An analytical solution for the ground reaction curve of brittle rocks, including gravity

Ground reaction curve, for the majority of rock masses, includes two parts as follows: first, the descending part which involves elastic and plastic behaviours; second, the ascending part which develops due to the collapse of perturbed zone. Within the ascending part, the main reason for increasing ground pressure is the down falling of upper-tunnel plastic zone. This phenomenon is expected in brittle rocks in which the residual strength parameters drop suddenly after peak strength. This trend finally leads to the collapse in tunnels. Finding ground reaction curve has been difficult since it requires considering the gravity which interrupts the axisymmetry of the problem while the broken zone tends to collapse due to loosening. In this study, a new analytical method is derived in order to obtain the radial displacement and pressure in the upper part of cylindrical tunnels including the gravity. The rock mass is supposed to behave as an elastic-brittle-plastic material compatible with Mohr–Coulomb’s linear criterion. Non-associative flow rule is used for plastic flow of the rock mass. The new solution is verified by applying to real examples and a comparison is held between the new method, P.Roussev solution and UDEC software modelling.