隧道围岩开挖及锚喷衬砌稳定可靠度计算

Calculation of stability reliability for the surrounding rock excavation and rockbolt-shotcrete support in tunnel structure

对隧道围岩开挖进行线弹性收敛分析,导出围岩径向位移计算公式;基于薄壁筒理论及锚杆端锚理论,确定隧道围岩锚喷衬砌支护抗力求解方法;进一步推演得到隧道围岩开挖及锚喷衬砌功能函数。针对功能函数表达式为高度非线性隐式导致常规SORM难以直接应用的问题,基于数值差分原理推导梯度矢量求解公式,以此置换常规SORM中梯度的解析求解方式,构建一种不受功能函数形式制约的隧道稳定可靠度直接计算途径。利用该方法对工程实例进行分析,与蒙特卡洛法计算结果进行对比,验证其精确性及广泛适用性,同时在标准独立正态空间内建议了具有普遍适用意义的步长系数取值v=0.01。

A calculation formula for the radial displacement of surrounding rock was derived according to the convergence analysis of linear elasticity of surrounding rock,and a solving method of the support resistance of shotcrete lining and rockbolts was determined based on the thin-wall cylinder theory and the point anchored reinforcement theory. Performance functions involving excavation of the surrounding rock as well as rockboltshotcrete support were deduced. Aiming at the problem that the common second order reliability method(SORM)could not be applied directly due to that the performance functions were highly nonlinear and implicit,a calculation formula of gradient vectors,instead of the analytical algorithm used in common SORM,was deduced based on the difference principle,and a direct calculation method for stability reliability of tunneling structure,which is free from the constraint of the performance function form,was proposed. A tunnel project was analyzed by the developed method,and comparison between the calculation results by the method and Monte-Carlo method was performed. It is shown that the developed method is widely applicable and accurate. Meanwhile,a suitable step length coefficient v = 0.01 which has universally applicable meaning in the independent standard normal space was suggested.