Upper bound analysis of three-dimensional progressive collapse mechanism of deep tunnel roof with weak surrounding rock

Tunnel roof collapse is a progressive failure process. In order to study the progressive collapse characteristics of deep tunnel roof with weak surrounding rock, we establish the three-dimensional progressive collapse mechanism of deep tunnel based on the limit analysis upper bound theorem and nonlinear Hoek-Brown failure criterion, derive the analytical solution of collapse surface in the whole process considering pore water pressure, and draw the three-dimensional surface diagram of roof progressive collapse. Furthermore, we analyze the morphological characteristics of the collapsed body when the relevant parameters are varied singularly, and the influence of each parameter on the collapsed body gravity and tunnel support force under different pore water pressures. The results show that the dimensionless parameters characterizing the rock mass, unit weight, pore water pressure and tensile stress have significant effects on the morphology, gravity and support force of progressive collapse. In the process of progressive collapse of deep tunnel, the physical and mechanical parameters of surrounding rock gradually weaken, which is mainly reflected in the gradual attenuation of the rock strength with the development of deformation up to a residual value. The attenuation of the strength of surrounding rock and the residual strength have a certain influence on the collapse gravity and tunnel support force. The theoretically calculated collapse shape of tunnel roof is basically consistent with the collapse range of tunnel roof in the F-3 fault fracture zone of actual tunnel engineering, which verifies the applicability of the theoretical results for predicting the collapse range of tunnel roof progressive collapse. The research results can provide a theoretical basis for the construction design and safety protection of deep tunnel with weak surrounding rock.