An analytical solution for shallow buried tunnel reinforced by point anchored rockbolts

摘要

In this paper, an analytical approach is presented, by focusing on the shallow buried tunnel reinforced by two-point anchored rockbolts, by considering the rockbolts as two identical concentrated forces acting in opposite directions, applied at both the ends of the rockbolts. It was assumed that the surrounding rock and the bolts were in an elastic state and the problem existed in a plane strain condition. The complex variable method was applied to reach a solution. While solving the problem, first, the problem of a circular shallow buried tunnel, with a concentrated force acting on the surrounding rock mass, was addressed. Afterwards, the solution for a tunnel reinforced by multiple rockbolts was obtained, based on the previous solution, considering that displacements between the rockbolts and rock mass were compatible. The case of pre-stressed rockbolts was also considered in this paper. The solution obtained in this paper provides the results for the axial load of the rockbolts and the stress and displacement of the surrounding rock. The analytical solution results were found to be similar to that of the finite element method obtained by ANSYS software. In addition, to quantify the mechanical contribution of the rockbolts, the stress and displacement distributions of the surrounding rock, for reinforced tunnel and non-reinforced tunnel, were also compared.