基于向量投影响应面法的隧道围岩变形稳定可靠度分析

Analysis of Deformation Stability Reliability of Tunnel Surrounding Rocks Based on Vector Projection Response Surface Method

围岩变形稳定是保证隧道施工安全的重要因素,由于影响围岩变形稳定因素众多,围岩变形稳定功能函数一般为隐式或为高度非线性,而采用向量投影响应面法可使计算简化且精度可得到保证。为了应用可靠度理论判定围岩变形稳定性,文章以Mohr-Coulomb强度理论作为围岩屈服条件求得的圆形隧道围岩位移解析解作为围岩位移函数,将圆形隧道毛洞围岩表面刚好达到剪切塑性极限时的洞顶沉降位移作为围岩变形的极限位移,建立了圆形隧道围岩变形稳定功能函数。利用向量投影取样法,通过响应面函数的梯度投影确定取样点,求解响应面函数,再用一次二阶矩法计算了某圆形隧道的围岩变形稳定可靠指标,并和蒙特卡洛法计算结果进行了对比,根据可靠指标对该隧道围岩变形稳定性进行了评定。

Stability of rock mass deformation is an important factor to ensure the safety of tunnel construction,the deformation stability function of surrounding rock is of implicit or highly nonlinear due to many factors affecting the stability of surrounding rock deformation,while the calculation can be simplified and the accuracy can be guaranteed by using vector projection response method.In order to judge the stability of surrounding rock by reliability theory,the performance function of rock mass deformation stability of the circular tunnel is established by taking the analytical solution of rock mass displacement of the circular tunnel as the rock mass displacement function which is obtained by taking the Mohr-Coulomb strength theory as the rock mass yield condition,and taking the crown settlement as the ultimate displacement of rock mass deformation when the rock mass surface of unsupported circular tunnel reaches shear plastic limit.Using the vector projection sampling method,the response surface function is solved by determining the sampling points based on gradient projection of response surface function,the reliability indexes of rock mass deformation stability are calculated by first-order second-moment method,a comparison with the results calculated with Monte Carlo method is conducted,and the reliability of tunnel rock mass deformation stability is evaluated.