多维量化记忆本构模型及其验证
摘要
一维量化记忆模型(SM)以经典的弹塑性模型为基础，将土体在单调加载情况下应力应变曲线的非线性剪切模量变换成量化模量在几何空间上的分段线性分布，这种变换建立了剪切模量与量化模量的映射关系。再以Masing准则为基础，在循环加载情况下，对这种简化后的几何分布进行变化调整，生成分段线性的量化模量。在进行土工结构动力计算时，可根据应力条件通过线性插值确定量化模量，再运用映射关系确定非线性的剪切模量。从而将剪切模量的非线性问题转化为量化模量的分段线性问题来处理，大大简化了非线性计算的复杂性。
本文将一维量化记忆模型中的记忆点对扩展为偏平面上的记忆面，将量化模量定义为当前应力点与破坏面之间距离的函数，构造了多维量化记忆模型(MDSM)，推导了多维应力条件下的本构关系。采用与一维量化记忆模型相同的映射函数来计算过程中塑性模量的变化。
在本构关系的数值实施中，利用大型非线性有限元软件ABAQUS提供的用户自定义接口平台，编写子程序UMAT，实现了多维量化记忆本构积分模块。最后对某大三轴试验进行了有限元模拟，得到的计算曲线与试验结果一致。因此，本文提出的多维量化记忆模型及其算法是可行的及合理的。
In this thesis, one-dimensional scaled memory(SM) model is introduced comprehensively for dynamic nonlinear analysis of soil structure. The SM translate the nonlinear variation of tangential modules during monotonic loading into a piecewise linear distribution geometrical relationship, which can easily be modified to simulate hysteretic characteristics of soil behavior during cyclic loadings, it also can simulate the dynamic stress-strain response of arbitrary cyclic loadings. The SM is applied to eliminate artificial ratcheting in bounding surface plasticity, and to produce closed stress-strain loops during cyclic loadings, without introducing a single material constant.
A multi-dimensional scaled memory (MDSM) model for pressure-dependent materials, based on the concept of scaled memory, is constructed. The constitutive relationship is deduced. In this thesis, the each dipole of memory points in one-dimensional SM would be generalized as a memory surface in multi-dimensional stress space for MDSM, the scaled modulus is defined as a function of distance between the current stress point and failure surface, and the mapping function of one-dimensional stress-strain relationship is adopted in the MDSM.
The constitutive integration module is completed through the user subroutine UMAT in numerically implementing of the proposed constitutive model, which based on the big nonlinear FEM software ABAQUS, and it will be applied for the dynamic nonlinear analysis of soil structure under multidimensional stresses. To simulate the dynamic triaxial test process with 300mm diameter's specimen, the dynamic stress-strain curves were agreement between calculation by MDSM and test results. It is demonstrated that the dynamic stress-strain relationship could be simulated commendably by multi-dimensional scaled memory model and its arithmetic.
本文将一维量化记忆模型中的记忆点对扩展为偏平面上的记忆面，将量化模量定义为当前应力点与破坏面之间距离的函数，构造了多维量化记忆模型(MDSM)，推导了多维应力条件下的本构关系。采用与一维量化记忆模型相同的映射函数来计算过程中塑性模量的变化。
在本构关系的数值实施中，利用大型非线性有限元软件ABAQUS提供的用户自定义接口平台，编写子程序UMAT，实现了多维量化记忆本构积分模块。最后对某大三轴试验进行了有限元模拟，得到的计算曲线与试验结果一致。因此，本文提出的多维量化记忆模型及其算法是可行的及合理的。
In this thesis, one-dimensional scaled memory(SM) model is introduced comprehensively for dynamic nonlinear analysis of soil structure. The SM translate the nonlinear variation of tangential modules during monotonic loading into a piecewise linear distribution geometrical relationship, which can easily be modified to simulate hysteretic characteristics of soil behavior during cyclic loadings, it also can simulate the dynamic stress-strain response of arbitrary cyclic loadings. The SM is applied to eliminate artificial ratcheting in bounding surface plasticity, and to produce closed stress-strain loops during cyclic loadings, without introducing a single material constant.
A multi-dimensional scaled memory (MDSM) model for pressure-dependent materials, based on the concept of scaled memory, is constructed. The constitutive relationship is deduced. In this thesis, the each dipole of memory points in one-dimensional SM would be generalized as a memory surface in multi-dimensional stress space for MDSM, the scaled modulus is defined as a function of distance between the current stress point and failure surface, and the mapping function of one-dimensional stress-strain relationship is adopted in the MDSM.
The constitutive integration module is completed through the user subroutine UMAT in numerically implementing of the proposed constitutive model, which based on the big nonlinear FEM software ABAQUS, and it will be applied for the dynamic nonlinear analysis of soil structure under multidimensional stresses. To simulate the dynamic triaxial test process with 300mm diameter's specimen, the dynamic stress-strain curves were agreement between calculation by MDSM and test results. It is demonstrated that the dynamic stress-strain relationship could be simulated commendably by multi-dimensional scaled memory model and its arithmetic.
引文
[1] Iwan W D. On a class of models for the yield behavior of continuous and composite system[J]. Journal of Applied Mechanics, 1967, 34(EM3):612-617.
[2] 郑大同，王惠昌．循环荷载作用下土的非线性应力应变模型[J]．岩土工程学报，1983，5(1)：65-76．
[3] 谢定义．土动力学[M]．西安交通大学出版社，1988．
[4] Lamb I, Tsai C F, Martin, G R. Determination of the dependent spectra using nonlinear analysis[A]. In: Proceedings of International Conference on Microzonation[C]. 1978.
[5] 符圣聪，江静贝，Iwan 模型用于场址动力分析[J]．地震工程与工程振动，1984，4(3)：48-59．
[6] Finn W G L．地震时地面和土构筑物的永久位移[J]．世界地震工程，1992，(1)：63-69．
[7] Finn W D L, Lee W K, Martin G R. An effective stress model for liquefaction[J]. Journal of Geotechnical Engineering, 1977, 103(6):517-534.
[8] 栾茂田．土动力非线性分析中的变参数Ramberg-Osgood本构模型[J]．地震工程与工程振动，1992，12(2)：69-78．
[9] 李小军，廖振鹏．土应力应变关系的粘—弹—塑模型[J]．地震工程与工程振动，1989，9(3)：65-72．
[10] 李小军．土动力本构关系的一种简单函数表达式[J]．岩土工程学报，1992，14(5)：90-94．
[11] 李小军，廖振鹏，张克绪．考虑阻尼拟合的动态骨架曲线函数式[J]．地震工程与工程振动，1994，14(1)：30-35．
[12] Pyke R. Nonlinear soil models for irregular cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE, 1979, 105(GT6).
[13] 栾茂田，林皋．土料非线性滞回本构模型的半解析半离散构造方法[J]．大连理工大学学报，1992，32(6)：694-701．
[14] 张克绪，李明宰，王冶琨．基于非曼辛规则的土动弹塑性模型[J]．地震工程与工程振动，1997，17(2)：74-81．
[15] 王志良，王余庆，韩清宇．不规则循环剪切荷载作用下土的粘弹性模型[J]．岩土工程学报，1980，2(3)：10-19．
[16] 王志良，韩清宇，．粘弹性土层地震反应的波动分析法[J]．地震工程与工程振动，1981，1(1)：117-137．
[17] 吴仲谋．饱和砂土两相动力有效应力分析方法研究[D]．水利水电科学研究院博士学位论文，1988．
[18] 郑大同，王天龙．土的滞回特性及其模型化[A]．见全国第四届土力学及基础工程学术会议论文[C]．
[19] 李万红，汪闻韶．无粘性土非线性动力剪应变模型[J]．水利学报，1993，(9)：11-17．
[20] 陈惠发[美]著，余天庆，王勋文等译．土木工程材料的本构方程(第二卷 塑性与建模)[M]．2001，武汉：华中科技大学出版社．
[21] Carter J P, Booker J R, Wrothu C P. A critical state soil model for cyclic loading[A]. In: Pande G N,
Zienkiewicz O C, eds. Soil Mechanics Transient and Cyclic Loadings[C]. London: John Wiley and Son, 1982, 35-62.
[22] Desai C S, Gallagher R H. Mechanics of Engineering Materials[M]. London: John Wiley and Sons, 1984, 96-103.
[23] Provest J H. Anisotropic undrained stress-strain behavior of clay[J]. Journal of Geotechnical Engineering Division, 1978, 104(8): 1075-1090.
[24] Provest J H. Plasticity theory for soil stress-strain behavior[J]. JEMD, 1978, 104(5):1177-1194.
[25] Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamic sand Earthquake Engineering, 1985, 4(1):9-17.
[26] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic critical state model for soil subjected to cyclic loading[J]. Geotechnique, 1981, 31 (4):451-470.
[27] Mroz Z, Zienkiewicz O C. Uniform for mulation of constitutive equation for clay and sands[A]. In: Desai C S, Gallagher R H, eds. Mechanics of Engineering Materials[C]. London: John Wiley and Son, 1984, 78-95.
[28] Dafalias Y F, Popov E P. A model of non-linearly hardening material for complex loadings[J]. Acta Mechanics, 1975, 21 (3): 173-192.
[29] Krieg R D. A practical two-surface plasticity theory[J]. Journal of Applied Mechanics, ASCE, 1975,42(2):641-646.
[30] Dafalias Y F. A model for soil behavior under monotonic and cyclic loading conditions[A]. In: Transactions of 5th International Conference on SmiRT[C]. Vol K, Paper No. K 1/8,West Berlin, Germany, 1979.
[31] Dafalias Y F, Herrmann L R. Bounding surface formation of soil plasticity[A]. Soil Mechanics-Transient and Cyclic Loads (Edited by Pande G N and Zienkiewicz O C)[C]. John Wiley and Sons, Chichester, U K, New York, 1982, 253-282.
[32] Dafalias Y F, Herrmarnn L R. Bounding surface plasticity. Ⅱ: Application to isotropic cohesive soils[J]. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12): 1263-1291.
[33] Anandarajah A, Dafalias Y F. Bounding surface plasticity Ⅲ: Application to anisotropic cohesive soils[J]. Journal of Engineering Mechanics, 1986, 112(EM12): 1292-1318.
[34] Dafalias Y F, Popov E P. Cyclic loading for materials with a vanishing elastic region[J]. Nuclear Engineering and Design, 1977,41(2):293-302.
[35] Bardet J P. Application of plasticity theory to sand behavior[D]. California Institute of Technology, Pasadena, 1983.
[36] Matsuoka H. Stress-strain relationship of sand based on the mobilized plane. Soil and Foundations, 1974, 14(2): 1-27.
[37] Aubry D, Hujeux J G, Lassoudiere F, et al. A double memory model with multiple mechanisms for cyclic soil behavior. Proc Inter Symp on Numeral Models in Geomechanics, 1982, 134-139.
[38] 谢定义，张建民．极限平衡理论在饱和砂土动力失稳过程中的应用[J]．土木工程学报，1981，14(4)：17-28．
[39] 张建民．饱和砂土瞬态动力学理论及其应用研究[D]．陕西机械学院学位论文，1991．
[40] 徐干成，谢定义，郑颖人．饱和砂土循环动应力应变特性的弹塑性模拟研究[J]．岩土工程学报，1995，17(2)：1-12．
[41] 王建华，要明伦．软粘土不排水循环特性的弹塑性模拟[J]．岩土工程学报，1996，18(30)：11-18．
[42] 吴兴征．堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D]．大连理工大学博士学位论文，2001．
[43] 丰土根．饱和砂土不排水动力特性及多机构边界面塑性模型研究[D]．河海大学博士学位论文，2002．
[44] Bardet J P. Scaled Memory Model for Undrained Behavior of Anisotropic Clays[J]. Journal of Geotechnical Engineering, 1995, 62(11): 755-765.
[45] Bardet J P.Scaled Memory Model for Cyclic Behavior of Soils[J]. Journal of Geotechnical Engineering, 1995, 62(11): 766-775.
[46] Barder J P.Scaled Memory Description of Hysteretic Material Behavior[J]. Journal of Geotechnical Engineering, 1996, 63(9): 750-757.
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[2] 郑大同，王惠昌．循环荷载作用下土的非线性应力应变模型[J]．岩土工程学报，1983，5(1)：65-76．
[3] 谢定义．土动力学[M]．西安交通大学出版社，1988．
[4] Lamb I, Tsai C F, Martin, G R. Determination of the dependent spectra using nonlinear analysis[A]. In: Proceedings of International Conference on Microzonation[C]. 1978.
[5] 符圣聪，江静贝，Iwan 模型用于场址动力分析[J]．地震工程与工程振动，1984，4(3)：48-59．
[6] Finn W G L．地震时地面和土构筑物的永久位移[J]．世界地震工程，1992，(1)：63-69．
[7] Finn W D L, Lee W K, Martin G R. An effective stress model for liquefaction[J]. Journal of Geotechnical Engineering, 1977, 103(6):517-534.
[8] 栾茂田．土动力非线性分析中的变参数Ramberg-Osgood本构模型[J]．地震工程与工程振动，1992，12(2)：69-78．
[9] 李小军，廖振鹏．土应力应变关系的粘—弹—塑模型[J]．地震工程与工程振动，1989，9(3)：65-72．
[10] 李小军．土动力本构关系的一种简单函数表达式[J]．岩土工程学报，1992，14(5)：90-94．
[11] 李小军，廖振鹏，张克绪．考虑阻尼拟合的动态骨架曲线函数式[J]．地震工程与工程振动，1994，14(1)：30-35．
[12] Pyke R. Nonlinear soil models for irregular cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE, 1979, 105(GT6).
[13] 栾茂田，林皋．土料非线性滞回本构模型的半解析半离散构造方法[J]．大连理工大学学报，1992，32(6)：694-701．
[14] 张克绪，李明宰，王冶琨．基于非曼辛规则的土动弹塑性模型[J]．地震工程与工程振动，1997，17(2)：74-81．
[15] 王志良，王余庆，韩清宇．不规则循环剪切荷载作用下土的粘弹性模型[J]．岩土工程学报，1980，2(3)：10-19．
[16] 王志良，韩清宇，．粘弹性土层地震反应的波动分析法[J]．地震工程与工程振动，1981，1(1)：117-137．
[17] 吴仲谋．饱和砂土两相动力有效应力分析方法研究[D]．水利水电科学研究院博士学位论文，1988．
[18] 郑大同，王天龙．土的滞回特性及其模型化[A]．见全国第四届土力学及基础工程学术会议论文[C]．
[19] 李万红，汪闻韶．无粘性土非线性动力剪应变模型[J]．水利学报，1993，(9)：11-17．
[20] 陈惠发[美]著，余天庆，王勋文等译．土木工程材料的本构方程(第二卷 塑性与建模)[M]．2001，武汉：华中科技大学出版社．
[21] Carter J P, Booker J R, Wrothu C P. A critical state soil model for cyclic loading[A]. In: Pande G N,
Zienkiewicz O C, eds. Soil Mechanics Transient and Cyclic Loadings[C]. London: John Wiley and Son, 1982, 35-62.
[22] Desai C S, Gallagher R H. Mechanics of Engineering Materials[M]. London: John Wiley and Sons, 1984, 96-103.
[23] Provest J H. Anisotropic undrained stress-strain behavior of clay[J]. Journal of Geotechnical Engineering Division, 1978, 104(8): 1075-1090.
[24] Provest J H. Plasticity theory for soil stress-strain behavior[J]. JEMD, 1978, 104(5):1177-1194.
[25] Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamic sand Earthquake Engineering, 1985, 4(1):9-17.
[26] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic critical state model for soil subjected to cyclic loading[J]. Geotechnique, 1981, 31 (4):451-470.
[27] Mroz Z, Zienkiewicz O C. Uniform for mulation of constitutive equation for clay and sands[A]. In: Desai C S, Gallagher R H, eds. Mechanics of Engineering Materials[C]. London: John Wiley and Son, 1984, 78-95.
[28] Dafalias Y F, Popov E P. A model of non-linearly hardening material for complex loadings[J]. Acta Mechanics, 1975, 21 (3): 173-192.
[29] Krieg R D. A practical two-surface plasticity theory[J]. Journal of Applied Mechanics, ASCE, 1975,42(2):641-646.
[30] Dafalias Y F. A model for soil behavior under monotonic and cyclic loading conditions[A]. In: Transactions of 5th International Conference on SmiRT[C]. Vol K, Paper No. K 1/8,West Berlin, Germany, 1979.
[31] Dafalias Y F, Herrmann L R. Bounding surface formation of soil plasticity[A]. Soil Mechanics-Transient and Cyclic Loads (Edited by Pande G N and Zienkiewicz O C)[C]. John Wiley and Sons, Chichester, U K, New York, 1982, 253-282.
[32] Dafalias Y F, Herrmarnn L R. Bounding surface plasticity. Ⅱ: Application to isotropic cohesive soils[J]. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12): 1263-1291.
[33] Anandarajah A, Dafalias Y F. Bounding surface plasticity Ⅲ: Application to anisotropic cohesive soils[J]. Journal of Engineering Mechanics, 1986, 112(EM12): 1292-1318.
[34] Dafalias Y F, Popov E P. Cyclic loading for materials with a vanishing elastic region[J]. Nuclear Engineering and Design, 1977,41(2):293-302.
[35] Bardet J P. Application of plasticity theory to sand behavior[D]. California Institute of Technology, Pasadena, 1983.
[36] Matsuoka H. Stress-strain relationship of sand based on the mobilized plane. Soil and Foundations, 1974, 14(2): 1-27.
[37] Aubry D, Hujeux J G, Lassoudiere F, et al. A double memory model with multiple mechanisms for cyclic soil behavior. Proc Inter Symp on Numeral Models in Geomechanics, 1982, 134-139.
[38] 谢定义，张建民．极限平衡理论在饱和砂土动力失稳过程中的应用[J]．土木工程学报，1981，14(4)：17-28．
[39] 张建民．饱和砂土瞬态动力学理论及其应用研究[D]．陕西机械学院学位论文，1991．
[40] 徐干成，谢定义，郑颖人．饱和砂土循环动应力应变特性的弹塑性模拟研究[J]．岩土工程学报，1995，17(2)：1-12．
[41] 王建华，要明伦．软粘土不排水循环特性的弹塑性模拟[J]．岩土工程学报，1996，18(30)：11-18．
[42] 吴兴征．堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D]．大连理工大学博士学位论文，2001．
[43] 丰土根．饱和砂土不排水动力特性及多机构边界面塑性模型研究[D]．河海大学博士学位论文，2002．
[44] Bardet J P. Scaled Memory Model for Undrained Behavior of Anisotropic Clays[J]. Journal of Geotechnical Engineering, 1995, 62(11): 755-765.
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