基于Kriging算法的隧道衬砌稳定可靠度分析

Reliability Analysis of Tunnel Lining Stability Based on Kriging Algorithm

根据以往的变形压力理论增加了塑性-分离阶段,由此提出了围岩变形压力发展过程的4个阶段,并在上述理论基础上建立了隧道衬砌结构稳定的功能函数,指出了该功能函数的隐式特征在求解可靠度时的困难。利用Kriging算法中变异函数对随机变量特征的表达能力和Kriging算法的插值技术,结合拉丁超立方试验设计抽样方法,推导出了隧道围岩最小支护阻力的变异函数建立方法以及隧道衬砌结构稳定功能函数的插值方法,并给出了建立变异函数和实现隐式函数插值的具体操作流程,从而解决了当隧道衬砌结构稳定功能函数为隐式函数时无法直接求解其可靠度的问题。将此算法分析结果与Monte-Carlo算法精确解相比较,其迭代次数大大减少,而失效概率的绝对误差仅为0.0049%,相对误差为2.523 8%,表明Kriging算法不仅计算效率高,并且能够满足计算结果的精度要求。

According to the conventional theory of deformation pressure, the four-stage idea for evolution of deformation pressure of surrounding rock was proposed when adding the plasticity-separateness process to it. On this basis, the performance function for structural stability of tunnel lining was developed, and the fact that the reliability evaluation is hampered by the implicit form of performance function was indicated. By using the expression capability of variance function for the characteristics of random variables and the interpolation technique in Kriging algorithm as well as Latin hypercube sampling method, both the formulation of variance function for minimum support resistance of surrounding rock and the interpolation of performance function for tunnel lining stability were derived, and then the corresponding process for accomplishing abovementioned tasks was also presented, thus the problem of the calculation of reliability index in the context of the non-explicit expression of performance function for tunnel lining stability was resolved. In comparison with Monte-Carlo simulation method, the iterations of computation process in this illustrative example through the proposed procedure were alleviated to a large extent, the absolute error of failure probability is only 0.004 9% and the relative error is approximate to 2.523 8 %, which demonstrates that the Kriging algorithm is not only efficient but also can fulfill the precision level of calculated results.