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Probabilistic Slope Stability Analysis with the

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Presentation on theme: "Probabilistic Slope Stability Analysis with the"— Presentation transcript:

1 Probabilistic Slope Stability Analysis with the
“Response Surface Methodology” (Henry T. Chiwaye)

2 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

3 Slope Design Approaches
Deterministic Factor of Safety (FOS) Probabilistic Probability of Failure(POF) Risk Analysis Economic / Safety impact Uncertainty: Geology Strength Water

4 Probabilistic Analysis
Monte Carlo Simulation Point Estimate Method (PEM)

5 Monte Carlo Simulation
CC Friction angle Cohesion Frequency INPUT DATA MONTE CARLO ANALYSIS (SLIDE, Phase2, FLAC, UDEC ) Model OUTPUT RESULTS 1.0 Frequency FOS POF model = P ( FOS < 1.00 ) POF Highlights Large no. of runs (103). Reveals Sensitivities Very Flexible

6 Point Estimate Method (PEM)
CC Friction angle Cohesion Frequency INPUT DATA 2n MODEL RUNS (SLIDE, Phase2, FLAC, UDEC ) Model OUTPUT RESULTS FOS Statistics Mean Variance POF Highlights Evaluate model at 2n points. Assume a form for the FOS probability distribution No sensitivity information

7 Response Surface Methodology
Response Surface Techniques Monte Carlo Simulation Probability Of Failure (%)

8 Response Surface Techniques

9 Response Surface Techniques
Concept Var 1 Var 2 FOS Evaluate model at selected points Use interpolation scheme to generate response surface

10 Response Surface Generation
RSM Overview Response Surface Generation Model (SLIDE, UDEC etc) MONTE CARLO ANALYSIS EXCEL 1.0 POF OUTPUT RESULTS FOS Frequency

11 RSM Verification Approach RSM vs. Model (SLIDE)
Cohesion & friction angle uncertain variables RSM using linear interpolation Models 90m

12 Model vs. RSM (POF %) Homogeneous Slope: (Normal)

13 Model vs. RSM (POF %) Homogeneous Slope : (Lognormal)

14 Model vs. RSM (POF %) 3 Material Slope : (Normal)

15 RSM vs. PEM (POF %) Requires 2n + 1 points vs. 2n for PEM

16 RSM Guidelines Piecewise Linear / Quadratic interpolation can be used.
Grouping Variables Strength Cohesion Friction Angle Evaluation points must be in region of interest (+ / - 1 std dev).

17 Remarks Use of RSM with strongly correlated variables

18 Conclusions Good agreement between RSM and Monte Carlo Simulation
Low computational times Practical way to incorporate numerical analysis in probabilistic slope design Reveals Sensitivities Very flexible

19 Questions?

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