Extended finite element method (XFEM) for analysis of cohesive rock joint

Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock mass without any numerical illposedness. XFEM is based on partition unity principle and can be used for cohesive rock joints. Equilibrium equation and traction condition are solved by Newton-Raphson method to obtain nodal displacements and external load simultaneously. This paper summarizes mathematical frameworks for implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of application of XFEM in one and two dimensional problems with single joint. Results obtained from XFEM are in good agreement to those of analytical as well as experimental results.

[1]  E. T. Brown,et al.  Rock Mechanics: For Underground Mining , 1985 .

[2]  Nick Barton,et al.  Experimental studies of scale effects on the shear behaviour of rock joints , 1981 .

[3]  Nick Barton,et al.  The shear strength of rock and rock joints , 1976 .

[4]  J. Oliver.  MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 2: NUMERICAL SIMULATION , 1996 .

[5]  J. Oden,et al.  H‐p clouds—an h‐p meshless method , 1996 .

[6]  Fred A. Donath,et al.  Effects of Cohesion and Granularity on Deformational Behavior of Anisotropic Rock , 1972 .

[7]  Bernard Amadei,et al.  Modelling rock joints under shear and normal loading , 1992 .

[8]  N. Barton,et al.  The shear strength of rock joints in theory and practice , 1977 .

[9]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

[10]  Gernot Beer,et al.  Numerical methods in rock mechanics , 1990 .

[11]  J. Oliver.  MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 1: FUNDAMENTALS , 1996 .

[12]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[13]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[14]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[15]  F. Patton.  Multiple Modes of Shear Failure In Rock , 1966 .

[16]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[17]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .