An investigation into application of jointly distributed random variables method in reliability assessment of rock slope stability

Abstract Analysis of stability of rock slopes is a branch of rock engineering that is highly amenable to probabilistic treatment. Probabilistic analysis of rock slope stability has been used as an effective tool to evaluate uncertainty so prevalent in variables and has received considerable attention in the literature. In this research the application of the Jointly Distributed Random Variables (JDRVs) method for probabilistic analysis and reliability assessment of rock slop stability with plane sliding is investigated. The selected probabilistic parameters are friction angle of sliding surface and apparent cohesion which are modeled using a truncated normal probability distribution function and the depth of water in tension cracks and earthquake acceleration ratio which are considered to have truncated exponential probability distribution function. The parameters related to geometry and unit weight are regarded as deterministic parameters. The results are compared with the Monte Carlo (MC) simulation. Comparison of the results indicates that the results of the JDRV method include a degree of error, primarily due to the interdependency of some of the variables in the formulation. It is also shown that due to this interdependency of the variables, the application of JDRV method in reliability assessment of rock slope stability will result in errors and hence, the MC method will be the preferable method. The results of sensitivity analysis using Monte Carlo simulation show that the friction angle of sliding surface is the most effective parameter in rock slope stability with plane sliding.

[1]  P. Kulatilake,et al.  Stochastic fracture geometry modeling in 3-D including validations for a part of Arrowhead East Tunnel, California, USA , 2003 .

[2]  Paul G. Hoel,et al.  Introduction to Probability Theory , 1972 .

[3]  R. Jurado-Piña,et al.  A Simple Genetic Algorithm for Calibration of Stochastic Rock Discontinuity Networks , 2012, Rock Mechanics and Rock Engineering.

[4]  Dan M. Frangopol,et al.  Monte Carlo simulation of rock slope reliability , 1989 .

[5]  N. Sitar,et al.  Rock Wedge Stability Analysis Using System Reliability Methods , 2007 .

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

[7]  Nicholas Sitar,et al.  System reliability approach to rock slope stability , 2006 .

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

[9]  Herbert H. Einstein,et al.  Geologic Stochastic Modeling and Connectivity Assessment of Fracture Systems in the Boston Area , 2002 .

[10]  P Starzec,et al.  Application of two-level factorial design to sensitivity analysis of keyblock statistics from fracture geometry , 2002 .

[11]  Fulvio Tonon,et al.  Closed-form and numerical solutions for the probability distribution function of fracture diameters , 2007 .

[12]  Gordon A. Fenton,et al.  Probabilistic methods in geotechnical engineering , 2007 .

[13]  N. Sitar,et al.  Inference of discontinuity trace length distributions using statistical graphical models , 2006 .

[14]  Graeme Major,et al.  Application Of Monte Carlo Techniques To Slope Stability Analyses , 1978 .

[15]  Jeffrey K. Whyatt,et al.  Applications Of The Point Estimation Method For Stochastic Rock Slope Engineering , 1900 .

[16]  A. Karakas Practical Rock Engineering , 2008 .

[17]  R. Jimenez,et al.  Fuzzy spectral clustering for identification of rock discontinuity sets , 2008 .

[18]  J. Christian,et al.  The point‐estimate method with large numbers of variables , 2002 .

[19]  Dian-Qing Li,et al.  Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables , 2011 .

[20]  B. Moshiri,et al.  Investigating the validity of conventional joint set clustering methods , 2011 .

[21]  W. Wittke Rock Mechanics: Theory and Applications With Case Histories , 1990 .

[22]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[23]  L. Faravelli Response‐Surface Approach for Reliability Analysis , 1989 .

[24]  N. Sitar,et al.  Influence of Stochastic Discontinuity Network Parameters on the Formation of Removable Blocks in Rock Slopes , 2006 .

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

[26]  R. E. Hammah,et al.  Probabilistic Slope Analysis with the Finite Element Method , 2009 .

[27]  Hedi Hassis,et al.  Reliability analysis of slope Stability using stochastic finite element method , 2011 .

[28]  Hyuck-Jin Park,et al.  The evaluation of the probability of rock wedge failure using the point estimate method , 2011, Environmental Earth Sciences.

[29]  Alfredo Ang H.-S.,et al.  Probability concepts in engineering planning and design, vol i : basic principles , 1979 .

[30]  Richard E. Goodman,et al.  Block theory and its application to rock engineering , 1985 .

[31]  A. J. Hendron Engineering of rock blasting on civil projects : Structural and Geotechnical Mechanics (Englewood Cliffs, NJ: Prentice-Hall, 1977), P242–277 , 1978 .

[32]  R. Goodman Introduction to Rock Mechanics , 1980 .

[33]  P. R. La Pointe,et al.  Derivation of parent fracture population statistics from trace length measurements of fractal fracture populations , 2002 .

[34]  E. Hoek,et al.  Rock slope engineering , 1974 .

[35]  David Stirzaker Probability and Random Variables: A Beginner's Guide , 1999 .

[36]  Bak Kong Low Reliability analysis of rock slopes involving correlated nonnormals , 2007 .

[37]  Pinnaduwa Kulatilake,et al.  Factor of safety of tetrahedral wedges: A probabilistic study , 1987 .

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

[39]  Hyuck-Jin Park,et al.  Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA , 2005 .