A hybrid boundary element—finite element method of stress analysis for bolt-reinforced inhomogeneous ground

Abstract

A numerical implementation of stress analysis for bolt-reinforced ground is presented by combining the use of boundary and finite elements. The stresses and deformations around underground openings are derived by considering the interactions between rock movement, bolt tension and bending. The rocks are piecewise inhomogeneous and contain planes of weakness. Boundary elements are used to represent the openings and interfaces between strata, while rock bolts which can be fully grouted or partially grouted are represented by finite elements. The reinforcements of bolts are related to the movements of rocks and the displacement discontinuities along the planes of weakness. Furthermore, the effect of the bearing plates is simulated by using additional boundary elements in contact with the surface of the openings. With the use of an indirect formulation method for inhomogeneous solids, all the effects of rock inhomogeneities, unloading along opening surfaces, sliding and/or separations along planes of weakness, bolt reinforcements at axial and transverse directions, and the reactions of bearing plates are incorporated into a mechanical model for the entire domain of interest. Several examples are presented which show that the numerical method developed and adopted in this paper is very efficient in solving the rock bolting problems.