Reliability analysis of ground–support interaction in circular tunnels using the response surface method

Abstract The first-order and the second-order reliability method (FORM/SORM) are used to evaluate the failure probability of three performance functions of the ground–support interaction in circular tunnels subjected to hydrostatic stresses. The response surface method (RSM) is used to enable reliability analysis of the implicit convergence-confinement method. The friction angle, cohesion and elastic modulus of the rock mass are considered as basic random variables and are first assumed to obey normal distributions. The quadratic polynomial with cross terms is employed as response surface function to approximate the limit state surface (LSS) at the design point. The strategies for the RSM are presented. The failure probability with respect to different criteria are obtained from FORM/SORM and compared to those generated from Monte Carlo simulations. The results show that the support installation position has great influence on the probability of the three failure modes under consideration. Comparison between analysis using correlated and uncorrelated friction angle and cohesion indicates that the influence of the correlation on the reliability analysis depends on the support installation position and the orientation of the LSS. The reliability analysis involving correlated non-normal distributions and the reliability-based design of the support are also investigated.

[1]  E. T. Brown,et al.  Underground excavations in rock , 1980 .

[2]  Bruce R. Ellingwood,et al.  A new look at the response surface approach for reliability analysis , 1993 .

[3]  Evert Hoek,et al.  Big Tunnels in Bad Rock , 2001 .

[4]  C. Fairhurst,et al.  APPLICATION OF THE CONVERGENCE-CONFINEMENT METHOD OF TUNNEL DESIGN TO ROCK MASSES THAT SATISFY THE HOEK-BROWN FAILURE CRITERION , 2000 .

[5]  Ove Ditlevsen,et al.  Uncertainty modeling with applications to multidimensional civil engineering systems , 1981 .

[6]  M. Sato,et al.  Application of Convergence Confinement Analysis to the study of preceding displacement of a squeezing rock tunnel , 1991 .

[7]  John A. Hudson,et al.  Comprehensive rock engineering , 1993 .

[8]  A. Kiureghian,et al.  Second-Order Reliability Approximations , 1987 .

[9]  Carlos M Carranza-Torres,et al.  Elasto-plastic solution of tunnel problems using the generalized form of the hoek-brown failure criterion , 2004 .

[10]  Pierpaolo Oreste,et al.  The Convergence-Confinement Method: Roles and Limits in Modern Geomechanical Tunnel Design , 2009 .

[11]  Isaac Elishakoff,et al.  Refined second-order reliability analysis☆ , 1994 .

[12]  N. Vlachopoulos,et al.  Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels , 2009 .

[13]  Kok-Kwang Phoon,et al.  Reliability-Based Design in Geotechnical Engineering: Computations and Applications , 2009 .

[14]  Yan-Gang Zhao,et al.  A general procedure for first/second-order reliabilitymethod (FORM/SORM) , 1999 .

[15]  Bak Kong Low.  Efficient Probabilistic Algorithm Illustrated for a Rock Slope , 2008 .

[16]  M. Hohenbichler,et al.  Improvement Of Second‐Order Reliability Estimates by Importance Sampling , 1988 .

[17]  E. Hoek.  Reliability of Hoek-Brown estimates of rock mass properties and their impact on design , 1998 .

[18]  M. D. Stefano,et al.  Efficient algorithm for second-order reliability analysis , 1991 .

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

[20]  Bak Kong Low,et al.  Reliability analysis of circular tunnel under hydrostatic stress field , 2010 .

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

[22]  M. Evans.  Statistical Distributions , 2000 .

[23]  Tugrul Unlu,et al.  Effect of Poisson's ratio on the normalized radial displacements occurring around the face of a circular tunnel , 2003 .

[24]  Bak Kong Low,et al.  Reliability Analysis of Laterally Loaded Piles Involving Nonlinear Soil and Pile Behavior , 2009 .

[25]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

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

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

[28]  C. Fairhurst,et al.  The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion , 1999 .

[29]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[30]  R. Rackwitz,et al.  Quadratic Limit States in Structural Reliability , 1979 .

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

[32]  H. U. Köylüoglu,et al.  New Approximations for SORM Integrals , 1994 .

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

[34]  Ramana V. Grandhi,et al.  Improved two-point function approximations for design optimization , 1995 .

[35]  Guo Jun Li,et al.  Soft clay consolidation under reclamation fill and reliability analysis. , 2000 .

[36]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[37]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

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

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

[40]  Ramana V. Grandhi,et al.  Reliability-based Structural Design , 2006 .

[41]  Yan-Gang Zhao,et al.  New Approximations for SORM: Part 2 , 1999 .

[42]  C. Bucher,et al.  A fast and efficient response surface approach for structural reliability problems , 1990 .

[43]  Pierpaolo Oreste,et al.  Analysis of structural interaction in tunnels using the covergence–confinement approach , 2003 .

[44]  Abdul-Hamid Soubra,et al.  Probabilistic Analysis of Circular Tunnels in Homogeneous Soil Using Response Surface Methodology , 2009 .