Lower bound solutions for circular tunnels in two and three dimensions

SummaryComplete statically admissible stress fields are evaluated for the problem of tunnel stability. The tunnels are supported by uniform internal pressure due to a lining or rock bolts. In both cases plane deformations are assumed. Additionally, a complete stress field is derived for the problem of the stability of the unsupported span of a tunnel. The latter problem is formulated three dimensionally. In all cases the Mohr Coulomb yield criterion is used. The solution is based on the lower bound theorem of plasticity, which states that the stability of a statical system is proved if at least one admissible stress field exists.