Numerical and Analytical Solutions to Benchmark Problems Related to TunnelMechanics

摘要

In this report, five numerical approaches to problems of tunnel dynamics arecompared with each other and--wherever possible--with exact analytic solutions. The medium is an idealization of a jointed rock mass. The intact rock is linear elastic-plastic with a pressure-dependent failure surface and associated plastic flow law. There are two orthogonal sets of equally spaced joints. Each joint is nonlinear elastic in the normal direction and linear elastic with Coulomb friction in shear. All the methods but one represent the intact rock by continuum elements; the other treats it as rigid and lumps its compliance in the joints. Most methods represent the joints as sliding interfaces, but one models them also as finite elements. Most methods have two different types of models for jointed rock, an explicit one where the joints are treated separately, and an implicit one where their properties are lumped together with those of the intact rock. Seven problems are posed. In the simplest of the problems a strain history is specified for a block of intact rock. In the most complex, a lined tunnel in jointed rock mass is engulfed by a cylindrically divergent stress wave. A complete analytic solution is derived for the first problem, incrementally analytic ones for the next four, and an idealized static orthotropic elastic solution for the last one. Based on a combination of physical understanding (of wave propagation and material behavior) and comparison with the analytic solutions, three of the numerical approaches are judged to have produced credible results to final problem. Benchmark, Tunnel Mechanics, Tunnel Deformation, Tunnel Vulnerability.