An enriched finite element procedure is proposed for formulating interaction of steel rock bolt along with multiple joints in a rock mass. This numerical method involves analysis of bolt behavior with varying joint dip angle, bolt angle, joint-bolt-grout properties in extended finite element platform. This paper presents the procedures and derivation of stiffness matrices of the bolt crossing multiple joints (BCMJ) at any arbitrary orientation. Multiple joints and a bolt can intersect an element enriching nodal degrees of freedom. In this case, constitutive model of rock, rock-joint rock-bolt and joint-bolt are incorporated into the formulation of stiffness matrix. The proposed method is implemented using 3-noded triangular elements and can be upgraded for higher order elements. This procedure is then applied to evaluate the behavior of a bolted joint sample under direct shear test. The method is also applied to analyze reinforced circular tunnel made in rock mass having multiple intersecting joints at different orientations. The results in terms of displacements and stresses are compared with unbolted rock mass model. The proposed method shows the efficacy of enriched finite element method for incorporating discrete discontinuities and rock bolts in finite element platform.


Rock mass in general contains large number of joint sets, strength of which is characterized by the joint spacing, aperture, joint fill strength and intact rock strength. In underground excavations and sometimes open pit slopes, rock bolt is widely used primary support system to stabilize the rock mass. Accurately modelling the rock bolt in rock mass is complex if interaction behaviour between rock, joint and bolt are to be considered. In general, rock bolt reinforces rockmass through restraining deformation within rock mass (Li & Stillborg 1999) and reduces the yield region around the excavation boundary. For a fully grouted passive rock bolt installed in a deformable rock mass, the axial load distribution along the bolt length indicates a neutral point where the shear stress at the interface between the bolt and grout material vanishes. Closed form elasto-plastic analytical solution of grouted bolt around a circular tunnel have been presented by many researchers (Stille et al. 1989, Cai et al. 2004, Carranza-Torres 2009, Osgoui & Oreste 2010). Modelling of rock bolt in jointed rock mass becomes a challenging task if complex mechanisms of rock bolt behaviour and dowel effects due to joint crossing bolt are taken into consideration. A three dimensional elasto-viscoplastic constitutive model has been derived to take special attention of bolt behaviour at a joint (Chen & Egger 1999).

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