CPTU数据校准黏土和砂土统一模型本构参数的随机力学-贝叶斯方法  

Stochastic mechanics based Bayesian method of calibrating the constitutive parameters of Clay and Sand Model with CPTU data

作　　者：王长虹 马铖涛 吴昭欣 王昆[1] 汤道飞 Wang Changhong;Ma Chengtao;Wu Zhaoxin;Wang Kun;Tang Daofei(Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学,上海200444

出　　处：《土木工程学报》2022年第10期101-116,共16页China Civil Engineering Journal

基　　金：上海高校特聘教授岗位计划(TP2018042);上海市浦江人才计划(18PJ1403900);上海市社会发展科技攻关项目(21DZ1204300)。

摘　　要：黏土-砂土统一本构模型CASM(Clay And Sand Model)与剑桥模型相比引入了状态参数,可描述黏土和砂土的复杂力学状态,但其本构参数(一类精细的岩土参数)因存在天然的变异性和认知的不确定性,难以精细确定。以CASM模型为基础推导球孔扩张和孔压静力触探试验CPTU(Piezocone Penetration Test)贯入机理,结合原位测试数据,采用随机力学-贝叶斯方法校准关键本构模型参数,如间隙比、应力状态系数、临界状态应力比和超固结比。首先推导基于CASM模型的球孔扩张理论,解释极限扩孔应力与CPTU数据的贯入力学机理。然后提出基于MCMC(Markov Chain Monte-Carlo)法的贝叶斯抽样算法。最后采用以上随机力学-贝叶斯方法校准上海苏州河段深层排水调蓄管道系统工程云岭西地区第(8)层土和第(8)层土的本构模型参数,并通过数值模拟评估本构模型参数后验分布的准确性。研究结果表明:本构参数经过贝叶斯理论校准后,其变异性减小,且具有一定的统计相关性。利用校准后的本构参数进行基坑开挖模型数值计算,得到的结果更加符合工程监测值,证明了利用原位测试数据校准本构参数的随机力学-贝叶斯方法的有效性。以上研究揭示了CASM本构模型与CPTU数据之间的力学机理和数学统计规律,并为其他本构模型的开发和参数校准提供了新的研究思路。Compared with the Cam-clay model, the state parameters of describing the complicated mechanical states of clay and sand are introduced into Clay And Sand Model(CASM).However, it is difficult to precisely determine the constitutive parameters(including model parameters and geomaterial parameters) due to the natural variability and epistemic uncertainty of these parameters.Based on the CASM, the spherical cavity expansion theory and Piezocone Penetration Test(CPTU) mechanism are derived.By referring to in-situ test data, the key constitutive parameters, such as spacing ratio, stress-state coefficient, critical stress ratio and overconsolidation ratio, are calibrated by the stochastic mechanics based Bayesian method.Firstly, the theory of spherical cavity expansion based on CASM is derived, and the mechanical conversion between the limit cavity expansion stress and CPTU data is explained.Secondly, a Bayesian sampling algorithm based on Markov chain Monte-Carlo(MCMC) method is proposed.Finally, the stochastic mechanics based Bayesian method is used to calibrate the constitutive parameters of the soil layers(8)and(8)in West Yunling shaft of Suzhou river drainage and storage pipeline project of Shanghai, and the accuracy of posterior distributions of constitutive parameters are evaluated by numerical simulation.The results indicate that the uncertainties of constitutive parameters are reduced after calibration of Bayesian method with certain statistical correlations.The results from numerical simulations of foundation excavation using the calibrated constitutive parameters are more consistent with theengineering measurements, validating the effectiveness of the stochastic mechanics based Bayesian method of calibrating constitutive parameters with in-situ test data.The above studies reveal the mechanical and statistical laws between the CASM and CPTU data, and hence provide reference for the development of other constitutive models and parameter calibration.

关 键 词：球孔扩张理论 本构参数 贝叶斯方法 参数校准 孔压静力触探试验 

分 类 号：TU441[建筑科学—岩土工程]