Stability of Asymmetric Parallel Tunnels in Cohesive-Frictional Soils

In this paper, finite-element limit analysis (FELA) in conjunction with nonlinear programming was developed and applied to evaluate the stability of asymmetric parallel circular tunnels in cohesive-frictional soils subjected to surcharge pressure. Based on the feasible arc interior point algorithm, a new imprecise step search algorithm was proposed to improve the speed of solving the optimization models. Meanwhile, an empirical judgment criterion was established for detecting the infeasibility of the problem. Based on the FELA method, the lower bound and upper bound for the dimensionless stability number were obtained, which account for the influence of material properties, including the overburden stress factor gamma D/c and the soil internal frictional angle phi, and geometric parameters, such as the normalized spacing ratio S/D, cover depth ratio H/D, and diameter ratio R/D of two tunnels. To obtain tight bounds for the failure load of the problem, an adaptive remeshing strategy was used in all of the numerical simulations. To facilitate practitioners' use, the calculated results were presented in the form of design tables and charts, and the failure modes for different parameters were compared and discussed. The stability numbers obtained from the present analysis are applicable to estimate the stability of asymmetric parallel circular tunnels in cohesive-frictional soils subjected to surcharge pressure. From the failure modes, engineers can identify critical sections of the asymmetric parallel tunnels where additional reinforcement or support may be required. This information can help to ensure that the asymmetric parallel tunnels remain stable during construction and in service, reducing the potential for failure and increasing the safety of the tunnels.