Upper bound limit analysis of support pressures of shallow tunnels in layered jointed rock strata

• The range of the loose zone can be determined by the states of the joints.
• The loose zone failure mode is classified into arch collapse and caving collapse.
• Failure mechanisms of the caving collapse failure mode were analyzed.
• The boundaries of the caving collapse failure modes were analyzed.
• Support pressures of shallow tunnels were analyzed by using limit analysis method.

With more and more large-span shallow underground projects being built in layered jointed rock strata, there is an increasing interest in the study of stability problems of such projects. The upper bound theorem of limit analysis has been found to be a valid method for analyzing such problems and it is crucial to ensure the accuracy of the failure mode when applying this method. In the present paper, for tunnels in layered jointed rock strata, 8 factors including the thickness of the weathered overburden, the states of the rock joints, and the depth of the tunnel were considered by analyzing the failure mode. By using the orthogonal array testing strategy and the distinct element method, 64 different numerical simulation models based on an actual tunnel project were simulated. The test results showed that the range of the loose zone was determined by the stretch, slippage, and fracture area of the joints. Two kinds of loose zone were obtained, i.e. the arch collapse loose zone and the caving collapse loose zone. The loose zone boundary was analyzed and fitted with linear and non-linear models; such as parabola and power function curves, respectively. The rational failure mode was studied by analyzing the recognition method, the classification, and the failure mechanism of the caving collapse loose zone. By using the liner least squares method, an empirical formula of the boundary of the caving collapse loose zone was obtained, and its boundary were divided equally with identical angles, then a kinematically admissible velocity field was established. Based on the virtual power principle and virtual work principle, the upper bound theorem of limit analysis was adopted to study the support pressures and a limit analysis model was established. A real tunnel project case was studied as an example, and the results were compared with the Terzaghi theory and the Fraldi theory, so as to demonstrate the applicability of the proposed method.