基于可靠度理论与Matlab的隧道衬砌结构设计与分析

Design and Analysis of Tunnel Lining Structure Based on Reliability Theory and Matlab

针对隧道衬砌结构稳定性的极限状态功能函数具有高度非线性和其参数具有随机性的特征,提出在Matlab环境下采用蒙特卡罗法进行隧道衬砌结构设计的方法.该计算和设计方法编程过程简化,计算速度快,精度高,且不受极限状态方程非线性、随机变量非正态的限制.结合工程实际,给出了具体的可靠性设计步骤,建立了各参数与可靠度的关系,指出了提高隧道衬砌结构可靠度的方法和措施,为隧道衬砌结构参数设计和优化提供科学依据.结果表明:该计算和设计方法所得到的结果比传统的经验分析法、安全系数法得到的结果更加科学、经济、高效.

Aiming at the characteristic that the limit state functions are highly nonlinear and that the parameters are random,we put forward a new design method of tunnel lining structure based on the method of Monte-carlo in Matlab.This design method,with a high precision,is not only simple in programing and quick in calculation,but also not being limited by nonlinearity of limit state equations and by non-normal random variables.Then we put forward the design procedures and examples.Besides,the relationship between parameters and reliability is established,and the methods of improving the reliability of tunnel lining structure analyzed,which provides a scientific evidence for the design and optimization of tunnel lining parameters.The results show that the calculation use this method is more scientific,more economical,and more efficient,compared with the conventional empirical analysis method and the safety factor method.