Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet

This paper develops a Monte Carlo simulation (MCS)-based reliability analysis approach for slope stability problems and utilizes an advanced MCS method called “subset simulation” for improving efficiency and resolution of the MCS at relatively small probability levels. Reliability analysis is operationally decoupled from deterministic slope stability analysis and implemented using a commonly available spreadsheet software, Microsoft Excel. The reliability analysis spreadsheet package is validated through comparison with other reliability analysis methods and commercial software. The spreadsheet package is then used to explore the effect of spatial variability of the soil properties and critical slip surface. It is found that, when spatial variability of soil properties is ignored by assuming perfect correlation, the variance of the factor of safety (FS) is overestimated, which may result in either over (conservative) or under (unconservative) estimation of the probability of failure (Pf = P(FS < 1)). When...

[1]  Bak Kong Low,et al.  Probabilistic Stability Analyses of Embankments Based on Finite-Element Method , 2006 .

[2]  Wilson H. Tang,et al.  New methods for system reliability analysis of soil slopes , 2011 .

[3]  Jin-Jian Chen,et al.  Effect of Spatial Correlation of Cone Tip Resistance on the Bearing Capacity of Piles , 2013 .

[4]  D. Cruden,et al.  Probabilistic slope stability analysis for practice , 2002 .

[5]  Gordon A. Fenton,et al.  Probabilistic slope stability analysis by finite elements , 2004 .

[6]  J. Y. Ching,et al.  Reliability analysis of a benchmark problem for 1-D consolidation , 2009 .

[7]  S. K. Au,et al.  Reliability analysis of slope stability by advanced simulation with spreadsheet , 2009 .

[8]  G. L. Sivakumar Babu,et al.  Effect of soil variability on reliability of soil slopes , 2004 .

[9]  Yu Wang,et al.  Reliability analysis of a benchmark problem for slope stability , 2009 .

[10]  Han Ping Hong,et al.  Reliability Evaluation of Earth Slopes , 2008 .

[11]  Thomas F. Wolff,et al.  Search Algorithm for Minimum Reliability Index of Earth Slopes , 2001 .

[12]  Kok-Kwang Phoon,et al.  Application of the Kriging-Based Response Surface Method to the System Reliability of Soil Slopes , 2013 .

[13]  E. Vanmarcke.  Probabilistic Modeling of Soil Profiles , 1977 .

[14]  Tien H. Wu,et al.  System reliability of slope stability , 1990 .

[15]  Douglas J. Kamien.  Engineering and Design: Introduction to Probability and Reliability Methods for Use in Geotechnical Engineering , 1997 .

[16]  Zhe Luo,et al.  Reliability analysis of basal-heave in a braced excavation in a 2-D random field , 2012 .

[17]  W. H. Tang,et al.  Probability-based short term design of soil slopes , 1976 .

[18]  A. Bishop.  The use of the Slip Circle in the Stability Analysis of Slopes , 1955 .

[19]  Yu Wang,et al.  Uncertain parameter sensitivity in Monte Carlo Simulation by sample reassembling , 2012 .

[20]  Melvin J. Dubnick.  Army Corps of Engineers , 1998 .

[21]  R. N. Chowdhury,et al.  Geotechnical system reliability of slopes , 1995 .

[22]  Dian-Qing Li,et al.  Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis , 2012 .

[23]  J. Christian,et al.  Reliability Applied to Slope Stability Analysis , 1994 .

[24]  Yu Wang,et al.  Implementing advanced Monte Carlo simulation under spreadsheet environment , 2010 .

[25]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[26]  R. D'Andrea,et al.  Safety Factors for Probabilistic Slope Design , 1982 .

[27]  E. Spencer.  A Method of Analysis of the Stability of Embankments Assuming Parallel Inter-Slice Forces , 1967 .

[28]  Norbert R. Morgenstern,et al.  PROBABILISTIC ASSESSMENT OF STABILITY OF A CUT SLOPE IN RESIDUAL SOIL , 2005 .

[29]  Siu-Kui Au,et al.  Application of subset simulation methods to reliability benchmark problems , 2007 .

[30]  Keh-Han Wang,et al.  Flexible Porous Wave Barrier for Enhanced Wetlands Habitat Restoration , 2003 .

[31]  N. R. Morgenstern,et al.  Extensions to the generalized method of slices for stability analysis , 1983 .

[32]  Gordon A. Fenton,et al.  Influence of spatial variability on slope reliability using 2-D random fields. , 2009 .

[33]  Akbar A. Javadi,et al.  Reliability assessment of infinite slope stability using the jointly distributed random variables method , 2012 .

[34]  N. Morgenstern,et al.  The analysis of the stability of general slip surfaces , 1965 .

[35]  J. M. Duncan,et al.  Factors of Safety and Reliability in Geotechnical Engineering , 2000 .

[36]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[37]  J. M. Duncan,et al.  Soil Strength and Slope Stability , 2005 .

[38]  W. Tang,et al.  Efficient Spreadsheet Algorithm for First-Order Reliability Method , 2007 .

[39]  Claudio Cherubini,et al.  Reliability Analysis Of Slopes , 1970 .

[40]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[41]  Robert B. Gilbert,et al.  SLOPE RELIABILITY ANALYSIS USING GENERALIZED METHOD OF SLICES , 1998 .

[42]  P. Lumb,et al.  Probabilistic design of slopes , 1987 .

[43]  James L. Beck,et al.  SUBSET SIMULATION AND ITS APPLICATION TO SEISMIC RISK BASED ON DYNAMIC ANALYSIS , 2003 .

[44]  Robert V. Whitman,et al.  Organizing and evaluating uncertainty in geotechnical engineering , 2000 .

[45]  K. Phoon,et al.  Reliability Analysis of Infinite Slope using Subset Simulation , 2009 .

[46]  N. Janbu,et al.  SLOPE STABILITY COMPUTATIONS , 1973 .

[47]  Bak Kong Low,et al.  Reliability analysis of reinforced embankments on soft ground , 1997 .

[48]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[49]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.