslide.

Manning's equation for turbulent flow has a coefficient based on the roughness of

the base of the flow. This coeffcîent varies in value and typical values are shown

in Table 2.2.

Forested Manninri's coefficient - n Dense forest with dense underbrush O. 1 50 Cleared land with no stumps 0.040 Cleared land with new growth 0.060

Table 2.2 Manninq's Coefficient for various forest conditions. {Ada~ted from- Roberson and Crow. 1993)

In some empirical models developed for calculating landslides travel

distances, numerical values dependent on the type of vegetation cover are

assigned. For example, Cannon (1993) uses values ranging from 10 to 60 in

increments of 10, with 60 being the numerical representation of trees. These

numerical values where used in a regression analysis to develop an empirical

mode1 for landslide travel distances.

2.3.3 Geological and Topographic Factors

Another important factor that influences landslides is the general geology

and topography of the surrounding area. Wieczorek (1993) states that in the San

Francisco Bay following a storm in 1992 that most debris Rows started in hollows.

Hollows are topographic concave depressions in the slope. Hollows end up

having well defined failure surfaces and become unstable as colluvial material is

deposited. Forty-four debris flow sites examined by Benda and Cundy (1990),

had colluvial material deposited in hollows ranging from 0.4 to 3.5 m thick.

Topography is also important in that it defines the general path the motion

of the landslide must take. Most debris fiows run through channels and valleys.

However, once the debris flow exits the channel it tends to fan out and begin to

deposit the entrained material. Once deposition begins, there is less momentum

driving the slope movement. The slope along which the movement occurs is

probably the most critical in that it effects the driving force of the landslide.

Reducing the slope of a hill can reduce the chances of landslides occurring.

Geological formations and deposits have also been examined with respect

to rock avalanches. Evans et al. (1997) examined two slope failures that followed

bedding planes along the upper half of the slope and then sheared through intact

rock at the bottom of the slope. The failure surface of the two avalanches

occurred within the same geological formation. The shear strength between the

bedding planes of the rock can be exarnined to deterrnine zones of weakness

within specific geological formations. By identifying landslide prone geological

formations, identification of possible landslide sites can be easily determined.

For example. in Figure 2.1. the failure surface follows the bedding planes

the Palliser formation along the upper portion of the failed mass. This occurs

although there are two faults within the formation. The failure surface shears

through the Banff formation at the toe of the landslide.

Fiaure 2.1 Beddina Planes and Failure Surface (from Evans et al. 1997)

2.3.4 Volcanoes and Earthquakes

Volcanoes and earthquakes are damaging by thernselves. Couple

volcanoes or earthquakes with landslides and there is a possible catastrophe in

the making. In Table 2.1, the three most damaging landslide events are linked to

earthquakes or volcanoes.

Earthquakes a n lead to liquefaction of soils causing debris fiows.

Vibration of the soi1 structure to leads to a collapse of the soi1 structure causing

the generation of excess pore-water pressures. Movements along failure planes

in the rock mass can destroy any whesion or residual shear strength resulting in

rockslides or avalanches.

Volcanoes also generate dope rnovements caused by pressure being built

up within the magma-system (Nisbett and Collins, 1997). Enough pressure within

the volcano c m cause outward rnovement of the slopes. This outward movement

can lead to an unstable slope configuration, which can lead to slope failures. Of

some interest is the fact that the Mount St. Helens rockslide-avalanche occurred

before the actual eruption of material from the mountain. The rockslide-

avalanche lead to the weakened Rank blowing out when the eruption occurred

(Nisbett and Collins, 1997). Also within a volcano, erupted material can rnelt the

snow or ice present causing large amounts of water to enter the slope and cause

debris fiows or rock slides. This was the case in the Nevado del Ruiz debris flow

in Colombia where over 23000 people died.

2.4 Landslide Models

Research into landslides has focused mainly on the use of different

models to project fun-out distances and landslide risk. The formulation of these

models is based prirnarily on empirical or dynarnic modeling. There has been

some work on physical scale modeling but there has been limited research with

large-scale models.

First. a clarification of some terms is in order. The term angle of reach or

fahrboschung refers to the angle between the head of the landslide and the

furthest displaced mass. The angle of apparent friction is the angle between the

initial centre of gravity and the final centre of gravity. If the apparent friction angle

is equal to the angle of reach then the apparent angle of friction is the friction

angle on the sliding plane (Geotechnical Engineering Office, 1997). Figure 2.2

shows a visual representation of the angle of reach and the angle of apparent

friction. The angle of reach is often used to represent the mobility of a landslide.

8 - Angle of Reach 4 -Apparent friction angle

Vol-volume of slide

F i~u re 2.2 The Anale of Reach and Apparent Friction

2.4.1 Physical Modeling

Physical modeling typically involves using scale models to capture the

motion of landslides. Unfortunately, the majority of the research done so far has

involved small scale laboratory testing. Skermer (1 983) presented two models of

the Frank slide in British Colombia. One model has a scale of 1 :IO00 and the

other a 12000 s a l e model. The 1 :2000 scale model gave an angle of reach of

13" that was similar to that attained in the actual Frank landslide.

Large-scale debris flow tests have also been conducted recently. Iverson

and LaHusen (1993) conducted test using a 95 m long, 2 m wide and 1.2 m

deep. The slope of the model is 31 O in the top 88 m and flattens to 2.1 5 O at the

bottom. The model can hold 20 m3 of material. Iverson found from initial test

results for a sand-gravel-water mixture indicate that grain friction dominates the

shear resistance in a debris Row rather than grain collisions and liquid viscosity.

The motion of debris flows is thought to be controlled by three basic

mechanisms: grain friction, liquid viscosity, and grain collision. These

mechanisms affect the shear resistance and momentum transportation in debris

Rows (Iverson and LaHusen, 1993). One must remember that debris flows are a

mixture of water, soil, rock and other debris. lverson and LaHusen present

results from one test run at the flume, as well as two hypothetical flows. The

viscosity of the test run was taken as 0.001 Pa-S. The two hypothetical fiows had

a viscosity of 1 Pas and 0.1 Pabs, respectively. Iverson's observations lead to an

interesting aspect that must be looked at in further studies: at what ratio of solid

to Iiquid does the Iiquid viscosity component begin to dominate. Understanding

this aspect would help in further classifying debris fiows and mudslides since the

proper mechanism depends on material concentrations. With further large-scale

tests, further variables can be loaked at and emphasis can be placed on what is

the appropriate mechanism.

Hashimoto and Hirano (1993) also conducted tests to determine

sedimentation deposition of debris flows. The model used was 9.5 m long and 10

cm wide with a 1 6 O upper slope and a bottom siope 1.95 m long, 1.23 m wide

and various angles ranging from 2 O to 8 O . Different coloured grains were placed

in vertical bands across the width of the model. This allowed the visual

examination of where various grains dispersed to from the Row. Hashimoto and

Hirano (1 993) also developed equations based on observations and conservation

of mass. The equations developed predicted the same deposition pattern as was

developed in the expenment.

Until the actual mechanisms behind landslides are better understood,

small-scale lab testing can be difficult to interpret accurately. For instance, in the

case of Skermer's model the angle of reach is determined from the farthest

particle. In this case, the grain collisions and grains rolling over the çmooth

surface of the model may not be entirely acwrate due to low particle inertia and

poor modeling of the bed friction. In Skermer's model, the angle of reach was

based on an individual particle that traveled to the edge of the model.

Fiaure 2.3 L a r ~ e Scale Landslide Test Slope Ifrom Iverson and LaHusen, 1993)

2.4.2 Ernpirical Modeling

Empirical models are generated by examining previous landslide data

involving slope rnorphology, slope angle, travel distance and initial and final

landslide volumes. These models are typically developed for specific locations

generated frorn local data. Some models can be transferred to other locations but

calibration is required. These models typically predict travel distances andlor

landslide volumes. The deformation characteristics or the slide velocities of the

landslide are not predicted. Landslide initiation for a specific site is often not

predicted but the probability that a landslide will occur in certain areas may occur

is given for some empirical models.

Quite ofien ernpirical models are generated from digital photographs

andlor direct field measurements. Cannon (1 993) derived an empirical model for

debtis Rows and the volume-change. Twenty-six debris Rows were chosen and

using regression analysis equation 2.1 was derived.

where: 8 = dope angle, (degrees);

R = transverse radius of channel, (m);

Vi = initial debris flow volume. (mA3);

Vf = final debris fiow volume, (mA3);

D = run-out distance, (m).

Vegetation type was measured but did not contribute significantly to

becume a part of the equations developed. No results were given but analysis

with this equation is supposedly quite simple when applied to digitized maps.

Motion of the landslide stops when the volume of the debris flow is negligible.

Benda and Cundy (1990) propose a simple empirical model for debris

flows based on hollows and first and second-order channels. A first-order

channel is a channel receiving material from a landslide occurring in a hollow. A

second-order channel receives two or more first-order channels. This pattern

continues until al1 influencing channels have been looked at. Forty-four debris

f i w s were examined and a simple empirical model based on the slope angle and

the junction angle determined. The junction angle is the angle between

intersecting channels. The volume of the debris flow may also be estirnated.

Benda and Cundy (1990) assume that flow requires a minimum slope of 20" and

continues until the slope is less than 3.5" or a junction angle greater than 70°.

Deposition sites and travel distances are then calwlated.

Using this model Benda and Cundy examined 21 debris flows. This model

under predicted the run-out distance of the slides. The under-predicted travel

distance is due to the model not considering the momentum of the debris flow as

it travels down the slope.

Corominas (1996) looked ai the angle of reach of a landslide. Corominas

referred to the angle of reach as a mobility index. Landslides were classified

according to the type of slide: earthflows, translational slide, debris flows or rock

falls. In general, as the volume of material increased, the angle of reach

decreased. This is most likely due to the momentum of the landslide being able

to overcome obstacles present on the landslide path. Corominas found that earth

Rows are more mobile than other flows at smaller volumes, while at higher

volumes al1 flows had similar angles of reach. Regression analysis was

perfomed and equations relating the volume of the slide to the height and fun-

out of the slide were detem~ined. Equation 2.2 shows the relationship given for al1

204 landslides examined.

where: H = height of fall in metres,

L = horizontal distance traveled by fall in metres,

vol = volume of slide.

Other empirical models look at rainfall duration and intensity forecasts and

relate that to current soi1 moisture and slope conditions. As mentioned in section

2.3.1, rainfall is considered a major infiuencing factor on landslides. Wilson et al.

(1 993) used rainfall predictions to develop real-time warning systems (see

section 2.6). Although no equations are given in Wilson's paper, it seerns that it

may be helpful to determine rainfall duration or intensity versus landslide

volumes or probability of landslides occurring. This would allow simple

calculations based on rainfall forecasts to determine the expected landslide

volumes and probability of slope failures.

2.4.3 Dynarnic or Continuum Analysis

With dynamic analyses, the landslide velocity andor defomation can be

predicted over time. Predidion of the defomation is especially important if one is

dealing with debris flow because the depth of flow can range up to several

metres in height. Currently most models make the assumption that steady,

unifom flow is occurring.

Hutchinson (1 986) proposed a rigid-block sliding-mnsolidation model. In

the derivation, Hutchinson assumes that interslice forces are equal and opposite

and that the resistance along the base is purely frictional. This mode1 uses

Terzaghi's one-dimensional consolidation equation to predict the reduction of the

pore-water pressure along the base of the sliding-block. This model does not

allow for deformation of the block If the block were allowed to deform, equation

2.3 would have the height of the block as a variable and some iteration would be

required. Figure 2.4 shows the forces acting on Hutchinson's element and

equation 2.3 gives the acceleration.

From Hutchinson (1 987):

where: acc - acceleration of block (m/sA2), h - height of block (m),

y - unit weight ( ~ l m ~ 3 ) , Ysat - saturated unit weight ( ~ l r n ~ 3 ) ,

g - acceleration due to gravity (m/sA2),

ai - slope angle (rads), ub - basal pore water pressure,

t& - basal fiction angle,

s - ratio of saturated layer to complete block height.

U = Ub bseca where %= basal pore water pressure

Ficrure 2.4 Hutchinson's Sliding Block Model

Hutchinson uses this model to examine the Aberfan flow slide. This model

accurately predicted the actual travel distance and velocity of the flow slide.

Kinematic waves have also been used to model debris flows by Arattano

and Savage (1994). Kinematic wave equations are derived from the continuity

and momentum equations. Rapid changes in height invalidate the theory but

Arattano and Savage show that at a certain distance downstream the solution

applies. This and the development of a shock front over time allow neglected

terms in the equation to become apparent. In addition, travel distance cannot be

modeled accurately since kinematic waves, in theory, propagate indefinitely. Both

of these issues should be addressed before further use of this model. The rnodel

does have some potential in modelling debris flows. Arattano and Savage

modelled the Mount St. Helens debris flow and produced results that agreed with

the observed motion of the debris flow.

The characteristic equation developed by Arattano and Savage (1 994)

(equation 14 in reference) in dimensional fom is:

where: h = flow height,

u = velocity,

x = displacement along slope,

t = time,

k = constant depending on flow channel.

Arattano and Savage used this model to model the debris

on the Muddy River on the Rank of Mount St. Helens. The mode

shape of the debris fiow quite accurately with observed data

stations.

flow occurring

I predicted the

from gauging

Chen (1988) develops a model for debris fiows in wide channels using a

generalized viscoplastic fluid. This is applied to solving steady, uniform debris

flows. This model accounts for normal stress effect and soi1 yield criteria.

Unfortunately, the equations derived are difficult to relate to material properties

and are thus difficult to use. From Chen (1 998):

wt-tere: Tzx = total shear stress at a point,

T n = total normal stress at a point.

Txx = total longitudinal stress at a point

c = cohesion, p = pressure,

4 = internai friction angle, pl 4 2 = consistency indices,

q = flow-behaviour index, u = flow velocity.

The consistency indices, 1-11 and pz, are difficult to calculate. The indices

rely on various properties such as linear grain concentration, grain diameter and

intergranular fluid viscosity. This leads to sorne diffÏculty in using this model since

some of these properties are rarely known.

Takahashi (1978) presents a Bagnold's dilatant fluid model for debris

flows. The same problem in determining suitable coefficients for the equations

occurs as in Chen's model in that determining some values is quite difftcult.

Takahashi's model provides equations for the height and velocity of the front of

the debris flow as it progresses down the slope. Takahashi (1978) derives his

model by considering the static tangential stress (r) and the resisting shear

stress (r,), equations 2.7 and 2.8 respectively.

Takahashi then relates the normal (P) and shear (T) stresses by equations 2.9

and 2.10, respectively.

where: g = gravity, 8 = siope angle,

a = grain density (g/cmA3), p = fluid density,

ho = depth of water over bed,

4 = internal friction angle,

ai = a constant, h = linear concentration,

d = representative grain diameter,

or = dynamic internal angle of friction,

ai = depth at which stresses are taken at,

c = grain concentration in volume,

du/dy = velocity gradient normal to shearing plane.

Eqn. 2.9 is similar to eqn. 2.5, which is from Chen's rnodel. Chen (1988)

also found that Bagnold's dilatant fluid model (the basis of Takahashi's model) is

a more specific case of the generalized viscoplastic fiuid.

Combining both the rigid block madel and continuum equations was done

by Hungr (1995). Hungr's model uses both boundary blocks and mass blocks.

The wntinuity equation is applied to the rnass block while the rnomentum

equation is applied to the boundary block. Various rheological terms can be

applied depending on the type of landslide being looked at. Hungr's model was

used as a partial basis for the cornputer rnodel developed for this thesis and

portions of it will be described in the next chapter.

Various other theories abound for the modelling of landslides. Nisbett and

Collins (1997) mention models that include acoustic fluidization where sound

induœd vibrations reduce material strength and another theory where the

landslide runs on a cushion of air like a hovercraft.

2.5 Landslide Risk Assessment and Hazard Ma~ping

Once the most appropriate empirical or continuum model of the landslide

has been decided on, landslide hazard rnaps can be created and risk

assessments performed. Landslide hazard mapping allows for rapid assessrnent

of the local terrain that during rainstons may cause problem as well as allowing

developers to determine if it is financially viable to develop the property. Risk

assessments also require an understanding of people's acceptance of landslide

occurrences and damages.

The digital elevation model (DEM) is discussed by Ellen and Mark, 1993.

Ellen and Mark state that the DEM is a numerical representation of topography

that consists of elevations interpolated at 10-rn X, Y spacing from 12.2-rn

elevation contours. The DEM coupled with Cannon's equation (eqn. 2.1) allow

easy evaluation of the topographic area. One must be careful in applying this

equation to other areas since the regression perforrned may be location

dependent, in this case for Honolulul Hawaii. In this way hazard mapping can be

easily accomplished and then further nsk assessment done in the critical areas.

Finlay and Fell (1997) looked at the issue of people's acceptance of

landslides in Australia and Hong Kong. Ten different groups were looked at with

various exposures to landslides. This exposure ranges from no exposure to

exposure to various different landslide types. Some groups consisted of staff

dealing with landslides on a regular basis.

Not surprisingly, people's perception of landslides depends on their

exposure to them. Acceptable landslide probabilities are low at about 10- 6 per

year. The groups interviewed that lived in landslide prone areas mentioned the

same acceptable probability but the actual probability of landslides was far

higher. Finlay and Fell (1997) notes that this is because people who tolerate the

risk of landslides do not necessarily accept it. Finlay's study groups perceive that

acceptable losses of lives range from 1 in 100 000 to 1 in 1 million per year. This

is sirnilar to the accepted losses for petrochemical plants and dams (Finlay and

Fell, 1997).

People's perception that landslides pose a minor risk is highlighted in

Finlay and Fell's study. One study group that lived in a debris flow prone region

ranked landslides a far less risk then was actually the case for that area. The

probability of landslides occurring in the region was in the order of 1 in 100 to 1 in

1000 but the group ranked the hazard from landslides below al1 of the hazards

presented. For example, the probability of being struck by a car and being killed

is 40 in 1 million, which is less likely then being affected by a landslide in that

region.

Finlay and Fell (1 997) also found that most people have a lower maximum

acceptable probability for fast rnoving landslides then frorn slower developing

landslides. This result came from the groups examining various conditions with

varying landslide types and chances of being killed.

2.6 Landsfide W a m i n ~ Systems. Countenneasures and Prevention

The use of warning systems and countermeasures for landslides can be

effective in reducing the damage to buildings and lives at risk. Landslide

prevention is beneficial in that the risk of a landslide occumng is reduced.

Waming systems are usually based on meteorological data andlor on-site

measures. Landslide countermeasures include diversion channels, dams and

other camponents. Landslide prevention techniques are similar to ones used to

increase slope stability.

2.6.1 Warning Systems

A warning system used in the San Francisco area (Wilson, 1993) involves

the use of rainfall forecasts for the area. The amount of rainfall and rainfall

intensity are projected to detenine if the antecedent threshold is exceeded.

Once this threshold is exceeded, the storrn threshold is determined to see if there

is a possibility of dope failures. These observations are coupled with piezometric

readings of critical areas. Different warning levels are issued depending on the

projected rainfall intensities. This method must be developed in conjunction with

developing relationships between rainfall intensity and duration and landslide

occurrences. People effected by the wamings must also be willing to deal with

the occasional false alarrn,

This is one possible type of warning system, other types of warning

systems include trip wires or vibration sensors to give immediate waming of an

occurring landslide. Coupling rainfall forecasting landslide warning systems and

these methods would be beneficial in protecting people. If the rainfall is projected

to exceed threshold Iirnits, a warning is issued in the affected area. The trip wires

and vibration sensors can be used as a final warning before the landslide effects

the area. However, this warning may not be soon enough if the landslide is fast

moving, as is the case Mth debns flows. With this instrumentation, possible

bridge or road closures can be issued immediately when the slide begins so

premature road closure may not be necessary.

Visual signs can also be used as a warning systern or rather warning

signs of possible problems with landslides. Some visual warning signs are old

landslide scars and tension cracks on the slope. Leaning trees also suggest

hillslope creep. Signs of pooled water or wetness indicate poor drainage that can

be a sign of a high water table. The sign of a high water table can lead to

problems with dope stability.

2.6.2 Counterrneasures

Landslide countermeasures involve physical structures impeding the

movement of landslides or reducing the possibility of landslides occurring.

Reducing the possibility of a landslide ocairring involves similar methods used

for increasing slope stability, which are discussed in the next section.

To reduce the effects of landslides while motion is occumng certain

interesting methods are available. Some of these measures are called debris-

flow capturing works (Mizuyarna, 1993) (Fig. 2.5). These measures include

checkdams and sabo dams. Check-dams and ordinary sabo dams are just dams

on hillsides and retain the debris from slope movements behind them. Open-type

sabo dams consist of slits or grids of steel pipes and help reduce the peak

discharge rate of a debris flow (Fig. 2.6). Mizuyama (1993) also states that the

open-type of sabo dam is also beneficial in that the capture basin behind ernpties

during successive events.

Of note is that check-dams have the problem that the catch basins are

filled with smaller events and may not be able to handle a larger landslide when it

occurs. Davies (1993) noted that the long-term effect of check-dams could cause

a major event to being magnified. Once a dam is destroyed during a landslide the

sediment that has been held back becomes part of the slide creating a larger flow

then would of originally occurred. (This is analogcus to flood control dams that

break during major storms thus causing more damage then if the dams were not

there to begin with.) Davies also suggested that the average landslide volume

per year is constant over the long term and is restored by large landslide events.

Other structural countermeasures include debris-flow dykes, deflection

walls and a debris flow dispersing forest zone (Mizuyama, 1993). The dispersive

forest zone is interesting in that it helps emphasis the role of forests and

vegetation on landslides not only on the landslide initiation but also on the motion

of the slide itself.

Fiqure 2.5 Debns flow countermeasures. (From Mizuvama, 1993)

Fioure 2.6 Open Tvpe. Steel Pipe Sabo Dam. (From Mizuvama. 1993)

2.6.3 Prevention

For specific landslide sites, any type of slope stabilization method would

be of benefit. Typical dope stabilization methods end up increasing the effective

shear resistance along the failure plane of the slope. These methods quite often

consist of dewatering, soi1 reinforcement, reducing of slope angle and reduction

of slope overburden. These methods are typically only viable for specific sites.

In general, landslides may be reduced by development of rigid land use

plans. These plans could be fomulated for subdivisions, roads or for altemate

land-use plans. For subdivisions, reducing the amount of water entering the soil,

limiting building on marginal slopes and keeping existing vegetation on the

slopes would al1 be beneficial in reducing the probability of landslide failures.

For roads, well-designed routes and adequate cut and fiIl dope angles

would help reduce possible failures. With the construction of roads, Oregon State

requires full-bench construction on slopes steeper than 26O (Sidle et al.. 1985).

Bench construction, (Figure 2.7) although desirable is wstly due to haulage of

materials. Sliver fiIl construction is ta be avoided since compaction of materials is

difficult.

Full Bench Sliver FiII

Figure 2.7 Examples of Different Road Construction

CHAPTER 3

3.1 The Cornputer Model

The cornputer program SLIDER was developed in conjunction with this

thesis to give a visual output of a landslide occurring and to allow a comparison

of the results of the analysis using different resistanœ terms. SLIDER also allows

for the easy of simple input to detenine the effects of various variables. SLIDER

is an acronym for See Landslides lnvolving a Discrete EIement and Rheology.

SLIDER is similar to a prograrn proposed by Hungr (1995) or HUtchinson (1986)

but has been deveioped to allow visual output of the slide to the screen as it

moves and incorporation of rigid-block earthquake loading. SLIDER's use of a

semi-rigid block allows for the incorporation of erosion/deposition of material

within the model affeding the resisting force.

Benefits of visually displaying the landslide include allowing the user a

visual representation of the slide. This allows the user to determine if the

movement of the landslide related to the material properties or model chosen are

reasonable.

mg = force due to gravity, N = normal force, R = resisting force, Q = quake force, Ki = earthquake direction, D = driving force, F = resultant force dong the slope.

Fia 3.1 Forces Actina on 8lock

3.2 Dnvina and Resistinq Terrns

3.2.1 Basic Principles

Far motion to begin the driving force must be greater than the resisting

force. This is determined from Newton's second law:

F=ma

m = rnass of the block, (kg). where:

a = acceleration, (m/sA2),

However, summing the forces along the slope in Figure 3.1 gives:

where: D = driving force = mgsin(a).or

Q if the earthquake loading is chosen,

R = resisting force.

Velocity is detemined by rearranging then integrating equation 3.1.

FAt v = v , +-

rn

where: v = new velocity (mls),

vo = velocity of previous time step,

At = implicit time step provided by user (s),

m = mass (kg).

For deposition and erosion, a momentum term, M is applied to equation

3.2a. This then leads to:

where: M = O for erosion.

M = Amv for deposition.

M=O for erosion since it is assumed that the rnass gained by the rnoving

block has no motion. For deposition, the mass removed is moving at a specific

velocity so some momentum is removed from the block. The full derivation of the

momentum term is contained in Hungr (1995). Hungr only shows the derivation

of this terni but does not give any calculations or results using the momentum

term.

lntegrating equation 3.2a gives the displacement term in equation 3.3a.

This displacement is along the dope and is relative to the starting position of the

block. Due to the possibility of the block running uphill and back down if the

parabolic geometry is chosen, the cumulative displacement is calculated

(equation 3.2 b).

di,d,, = displacement - cunent and previous time step

respectively .

q,ql = cumulative displacement - curent and previous time

step, respectively.

At = time step (s);

3.2.2 Driving Force

Other than the earthquake loading, whidi will be discussed in section

3.2.4, the driving force is due to gravity. The forces acting on the block are given

in Fig. 3.1. The driving force is given below:

Di = Hi W L p g sina,

where: Di = driving force (N),

Hi = height at time step (m),

W,L = width and length, respectively (m),

p = material density (kglm3).

a, = slope angle, and g = gravity (mlsz) .

3.2.3 Resisting Forces

The reason for incorporating different resistance terms in the computer

model was to allow for the different types of slope movements ranging frorn rock

avalanches to debris flows. In Appendix B, Figure B1.l shows the resisting

forces dialog box. The user must choose one of the following rheologies: (The

terrns are defined at the end of this section and al1 the terms are taken frorn

Hungr, 1 995.)

Friction flow:

I; = AH, y ( ~ - ru, )tan 4, cosa, + 9

Plastic flow

Newtonian Laminar flow:

Turbulent flow:

Voellrny fluid:

Items that contain subscnpts are variable material or geometric properties

that will be described in section 3.3.

Terminolog y:

Ti - resistance force (N), A - base area of block (mA2),

Hi - height of block at current time step (m),

y -unit weight (NlmA3),

g - acceleration due to gravity (mlsA2),

Ct i - slope angle at current time step (rads),

ruj - pore water pressure coefficient,

éi - basal friction angle at current tirne step,

aci - centrifuga1 acceleration (rnlsA2),

c - constant shear strength (~lm"Z),

V i - velocity at current time step (mis),

p - dynamic viscosity (N s l d ) ,

n - Manning's number,

6 - Voellrny turbulence coefficient (mlsA2),

3.2.4 Earthquake Loading

Earthquake loading is incorporated in the model to better represent actual

loading situations. The earthquake loading is based on work done by Crawford

(1980). The derivation of the earthquake loading incorporates the gravitational

and resisting forces and is derived only for the frictional fiow resistance model.

The basic principle of this model is that for the block to start moving the

ground acceleration must exceed a critical acceleration. Once motion occurs, the

block rernains in motion until the relative motion of the block and slope are equal.

Figure 3.2 shows a flow-chart for the solution procedure. The earthquake data is

derived frorn modifying digitized earthquake data files. The format is shown in

Table 3.1. Frorn this data the resultant earthquake acceleration and direction is

calculated. This in tum affects the critical acceleration, which is shown in

equation 3.12.

The ternis are descnbed above in section 3.2.3 except,

where: âcrit = critical resisting acceleration,

Kj = earthquake direction in the plane of the failure

plane as calwlated ftom the earthquake data table.

Crawford (1980) derived an equation similar to equation 3.12. This

equation is derived from determining the resultant forces acting on the block.

These forces are shown in Figure 3.1. Crawford's equation had a frictional

component only and no allowance waç made for centrifuga1 acceleration or pore-

water pressure reduction. In equation 3.12, the frictional resistance component in

Crawford's equation was replaced by equation 3.5. The mass (AHî() cancels out

of the equation.

Model runs using an earthquake data file will be shown in Chapter 4 along

with mode1 runs for the other resistance terms.

Line - Description

2 3->x X-> end

n = (total data points)/2 time step horizontal earthqua ke force vertical earthquake force

Table 3.1 Earthauake Data File Format

Set Initial Values of Accelerations. Velocities and Displacements for ground and sliding block for t = 0.

Calculate Acceleration and Velocity of ground from

1 Accelerogram for time t to t + ~ t . 1

Calculate Relative Velocity and Displacernent of ground and sliding block at time, t.

Calculate resistance on sliding surface as a function of displacement.

Calculate Velocity and Displacement of sliding block in time t+At.

. Fiaure 3.2 Flow chart for Solution to Earthquake Loadinq

3.3 Geornetn'c and Material Properties and Options

As a landslide travels downhill, variability in the geometry and material

properties is encountered. This requires that the cornputer program have the

flexibility and the ability to Vary these properties.

The program developed allows for variation of a majority of the geometric

and material properties.

3.3.1 Geometric Properties

The geometric layout of the slope is important and should allow for

variability in the slope angle as well as the starting height of the block. Two

different slope types are available:

i) Flat slope (constant slope angle) - with or without a flat ninout,

2) A parabolic slope (variable slope angle).

It is important to allow a flat (zero slope angle) section to provide some

idea of the runout distance available for a moving landslide mass. The parabolic

slope option is interesting since it shows the possibility of substantial opposite

slope run-up. This option can help modal a case like the Avalanche Mountain

avalanche (Evans et al., 1994). At Avalanche rnountain, the rock avalanche

started at a maximum height of 1220 m and travelled 640 rn up the opposite side

of the valley.

The geometric model also shows that the starting height of the block is

important as it controls the distance that can be travelled on the initial downhill

portion. For the computer program developed, calculations for the constant dope

angle case are not affeded if the block does not reach the toe of the slope. In

Appendix B. Figure 81.2 shows geometric properties dialog box from the

computer model.

3.3.2 Matenal Properties

For any type of modelling, assigning proper material properties is vital to

perfonn proper and sensible calculations. Of course, the material properties

specified depend on the resistance term chosen. Material properties should be

chosen based on field observations and practical experience. Quite often

material properties can only be deterrnined through calibrations from surrounding

landslide sites. Figure B I -3 in appendix B shows the material properties dialog

box.

3.3.3 Modelling Options

Basal Friction Angle

Most material properties change as the landslide travels down the slope.

The computer program developed offers variation in the basal friction angle,

pore-water pressure and rnaterial erosion or deposition.

By allowing for a change in the basal friction angle, one can allow for a

change in dope morphology. This change oflen occurs due to changes in slope

vegetation, snow or ice along the slope. Currently, the computer rnodel is based

on a change in the friction angle per metre travelled (radslm). The friction angle

can either increase or decrease depending on the value for the change in friction

angle entered. Equation 3.13 shows how the new basal friction angle is

calwlated.

di = basal fnction angle of current time step (radians),

do = initial basal friction angle (radians),

A$ = change in basal fiction angle (radlm),

ci = cumulative displacement at current time step (m).

Pore- water Pressure

Pore-water pressure is inwrporated into the computer model by allowing a

pore-water pressure coefficient reduction factor that affect the effective stress

along the block slope interface. This pore water pressure coefficient (fui) is the

ratio of pore-water pressure to the total normal stress along the base of the

block. The reduction of the pore-water pressure is related to Terzaghi's one-

dimensional consolidation theory. In the computer model the user specifies the

basal pore-water pressure and this is checked to see if it exceeds the maximum

pore water pressure with the limiting condition being when the effective normal

stress is zero.

From Hutchinson (1 986), the maximum pore water pressure is:

(% ), = [(1 - S)Y + Va b, cosZ a, (3.13)

the ternis are described above in section 3.2.3 except,

where: s - ratio of height of saturated soi1 to height of soil.

y - unit weight of soi1 above the water table ( ~ l m " 3 ) .

The dissipation of the pore-water pressure is based on Terzaghi1s one-

dimensional consolidation theory and considers only upward drainage.

From Hutchinson (1 986),

where: t = elapsed time (s),

d = length of drainage path (m),

= s h j ~ ~ s ( a i ).

cv = coefficient of consolidation,

T = 1 - ubihbo, where Ubi = curent pore-water pressure

u b ~ = initial pore-water pressure.

Rearranging the terms:

.. = [i- Td' Il,,

Deposition and Erosion

Deposition or erosion is specified at a constant rate, kilograms per metre

travelled (kglm). This leads to the development of the momenturn equations.

From Hungr (1995). the momentum t e n (M). is derived from Newton's second

law of momenturn. lgnoring some second order terms results in the following:

M =Amjvi for erosion (3.15a)

and M = O for deposition. (3.1 Sb)

Of note is that as material is deposited or rernoved, the height of the

moving block changes. This results from the assumption of a constant material

density and a constant base area (length and width) of block. Thus. the height of

the moving biock is the only dimension that is allowed to change. The change in

height can have a pronounced effect on the resistance terms. In the laminar and

turbulent resistance terrns. the height is an essential component of the flow term

so that any change in height is magnified.

Conservation of Enem y

A conservation of energy check is carried. The total, potential and kinetic

energies are calculated. Note, however, that this check only gives a constant

total energy if the constant mass model (no deposition or erosion) is chosen.

One final item considered that is not related to a material property is the

important effect of centrifugal acceleration. Of course. the centrifugal acceleration

terni is only used on the parabolic geometric model. This is due to the

formulation of the centrifugal acceleration term and the radius of curvature

component. The centrifugal acceleration (aci) is derived in Saneinejad, (1997)

and is given by the following equation.

where: Ri = radius of curvature (m),

vi = velocity at current time step (m/s).

Various cornputer analyses will be presented in the next chapter along

with an examination of the effects of the variables on the resistance terrns used.

Refer to Figure B I -4 to see the modelling options dialog box.

3.4 Model Output

The model output consists of three components. These components

include: i) a visual display of the block motion, ii) a simple graphical component.

and iii) output to file in comma separated value (CSV) format.

The visual display of the moving block is very helpful to the user.

Displaying the motion allows the user to determine if the motion looks right. The

time-step can be specified to allow the rnoving block to proceed more rapidly on

the cornputer screen. This is valuable for viewing long model runs of long

duration. See Figure B2.1 for the screen printout of the moving block view.

A simple graphical selection is available and gives the user another type

of visual representation of the motion of the block. The user can specfy the x-

axis and y-ais and whether the plot is related to energy or kinematics of the

block. Figure 82.2 shows a plot with the simple graphical program available.

For exporting data to another program, such as ExcelTM, the data from the

model is saved as a comma separated value (CSV) file format. The CSV file

format is widely recognizable by readily available spreadsheet programs. The

simple transfer of the results can allow further data manipulation in a common

format.

CHAPTER 4

4.1 introduction to the Aberfan Landslide

The Aberfan debris flow that occurred on October 21, 1966, caused the

death of 144 people and initiated a renewed effort into landslide research

especially in Wales (Bently and Siddle, 1996). At Aberfan, the debris flow was

caused by the failure of loose coal mine waste, which was saturated by both an

artesian water table and the wet weather. Extensive research and modelling of

the Aberfan fIow has occurred (Hutchinson 1986) and there is sufficient

information to allow validation of the computer mode1 proposed.

Figure 4.1 is from Hutchinson (1986) and a similar dope profile was

chosen by using the parabolic geometry option in the computer model.

A computer model validation will be presented using each of the

resistance models presented in section 3.2.3. The material properties will be

selected for each of the resistance terms so that the runout is distance is similar

for each case. Table 4.1 shows the material properties used in the initial fun of

the model.

Validation of the computer model will also present a sensitivity analysis to

determine the effect of variation of material properties on the model.

Initial Startina Point and Velocities Material Properties Starting Height 100 m from river phi (cv) 36 deg Parabolic Shape 0.0001434 height of block 2 m Initial Velocity 3 mls Height of water 0.2 m Velocity at x=430 m 9-1 3 m/s Coef. Of Consolidation 6.34e-5 (mA2/s)

8ulk Unit Mass 1764 kglmA3 Saturated Unit Mass 1898 kg/mA3

Table 4.1 Aberfan Landslide Data ( Hutchinson . 1 986)

Narurai rcaie (ml 'Aberfan &ad

i Gtimated mar errent tf no 00s truc tions 1

1 1

2 5 ' * 0,.

i i J Constanr siope of t la

Figure 4.1 Aberfan Slope Profiie (Hutchinson. 1986)

4.2 Result of Cornputer Analysis of Aberfan Landslide

Analysis of the Aberfan Landslide was carried out by trying to match the

total unobstructed travel distance of 760 metres. The use of the different

resistance terms resulted in a wide range of velocities and total time for the slide

to occur (Figure 4.2). The terms varied in each resistance term for this initial run

are listed in Table 4.2. Surprisingly, the best results are given by the Voellmy

model (which is surprising since this is a semi-empirical model) based on

observations of snow avalanches. The velocities at about 430 metres were

observed by witnesses to range from 5-15 mls. The values for the material

properties and peak velocities for each resistance t e n run are given in Appendix

A in Table Al. 1 to A1 -5.

Problems were encountered with the Laminar and Turbulent fiow

resistance ternis. The fact the each term (refer to equations 3.7 and 3.8) relies on

velocity in some fashion leads to the resistance dropping to zero if the velocity is

zero. This gives very long run times and difficulty in achieving convergence of

results.

1 Friction 1 1Basal Water Pressure 1

Resisitance Term Plastic

Material Propertv Va tied Yield Strength

1 Laminar 1

s Voellrn y

5 L

Table 4.2 Resistance Term and Material Pro~ertv Varied

Friction Angle and Turbulence Coefficient

4.3 Effect of Variation of Resistance Terrns

The results from each resistance term were modified to determine the

effects on both maximum velocity and travel distance. Different starting

velocities, slope morphology and centrifuga1 acceleration are analysed. No

modifications of soi1 density or block height are examined as these values are

well known for this problem. The effects of erosionldeposition are also

considered. The cumulative travel distance was made identical and the

parameters in Table 4.2 were modified accordingly to achieve this result. Table

4.3 shows which parameter was varied and what was the effed on the peak

velocity. Further results are given in Appendix A in Table A3 - A8. Figure 4.3 to

4.8 shows the resulting velocity versus displacement plots of the resul ts.

Turbulent Manning's Coefficient i

Fiaure 4.3b Desposition of 2.25 kcilm

Laminar (2500s) -'+

Resistance Terni

Plastic

Friction - 1

Water Press. 1.47E+04 22 42 4.2 A1.2 Deposition 4.5 24 46 4.3a A22

Water Press. 1 SOE+O4 De position 2.25 22.5 51 4.3b A3.2

Water Press. 1.48€+04 t

Erosion 2.25 22.5 58 4 . 3 ~ A5.2 Water Press. 1.65E+04

Erosion 2.25 20.3 68 4 . 3 ~ A5.4 Water Press. 1.65E+04

Paramter/Option Examined

Sat. Height .6m Slope Morph 3.40E-04 29.7 40 4.4 A4.1

lntial Fric. Ang. O Slope Morph 1 SOE-03 32.3 44 4.4 A4.2 Consolidation hsat = 0.2 Slope Morph 1 -40E-03 32.1 44 - A4.3a Consolidation hsat = 0.2

Intial Vel. 3 Deposit 2.25 Slope Morph 1.40E-03 31.9 44 - A4.3b Consolidation hsat = 0.2

lntial Vel. O Deposit 2.25 Slope Morph 1.40E-03 32.4 44 - A 4 . 3 ~

1 Yield Stength 4500 20 58 4.2 A1.l De position 4.5 32.8 34 4.3a A21

Yield Stength 6500 De position 2.25 23 -6 49 4.3b A3.1

1 Yield Stength 6500 Erosion 2.25 17.3 76 4 . 3 ~ AS.l

Yield Stenath 6500

Value of Parameter

Turbulent r

Peak Vel. (mls)

Voellmy

Turbulence 1500 Manning's Coef. 0.1 15 5.82 282 4.2 A1.4

Deposition 4.5 5.73 535 4.3a A24 Manning's Coef. 0.1 1 5

Deposition 2.25 5.77 358 4.3b A3.4 Mannino's Coef. 0.1 15

Consolidation hsat = 0.2 Intial Vel. 5 Deposit 2.25

Turbulence 1.00€+03 15.9 8 1 4.2 A1.3 Friction Angle 3

Deposition 4.5 23.6 59 4.3a A23 Turbulence 5000 Deposition 2 -25 17.7 59 4.3b A3.3 Turbulence 1500

Erosion 2.25 11.8 110 4 . 3 ~ A53

Run Time (s)

Table 4.3 Summarv of Varied Material Properties and Results

Laminar

Figure

L - Erosion Could not get model to match flow distance

Wscosity 2.80E+04 3 10000 4.2 A1 .S Deposition 4.5 20.9 2370 4.3a A 2 5 Viscosity 1.00€+02

Deposition 2.25 3 2500 4.3b A3.5 Wscosity 2.50E+03

Erosion Could not get model to match flow distance

Table

From Table 4.3 and Figures 4.2-4.4, one can see that there is a wide

range of velocities calculated from the various models. These velocities range

from 33 mis for Plastic Flow to 3 mis for the Laminar flow. Also the time for the

flow to take place is given beside the mode1 and ranges from 34 seconds to

greater then 10 000 seconds. In the following sections, the results from analyses

using different resistance terms will be discussed.

4.3.1 Plastic Flow Model

The Plastic flow model is the simplest. at least conceptually, as it only

relies on a constant yield strength term. The Plastic flow model typically gave

higher peak velocities than the other rnodels (see Table 4.3). The closest

possible result to the Aberfan observations was achieved with the inclusion of the

erosion term. This value was set at 2.25 kglm and resulted in a peak velocity of

17.3 mls. However, site investigation at Aberfan indicated that the landslide

typically deposited material instead of eroding material from the slope. Refer to

Tables A l . 1, A2.1, A3.1, A5.1 and Figures 4.3a-c.

4.3.2 Friction Flow Model

Wth more parameters to Vary, the friction fiow model offers more opportunity for

insight into the flow of landslides. The effects of consolidation, slope morphology,

deposition and erosion, and initial velocity were al1 considered. The peak

velocities given by these models were typically higher than those observed at

Aberfan. Other than for the slope morphology model, the friction angle was set at

36". See Table 4.3 and Figure 4.2.

The basal pore-water pressure influences the effect of consolidation. With

increased saturated height the drainage path is increased. which increases the

time for the pore-water pressure to dissipate. In this case. a saturated height of

0.6 metres had a slightly lower velocity than a saturated height of 0.2 rn when

inciuding erosion. See Table A5.2 and 5.4.

For the dope morphology rnodel, the peak velocity was increased. This is

due to the initial friction angle being set to zero (the friction angle increases as it

travels along the slope) and the steepest slope being at the beginning of the run.

See Figure 4.4.

The initial velocity made little difference. Initial velocities of 0. 3 and 5 rnls

were chosen and the results varied only marginally. Due to the slight difference,

the other velocities were not plotted on Figure 4.4. The input data is given in

Table 4.3b, 4 . 3 ~ .

4.3.3 Voellmy Fluid Flow

Figure 4.2 shows that the Voellmy ffuid flow model most accurately depicts

the actual landslide. However, a low friction angle had to be chosen since the

model did not have a pore-pressure reduction term. If $cv (constant volume

friction angle) were used, motion would not occur. This suggests that perhaps a

consolidation term should be placed in the Voellmy fluid model to effectively

reduce the sliding resistance. Deposition and erosion have different effects on

the Voellmy flow model. Erosion lowers the peak velocity to 11.8 mls while

deposition increases the velocity.

4.3.4 Turbulent Flow

Turbulent flow relies on Manning's number as one of the components of

the resistance term. Unfortunately, the resistance term is dependant on velocity

the block will not stop unless the slope is zero. This leads to slides with the

laminar and turbulent fiow ternis travelling further than the actual landslide. With

deposition and erosion, the peak velocities are approximately the same. See

Figure 4.3a to Figure 4 . 3 ~ .

4.3.5 Laminar Flow

The problems with laminar flow are similar to those of the turbulent flow

model. With the laminar flow model, the time-step is important in that the velocity

decays rapidly and requires a small time-step to model it properly. From Figure

4.3a, the laminar flow term actually gives a very good representation of the

observed velocities. This is due to the deposition of the block reducing the height

and the velocity of the block. As the height of the block goes to zero. the

resistance term goes to infinity. Since the deposition rate was set to give a

completely deposited mass, the velocity quickly reduces.

4.4 Earthquake Loading

In this cornputer program, earthquake loading is only applied to the

frictional resistance model. As an example of the earthquake loading capabilities

of this rnodel, a sample calwlation is done using a slope angle of 20' and a

friction angle of 45'. This block would be stable if no earthquake loading

ocwrred. Table 4.4 gives the general definition of the problem.

The earthquake chosen was the Northridge Earthquake of January 17,

1994. The earthquake data is from the Tarzana - Cedar Hill Nursery A station

(No. 24436). This station is with 12 km of the epicentre and experienced a peak

acceleration of 17.4 m2/s. The earthquake acceleration is given in Figure 4.5.

Figure 4.6 shows the movernent of the block.

The results seem quite reasonable in that there is minimal uphill

movernent. This is to be expected due to the combined effect of the slope angle

and the basal friction angle creating an asyrnmetric critical acceleration.

Model Choice: Friction Flow

Geometric Data Material Properties Geometric Model: Straight flat nin-out Unit Mass(kg/mA3) = 1835 Slope Angle(rads): 0.4363 Friction Angle(rads) = 0.7854 Starting Height(m): 15

ModeIlina Options Enabled. Kinetics. Calculation Tolerance = 1.00E-05 lnital Velocity (rnls) = O Initial Block Height(m) = 1 Time Step(s) = 2.00E-02 Block Width(m) = 1 Max Acc. (m/ses) Max Vel(m/s) Disp (m) Block Length(m) = 1 93.3 3.93 15.3

Min Acc. (m/s*s) Min Vel (m/s) -53.3 -0.71

Table 4.4 Earthquake Data Table

CHAPTER 5

5.11 Conclusions

The wmputer model developed is able to realistically model various

landslide situations including slope morphology, geometry and sliding resistance

models. The material property parameters are simple to input and easy to

understand. Landslide motion can be govemed by different rheologies and the

computer program has the required flexibility to handle the different types of

resistance terms. Visual display of the block motion is done quickly. Displaying

the motion allows for rapid assessment of the movement of the landslide.

The cornputer mode1 is very good for calculating the general motion of the

landslide. This is useful to an engineer because it allows rapid assessment of

critical areas that may be affected by landslides. However, the model failç to

capture the deformation of the landslide as it travels down the slope, which may

be detrimental in that some of the resistance terms depend on the height of the

block.

For the Aberfan landslide, the model allows for a good assessment of the

most appropriate resistance terms. The Voellmy resistance term gives very good

results when compared to obsewed velocities. The results given by the laminar

resistance terni are poor except in the case of deposition were the motion of the

block accurately models the observed velocities. The plastic and frictional

resistance terms constantly over predicted the block's velocity while the turbulent

resistance term predicts a lower block velocity.

Earthquake loading is very influential on dope failures. The modelling

shows that seerningly stable blocks will quite easily begin to move under

earthquake loading.

The main contribution to landslide modelling is that this computer model is

simple to use and is based on fundamental relationships of motion. The

computer model also lays down the basis for further work.

5.2 Recommendations

Although the affects of landslides have been looked at for sometime there

is extensive work still required. The mechanisms of motion of the landslide are

still not well known. Fumer work is required to better define which resistance

terms are best for use in computer models.

Some other future work involves look at modelling retrogressive slides,

examination of the effectiveness of landslide countermeasures and

instrumentation of an adual landslide. For retrogressive landslides to occur it is

important that the failing material flow away from the toe of the slope. Once the

material has flown away from the toe, it allows another potential failure surface to

be generated. The coupling of a landslide computer model and a static anaiysis

program to determine the movement of slopes along critical slip surfaces would

help determine how far a retrogressive landslide might regress.

Examining the effectiveness of landslide countermeasures should be

looked at in terms of both physical effectiveness and economic feasibility.

Counteneasures will become increasingly important in the future as more

property and lives are impacted by landslides.

Instrumentation of an actual landslide would be desirable but extremely

difficult as the specific landsiide site is not known and extensive and rugged

instrumentation would most likely be quite expensive. The use of large scale

testing may be the best alternative in that the geometric conditions and material

properties are clearly defined.

Development of a cornputer model that models the initiation, complete

length of the flow and the deformation of the landslide would be extremely

beneficial. This is because some of the parameters within the resistance models

are height and basal area dependent. With a deformable multi-block model, the

results of the analyses would most Iikely be more reliable. Other work on the

cornputer model is to allow further variance of the material properties, specifically

in terms of the slope morphology model and the deposition/erosion terrn.

CHAPTER 6

References

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Chen, C. 1988. Generalized Viscoplastic Modelling of Debris Flow. Journal of Hydraulic Engineering. v. 114, No. 3, pp. 237-258.

Corominas. J. 1996. The angle of reach as a mobility index for small and large landslides. Canadian Geotechnical Journal. v. 33. pp. 260-271.

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Davies, T.R. 1993. Research Needs for Debris Flow Disaster Prevention. Hydraulic Engineering '93 - Proceedings of the 1993 Conference. v. 2, pp. 1284-1 289.

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Appendix A

Input Data for Different Resistance Ternis

Title: Table A t 1

Model Choice: Date:

Plastic Flow Wednesday

Geomettic Data Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Starting Heig ht(m): 100

Material Pro~erlies Bulk Unit Mass(kgJmA3) = 1764 Initial Block Height( 2 Depostion/Erosion Rate(kg1m) O Block Width(m) = 1 Yield Strength(N/mA2) =

ModeIlino O~tions Enabled.

Kinetics. Inital Velocity (m/s) = Calculation Time Step(s) = Max Acc. (mJs*s)

1.49 Min Acc. (m/s*s)

-1 .O6

4500 Block Length(m) = 1

3 1.00E-02 Calculation Toleranc 1.00E-06 Max Vel(m/s Disp (m)

20 766 Min Vel(m1s)

-4.1 SE-03

Title: Table A i .2

Model Choice: Date:

Friction Flow Wednesday Mar-1 8

Geometric Data Geometric Model: Para bolic Parabolic shape fundion: 1.43E-04 Starting Height(m): 1 O0

Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height( 2 DepostionIErosion Rate(kg/m) O Block Width(m) = 1 Friction Angle(rads) = O .6283 Block Length(m) = 1

Modellina Options Enabled. Consolidation Enabled. Coef. of Consolidation(mA21s 6.34E-05 Saturated Mass Density(kg/m 1898 Height of Water(m) = 0.2 Initial Pore-Water Press.(N/m 1.47E+04 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mls) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-06 Max Acc. (mls*s) Max Vel(m/s Disp (m)

1 -86 22.2 754 Min Acc. (m/s*s) Min Vel(m/s)

-1 -36 -1 .ME-02

Table A 1 3

Model Choice: Date:

Geornetric Data

Voellmy Fluid Flow Wednesday Mar4 8

Geometric Model: Parabolic Pambolic shape fundion: 1.43E-04 Starting Height(rn): 1 O0

Initial Block Height( 2 BIock Width(m) = 1 Slock Length(m) = 1

Material Prooerties Bulk Unit Mass(kglmA3) = 1 764 Friction Ang le(rads) = 5.24E-02 Turbulence Coef(m/sA2) = 1000 Depostion/Erosion Rate(kg/m) O Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mis) = 3 Calculation Tirne Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s*s) Max Vel(m/s Disp (m)

1 -74 15.9 762 Min Acc. (m/s*s) Min Vel(m/s)

-0.284 -4.60E-04

Model Choice: Turbulent Flow Date: Wednesday

Geometric Data Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(m): 1 O0

Material Pro~erties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height(m 2 DepostionfErosion Rate(kg/ O Block Width(m) = 1 Mannings Coef. = 0.1 15 Block Length(m) = 1

Kinetics. lnital Velocity (m/s) = 3 Calculation Tirne Step(s) = 1.00E-02 Calculation Toleranc ###### Max Acc. (m/s*s) Max Vel(m/s) Disp (m)

1.7 5.82 852 Min Acc. (rnls's) Min Vel(m/s)

-2.1 6E-O2 -6.87E-04

Title: Table A1 -5

Model Choice: Date:

Laminar Flow Wednesday

Geometn'c Data Geomettic Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(rn): 100

Material Properties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height(rn 2 DepostionIErosion Rate(kg1 O Block Width(m) = 1 Viscosity(Ns/mA2) = 2.80E+04 Block Length(m) = 1

Modelling Options Enabled.

Kinetics. lnital Velocity (mls) = 3 Calculation Tirne Step(s) = 0.5 Calculation Toleranc Max Acc. (rn/s*s) Max Vel(rn/s) Disp (m)

16.6 3 763 Min Acc. (rn/s*s) Min Vel(m1s)

-33.4 -1 -21

Title: Table A2.1 Plastic Flow Deposition

Model Choice: Plastic Flow

Geornetric Data Geometric Modsl: Parabolic Parabolic shape function: 1.43E-04 Starting Heighl(m): 100

Material Pro~erties Bulk Unit Mass(kg/rnA3) = 1764 Initial Block Height( 2 DepostionlErosion Rate(kg/m) -4.5 Block Width(m) = 1 Yield Strength(N/mA2) = 6500 8lock Length(m) = 1

Kinetics. lnital Velocity (mis) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s*s) Max Vel(m1s Disp (m)

12.1 32.8 761 Min Acc. (mls's) Min Vel(m/s)

-1 1.7 -0.1 14

Title: Table A2.2 Friction Flow with Depositi

Model Choice: Friction Flow

Geornetric Data Geornetric Model: Parabolic Parabolic shape fundion: 1 -43E-04 Starting Heig ht(m) : 100

Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height( 2 DepostionfErosion Rate(kg/m) 4 . 5 Block Width(rn) = 1 Friction Angle(rads) = 0.6283 Block Length(rn) = 1

Modellino O~tions Enabled. Consolidation Enabled. Coef. of Consolidation(mA2/s) 6.34E-05 Saturated Mass Density(kg1m 1.90E+03 Height of Water(m) = 2.00E-01 Initial Pore-Water Press.(N/m 1.50E+04 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mls) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s"s) Max Vel(m1s Disp (m)

2.97 24 765 Min Acc. (rn/s*s) Min Vel(rn/s)

-2.53 -0.01 59

Title:

Model Choice:

Geometric Data

Table A 2 3 Voellmy with Deposition

Voellmy Fluid Flow

Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(rn): 1 O0

Initial Block Height( 2 Block Width(m) = 1 Block Length(m) = 1

Material Pro~erties Buik Unit Mass(kg/mA3) = 1 764 Friction Angle(rads) = 5.24E-02 Turbulence Coef(mlsA2) = 5000 DepostioniErosion Rate(kg/m) -4.5 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. Inital Velocity (mis) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (mis's) Max Vel(m/s Disp (m)

1.77 23.6 763 Min Acc. (m/ses) Min Vel(m/s)

-0 -928 -5.64E-04

Title: Table A2.4 Turbulent Flow Deposition

Model Choice: Turbulent Flow

Geometnc Data Geometn'c Model: Parabolic Parabolic shape fundion: 1.43E-04 Starting Height(m): 100

Material Pro~erties Bulk Unit Mass(kg/rnA3) = 1764 DepostionErosion Rate(kg1 -4.5 Mannings Coef. = 0.115

Initial Block Height(m 2 Block Width(m) = 1 Block Length(m) = 1

ModeIlinci Options Enabled.

Kinetics. Inital Velocity (mis) = 3 Calculation Time Step(s) = 1.00E-02 Ca lcutation Toleranc #MW## Max Acc. (m/s*s) MaxVel(m/s) Disp(m)

1.7 5-73 784 Min Acc. (mis%) Min Vel(m/s)

-0.24 -0.00044 1

Table A2.S Laminar with Deposition

Model Choice: Laminar Flow

Geometric Data Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Startirig Height(m): 1 O0

Material Pro~erties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height(m 2 Depostion/Erosion Rate(kg1 -4.5 Block Width(m) = 1 Viscosity(Ns/mA2) = 1.00E+02 Block Length(m) = 1

Modelling Options Enabled.

Kinetics. lnital Velocity (m/s) = 3 Calculation Time Step(s) = 0.2 Calculation Toleranc ##WH## Max Acc. (m/s*s) Max Vel(rn/s) Disp (m)

2.1 5 20.9 754 Min Acc. (m/sœs) Min VeI(m/s)

-1 .#J -1 .#J

Title: Table A3.1 Plastic Flow and Depositio

Model Choice: Plastic Flow

Geometnc Data Geometric Model: Para bolic Parabolic shape function: 1.43E-04 Starting Height(m): 100

Material Pro~erties Bulk Unit Mass(kg/rnA3) = 1764 Initial Block Height( 2 Depostion/Erosion Rate(kg1m) -2.25 Block Width(m) = 1 Yield Strength(NlrnA2) =

Modellina O~tions Enabled.

Kinetics. lnital Velocity (mls) = Calculation fime Step(s) = Max Acc. (rnls's)

2.05 Min Acc. (mls's)

-1.59

6500 Block Length(m) = 1

3 1.00E-02 Calcufation Toleranc 1 .OOE-05

Max Vel(m/s Disp (m) 23.6 762

Min Vel(m1s) -0.00599

Titîe: Table A3.2 Fricton with Deposition B

Model Choice: Friction Flow

Geometnc Data Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(m): 1 O0

Bulk Unit Mass(kg/mA3) = 1 764 Initial Block Height( 2 DepostionIErosion Rate(kg1m) -2.25 Block Width(m) = 1 Friction Angle(rads) = 0.6283 Bloclc Length(rn) = 1

Modellinq Options Enabled. Consolidation Enabled. Coef. of Consolidation(mA2/s) 6.34E-05 Saturated M a s Density(kg/rn 1.90€+03 Height of Water(m) = 2.0OE-O1 Initial Pore-Water Press.(N/rn 1.48E104 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mls) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (mls's) Max Vel(m/s Disp (m)

1 -86 22.5 757 Min Acc. (mls's) Min Vel(m1s)

-1.38 -0.001 24

Title:

Model Choice:

Table A 3 3 Voellmy with Deposition B

Voellmy Fluid Flow

Geometric Data Geometnc Modek Parabolic Initial Block Height( 2 Parabolic shape function: 1.43E-04 Block Width(m) = 1 Starting Heig ht(m): 1 00 Block Length(m) = 1

Mat erial Pro~erties Bulk Unit Mass(kg/mA3) = 1 764 Friction Angle(rads) = 5.24E-02 Turbulence Coef(m/sA2) = 1 500 DepostionlErosion Rate(kg/m) -2.25 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. Inital Velocity (mk) = 3 Calculation Time Step(s) = 5.00E-02 Calculation Toleranc 1.00E-OS Max Acc. (rn/s*s) Max Vel(m1s Disp (m)

1-75 17.7 757 Min Acc. (m/ses) Min Vel(m/s)

-0.366 -2.1 8E-02

Title: Table A3.4 Turbulent with Deposition B

Model C hoice: Turbulent Flow

Geometric Data Geometric Model: Parabolic Parabolic shape function: 1 -436-04 Starting Height(m): 100

Maten'al Properties BulkUnitMass(kg/mA3)= 1764 Initial Block Height(m 2 Depostion/Erosion Rate(kgf -2.25 Block Width(m) = 1 Mannings Coef. = 0.115 Block Length(m) = 1

Modellina Options Enableci.

Kinetics. Inital Velocity (mis) = 3 Caiculation Time Step(s) = 1.00E-02 Calculation Toleranc *CIUCCUm Max Acc. (m/sUs) Max Vel(m/s) Disp (m)

1.7 5.77 848 Min Acc. (m/s*s) Min Vel(m/s)

-0.0293 -0.000221

Title: Table A3.5 Laminar with Deposition B

Model Choice: Laminar Flow

Geometnc Data Geometnc Model: Parabolic Parabolic shape function: 1 -43E-04 Starting Height(m): 100

Material Prooerties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height(m 2 Depstion/Erosion Rate(kg1 -2.25 Block Width(m) = 1 Viscosity(Ns/mA2) = 2,506+03 Block Length(m) = 1

Modelling Options Enabled.

Kinetics. lnital Velocity (mis) = 3 Calculation Time Step(s) = 0.05 Caiculation Toleranc MW#### Max Acc. (m/s*s) Max Vel(m/s) Disp (m)

-0.000035 3 778 Min Acc. (m/s*s) Min Vel(m1s)

-0.907 0.0446

Title: Table A4.i Slope Morpholocrv

Mode1 Choice: Friction Flow

Geometric Data Geometric Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(m): 100

Material Prooerties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height( 2 DepostiorVErosion Rate(kg/m) O Block Wdth(m) = 1 Friction Angle(rads) = O Block Length(m) = 1

ModeIlina Ootions Enabled. Slope Morphology Enabled. Change in Friction Angle(rads 3.40E-04 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. Inital Velocity (rn/s) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s*s) Max Vel(rn/s Disp (m)

2.83 29.7 756 Min Acc. (m/sgs) Min Vel(m/s)

-2.33 -1.36E-02

Titl e: Table A4.2 S l o ~ e Momh. + Consolidati

Mode! Choice: Friction Flow

Geometric Data Geometric Model: Para bolic Parabolic shape function: 1.43E-04 Starting Height(m): 1 O0

Material Promrties Bulk Unit Mass(kg/mA3) = 17 64 Initial Block Height( 2 Depostion/Erosion Rate(kg/m) O BlockWidth(m)= 1 Friction Angle(rads) = O Block Length(m) = 1

Modellinq O~t ions Enabled. Consolidation Enabled. Coef. of Consolidation(mA2/s) 6.34E-05 Saturated Mass Density(kg1m 1898.00 Height of Water(m) = 0.20 lnitialPoreWaterPressure(N1 1.SOE+04 Slope Morphology Enabled. Change in Friction Angle(rads 1 -50E-03 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mk) = 3 Calculation Tirne Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (rn/s's) Max Vel(m1s Disp (rn)

4.24 32.3 760 Min Acc. (m/s*s) Min Vel(m/s)

-3.77 -1.16E-02

Model Choice:

Table A4.3a Slope Momholociv +Consolidation and Deposition

Friction Flow

Geometric Data Geometric Model: Para bolic Parabolic shape fundion: 1.43E-04 Starting Height(m): 100

Material Properties Bulk Unit Mass(kg/mA3) = 1 764 Initial Block Height( 2 Depostion/Erosion Rate(kg1m) -2.25 Block Width(m) = 1 Friction Angle(rads) = O Block Length(m) = 1

ModeIlina O~tions Enabled. Consolidation Enabfed. Coef, of Consolidation(mA2/s) 6.34E-05 Saturated Mass Density(kg1rn 1.90E+03 Height of Water(m) = 2.00E-O1 Initial Pore-Water Pressure(N1 1.47E+04 Slope Morphology Enabled- Change in Friction Angle(rads 1.40503 Centrifuga1 Acceleration Reduction Ena bled.

Kinetics. Inital Velocity (m/s) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s's) Max Vel(m/s Oisp (m)

3.99 32.1 763 Min Acc. (rn/s*s) Min Vel(m/s)

-3.53 -3.30E-02

Title: Table A4.3b Different Startincr Velocitv

Mode! Choice: Friction Flow

Geometric Data Geornetn'c Model: Parabolic Parabolic shape function: 1.43E-04 Starting Height(m): 1 O0

Material Pro~erties Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height(m 2 DepostionIErosion Rate(kg/m -2.25 Block Width(m) = 1 Friction Angle(rads) = O Block Length(m) = 1

Modellina Options Enabled. Consolidation Enabled. Coef, of Consolidation(mA2/s) 6.34E-05 Saturated Mass Density(kg/m 1.90€+03 Height of Water(m) = 2.00E-01 Initial Pore-Water Pressure(N 1.47E+04 Slope Morphology Enabled. Change in Friction Angle(rads 1.4OE-03 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mls) = O Calculation Time Step(s) = 1.00E-02 Calculation Toleranc ##WH# Max Acc. (m/s*s) Max Vel(m1s) Disp (m)

3 -97 31.9 759 Min Acc. (m/s*s) Min Vel(m1s)

-3.49 -0.0246

Title: Table A 4 . 3 ~ Initial Velocitv of 5 m/s

Model Choice: Friction Flow

Geometric Data Geornetric Modef: Parabolic Parabolic shape function: 1.43E-04 StaRing Height(m): 100

Bulk Unit Mass(kglmA3) = 1764 Initial Block Height(m 2 Depostion/Erosion Rate(kg1m -2.25 Block Width(rn) = 1 Friction Angle(rads) = O Block Length(m) = 1

Modellinq Options Enabled. Consolidation Enabled. Coef. of Consolidation(mA2/s) 6.34E-05 Saturated M a s Density(kg1m 1.90E+03 Height of Water(m) = 2.0OE-O1 Initial Pore-Water Pressure(N 1 -47 €+O4 Slope Morphology Enabled. Change in Friction Angle(rads 1 -40E-O3 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mis) = 5 Calculation Tirne Step(s) = 1.00E-02 CaIculation Toleranc #HM## Max Acc. (m/s*s) Max Vel(m1s) Disp (m)

4 32.4 767 Min Acc. (m/s*s) Min Vel(m1s)

-3.56 -0.0238

Title: Table A5.1 Erosion (2.25 kslrnl

Model Choice: Plastic Ffow

Geometric Data Geometnc Model: Pambolic Parabofic shape function: 1.43E-04 Starting Height(m): 1 O0

Material Properties Bulk Unit Mass(kg/mA3) = 1 764 Initial Block Height( 2 Depostion/Erosion Rate(kg/m) 2.25 Block Width(m) = 1 Yield Strength(N/mA2) = 6500 Block Length(m) = 1

Kinet ics. lnital Vefocity (mis) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc 1.00E-05 Max Acc. (m/s*s) Max Vef(m/s Disp (m)

1 -2 17.3 753 Min Acc. (m/s9s) Min Vel(m/s)

-0.31 5 -0.001 83

Title:

Moâel Choice:

Table A5.2 Erosion (2.25 kzilml with Consolidation (saturated height = .2 m)

Friction Flow

Geometnc Data Geometric Model: Parabolic Parabolic shape function: 1 -43E-04 Starting Height(m): 1 O0

Bulk Unit Mass(kg/mA3) = 1764 Initial Block Height( 2 Depostion/Erosion Rate(kg/m) 2.25 Block Width(m) = 1 Fn'ction Angle(rads) = 0.6283 Block Length(m) = 1

ModeIlinci Options Enabled. Consolidation Enabled. Coef. of Consolidation(mA2/s) 6.34E-05 Saturated M a s Density(kg1rn 1.90E+03 Height of Water(m) = 2.00E-01 Initial Pore-Water Press.(N/m 1.65E+04 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. M a l Velocity (mls) = 3 Calcufation Time Step(s) = 1 .O0502 Calculation Toleranc 1.00E-05 Max Acc. (rn/s*s) Max Vel(m/s Oisp (m)

2.09 22.5 765 Min Acc. (m/s*s) Min Vel(m/s)

-0 -604 -0.00502

Title:

Model Choice:

Table A5.3 Erosion 12.25 kslm)

Voellmy Fluid Flow

Geomettic Data Geometn'c Modef: Parabolic Initial 8lock Height( 2 Parabolic shape function: 1.43E-O4 6lock Width(rn) = 1 Starting Height(m): 100 Bfock Length(m) = 1

Material Prooerties Bulk Unit Mass(kg/mA3) = 1764 Friction Angle(rads) = 5.24E-02 Turbulence Coef(m/sA2) = 450 Depostion/Erosion Rate(kg/m) 2.25 Centrifuga1 Acceleration Reduction Enabled.

Kinetics. lnital Velocity (mis) = 5 Calculation Time Step(s) = 1 -00E-02 Calculation Toleranc 1.00E-05 Max Acc. (mls's) Max Vel(m/s Disp (m)

1 .SI 11.8 774 Min Acc. (mls's) Min Vel(m/s)

-0.1 52 -7.75E-05

Title:

Mode1 Choice:

Geometric Data Geometnc Model: Parabolic shape function: StaRing Height(m):

Material Pro~erties Bulk Unit Mass(kg/mA3) = Depostion/Erosion Rate(kg1 Friction Angle(rads) =

Table A5.4 Erosion 12.25 kalm1 wîth Consolidation (saturated height 0.6 m)

Friction Flow

Para bolic 1 -43504 100

1764 Initial Block Height(rn 2 2.25 Block Width(m) = 1

0.6283 Block Length(rn) = 1

Modellina O~tions Enabled. Centrifuga1 Acceleration Reduction Enabled.

Kinetics. Inital Velocity (mis) = 3 Calculation Time Step(s) = 1.00E-02 Calculation Toleranc #### Max Acc. (m/ses) Max Vel(m/s) Disp (m)

1.69 20.3 759 Min Acc. (rn/s*s) Min Vel(m/s)

-0.408 -1.32E-03

Dialog Boxes and Output Screens from Cornputer Modal

Figure E3 1.1 Resistance Term Dialoa Box

Figure B 1.2 Geometric Properties Dialog Box

fime (s): 51.1 I

Oispiacernem

1.5834

Sliding Bock Not tn Scaie.

Fieure B2.1 Block Motion Outout Screen

Fimire B2.2 Granhine Program Output Screen

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