基于位移释放系数的深埋圆形压力隧道力学行为的解析解

An Analytical Solution of Mechanical Behaviors of a Deep Circular Pressure Tunnel Based on Displacement Release Coefficient

为解决含有孔隙水的可渗透岩层中隧道围岩的力学行为,采用复变函数法与Biot孔隙弹性理论相结合的方法,建立了一个基于位移释放系数的可渗透深埋圆形压力隧道的应力和位移的解析模型。根据应力应变本构方程及平面应变协调方程导出了应力函数的非齐次双调和方程。选取计算参数进行算例计算,并将计算结果与商业有限元软件的计算结果进行对比,两者基本一致。通过选取不同的隧道参数及远场应力比进行敏感性分析,发现隧道在软衬砌和硬衬砌条件下会产生较大差异的力学行为。位移释放系数和孔隙压力对围岩中的环向应力和径向应力有显著的影响。

To investigate the mechanical behaviors of tunnel surrounding rock in permeable rock stratum,an analytical model of stress and displacement of permeable deep buried circular pressure tunnel based on displacement release coefficient is established using the complex function method combined with Biot′s poro-elastic theory.Based on the stress-strain constitutive equation and plane-strain compatibility equation,the non-homogeneous biharmonic equation of stress function is derived.Then,the stress function is expressed by complex potential function,and the coefficients of complex potential function are determined according to the boundary condition at the inner surface of liner and rock/liner interface.An example is calculated according to the given parameters,and the calculation results are compared with those of commercial finite element software,which shows excellent agreements.Meanwhile,by selecting different tunnel parameters and far-field stress ratio for sensitivity analysis,it is found that the tunnel has great differences in mechanical behavior under the conditions of soft liner and hard liner.The displacement release coefficient has a significant impact on the hoop stress and radial stress in the surrounding rock.The increase of displacement release may lead to tensile stress in the rock.