Stability of twin circular tunnels in cohesive-frictional soil using the node-based smoothed finite element method (NS-FEM)

This paper presents an upper bound limit analysis procedure using the node-based smoothed finite element method (NS-FEM) and second order cone programming (SOCP) to evaluate the stability of twin circular tunnels in cohesive-frictional soils subjected to surcharge loading. At first stage, kinematically admissible displacement fields of the tunnel problems are approximated by NS-FEM using triangular elements (NS-FEM-T3). Next, commercial software Mosek is employed to deal with the optimization problems, which are formulated as second order cone. Collapse loads as well as failure mechanisms of plane strain tunnels are obtained directly by solving the optimization problems. For twin circular tunnels, the distance between centers of two parallel tunnels is the major parameter used to determine the stability. In this study, the effects of mechanical soil properties and the ratio of tunnel diameter and the depth to the tunnel stability are investigated. Numerical results are verified with those available to demonstrate the accuracy of the proposed method.

[1]  A. S. Osman,et al.  Stability of unlined twin tunnels in undrained clay , 2010 .

[2]  H. -B. Mühlhaus.  Lower bound solutions for circular tunnels in two and three dimensions , 1985 .

[3]  E. Davis,et al.  The stability of shallow tunnels and underground openings in cohesive material , 1980 .

[4]  Scott W. Sloan,et al.  Collapse Analysis of Square Tunnels in Cohesive–Frictional Soils , 2001 .

[5]  Robert J. Mair,et al.  Centrifugal modelling of tunnel construction in soft clay , 1980 .

[6]  Chris Martin,et al.  Upper bound limit analysis using simplex strain elements and second‐order cone programming , 2007 .

[7]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[8]  J. Bonet,et al.  A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications , 1998 .

[9]  E. Leca,et al.  Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material , 1990 .

[10]  Scott W. Sloan,et al.  Undrained Stability of Dual Circular Tunnels , 2014 .

[11]  Stéphane Bordas,et al.  A cell‐based smoothed finite element method for kinematic limit analysis , 2010 .

[12]  H. Nguyen-Xuan,et al.  Adaptive selective ES-FEM limit analysis of cracked plane-strain structures , 2015 .

[13]  Scott W. Sloan,et al.  Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading , 2011 .

[14]  Hung Nguyen-Xuan,et al.  A theoretical study on the smoothed FEM (S‐FEM) models: Properties, accuracy and convergence rates , 2010 .

[15]  Hung Nguyen-Xuan,et al.  Computation of limit and shakedown loads using a node‐based smoothed finite element method , 2012 .

[16]  Guirong Liu,et al.  A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems , 2009 .

[17]  E. Soliman,et al.  Two- and three-dimensional analysis of closely spaced double-tube tunnels , 1993 .

[18]  Guirong Liu,et al.  An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids , 2009 .

[19]  Long Chen.  FINITE ELEMENT METHOD , 2013 .

[20]  Chung-Jung Lee,et al.  Ground movements and collapse mechanisms induced by tunneling in clayey soil , 2003 .

[21]  K. Y. Dai,et al.  Theoretical aspects of the smoothed finite element method (SFEM) , 2007 .

[22]  Hung Nguyen-Xuan,et al.  An adaptive selective ES-FEM for plastic collapse analysis , 2016 .

[23]  Jeong Whan Yoon,et al.  Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one‐point quadrature solid‐shell elements , 2008 .

[24]  Scott W. Sloan,et al.  Stability of dual square tunnels in cohesive-frictional soil subjected to surcharge loading , 2011 .

[25]  Wai-Fah Chen.  Limit Analysis and Soil Plasticity , 1975 .

[26]  Isam Shahrour,et al.  Numerical analysis of the interaction between twin-tunnels: Influence of the relative position and construction procedure , 2008 .

[27]  Hung Nguyen-Xuan,et al.  An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis , 2015 .

[28]  Scott W. Sloan,et al.  UNDRAINED STABILITY OF A SQUARE TUNNEL IN A SOIL WHOSE STRENGTH INCREASES LINEARLY WITH DEPTH , 1991 .

[29]  Robert L. Taylor,et al.  Triangular finite elements with rotational degrees of freedom and enhanced strain modes , 2000 .

[30]  G. R. Liu,et al.  On Smoothed Finite Element Methods , 2010 .

[31]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[32]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[33]  Jyant Kumar,et al.  Stability of long unsupported twin circular tunnels in soils , 2013 .

[34]  B. Moran,et al.  Stabilized conforming nodal integration in the natural‐element method , 2004 .

[35]  Guirong Liu,et al.  A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements , 2009 .

[37]  Medhat A. Haroun,et al.  Reduced and selective integration techniques in the finite element analysis of plates , 1978 .