土的量化记忆模型参数确定与应用研究
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摘要
论文首先介绍了量化记忆(SM)模型的基本理论。SM模型以经典弹塑性理论作为基础，将单调加载情况下的应力－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，然后再以Masing准则作为基础，在循环加载情况下，对这种简化的几何分布进行变化调整，从而使其生成非线性变化的剪切模量。将非线性的问题转化为线性问题进行处理，大大简化了非线性计算的复杂性。
其次，采用高精度局部位移计，对筑坝材料进行了动三轴试验，采用Levenberg－Marquardt非线性最小二乘法，编写程序拟合了SM模型6个材料参数：E，(max，(min，h0，r，s，并将量化记忆模型生成的应力应变关系曲线、模量衰减和阻尼曲线与试验曲线进行了比较。结果证明，量化记忆模型生成的曲线和试验曲线之间是相互吻合的。探讨了不同应变水平下滞回圈的SM模型参数的拟合情况，得到了h0，r，s三个参数随动应变幅值变化的规律。同时，本文对双线性SM模型（BSM）模型进行了初步探讨，通过试验初步验证了BSM模型应用的可行性。
最后，编写了考虑应力应变切线模量的衰减的真非线性地震反应分析程序。计算了一实际工程，并和等价非线性法进行了对比。计算表明，由试验参数计算得到的真非线性地震响应分布规律和等价线性法得到的响应基本一致，但是要略大于等价线性法得到的结果。由试验参数得到的真非线性地震响应能较好地体现坝体的真实地震响应。
Firstly, the scaled memory (SM) model is introduced for dynamic nonlinear analysis of soil structures. The SM translates 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.
In order to determine the parameters of the SM model, the analysis program of nonlinear Levenberg－Marquardt least squares method is developed. The parameters of the SM model , such as ,,,,,, is defined by fitting test results. To compare the dynamic stress-strain relationships, modules attenuation and damp ratio curve between the tests and the calculated results by SM model, it is shown that the SM model is capable and practicable. Because the hysteretic loops are varied as the axial dynamic strain increased, so the SM model parameters will be changed during dynamic loading. The relationship between h0，r，s and axial dynamic strain is induced by the fitting test results. In addition, the parameter of binary scaled model (BSM) is discussed which mean the skeleton curve is different between tensile branch and compression branch.
Lastly, a seismic response analysis program of embankment, which combines step-by-step scheme with unbalanced load transfer method, was developed. It has thought of the degradation of soils and can use the parameters of the SM model that has been calculated by the least squares program. Taking a embankment as example, a comparison between the incrementally-iterative numerical technique and the equivalent linearization approach was carried out .It is shown that distribution of dynamic response of dam is mainly alike, but the dynamic response of incrementally-iterative numerical technique using experimental parameter is greater than that of the equivalent linearization approach.
其次，采用高精度局部位移计，对筑坝材料进行了动三轴试验，采用Levenberg－Marquardt非线性最小二乘法，编写程序拟合了SM模型6个材料参数：E，(max，(min，h0，r，s，并将量化记忆模型生成的应力应变关系曲线、模量衰减和阻尼曲线与试验曲线进行了比较。结果证明，量化记忆模型生成的曲线和试验曲线之间是相互吻合的。探讨了不同应变水平下滞回圈的SM模型参数的拟合情况，得到了h0，r，s三个参数随动应变幅值变化的规律。同时，本文对双线性SM模型（BSM）模型进行了初步探讨，通过试验初步验证了BSM模型应用的可行性。
最后，编写了考虑应力应变切线模量的衰减的真非线性地震反应分析程序。计算了一实际工程，并和等价非线性法进行了对比。计算表明，由试验参数计算得到的真非线性地震响应分布规律和等价线性法得到的响应基本一致，但是要略大于等价线性法得到的结果。由试验参数得到的真非线性地震响应能较好地体现坝体的真实地震响应。
Firstly, the scaled memory (SM) model is introduced for dynamic nonlinear analysis of soil structures. The SM translates 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.
In order to determine the parameters of the SM model, the analysis program of nonlinear Levenberg－Marquardt least squares method is developed. The parameters of the SM model , such as ,,,,,, is defined by fitting test results. To compare the dynamic stress-strain relationships, modules attenuation and damp ratio curve between the tests and the calculated results by SM model, it is shown that the SM model is capable and practicable. Because the hysteretic loops are varied as the axial dynamic strain increased, so the SM model parameters will be changed during dynamic loading. The relationship between h0，r，s and axial dynamic strain is induced by the fitting test results. In addition, the parameter of binary scaled model (BSM) is discussed which mean the skeleton curve is different between tensile branch and compression branch.
Lastly, a seismic response analysis program of embankment, which combines step-by-step scheme with unbalanced load transfer method, was developed. It has thought of the degradation of soils and can use the parameters of the SM model that has been calculated by the least squares program. Taking a embankment as example, a comparison between the incrementally-iterative numerical technique and the equivalent linearization approach was carried out .It is shown that distribution of dynamic response of dam is mainly alike, but the dynamic response of incrementally-iterative numerical technique using experimental parameter is greater than that of the equivalent linearization approach.
引文
陈云敏.土的动力特性及测试方法的现状与发展.见：袁驷，张跃，茹继平主编，二十一世纪土木工程学科的发展趋势[M].北京：科学出版社,144－151
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.
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.
谢定义. 土动力学[M]. 西安交通大学出版社, 1988.
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.
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.
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.
刘汉龙, 余湘娟. 土动力学与岩土地震工程研究进展. 河海大学学报, 1999, 27(1):6-15.
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.
Desai C S, Gallagher R H. Mechanics of Engineering Materials[M]. London: John Wiley and Sons, 1984, 96-103.
Provest J H. Anisotropic undrained stress-strain behavior of clay[J]. Journal of Geotechnical Engineering Division, 1978, 104(8):1075-1090.
Provest J H. Plasticity theory for soil stress-strain behavior[J]. JEMD, 1978, 104(5):1177-1194.
Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamic sand Earthquake Engineering, 1985, 4(1):9-17.
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.
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.
Dafalias Y F, Popov E P. A model of non-linearly hardening material for complex loadings[J]. Acta Mechanics, 1975, 21(3):173-192.
Krieg R D. A practical two-surface plasticity theory[J]. Journal of Applied Mechanics, ASCE, 1975,42(2):641-646.
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.
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.
Dafalias Y F, Herrmann L R. Bounding surface plasticity. II: Application to isotropic cohesive soils[J]. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12):1263-1291.
Anandarajah A, Dafalias Y F. Bounding surface plasticity III: Application to anisotropic cohesive soils[J]. Journal of Engineering Mechanics, 1986, 112(EM12):1292-1318.
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.
Bardet J P. Application of plasticity theory to sand behavior[D]. California Institute of Technology, Pasadena, 1983.
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.
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.
Hardin B O, Drnevich V P. Shear moduli and damping ratios in soils: design equations and curves[J]. Journal of the Soil Mechanics and Foundations Division, ASCE,1972,98(7):667-692.
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.
Martin P P, Seed H B. One-dimensional dynamic ground response analysis[J]. Journal of Geotechnical Engineering Division, ASCE,1982,108(GT7):935-952.
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.
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.
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.
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.
Provost J H, Catherine M K. Shear stress-strain curve generation from simple material parameters[J]. Journal of Geotechnical Engineering, 1967, 34(3):11-19.
Pyke R. Nonlinear soil models for irregular cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE, 1979, 105(GT6).
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.
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.
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.
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.
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.
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].
1983,302-308.
Hardin B O. Plane strain constitutive equations for soils[J]. Journal of Geotechnical Engineering Division. 1983,109(3).
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.
Bardet J P. Scaled Memory Model for Undrained Behavior of Anisotropic Clays [J]. Journal of Geotechnical Engineering, 1995, 62(11): 755-765.
Bardet J P. Scaled Memory Model for Cyclic Behavior of Soils [J]. Journal of Geotechnical Engineering, 1995, 62(11): 766-775.
Bardet J P. Scaled Memory Description of Hysteretic Material Behavior[J]. Journal of Geotechnical Engineering, 1996, 63(9): 750-757.
Burland J B, Symes M J. A simple axial displacement gauge for use in the triaxial apparatus [J]. Geotechnique , 1982,32(1) :62-65.
Clayton C R I, Khatrush S A, Bica A, Siddiue A. The use of hall effect semiconductor s in geotechnical in strumentation [J].Geotechnical Testing Journal, ASTM,1989,12(1) :69-76.
Goto S, Tatsuoka F, etal. A simple gauge for local small strain measurements in the laboratory [J]. Soil sand Foundations, 1991.31(1) : 169-180.
Shibuya S, Tatsuoka F, Teachavorasinskuns, Kong X J, etal . Elastic deformation properties of geomaterials [J]. Soils and Foundations, 1992, 32(3) : 26-46.
孔宪京,贾革续,邹德高,娄树莲,韩国城.微小应变下堆石料的变形特性 [J].岩土工程学报,2001, 23(1): 32-37.
孔宪京,娄树莲,邹德高,贾革续,韩国城.筑坝堆石料的等效动剪切模量与等效阻尼比[J].水利学报,2001,(8),20-25.
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Mladen Vucetic, Ricardo Dobry. Degradation of marine clays under cyclic loading[J]. Journal of geotechnical engineering,1988,114(2),133-149.
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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.
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.
谢定义. 土动力学[M]. 西安交通大学出版社, 1988.
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.
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.
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.
刘汉龙, 余湘娟. 土动力学与岩土地震工程研究进展. 河海大学学报, 1999, 27(1):6-15.
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.
Desai C S, Gallagher R H. Mechanics of Engineering Materials[M]. London: John Wiley and Sons, 1984, 96-103.
Provest J H. Anisotropic undrained stress-strain behavior of clay[J]. Journal of Geotechnical Engineering Division, 1978, 104(8):1075-1090.
Provest J H. Plasticity theory for soil stress-strain behavior[J]. JEMD, 1978, 104(5):1177-1194.
Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamic sand Earthquake Engineering, 1985, 4(1):9-17.
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.
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.
Dafalias Y F, Popov E P. A model of non-linearly hardening material for complex loadings[J]. Acta Mechanics, 1975, 21(3):173-192.
Krieg R D. A practical two-surface plasticity theory[J]. Journal of Applied Mechanics, ASCE, 1975,42(2):641-646.
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.
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.
Dafalias Y F, Herrmann L R. Bounding surface plasticity. II: Application to isotropic cohesive soils[J]. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12):1263-1291.
Anandarajah A, Dafalias Y F. Bounding surface plasticity III: Application to anisotropic cohesive soils[J]. Journal of Engineering Mechanics, 1986, 112(EM12):1292-1318.
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.
Bardet J P. Application of plasticity theory to sand behavior[D]. California Institute of Technology, Pasadena, 1983.
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.
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.
Hardin B O, Drnevich V P. Shear moduli and damping ratios in soils: design equations and curves[J]. Journal of the Soil Mechanics and Foundations Division, ASCE,1972,98(7):667-692.
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.
Martin P P, Seed H B. One-dimensional dynamic ground response analysis[J]. Journal of Geotechnical Engineering Division, ASCE,1982,108(GT7):935-952.
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.
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.
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.
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.
Provost J H, Catherine M K. Shear stress-strain curve generation from simple material parameters[J]. Journal of Geotechnical Engineering, 1967, 34(3):11-19.
Pyke R. Nonlinear soil models for irregular cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE, 1979, 105(GT6).
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.
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.
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.
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.
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.
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].
1983,302-308.
Hardin B O. Plane strain constitutive equations for soils[J]. Journal of Geotechnical Engineering Division. 1983,109(3).
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.
Bardet J P. Scaled Memory Model for Undrained Behavior of Anisotropic Clays [J]. Journal of Geotechnical Engineering, 1995, 62(11): 755-765.
Bardet J P. Scaled Memory Model for Cyclic Behavior of Soils [J]. Journal of Geotechnical Engineering, 1995, 62(11): 766-775.
Bardet J P. Scaled Memory Description of Hysteretic Material Behavior[J]. Journal of Geotechnical Engineering, 1996, 63(9): 750-757.
Burland J B, Symes M J. A simple axial displacement gauge for use in the triaxial apparatus [J]. Geotechnique , 1982,32(1) :62-65.
Clayton C R I, Khatrush S A, Bica A, Siddiue A. The use of hall effect semiconductor s in geotechnical in strumentation [J].Geotechnical Testing Journal, ASTM,1989,12(1) :69-76.
Goto S, Tatsuoka F, etal. A simple gauge for local small strain measurements in the laboratory [J]. Soil sand Foundations, 1991.31(1) : 169-180.
Shibuya S, Tatsuoka F, Teachavorasinskuns, Kong X J, etal . Elastic deformation properties of geomaterials [J]. Soils and Foundations, 1992, 32(3) : 26-46.
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