Analytical and Numerical Analyses of Tunnel Excavation Problem Using an Extended Drucker–Prager Model

This paper presents a semi-analytical solution as well as finite element numerical simulations for the tunnel excavation problem, based on an extended Drucker–Prager model and under the drained condition. The adopted plasticity model is capable of accounting for the strain-hardening behavior of soils/rocks through both the internal friction angle and the cohesion. The analytical formulations show that this problem can be reduced to solving a system of ordinary differential equations, with the radial, tangential and vertical stresses, as well as the specific volume being the basic unknowns. Parametric studies are conducted to illustrate mainly the tunnel support pressure–displacement curve and the distributions of stress components, and, in particular, the critical support pressure required to stabilize the tunnel on the basis of three different collapse criteria. With regards to the numerical aspect, an integration algorithm has been developed by employing the return mapping scheme for the extended Drucker–Prager model and subsequently implemented into ABAQUS through the user subroutine UMAT. The agreement between the ABAQUS numerical results and the analytical solution predictions is overall excellent, which demonstrates the accuracy and reliability of the proposed integration scheme.