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.

Compatibility of the Support System Consisting of Yielding Elements and Shotcrete Lining in Highly Faulted Grounds

The design procedure is made for a mine shaft where permanent underground facilities are interconnected. The highly faulted grounds were identified using empirical and semi-empirical theories. Furthermore, the behavior types are presented. This paper presents excavation and support methods in such ground conditions and the calculations results show that the installation of the yielding elements have an effect on support elements and prevent shotcrete damage during the curing stage. Different numerical analyses carried out showed that, with the yielding elements installed, the total displacements increase but the final axial force reduces, and therefore, the characteristic compressive strength of shotcrete is not exceeded. The calculation results of ground loads and displacements on the designed support system are presented with a 3D numerical geo-mechanical model adopted for highly faulted ground surrounding deeper complex underground structures.

Influences of strain softening and seepage on elastic and plastic solutions of circular openings in nonlinear rock masses

Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.

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.