Influence of spatial variability on slope reliability using 2-D random fields.

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.

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

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

[3]  J. Christian.  Reliability Methods for Stability of Existing Slopes , 1996 .

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

[5]  T. Parkin,et al.  Analysis of Lognormal Data , 1992 .

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

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

[8]  Bak Kong Low,et al.  Reliability-based design applied to retaining walls , 2005 .

[9]  A. Soubra,et al.  Bearing capacity of foundations resting on a spatially random soil , 2008 .

[10]  M. Shinoda.  Quasi-Monte Carlo Simulation with Low-Discrepancy Sequence for Reinforced Soil Slopes , 2007 .

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

[12]  W. Tang,et al.  Reliability analysis using object-oriented constrained optimization , 2004 .

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

[14]  Bak Kong Low.  Practical Probabilistic Approach Using Spreadsheet , 1996 .

[15]  G. Fenton,et al.  Simulation of random fields via local average subdivision , 1990 .

[16]  J. Meisinger,et al.  Evaluation of statistical estimation methods for lognormally distributed variables , 1988 .

[17]  Bak Kong Low,et al.  Reliability Analysis of Rock Wedges , 1997 .

[18]  R. Rackwitz,et al.  Reviewing probabilistic soils modelling , 2000 .

[19]  Cee Ing Teh,et al.  Reliability analysis of laterally loaded piles using response surface methods , 2000 .

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

[21]  M. Matsuo,et al.  PROBABILISTIC APPROACH TO DESIGN OF EMBANKMENTS , 1974 .

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

[23]  P Lumb.  SOIL MECHANICS - NEW HORIZONS. CHAPTER 3: APPLICATION OF STATISTICS IN SOIL MECHANICS , 1974 .

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

[25]  Peter Lumb,et al.  Application of statistics in soil mechanics , 1974 .

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

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

[28]  Suzanne Lacasse,et al.  Slope reliability analysis accounting for spatial variation , 2007 .

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

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

[31]  Achintya Haldar,et al.  Reliability Assessment Using Stochastic Finite Element Analysis , 2000 .

[32]  K. Low,et al.  Practical Probabilistic Slope Stability Analysis , 2003 .

[33]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

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

[35]  Abdul-Hamid Soubra,et al.  Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure , 2008 .

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

[37]  E. Vanmarcke.  Reliability of Earth Slopes , 1977 .

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

[39]  W. Tang,et al.  EFFICIENT RELIABILITY EVALUATION USING SPREADSHEET , 1997 .

[40]  D. Stoyan,et al.  On the probability of failure of slopes , 1979 .

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

[42]  Gautam Bhattacharya,et al.  Direct search for minimum reliability index of earth slopes , 2003 .

[43]  Douglas L. Karlen,et al.  Distribution and Variability of Surface Soil Properties at a Regional Scale , 2000 .

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

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

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

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

[48]  Gordon A. Fenton,et al.  Seeking Out Failure: The Random Finite Element Method (RFEM) in Probabilistic Geotechnical Analysis , 2006 .

[49]  A. Nour,et al.  Foundation settlement statistics via finite element analysis , 2002 .

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