Mechanical response of tunnels crossing active fault zones under normal or reverse faulting: A refined nonlinear analytical approximate solution

Tunnels crossing active fault zones will be severely damaged under normal or reverse faulting. The tunnel-stratum interaction is nonlinear, and the fault zone width significantly affects the tunnel response. Nevertheless, the existing analytical models neglect the effect of nonlinear tunnel-stratum interaction or fault zone width and adopt unrealistic assumptions. This work proposes a refined nonlinear solution, considering the nonlinear tunnel-stratum interaction and fault zone width, and some widely employed assumptions are removed. Specifically, a tunnel under normal or reverse faulting is simplified to an elastic beam acting on a nonlinear foundation, the nonlinear tunnel-stratum interaction is considered by setting a series of nonlinear axial and vertical springs, and the fault zone width is considered by reducing the spring stiffness. Additionally, the nonlinear axial force and geometrical nonlinearity terms are considered in the governing equations. The comparison results indicate that the results obtained from the proposed model agree well with those from model tests and numerical models and have a better accuracy than the existing analytical models. Finally, the effects of fault, stratum, and lining parameters on the response of tunnels crossing normal or reverse faults are discussed regarding stress distribution and failure scope.