基于差分原理的喷锚支护水工隧洞稳定可靠度分析

Analysis of Stability Reliability of Hydraulic Tunnel with Shotcrete-anchor Supports Based on Difference Principle

由于围岩与喷锚支护的相互作用机理极其复杂,隧洞稳定可靠度分析的功能函数一般具有隐式非线性特征,传统的可靠度二阶矩算法因对功能函数求导困难而不便直接运用,因此,提出了基于差分原理的一次二阶矩和二次二阶矩可靠度算法。推导了水工隧洞围岩与支护共同作用可靠度计算功能函数,针对喷锚支护水工隧洞稳定可靠度计算问题,介绍了基于差分原理的一次二阶矩和二次二阶矩计算方法原理及步骤,并对工程实例水工隧洞进行稳定可靠度计算分析,与工程中通常采用的蒙特卡洛直接抽样法和重要抽样法计算结果进行对比分析。研究结果表明,基于差分原理的一次二阶矩和二次二阶矩可靠度算法精确且高效,计算成果能够满足实际工程要求。

Because the interaction mechanism between surrounding rock and shotcrete support is extremely complicated,the function of tunnel stability reliability analysis generally has implicit and nonlinear characteristics.The traditional reliability second-order moment algorithm is inconvenient to use directly because it is difficult to derive the partial derivatives of functional function.Therefore,the first order second moment method(FOSM)and second-order reliability method(SORM)based on the difference principle are proposed.First,the reliability calculation function considering the interaction between surrounding rock and support of hydraulic tunnel is derived.Then,aiming at the calculation of the stability reliability of the shotcrete-anchored-supported hydraulic tunnel,the calculating principle and steps of FOSM and SORM based on the difference principle are introduced in detail.Finally,the stability reliability calculation and analysis of the hydraulic tunnel of a engineering example are carried out,and the calculation results are compared with the Monte Carlo direct sampling method(MC-DS)and the importance sampling method(MC-IS).The research results show that,compared with MC-DS and MC-IS,the reliability algorithms of FOSM and SORM based on the difference principle are accurate and efficient,and the calculation results can meet the actual engineering requirements.