Extended finite element procedures for analysis of bolt crossing multiple intersecting rock joints

An enriched finite element procedure is proposed for formulating interaction of rock bolts with multiple intersecting/ non-intersecting joints in a rock mass. The numerical method involves analysis of reinforced rock mass having arbitrary joint dip angle, bolt angle and joint-bolt-grout properties in extended finite element (XFEM) platform. Shifted Heaviside and junction enrichment is incorporated for the intersecting jointed element. The paper presents procedures and formulation of stiffness matrices of a bolt crossing multiple joints (BCMJ) which may or may not intersect each other. Hence an element may contain two intersecting joints and a bolt. In that case for a 2D element, each node is enhanced to eleven degrees of freedom, 2 for rock displacements, 2 each for displacements of rock joints, 2 for displacements of the junction of joint intersection and 3 for displacements and rotation of bolt. The procedure also allows traction to be applied to a side of an enhanced element and to be transformed as nodal forces at enhanced degrees of freedom. The paper considers elastoplastic behaviour of joint surface and bolt-grout interface using Mohr-Coulomb criterion. For yielding of bolt rod unified tensile and bending criterion is adopted. The proposed method is implemented using 3-noded triangular elements and can be upgraded for higher order elements. The efficacy of the proposed procedure is evaluated by analyzing behaviour of a bolt reinforced jointed sample under direct shear test. The method is also applied to analyze displacements and stresses around a circular tunnel made in rock mass having multiple intersecting joints at different orientations, reinforced by bolts along the periphery of the tunnel. The results in terms of displacements and stresses are compared with those of unbolted rock mass model. The proposed method shows that effect of an individual joint, bolt and their interaction can be analyzed to understand the stability of excavation under given loading conditions and can be applied in wide variety of applications.