Probabilistic Analyses of Slopes: A State of the Art Review

Slope stability analyses are evolving from deterministic analyses, which rely only on the mean value of each parameter, to more advanced probabilistic methods. Moreover, many researchers have shown the benefits of considering spatial variability of soil properties in probabilistic analyses of slopes that may lead to a more economical and/or safer design . Spatial variability is usually modeled by random fields theory in both limit equilibrium and finite element based probabilistic analyses. This paper presents a state of the art review of the literatures on probabilistic analyses of slopes that may help researchers to choose a suitable probabilistic method for their problems.

[1]  R. Rackwitz Reliability analysis—a review and some perspectives , 2001 .

[2]  D Y Zhu,et al.  A new procedure for computing the factor of safety using the Morgenstern-Price method , 2001 .

[3]  K. Phoon,et al.  Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams , 2010 .

[4]  R. Suchomel,et al.  Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c–φ soil , 2010 .

[5]  T. Wolff Probabilistic Slope Stability in Theory and Practice , 1996 .

[6]  J. M. Duncan THE USE OF BACK ANALYSIS TO REDUCE SLOPE FAILURE RISK , 1999 .

[7]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

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

[9]  Sung-Eun Cho,et al.  Effects of spatial variability of soil properties on slope stability , 2007 .

[10]  Kok-Kwang Phoon,et al.  Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling , 2009 .

[11]  B. Satyanarayana,et al.  A Method of Analysis of the Stability of Embankments Assuming Parallel Inter-Slice Forces , 1967 .

[12]  R. Lewis,et al.  Associated and non-associated visco-plasticity and plasticity in soil mechanics , 1975 .

[13]  Donald E. Myers,et al.  Reliability and Statistics in Geotechnical Engineering , 2005, Technometrics.

[14]  D. V. Griffiths,et al.  Bearing capacity of spatially random soil: the undrained clay Prandtl problem revisited , 2001 .

[15]  M. Jaksa The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay. , 1995 .

[16]  Gautam Bhattacharya,et al.  Geotechnical Slope Analysis , 2010 .

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

[18]  Abdallah I. Husein Malkawi,et al.  Uncertainty and reliability analysis applied to slope stability , 2000 .

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

[20]  J. Ching,et al.  Efficient evaluation of slope stability reliability subject to soil parameter uncertainties using importance sampling , 2008 .

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

[22]  Gordon A. Fenton,et al.  Comparison of Slope Reliability Methods of Analysis , 2010 .

[23]  D. V. Griffiths,et al.  Risk Assessment in Geotechnical Engineering , 2008 .

[24]  D. V. Griffiths,et al.  SLOPE STABILITY ANALYSIS BY FINITE ELEMENTS , 1999 .

[25]  Gordon A. Fenton,et al.  Traditional and Advanced Probabilistic Slope Stability Analysis , 2007 .

[26]  E. Rosenblueth Point estimates for probability moments. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

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

[28]  Kok-Kwang Phoon,et al.  Evaluation of Geotechnical Property Variability , 1999 .

[29]  Siu-Kui Au,et al.  Effect of spatial variability on reliability evaluation of an earth slope , 2011 .

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

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

[32]  Kok-Kwang Phoon,et al.  Updating Uncertainties in Friction Angles of Clean Sands , 2012 .

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

[34]  John T. Christian,et al.  Geotechnical Engineering Reliability: How Well Do We Know What We Are Doing? , 2004 .

[35]  Kenneth Gavin,et al.  Simultaneous Determination of Critical Slip Surface and Reliability Index for Slopes , 2007 .

[36]  Eduardo Alonso,et al.  RISK ANALYSIS OF SLOPES AND ITS APPLICATION TO SLOPES IN CANADIAN SENSITIVE CLAYS , 1976 .

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