3D Limit Analysis of Progressive Collapse in Partly Weathered Hoek–Brown Rock Banks

Abstract

Because of the heterogeneous layered characteristics of geomaterials, analysis of tunnel stability may be complicated, and such characteristics increase the possibility of progressive failure of the surrounding rock banks. This paper offers an analytical upper-bound approach to the analysis of the progressive collapse of deep rectangular tunnels based on three-dimensional (3D) velocity discontinuity surfaces. A symmetric 3D rotational progressive failure mechanism that considers the presence of rock layers partly induced by weathering is initially proposed and analyzed with the upper-bound theorem. In this approach, the range and shape of potential falling blocks are determined with use of the variational principle and the partition optimization method. The results obtained with the proposed approach showed good agreement and consistency with existing literature. Sensitivity analysis was also conducted to assess the effects of relevant parameters on the scope of impending blocks. Such analysis can also shed light on the collapse mechanism at failure and can be applied to projects under stratified or deteriorated rock masses, areas in which studies are limited at present.