Ground reaction curves for circular excavations in non-homogeneous,axisymmetric strain-softening rock masses

Fast methods to solve the unloading problem of a cylindrical cavity or tunnel excavated in elasto-perfectly plastic, elasto-brittle or strain-softening materials under a hydrostatic stress feld can be derived based on the self-similarity of the solution. As a consequence, they only apply when the rock mass is homogeneous and so exclude many cases of practical interest. We describe a robust and fast numerical technique that solves the tunnel unloading problem and estimates the ground reaction curve for a cylindrical cavity excavated in a rock mass with properties depending on the radial coordinate, where the solution is no longer self-similar. The solution is based on a continuation-like approach(associated with the unloading and with the incremental formulation of the elasto-plastic behavior), fnite element spatial discretization and a combination of explicit sub-stepping schemes and implicit techniques to integrate the constitutive law, so as to tackle the diffculties associated with both strong strain-softening and elasto-brittle behaviors. The developed algorithm is used for two practical ground reaction curve computation applications. The frst application refers to a tunnel surrounded by an aureole of material damaged by blasting and the second to a tunnel surrounded by a ring-like zone of reinforced(rock-bolted) material.

The role of dilatancy in shallow overburden tunneling

The mechanical behavior of sandy ground during shallow circular tunneling is explored for various overburden heights H(=0.5D,1.0D,1.5D and 2.0D;D is the diameter of the tunnel)and various dilatancy coefficients(w//=0,1/3,1/2,and 1;/and w are the internal friction angle and dilation angle,respectively)through finite difference analyses.The ground is modeled as a linear elastic-perfectly plastic material that employs the Mohr-Coulomb yield criterion and obeys the non-associated flow rule.The ground reaction curve is applied in conjunction with the stress path as a conceptual tool for interpreting the mechanical response of the ground to tunneling.It is revealed that,at a certain relaxation value,a yield zone develops during tunneling and extends to the surface.This relaxation value increases with increases in the overburden and w//values for the cases of less shallow tunnels(i.e.,H=1.0D,1.5D and 2.0D),while for the shallowest case(H=0.5D),the extent of the yield zone to the ground surface is not sensitive to the w//value.The shear strain due to tunneling also increases with an increase in the w//value.Moreover,the w//value affects the radial displacement and the surface settlement due to tunneling.The magnitudes of the surface settlement and the radial displacement at the tunnel crown both decrease with an increase in the w//value.The relative difference in the displacement at the tunnel crown between the upper bound and lower bound values,w//(at the last computed stage),increases with an increase in the overburden height.It is recommended,therefore,that careful consideration be given to the dilatancy angle in the case of relatively less shallow tunnels.