基于敏感性分析的隧道围岩变形稳定可靠度计算

摘要

应用可靠度理论对隧道围岩稳定性进行评定的难点是围岩变形稳定功函数为隐式或为高度非线性,为解决这一问题,将影响隧道围岩变形的因素视为随机变量,结合敏感性分析原理和有限元分析方法,先通过有限元分析求解每一个随机变量单独变化时圆形隧道拱顶沉降位移,再根据围岩位移计算结果进行非线性拟舍得到拱顶沉降位移随单个因素变化时表达式,然后应用多元非线性回归求解围岩位移与多个随机变量之间的近似表达式.以圆形隧道洞室表面围岩刚好达到剪切塑性极限为临界条件时的洞顶沉降位移解析解作为围岩极限位移,根据围岩位移近似表达式和极限位移建立围岩变形稳定功能函数后进行围岩稳定可靠度计算.为了验证本方法的可行性,以某圆形断面隧道为例,采用设计点方法计算了围岩稳定可靠指标并对其稳定性进行了评定.本方法简单可行,计算精度能满足工程要求且具有一定的实用性.%It is difficult to evaluate the stability of tunnel surrounding rock by applying the reliability theory,for the stability function of surrounding rock is implicit or highly nonlinear.In order to solve this problem,the vault settlement displacement of the circular tunnel of each random variable changed seprately is calculated by the finite element analysis,combining the sensitivity analysis principle and finite element analysis method and considering the factors affecting the surrounding rock deformation of the support structure as random variables.Then the expression of the vault settlement displacement varying with the single factor is obtained by nonlinear fitting according to the calculation result of surrounding rock displacement.The approximate expression of surrounding rock displacement and multiple random variables is obtained by the multivariate non-linear regression.Taking the circular tunnel surrounding rock shear surface just reached the plastic limit for critical conditions,and regarding the roof subsidence displacement of surrounding rock calculated by elastic and plastic theory as the ultimate displacement of supporting structure,the surrounding rock and supporting structure deformation limit state function of stability is established.In order to verify the feasibility of the method,the reliability index of surrounding rock is calculated by design point method,and its stability is evaluated by taking a circular tunnel as an example.The results show that the method is simple and feasible,and the calculation accuracy can meet the requirements of the project.