考虑围岩–衬砌切向接触效应的穿越断层隧道结构纵向响应解析解

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

高烈度地震区断层的存在对工程结构产生严重影响,穿越断层隧道纵向响应有待深入研究。本文采用切向地基弹簧分析围岩–衬砌切向接触效应及隧道结构的轴向变形特征,建立断层错动作用下隧道纵向响应理论模型。首先,隧道被简化成有限长梁,采用切向地基弹簧和法向地基弹簧来体现围岩–衬砌的相互作用,在法向地基弹簧端部施加自由场位移来模拟断层错动,得到隧道结构纵向响应微分方程;通过格林函数法求解获得结构响应解析解;接着采用三维有限差分法对本文解析模型的有效性进行验证。结果表明:围岩–衬砌的切向接触效应对隧道结构的纵向响应存在显著影响,忽略导致得到的结构弯矩峰值误差达到35.33%。最后,探究断层宽度、断层弹性模量和衬砌混凝土等级对隧道纵向响应的影响;随着断层宽度增加,隧道结构内力减小;提高衬砌混凝土等级导致结构内力增大;断层区域围岩弹性模量的增加使得结构的弯矩、剪力减小,轴力增大。研究成果可为穿越断层隧道抗错断设计提供理论依据。

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.