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Probabilistic Slope Stability Analysis
with the
Scope of Presentation
 Overview of Response Surface Methodology (RSM)
 Implementation of RSM in probabilistic slope stability
analysis
 Verification Examples
 General guidelines for use of RSM
Slope Design Approaches
Deterministic
Factor of Safety
(FOS)
Uncertainty:
 Geology
 Strength
 Water
Probabilistic
Risk Analysis
Probability of
Failure(POF)
Economic / Safety
impact
Probabilistic Analysis
1) Monte Carlo Simulation
2) Point Estimate Method (PEM)
Monte Carlo Simulation
MONTE CARLO
ANALYSIS
Model
Friction angle
Cohesion
CC
(SLIDE, Phase2,
FLAC, UDEC )
OUTPUT
RESULTS
1.0
Frequency
Frequency
Frequency
INPUT
DATA
POF
FOS
POF model = P ( FOS < 1.00 )
Highlights
1) Large no. of runs (103).
2) Reveals Sensitivities
3) Very Flexible
Point Estimate Method (PEM)
INPUT
DATA
2n MODEL
Frequency
Frequency
RUNS
Model
Friction angle
Cohesion
OUTPUT
RESULTS
(SLIDE, Phase2,
FLAC, UDEC )
FOS Statistics
1. Mean
2. Variance
CC
Highlights
1) Evaluate model at 2n points.
2) Assume a form for the FOS probability distribution
3) No sensitivity information
POF
Response Surface Methodology
Response Surface Techniques
Response Surface Techniques
Concept
1) Evaluate model at
FOS
selected points
2) Use interpolation
scheme to
generate response
surface
RSM Overview
Response Surface
Generation
MONTE CARLO
ANALYSIS
OUTPUT
RESULTS
Model
(SLIDE,
UDEC
etc)
EXCEL
Frequency
1.0
POF
FOS
Approach
 RSM vs. Model (SLIDE)
 Cohesion & friction angle uncertain variables
 RSM using linear interpolation
Models
90m
Homogeneous Slope: (Normal)
Homogeneous Slope : (Lognormal)
3 Material Slope : (Normal)
 Requires 2n + 1 points vs. 2n for
PEM
 Piecewise Linear / Quadratic
 Grouping Variables
interpolation can be used.
b
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.0
0.2 must
0.4 be 0.6
0.4
0.6
0.8
1.0
Evaluation
points
in 0.8
Normalised Cohesion Normalised Cohesion
region of interest (+ / - 1 std dev).
0.0  0.2
Friction
Angle
Cohesion
Strength
1.0
 Use of RSM with strongly correlated variables
1) Good agreement between RSM and Monte Carlo Simulation
2) Low computational times
3) Practical way to incorporate numerical analysis in probabilistic
slope design
4) Reveals Sensitivities
5) Very flexible