Reliability analysis of circular tunnel under hydrostatic stress field

Abstract The first-order reliability method (FORM) is used to calculate the reliability index of a circular tunnel subjected to a hydrostatic stress field. The random variables are first assumed to follow the normal distribution. Comparison between analysis using negatively correlated and uncorrelated friction angle and cohesion indicates that the results of reliability analysis are conservative if negative correlation among strength parameters is not modeled. The reliability analysis involving correlated non-normal distributions is also investigated. The probability density functions are obtained from reliability indices and compared to those generated from Monte Carlo simulations. Reliability-based design of tunnel support pressure is also illustrated.

[1]  Wilson H. Tang,et al.  Decision, risk and reliability , 1984 .

[2]  Yarlong Wang,et al.  Ground Response of Circular Tunnel in Poorly Consolidated Rock , 1996 .

[3]  Poul V. Lade,et al.  Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces , 1977 .

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

[5]  E. Hoek,et al.  Predicting tunnel squeezing problems in weak heterogeneous rock masses , 2000 .

[6]  G. Baecher.  Reliability and Statistics in Geotechnical Engineering , 2003 .

[7]  M. Shinozuka.  Basic Analysis of Structural Safety , 1983 .

[8]  Shailendra K. Sharan,et al.  Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek–Brown rock , 2008 .

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

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

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

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

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

[14]  K Y Lo,et al.  EFFECTS OF DILATANCY AND YIELD CRITERIA ON DISPLACEMENTS AROUND TUNNELS , 1987 .

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

[16]  Diederichs,et al.  Underground Works In Hard Rock Tunnelling And Mining , 2000 .

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

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

[19]  C. Martin,et al.  Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength , 1997 .

[20]  Kiyoo Mogi,et al.  Fracture and flow of rocks under high triaxial compression , 1971 .

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

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

[23]  F. Rummel,et al.  Brittle Fracture of Rocks , 1972 .

[24]  Kyung-Ho Park,et al.  A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses , 2008 .

[25]  Mark D. Zoback,et al.  A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks , 2002 .

[26]  M. H. Yu,et al.  A NEW MODEL AND THEORY ON YIELD AND FAILURE OF MATERIALS UNDER THE COMPLEX STRESS STATE , 1992 .

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

[28]  Kiyoo Mogi,et al.  Effect of the intermediate principal stress on rock failure , 1967 .

[29]  V. Hajiabdolmajid,et al.  Modelling brittle failure of rock , 2002 .

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

[31]  E. Kreyszig,et al.  Advanced Engineering Mathematics. , 1974 .

[32]  Shailendra K. Sharan,et al.  Elastic–brittle–plastic analysis of circular openings in Hoek–Brown media , 2003 .

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

[34]  E. T. Brown,et al.  Ground Response Curves for Rock Tunnels , 1983 .

[35]  Bernard Amadei,et al.  Strength of a regularly jointed rock mass under biaxial and axisymmetric loading conditions , 1988 .

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

[37]  V. K. Mehrotra,et al.  Effect of intermediate principal stress on strength of anisotropic rock mass , 1998 .

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

[39]  A. McGarr,et al.  State of Stress in the Earth's Crust , 1978 .