Analytical solution for longitudinal response of tunnels with consideration of surrounding rock-concrete tangential interaction

The existence of faults in high-intensity earthquake areas has a serious impact on engineering structures and the longitudinal response of tunnels crossing faults needs to be studied further. The tangential foundation springs are used to analyze the tangential contact effect of surrounding rock-lining and axial deformation characteristics of tunnel，and an analytical solution for longitudinal response of tunnels crossing faults is presented. Firstly，the elastic foundation beam model is used to simulate the surrounding rock-tunnel structure interaction. Based on this，the differential equation for longitudinal response of tunnel structures is obtained. Wherein，the displacement of free field is applied on the distal end of normal foundation spring to simulate fault displacement. The analytical solution of the longitudinal tunnel response is gotten by using Green function. Secondly，the numerical solution from finite difference model of 3D is used to verify the validity of the proposed analytical solutions. The results show that the tangential contact effect of surrounding rock-lining has a significant impact on the longitudinal response of tunnel. Ignoring it，the peak bending moment error of structure reaches 35.33%. Finally，the effects of fault zone width，fault elastic modulus and lining concrete grade on the longitudinal response of tunnel are explored. As the fault zone width increases，the internal force of the tunnel structure decreases；increasing the lining concrete grade results in unfavorable effect on the structure；the increase in the elastic modulus of the surrounding rock in fault zone reduces the bending moment and shear force of structure，and increases the axial force，respectively. The research results can provide a theoretical basis for the anti-offset design of tunnels crossing faults. © 2024 Academia Sinica. All rights reserved.