UNITEN ICCBT 08 Probabilistic Approach of Rock Slope Stability Analysis Using

8/11/2019 UNITEN ICCBT 08 Probabilistic Approach of Rock Slope Stability Analysis Using

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ICCBT 2008 - E- (37) pp449-468

ICCBT2008

Probabilistic Approach of Rock Slope Stability Analysis Using

Monte Carlo Simulation

M. S. Mat Radhi,Universiti Putra Malaysia,MALAYSIA

N. I. Mohd Pauzi*, Universiti Tenaga Nasional,MALAYSIA

H. Omar, Universiti Putra Malaysia,MALAYSIA

ABSTRACT

___________________________________________________________________________

Probabilistic analysis has been used as a tool to analyze and model variability and

uncertainty for rock slope analysis. Uncertainty in rock slope may appear as scattered values

of discontinuity length and persistence. This study is to develop the probabilistic approach of

rock slope stability based on discontinuity parameters using Monte Carlo simulation. The

probabilistic analysis was done using kinematic and kinetic analysis. Kinematic analysis is

based on stereographic projection analysis and kinetic analysis is based on the deterministic

analysis. Factor of Safety (FOS) is determined for each type of failure i.e. planar and wedgefailure. The slope that has FOS less than 1.00 is considered as not stable and FOS more than

1.00 is considered as stable. Data of six slopes which is denoted as Slope S1, S2, S3, S4, S5

and S6 show that, Slope S2, Slope S4, and Slope S6 have FOS of 0.953, 0.991, and 0.891

respectively which show the slope as not stable. Whilst for wedge failure analysis, all the

slopes show FOS greater than 1.00 which is stable, although the kinematic analysis

(stereographic projection) shows otherwise. Probabilistic analysis is developed for rock slope

stability using Monte Carlo Simulation. Monte Carlo simulation calculate the probability of

failure for planar and wedge type of failure. The probability of failure (Pf) for planar failure

at slope S2, S4, and S6 are 51.6%, 17.8%, and 49% respectively. Wedge failure analysis show

0% probability of failure for dry slope cases while for wet slope cases, all slopes excluded the

S1 has the probability of failure (Pf) varies from 7.7% to 75.2%. This shows that theprobabilistic analysis will give relevant and enhance results which can help to determine

instability of rock slope. The development of probabilistic analysis using Monte Carlo

simulation is useful tool to get an accurate data in stability analysis of rock slope which have

great values of uncertainty.

Keywords: Probabilistic Approach, Monte Carlo Simulation, Rock slope stability

*Correspondence Authr: Nur Irfah Mohd Pauzi, Universiti Tenaga Nasional, Malaysia. Tel: +60389212020 ext

6254, Fax: +60389212116. E-mail: [email protected]
http://www.uniten.edu.my/newhome/content_list.asp?contentid=4017


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Probabilistic Approach of Rock Slope Stability Analysis Using Monte Carlo Simulation

ICCBT 2008 - E- (37) pp449-468450

1. INTRODUCTION

Uncertainty and variability are common in engineering geology studies dealing with natural

materials. This is because of rocks and soils are inherently heterogeneous, insufficient amount

of information for site conditions are available and the understanding of failure mechanism isincomplete. There are many researcher have made efforts to limit or quantify uncertainty of

input data and analysis results. Perhaps, slope engineering is the geotechnical subject most

dominated by uncertainty since slopes are composed of natural materials [2]. Uncertainty in

rock slope engineering may occur as scattered values for discontinuity orientations and

geometries such as discontinuity length and persistence. Therefore, one of the greatest

challenges for rock slope stability analysis is the selection of representative values from

widely scattered discontinuity data. Since geotechnical engineering problems are

characterized by uncertain variables, design is always subjected to uncertainties

Application of probabilistic analysis has provided an objective tool to quantify and model

variability and uncertainty. It makes the rock slope stability possible to consider uncertaintyand variability in geotechnical and geological parameters. There is several commercial

available limit equilibrium codes (such as SWEDGE, ROCKPLANE, SLIDE, SLOPE/W)

often incorporate probabilistic tools, in which variations in discontinuity properties can be

assessed.

Various probabilistic studies of rock slopes and mining areas have been carried out by these

researchers [10, 11, 1, 9, 5, 6, 7, 14].Though in Malaysia, such research are very few and

limited.

In summary, this study is to determine probabilistic analysis of rock slope stability based on

discontinuity parameters which is analyze and simulate probabilistic analysis method. Hence,

it would become helpful for the engineers to design and monitor the rock slope. The main aim

of this research is to determine probabilistic analysis of rock slope stability based on

discontinuity parameters which will help the slope engineers in rock slope design and stability

analysis.

2. BASIC THEORY

The development of road and highway constructions involved deep cutting into the slope, in

order to minimize the traveling time and distance between the two places. Besides, the need of

development on hilly areas for building and residential purpose has also increased and theselead to the concern of safety and stability of the slope for the public. The slope failure occur

due to human and natural causes which consist of improper planning, design and

implementation of the projects for human error while natural causes may be result of

weathering process, weak material and geological setting of the area.

In this research, cutting of rock slope is the major concern to be studied since a high degree of

reliability is required because slope failure or even rock falls can rarely be tolerated. Rock

slope stability is concern about analyzing the structural fabric of the site to determine if the

orientation of the discontinuities could result in instability of the slope under consideration.

Basically, there are four types of rock slope failures that always occurred at the rock slope

which are planar failure, wedge failure, toppling failure, and circular failure.


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M. S. Mat Radhi et. al.

ICCBT 2008 - E- (37) pp449-468 451

Planar failure is movement occurs by sliding on a single discrete surface that approximates a

plane and it is analyzed as two-dimensional problems which additional discontinuities may

define the lateral extent of planar failures, but these surfaces are considered to be release

surfaces, which do not contribute to the stability of the failure mass. Wedge failure happenedwhen rock masses slide along two intersection discontinuities both of which dip out of the cut

slope at an oblique angle to the cut face, forming a wedge-shaped block. Toppling failure

happened most commonly in rock masses that are subdivided into a series of slabs or columns

formed by a set of fractures that strike approximately parallel to the slope face and dip steeply

into the face. Circular failure is defined as a failure in rock for which the failure surface is not

predominantly controlled by structural discontinuities and that often approximately the arc of

a circle. Rock types that are susceptible to circular failures include those that are partially to

highly weathered and those that are closely and randomly fractured.

Applications of probabilistic analysis in geotechnical engineering have increased remarkably

in recent years. This is ranging from practical design and construction problems to advancedresearch publications. A lot of study and research have been conducted regarding probabilistic

analysis since geotechnical and geological engineering deal with material whose properties

and spatial distribution are poorly known. Consequently, a somewhat different philosophical

approach is necessary to overcome the uncertainty occurs in geotechnical and geological

engineering.

This paper explains on determining probability of failure of the rock slope which deals with

the uncertainty in geotechnical and geological engineering parameter using Monte Carlo

simulation. The Monte Carlo simulation used the extensive computational effort involved in

the simulations required researchers to develop their own software to solve slope stability

problems. The limitations and sometimes the complexities of probabilistic methods combined

with the poor training of most engineers in statistic and probabilistic theory have substantially

inhibited the adoption of probabilistic slope stability analysis in practice.

3. METHODOLOGY

Methodology of the research can be described by four stages; the first one is literature search

and formulation of objective, the second one is data collection at the field, the third one is

analysis and overview on the data collection and finally, the fourth stage is the developmentof the probabilistic approach using Monte Carlo simulation and finally suggestion for further

work to be done for this research. The flow chart of the methodology is shown in Figure 1.


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ICCBT 2008 - E- (37) pp449-468452

Figure 1. Methodology of the research

The data collections at site are such as discontinuity data on the cut slope, classification and

identification of grade weathering and lithology of the selected cut slope. Then, the analysis

on the fieldwork data is done using kinematic analysis and kinetic analysis. The kinematic

analysis is done using the data collection of geological structural at site. The DIPS 3.0

software is used to give the analysis in Rosette Plot, Scatter Plot, Pole Plot, and Potential

Instability.

Limit equilibrium method which is also known as kinetic analysis is carried out to determine

factor of safety for each cases of potential instability. The probabilistic approach is developed

using Monte Carlo Simulation Method for rock slope stability analysis. The development of

this probabilistic approach is done using spreadsheet software such as EXCEL and

probabilistic simulation is done using RISKAMP. These two software are link together and

the analysis is simulated which is called Monte Carlo Simulation.

Probabilistic approach is carried out by simulating the results according to number of

iteration. For each number of iteration, it would give the Factor of Safety (FOS) from where

the probability of failure can be obtained. The simulation carried out here are for 10, 100, 500,


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ICCBT 2008 - E- (37) pp449-468 453

1000, 5000, and 10000 no of iteration. The input data needed for the development of

probabilistic approach is the kinematic and kinetic analysis data. The kinematic analysis

inputs are the dip and dip direction data, friction angle, cohesion, and slope angle. The outputs

data are the type of failure of the slope whether it is planar, wedge, toppling or combination of

the two type of failure.

The kinetic analysis requires input data such as slope properties, cohesion, friction angle, and

groundwater table. The outputs from this analysis are the FOS of the slope. If FOS is less than

1, the slope is considered fail and if the FOS is more than 1, the slope is stable. The output

from kinetic analysis only gives one value of FOS. Then, when the simulation is carried out

for 10 times, 100 times, 500 times, 1000 times, 5000 times and 10000 times, the RiskAMP

software would gives many results of FOS and probability of failure, Pf for that particular

slope.

4. RESULTS AND ANALYSIS

4.1 Pos Selim Area

The probabilistic analysis which is developed for this study has been tested using data from

Pos Selim Highway. This probabilistic analysis is used to get accurate result and to determine

the uncertainties in geotechnical data. The probabilities of failure of the slope are the outcome

of this research.

Pos Selim Highway is located in Perak and can be accessed from Simpang Pulai or Cameron

Highland. The highway is part of the Malaysian Plan for East West second Link and divided

into eight packages. The highway starts from Simpang Pulai in Perak and ends at Kuala

Berang in Terengganu. Package two has been awarded to MTD Construction Sdn. Bhd. under

a Fixed Turnkey Lump Sum contract of total RM 282 million. The construction of the

highway in package two has started in May 1997 and was scheduled for completion in April

2000 [8]. Due to continuous cut slope failure along the highway, the construction of this

project was delayed [12]. Now in the year of 2005, the project has been opened to be used for

the public.

Along the terrain of Pos Selim Highway, there are two types of main lithological units which

are igneous and metasediment rock (Figure 4.1). The igneous rocks consist of granite and

metasediment rocks consist of quartz mica schist, quartz schist and closely foliated phylite.Granite rock covers over 65% while metasediment is about 35% [8].

Locations of slope study are distributed over three granite slopes and three schist slopes.

These slopes have been labeled as a S1, S2, and S3, which cover the granitic areas and S4, S5,

and S6 cover the schist areas (Table 1).


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ICCBT 2008 - E- (37) pp449-468454

S

S

Figure 2. Pos Selim Area with granite and schist formation

Table 1: Study Locations and Lithology

Slope Location Lithology

S1 Ch 2 + 960 Granite



S4 Ch 18 + 280 Schist



4.2 Kinematic Analysis

Kinematic analysis is done to plot the discontinuity data such as dip and dip direction into

graphical method. The graphical method which are discussed in this analysis are pole plot,

rosette plot, scatter plot. From these plots, the potential instability for each slope can be

determined.

4.2.1 Pole plot

From the six slopes that have been chosen for study, about 637 of discontinuity data have

been collected for analysis. From Figure 3, it can be seen that joint is the most dominant and

common at field, followed by fault and lastly foliation. The percentage occurrence of joint

from field measurement is 79.7%, while fault is 10.9% and another 9.4% is foliation. S1, S2


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ICCBT 2008 - E- (37) pp449-468 455

0

20

40

60

80

100

120

S1 S2 S3 S4 S5 S6

Joint Fault Foliat ion

(Figure 4), and S3 show that joint is dominant and higher which are 97%, 81%, and 97%

respectively from field measurement. S4, S5 (Figure 5), and S6 show that percentage of joint

decrease which is 63%, 70%, and 67% respectively.

Figure 3. Discontinuity data showing percentage of joint, fault and foliation at S1, S2, S3, S4,

S5 and S6.


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ICCBT 2008 - E- (37) pp449-468456

Figure 4. Pole Plot at S2

Figure 5. Pole Plot at S5

4.2.2 Scatter Plot Analysis

Scatter plot data (Figures 6) collected for six numbers of slopes, the total number of plot is

584. Table 2 has summarized scatter plot for each slope which shows three category of plot;

one, two, and three plots. The importance of the scatter plot is to distinguish any discontinuity

data that have the same value of dips and dips direction, where in pole plot it does not show

the poles that share the same value.


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ICCBT 2008 - E- (37) pp449-468 457

Figure 6: Scatter plot data

Table 2. No. of Scatter plot for each study slope

Slope One Plot() Two Plot() Three Plot() Total Plot

S1

S2

S3

S4

S5

S6

89

98

91

85

81

94

10

7

4

6

9

3

1

1

1

1

3

0

100

106

96

92

93

97

Total 538 39 7 584

4.2.3 Rosette PlotAnalysis

There are 525 of planes out of 637 discontinuities that have been plotted into rosette plot

(Figure 7) covering S1, S2, S3, S4, S5, and S6. Dips direction of each slope is plotted into

respected bin at interval of 10 degrees. Table 3 shows the maximum and minimum

frequencies of plotted plane for each slope, which are 10 and 1 respectively. Each slope has

only two bin of maximum frequency, whilst the number of bin for minimum frequency varies

between two and four.


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ICCBT 2008 - E- (37) pp449-468458

Figure 7. Rosette Plot

Table 3. No of plotted plane in Rosette Plot for each study slope

SlopePlotted

Planes

Maximum Plot

(Bin No)

Minimum

Plot (Bin No)

Total

Discontinuity

S1 92 6a& 24a 4c, 12c, 16c, 22c, 29c, &

34c112

S2 98 7b& 25b 1c, 5c, 13c, 19c, 23c,&

31c115

S3 92 13a& 31a 6c, 10c, 24c, & 28c 102

S4 79 7a& 25a 4c, 5c, 9c, 21c, 22c, &

27c100

S5 84 6a& 24a 4d, 11d, 14d, 22d, 29d, &

32d108

S6 80 18a& 36a 8c, 16c, 26c, & 34c 100

Total 525 118 38 637

a = frequency of 10, b = frequency of 9, c = frequency of 1, d = frequency of 2.

4.2.4 Potential Instability

Potential instability analysis is determined using stereoplot computer software, DIPS. This

analysis facilitates the determination of possible kinematic sliding of weathered rock slope in

types of planar, wedge, and toppling failure. Planar and wedge failure analysis is referred to

the work by Hoek and Bray [4], but toppling failure analysis is referred to Goodman and Bray

[3].


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ICCBT 2008 - E- (37) pp449-468460

Table 4 Continue

5-6% 86/122 J1 Joint Granite

S3 >10% 68/220 J2 Joint Granite

CH 17600 3-4% 52/79 J3 Joint Granite

7-8% 71/313 J4 Joint Granite

8-9% 45/87 J1 Joint Schist

S4 6-7% 65/322 J2 Joint Schist

CH 18280 6-7% 74/208 J3 Joint Schist

6-7% 66/237 J4 Joint Schist

>12% 35/98 J1 Foliation Schist

S5 10.5-12% 71/252 J2 Joint Schist

CH 18800 4.5-6% 87/176 J3 Joint Schist

4.5-6% 62/315 J4 Joint Schist

>10% 62/261 J1 Joint Schist

S6 7-8% 19/191 J2 Joint SchistCH 20750 6-7% 68/292 J3 Joint Schist

4.3 Kinetic Analysis

Kinetic analysis is carried out by applying direct formula using single fixed values (typically,

mean values). Therefore, the stability analysis is carried out using only one set of geotechnical

parameter. Factor of safety, based on limit equilibrium is widely used to evaluate slope

stability because of its simple calculation and results.

From this study, three slopes out of six slopes have been identified potential planar failure

which is S2, S4, and S6. Through these three slopes, only three joint sets have fall and satisfy

with conditions for planar failure. Table 5 below shows factor of safety for each joint set for

wet and dry case for planar failure.


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ICCBT 2008 - E- (37) pp449-468 461

Table 5. Results of Factor of Safety for Planar Failure

SlopeJoint Set

I.D.

Slope

Face

(deg)

Planar

Failure

(deg)

Mean Friction

Angle (deg)

Factor of

Safety

(Wet)

Factor of

Safety

(Dry)J1 77 30 Stable Stable

J2 80 30 Stable Stable


S1

J4

63

72 30 Stable Stable

J1 59 30 0.879 0.953



S2

J4

63

48 30 Stable Stable




S3

J4

73

71 30 Stable Stable

S4 J1 63 45 30 0.899 0.991




S5 J1 102 35 30 Stable Stable




S6 J1 63 62 30 0.767 0.891



For wedge planar failure case, five slopes have been identified potential to fail which are S2,

S3, S4, S5, and S6. Nine intersections of joint sets have been identified and satisfied for this

type of failure. The results for factor of safety for each intersection joints are shown in Table

6 below for wet and dry case.

Table 6. Results of Factor of Safety for Wedge Failure

SlopeIntersection

Joint

Slope Face

(deg)

Dip of

intersection

(deg)

Mean

Friction

Angle (deg)

Factor of

Safety

Factor of

Safety

(Dry)J1J2 58 30 1.296 Stable

J1J3 36 30 1.411 Stable

S2

J1J4

63

33 30 Stable Stable

J3J1 43 30 0.931 StableS3

J3J4

73

48 30 0.999 Stable

S4 J1J3 63 56 30 1.395 Stable

J2J3 17 30 1.434 StableS5

J3J4

102

38 30 0.831 1.572

S6 J1J3 63 30 30 Stable Stable


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ICCBT 2008 - E- (37) pp449-468 463

0

0.5

1

1.5

2

2.5

10 100 500 1000 5000 10000

No of Iter ation

Mean

ofFoS

Wet Slope Dry slope

Figure 9. Mean of FOS at J1J2, S2 for each iteration.

0

0.2

0.4

0.6

0.8

1

10 100 500 1000 5000 10000

No of Iteration

Pf

Wet Slope Dry Slope

Figure 10. Probability of wedge failure at J1J2, S2 for each iteration.


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ICCBT 2008 - E- (37) pp449-468464

0

0.5

1

1.5

2

2.5

1.44

1.56

1.68 1.

81.92

2.04

2.16

2.28 2.

42.52

2.64

Factor of Safety

Frequency

0

0.5

1

1.5

2

2.5

3

3.5

0.27

0.39

0.51

0.63

0.75

0.87

0.99

1.11

1.23

1.35

1.47

Factor of Safety

Frequency

0

2

4

6

8

10

12

14

1.38

1.54 1.

71.86

2.02

2.18

2.34 2.

52.66

2.82

2.98

Factor of Safety

Frequency

0

2

4

6

8

10

12

0.17

0.33

0.49

0.65

0.81

0.97

1.13

1.29

1.45

1.61

1.77

Factor of Safety

Frequency

0

10

20

30

40

50

60

70

1.29

1.47

1.65

1.83

2.01

2.19

2.37

2.55

2.73

2.91

3.09

Factor of Safety

Frequency

0

10

20

30

40

50

60

70

0.07

0.25

0.43

0.61

0.79

0.97

1.15

1.33

1.51

1.69

1.87

Factor of Safety

Frequency

(a) Wedge Failure Wet Slope (left) and Dry Slope (right) for 10 iteration

(b) Wedge Failure Wet Slope (left) and Dry Slope (right) for 100 iteration

(c) Wedge Failure Wet Slope (left) and Dry Slope (right) for 500 iteration

Figure 11. Histogram of FOS calculated in probabilistic analysis for combination of joint set 1

and 2 at S2.


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ICCBT 2008 - E- (37) pp449-468 465

0

200

400

600

800

1000

1200

1400

1 .2 4 1 .4 4 1 .6 4 1 .8 4 2 .0 4 2 .2 4 2 .4 4 2 .6 4 2 .8 4 3 .0 4 3 .2 4

Factor of Safety

Frequency

0

200

400

600

800

1000

1200

1400

0 .0 4 0 .2 4 0 .4 4 0 .6 4 0 .8 4 1 .0 4 1 .2 4 1 .4 4 1 .6 4 1 .8 4 2 .0 4

Factor of Safety

Frequency

0

20

40

60

80

100

120

1.31

1.49

1.67

1.85

2.03

2.21

2.39

2.57

2.75

2.93

3.11

Factor of Safety

Frequency

0

20

40

60

80

100

120

140

0.06

0.26

0.46

0.66

0.86

1.06

1.26

1.46

1.66

1.86

2.06

Factor of Safety

Frequency

0

100

200

300

400

500

600

700

1.2

1.4

1.6

1.8 2

2.2

2.4

2.6

2.8 3

3.2

Factor of Safety

Frequency

(d) Wedge Failure Wet Slope (left) and Dry Slope (right) for 1000 iteration

0

100

200

300

400

500

600

700

-0.01

0.19

0.39

0.59

0.79

0.99

1.19

1.39

1.59

1.79

1.99

Factor of Safety

Frequency

(e) Wedge Failure Wet Slope (left) and Dry Slope (right) for 5000 iteration

(f) Wedge Failure Wet Slope (left) and Dry Slope (right) for 10000 iteration

Figure 11: Histogram of FOS calculated in probabilistic analysis for combination of joint set 1

and 2 at S2 (continued).

The result could be interpreted that the increase in the number of iteration in Monte Carlo

simulation, the result becomes even details and thus increase the accuracy of calculation of

factor of safety of the rock slope. Probability of failure for dry slope at slope S2 is zero which

means the slope is stable and when the slope in wet condition, the probability of failure is in

the range of 0.752 to 0.802.


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ICCBT 2008 - E- (37) pp449-468466

5. CONCLUSIONS

For the planar failure shown in Table 8 for 10000 number of iteration, deterministic

analysis of J1 at S2 gives 0.879 and 0.953 for wet and dry slope cases, while in probabilistic

analysis it gives 76.3% and 51.6% respectively. For J1 at S4, deterministic analysisshows the lowest values of FOS; 0.899 and 0.991. But probabilistic analysis gives

the result of 38% and 17.8% for wet and dry slope cases. For planar failure of J1 at S6 gives

the high values of probability failure which is 62.9% and 49% and deterministic analysis

results are 0.767 and 0.891 respectively. These indicate that the slope has high possibility

of planar failure at J1 for S2 and S6, compare to J1 of S4. The Slope of S2, S4, and S6 also

show that probability of failure is high even the slopes are in dry condition.

For wedge analysis shown in Table 9 for 10000 number of iteration, high probability of

failure are determined at J1J2 and JIJ3 of S2, with 75.2 % and 57.9% respectively,

J3J4 of S3 with 48.2%, and J 1J3 o f S4 with 43% . Eve n deterministic values show

the FOS is more and equal to 1.00, it still has a higher probability to fail in these

circumstances. For example in slope S2 for wedge failure in Table 9, the FOS values is 1.434

but the probabilistic analysis result show otherwise where its probability of failure is 0.77 for

wet slope. This means that although factor of safety calculation said the slope is stable but the

probabilistic analysis run using Monte Carlo has detailed out the calculation and indicates the

slope is not stable.

Others intersection shows the lower results of probabilistic analysis with less than 40% for

each cases. The probabilistic analysis for wedge failure show that in dry condition, the value

of Pfis equal to 0, which mean that the slope is stable.

Table 8. Comparison of results for the deterministic and probabilistic analysis

(iteration of 10000) for planar failure

Deterministic ProbabilisticJoint Set Potential

Slope Analysis (FOS) Analysis (Pf)

InstabilityI.DWet Dry Wet Dry

J1 No Stable Stable 0 0

J2 NoStable Stable 0 0

S1J3 Planar Stable Stable 0 0


J1 Planar 0.879 0.953 0.763 0.516

S2 J2 No Stable Stable 0 0





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ICCBT 2008 - E- (37) pp449-468 467

Table 8 continue


J3 Planar Stable Stable 0 0


J1 Planar 0.899 0.991 0.38 0.178




J1 Planar Stable Stable 0 0




J1 Planar 0.767 0.891 0.629 0.49

S6 J2 No StableStable 0

0


Table 9. Results of wedge failure for the deterministic analysis and the

probabilistic analysis (iteration of 10000)

Deterministic Probabilistic

Set Set PotentialSlope No. I No. 2 Instability Analysis (FOS) Analysis (Pf)

Wet Dry Wet Dry

S1 J2 J3 No Stable Stable 0 0

J1 J2 Wedge 1.296 Stable 0.752 0

S2 J1 J3 Wedge 1.411 Stable 0.579 0

J1 J4 Wedge Stable Stable 0.203 0

J3 J4 Wedge 0.999 Stable 0.482 0



J3 J2 Wed e 1.434 Stable 0.77 0S5 J3 J4 Wedge 0.831 1.572 0.386 0

S6 J1 J3 Wedge Stable Stable 0.32 0


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ICCBT 2008 - E- (37) pp449-468468

Acknowledgements

The authors would like to thanks Universiti Putra Malaysia (UPM) for the funding of this

project and Universiti Tenaga Nasional (UNITEN) for their constant support andencouragement.

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