Progressive failure analysis of shallow circular tunnel based on the functional catastrophe theory considering strain softening of surrounding rock mass

Abstract

Collapse mechanism for the tunnel or underground cavern is important for the support system design. This paper investigates the progressive failure phenomenon of the shallow tunnel roof under the condition of plane strain by virtue of the functional catastrophe theory. Firstly, considering the plastic strain energy as an index for the state of the studied system, the analytical solutions for the profile curves of the collapsing blocks from the shallow tunnel roof including the ‘underground’ collapse and ‘spalling’ collapse are deduced on the basis of the nonlinear power-law failure criterion. Moreover, the criterions are derived to estimate whether the progressive failure phenomena including the ‘underground’ collapses and ‘spalling’ collapses for shallow tunnel roof would occurr or not. Then, the analytical prediction obtained from this paper for the shallow tunnels is compared with the existing analytical prediction for the deep tunnels. Finally, the comparisons of the results between analytical prediction obtained from this paper and two existing model tests are conducted to demonstrate the validity of the proposed analytical methodology.