隧道衬砌结构可靠度分析的三阶矩方法

Reliability Analysis of Tunnel Lining Structure Using Third-Moment Method

隧道衬砌结构的可靠度分析是隧道工程中的关键研究领域。传统的分析方法主要基于蒙特卡罗有限元法,通过将基本随机变量整合为两个综合变量,然后进行一次二阶矩法或二次二阶矩法来计算可靠度。该方法在处理综合变量之间的相关性时可能存在不足,导致分析结果的精确性受到影响。为了解决这一问题,本文提出了一种新的三阶矩方法来进行隧道衬砌结构的可靠度分析。该方法首先利用基于拉丁超立方抽样的蒙特卡罗有限元法来计算隧道衬砌结构极限状态功能函数的前三阶矩(包括均值、方差和偏度),然后使用三阶矩可靠度指标来估计衬砌结构的失效概率。通过算例验证,该方法不仅简化了计算流程,而且提高了结果的精确性,为隧道衬砌结构及其他隐式功能函数的结构可靠度分析提供了新的研究方法。

The reliability analysis of tunnel lining structures is a pivotal research domain in tunnel engineering.Traditional methodologies predominantly rely on the Monte Carlo finite element method,integrating basic random variables into two comprehensive variables,followed by a second-order moment method or a second-order second moment method for reliability computation.Nonetheless,this approach might exhibit inadequacies in addressing the correlation among integrated variables,potentially compromising the precision of the analysis outcomes.To counteract this limitation,this study introduces a novel third-order moment method for the reliability analysis of tunnel lining structures.Initially,the method employs the Monte Carlo finite element method based on Latin hypercube sampling to compute the first three moments(mean,variance,and skewness)of the limit state function of the tunnel lining structure.Subsequently,the third-order moment reliability index is utilized to estimate the failure probability of the lining structure.Validation through numerical examples demonstrates that this method not only streamlines the computational process but also enhances result accuracy,offering a novel research methodology for the reliability analysis of tunnel lining structures and other structures with implicit function forms.