基于随机有限元的修正剑桥模型可靠性研究

摘要

In this paper, the plastic slope of the initial normal consolidation line of the MCMwas deemed to be the dominant input random variable, and its effects to the reliability of foundation consolidation settlement was deeply researched. The Stochastic Finite Elements Methods analysis system of one dimensional consolidation of the foundation with the MCMwas constructed by the Python script process driving the ABAQUS main progress that based on the Monte Carlo theories.The plastic slope of the initial normal consolidation line of the MCMwas the dominant input ran-dom variable, and the consolidation settlement of soil foundation was the dominant output random variable. The probability distribution model and reliability index of foundation consolidation settlement were finally determined through the statistical regression of the relevance of above two random variables. The results showed that the ensuring probability of calculation result of consolidation settlement was only 60％ basing on the deterministic finite element analysis, and the reliability index of dominant output random variable would be improved by reducing the coefficient of variation of dominant input variable. When the distribution of plastic slope of the initial normal consolidation line obeyed Gauss distribution, the foundation consolidation settlement would obey Generalized Extreme Value-III distribution. The MCMnot only can reflect the stress-strain relationship under the complicated stress trajectory scientifically, but also reveal that the dispersion of the MCMparameters would lead to the random of the settlement of the foundation.%目的 研究修正剑桥模型中作为体系控制性输入随机变量的初始等向正常固结曲线斜率对作为控制性输出随机变量的地基土体宏观固结沉降量的可靠度影响.方法 基于Monte Carlo法的基本原理,编制Python脚本程序,驱动ABAQUS构建以修正剑桥模型为本构模型的一维地基固结沉降随机有限元分析体系.以修正剑桥模型中初始等向正常固结曲线INCL的斜率作为体系控制性输入随机变量,地基土体固结沉降量作为体系控制性输出随机变量.通过统计回归分析两者之间的相关性,最终确立了固结沉降量的概率分布模型与可靠度指标.结果 基于确定性有限元分析的固结沉降量计算结果仅有60％的保证率.降低控制性输入随机变量的变异系数大小可以提高控制性输出随机变量的可靠度指标.当正常固结曲线INCL的斜率服从Gauss分布时,土体宏观固结沉降量不拒绝Generalized Extreme Value-III分布.结论修正剑桥模型能够科学合理地再现复杂应力路径下土体的应力-应变关系,并揭示出模型参数的离散性将引起地基土体宏观沉降的随机性.