软黏土不排水循环应力应变关系的数值模拟
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摘要
对程星磊等提出的总应力形式增量弹塑性本构模型进行二次开发,以模拟复杂应力状态下软黏土的响应。通过Newton-Raphson算法,对材料非线性问题进行迭代求解;针对本构模型中应力反向等一系列关键性问题,应用欧拉切线算法编写了有限元程序,并结合子增量方法提高了计算精度。预测了软黏土在轴对称应力状态下的响应,得到了应力应变关系曲线,将其与单元预测结果进行比较,二者趋于一致,从而验证了有限元程序编写的合理性。利用该程序模拟三轴不固结不排水试验,模拟结果与试验吻合良好,表明该本构模型有限元程序可以反映轴对称应力状态下软黏土的不排水应力应变特性,可应用于更加复杂边值问题的模拟计算。
An incremental elasto-plastic constitutive model in the form of total stress developed by CHENG Xing-lei et al can effectively reflect the undrained cyclic stress-strain response of the saturated soft clay. In order to simulate the response of the soft clay under complex stress states,a secondary development for the constitutive model is conducted by use of the finite element method. The Newton-Raphson method is applied to solve iteratively the material nonlinear problem; considering a series of key problems such as stress reversing,in programming the model,Euler tangent algorithm is adopted,with a sub-incremental method improving calculation accuracy. The response of the soft clay under axisymmetric stress states is predicted,and the stress-strain relationship curves are received,which is compared with the results given by the unit predicting. The analysis comparison results show that it is in good agreement,verifying the rationality of the finite element program. The finite element program is applied to simulate unconsolidated undrained triaxial tests,and the results are in good agreement with the experiments,which indicates that the finite element program of the constitutive model can describe the undrained stress-strain behavior of the soft clay under triaxial stress states. Furthermore,it can be applied to solve more complex boundary value problems.
An incremental elasto-plastic constitutive model in the form of total stress developed by CHENG Xing-lei et al can effectively reflect the undrained cyclic stress-strain response of the saturated soft clay. In order to simulate the response of the soft clay under complex stress states,a secondary development for the constitutive model is conducted by use of the finite element method. The Newton-Raphson method is applied to solve iteratively the material nonlinear problem; considering a series of key problems such as stress reversing,in programming the model,Euler tangent algorithm is adopted,with a sub-incremental method improving calculation accuracy. The response of the soft clay under axisymmetric stress states is predicted,and the stress-strain relationship curves are received,which is compared with the results given by the unit predicting. The analysis comparison results show that it is in good agreement,verifying the rationality of the finite element program. The finite element program is applied to simulate unconsolidated undrained triaxial tests,and the results are in good agreement with the experiments,which indicates that the finite element program of the constitutive model can describe the undrained stress-strain behavior of the soft clay under triaxial stress states. Furthermore,it can be applied to solve more complex boundary value problems.
引文
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[10]程星磊,王建华,李书兆.软黏土不排水循环应力应变响应的弹塑性模拟[J].岩土工程学报,2014,36(5):933-941.(CHENG Xing-lei,WANG Jian-hua,LI Shu-zhao.Elastoplastic simulation for undrained cyclic stress-strain response of soft clay[J].Chinese Journal of Geotechnical Engineering,2014,36(5):933-941.(in Chinese))
[11]张学言,闫澍旺.岩土塑性力学基础[M].天津:天津大学出版社,2003:88-115.(ZHANG Xue-yan,YAN Shu-wang.Fundamentals of geotechnics plasticity[M].Tianjin:Tianjin University Press,2003:88-115.(in Chinese))
[12]王军祥,姜谙男.完全隐式返回映射算法对岩土地基问题的求解[J].工程力学,2013,36(8):83-89.(WANG Junxiang,JIANG An-nan.Fully implicit return mapping algrithm for solving the problems of geotechnical foundation[J].Engineering Machanics,2013,36(8):83-89.(in Chinese))
[13]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,1998:292-302.(ZHU Bo-fang.The finite element method theory and applications[M].Beijing:China Water Power Press,1998:292-302.(in Chinese))
[14]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1997:510-511.(WANG Xu-cheng,SHAO Min.The basic principles of the finite element method and numerical methods[M].Beijing:Tsinghua University Press,1997:510-511.(in Chinese))
[15]HU Cun,LIU Hai-xiao.Implicit and explicit integration schemes in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay[J].Computers and Geotechnics,2014,55:27-41.
[2]PRVOST J H.Anisotropic undrained stress-strain behavior of clays[J].Journal of the Geotechnical Engineering Division,ASCE,1978,104(GT8):1075-1090.
[3]DAFALIAS Y F,POPOV E P.A model of nonlinearly hardening materials for complex loading[J].Acta Mechanica,1975,21(3):173-192.
[4]DAFALIAS Y F,HEMNANN L R.A boundary surface soil plasticity model[C]∥Proceedings of International Symposium on Soils under Cyclic Transient Load.Rotterdam:Balkema Publ,1980:335-356.
[5]DAFALIAS Y F,POPOV E P.Cyclic loading for materials with a vanishing elastic domain[J].Nuclear Engineering and Design,1977,41(2):293-302.
[6]DAFALIAS Y F.Bounding surface plasticity Part I:Mathematical foundation and hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[7]DAFALIAS Y F,HERRMANN L R.Bounding surface plasticity.Part II:Application to isotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1263-1291.
[8]ANANDARAJAH A,DAFALIAS Y F.Bounding surface plasticity.Part III:Application to isotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1292-1318.
[9]花丽坤,孔亮.几种循环塑性模型的剖析和比较研究[J].宁夏工程技术,2003,2(1):19-23.(HUA Li-kun,KONG Liang.Analysis and comparison of several cyclic plastic models[J].Ningxia Engineering Technology,2003,2(1):19-23.(in Chinese))
[10]程星磊,王建华,李书兆.软黏土不排水循环应力应变响应的弹塑性模拟[J].岩土工程学报,2014,36(5):933-941.(CHENG Xing-lei,WANG Jian-hua,LI Shu-zhao.Elastoplastic simulation for undrained cyclic stress-strain response of soft clay[J].Chinese Journal of Geotechnical Engineering,2014,36(5):933-941.(in Chinese))
[11]张学言,闫澍旺.岩土塑性力学基础[M].天津:天津大学出版社,2003:88-115.(ZHANG Xue-yan,YAN Shu-wang.Fundamentals of geotechnics plasticity[M].Tianjin:Tianjin University Press,2003:88-115.(in Chinese))
[12]王军祥,姜谙男.完全隐式返回映射算法对岩土地基问题的求解[J].工程力学,2013,36(8):83-89.(WANG Junxiang,JIANG An-nan.Fully implicit return mapping algrithm for solving the problems of geotechnical foundation[J].Engineering Machanics,2013,36(8):83-89.(in Chinese))
[13]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,1998:292-302.(ZHU Bo-fang.The finite element method theory and applications[M].Beijing:China Water Power Press,1998:292-302.(in Chinese))
[14]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1997:510-511.(WANG Xu-cheng,SHAO Min.The basic principles of the finite element method and numerical methods[M].Beijing:Tsinghua University Press,1997:510-511.(in Chinese))
[15]HU Cun,LIU Hai-xiao.Implicit and explicit integration schemes in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay[J].Computers and Geotechnics,2014,55:27-41.
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