Influence of multiple random variables on the safety of cracked tunnels under earthquake action

Abstract

To explore the mechanical properties of cracked lining subjected to seismic loads based on wave theory and the extended finite element method, the dynamic viscoelastic boundary of a seismic wave and equivalent nodal force load were generated by MATLAB programming software to establish a simulation model of cracked lining structure. The internal force state change law of the lining structure was studied by varying the crack depth, crack length, secondary lining thickness, and other parameter values (including the layout between multiple cracks). Also, the safety factor of the lining crack section was obtained, and the functional relationship between the safety factor and parameter variables was established. Results show that the crack depth and secondary lining thickness were the main factors affecting the internal force of the crack section. Based on the least square method, the calculation formula and 95 % confidence interval between the minimum safety factor (Kmin) and each parameter of the crack section were obtained. Meanwhile, the Kmin prediction model was obtained via multiple nonlinear regression. When the crack depth value was 30 % of the lining thickness value, Kmin reduced 2.5 times. At 57 % crack depth of the lining thickness, the Kmin was less than the specification value, indicating that the lining structure’s safety reserve was low. Compared with the arrangement of the vertical distribution of the two cracks, the stress concentration generated when the two cracks were arranged in parallel would more likely affect the structure adversely. The findings can provide a reference for the safety study of cracked tunnels.