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In designing tunnels, rock-lining interactions are an important issue that needs to be accurately predicted and analyzed. For the closely located twin tunnels, the rock-lining interaction is more complex because of the interaction between tunnels. Based on the classical Schwarz alternating method, a new alternating procedure with fast convergence is presented, which can be used to solve the elastic problems of lined multiple holes. In consideration of the real interaction between tunnels and the interaction between rock and linings, an analytical model for the elastic mechanical responses of lined twin circular tunnels at great depths is proposed using the new analytical procedure. The solutions in all the alternating steps can be superposed to obtain the final solutions that satisfy all the boundary and continuity conditions and the solutions are efficiently calculated because of the analytical expressions. A good agreement between the analytical and numerical results indicates the correctness of the solutions. Based on the analytical model, the influences of the pillar width, relative tunnel radius, the lining stiffnesses and lateral pressure coefficient on the stress and displacement around the tunnels are obtained. The proposed method can be further applied to multiple-lined tunnel problems to quickly predict the supporting force.
Jia et al. (Sat,) studied this question.