Stress recovery procedure for discontinuous deformation analysis

The discontinuous deformation analysis (DDA) has been widely applied for rock engineering problems due to its special features in modeling the discontinuous rock mass. A linear polynomial function is often used in the standard DDA to ease the complex contact determination between the blocks. This linear displacement function generates a constant stress field within a block, which cannot be effectively used to model the stress variation within a block and across the block interface, especially in the region with a large stress gradient. In this paper, a stress recovery procedure is proposed for those DDA blocks which are glued together. Such a procedure can improve the stress accuracy along the block interface, and can be used for more accurate contact determination. Two numerical examples are presented to study the stress accuracy of the proposed method, and the results show that the proposed stress recovery method provides a better accuracy than the direct DDA and the averaging method.

[1]  Bijan Boroomand,et al.  RECOVERY BY EQUILIBRIUM IN PATCHES (REP) , 1997 .

[2]  K. A. Holsapple,et al.  Finite element solutions for propagating interface cracks with singularity elements , 1991 .

[3]  Yong-li Wu Variable power singular interface elements for a crack normal to the bimaterial interface , 1994 .

[4]  Lanru Jing,et al.  A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering , 2003 .

[5]  John S. Campbell,et al.  Local and global smoothing of discontinuous finite element functions using a least squares method , 1974 .

[6]  Y. Cheng,et al.  Coupling of FEM and DDA Methods , 2002 .

[7]  Zdeněk P. Bažant,et al.  New explicit microplane model for concrete: Theoretical aspects and numerical implementation , 1992 .

[8]  Bernard Amadei,et al.  Extensions of discontinuous deformation analysis for jointed rock masses , 1996 .

[10]  Abimael F. D. Loula,et al.  Local gradient and stress recovery for triangular elements , 2002 .

[11]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[12]  J. Z. Zhu,et al.  Superconvergence recovery technique and a posteriori error estimators , 1990 .

[13]  Erwin Stein,et al.  On the stress computation in finite element models based upon displacement approximations , 1974 .

[14]  S. Timoshenko,et al.  Theory Of Elasticity. 2nd Ed. , 1951 .

[15]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[16]  Ignacio Carol,et al.  On inter‐element forces in the FEM‐displacement formulation, and implications for stress recovery , 2006 .

[17]  Hui Rong Bao,et al.  Nodal-based discontinuous deformation analysis , 2010 .

[18]  D. Ngo,et al.  Finite Element Analysis of Reinforced Concrete Beams , 1967 .

[19]  A. Gens,et al.  AN INTERFACE ELEMENT FORMULATION FOR THE ANALYSIS OF SOIL-REINFORCEMENT INTERACTION , 1989 .

[20]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[21]  Xue-Cheng Tai,et al.  Superconvergence for the Gradient of Finite Element Approximations by L2 Projections , 2002, SIAM J. Numer. Anal..

[22]  J. Bramble,et al.  Higher order local accuracy by averaging in the finite element method , 1977 .

[23]  Yu-Yong Jiao,et al.  Viscous boundary of DDA for modeling stress wave propagation in jointed rock , 2007 .

[24]  I. Carol,et al.  Micromechanical analysis of quasi‐brittle materials using fracture‐based interface elements , 2001 .

[25]  Yossef H. Hatzor,et al.  Dynamic stability analysis of jointed rock slopes using the DDA method: King Herod's Palace, Masada, Israel , 2004 .