Functional Catastrophe Analysis of Progressive Failures for Deep Tunnel Roof Considering Variable Dilatancy Angle and Detaching Velocity

The phenomena of progressive failures are very common and important in geotechnical engineering. In this paper, a reliable prediction model is proposed to interpret the progressive failure phenomenon of roof collapse in deep tunnels using the functional catastrophe theory. The progressive collapse mechanisms and collapsing block shapes of deep circular tunnels under conditions of plane strain are investigated. The analytical solutions for the shape curves of the collapsing blocks of circular tunnels are derived based on the nonlinear power-law failure criterion considering variable dilatancy angle and detaching velocity. Moreover, criterions with variable dilatancy angle on progressive failure occurrence for deep tunnels are obtained. Then, the analytical predictions obtained in this paper are compared with experimental testing results, which indicate that the impacts of variable detaching velocity on the shape curves of the several continuous collapsing blocks should be considered to obtain more consistent prediction results with the corresponding experimental testing results.