考虑土骨架非线性的饱和土-结构相互作用分析
|
摘要
强地震作用下,饱和土体将进入非线性,有必要考虑非线性饱和土的地震响应以及非线性饱和土-结构相互作用问题。本文采用Biot饱和多孔介质模型,基于不规则加卸载准则的修正Davidenkov模型来描述近场区域内饱和土骨架的非线性特性,并采用集中质量显式有限元方法进行分析;远场区介质假定为线弹性饱和多孔介质,通过多次透射人工边界进行模拟;结构采用Newmark隐式时步积分方法进行分析。通过自编程序实现了非线性饱和土体的地震反应分析以及非线性饱和土-基础-结构相互作用分析。通过算例,对比分析了土体非线性对饱和土体、基础和结构反应的影响。
Under strong earthquakes, soil nonlinearity and pore water pressure have a great influence on the seismic response of soils. It is necessary to consider the seismic response of nonlinear saturated soils and the nonlinear saturated soil-structure interaction problem. In this paper, the soil is modeled by the Biot porous medium model. The Davidenkov model and the modified Masing rule is used to describe the nonlinear characteristics of the saturated soil skeleton in the near-field region which is analyzed by the lumped-mass explicit finite element method. Far-field region is assumed to be saturated poroelastic media, which is simulated by transmitting artificial boundaries. The structure is analyzed by Newmark implicit time integral method. The foundation is assumed to be rigid and the explicit time integral scheme is used to solve it. The corresponding code is programmed. Numerical examples for three-dimensional analysis of saturated half space and saturated soil-foudation-frame structure system under earthquake are presented. The linear elastic and nonlinear saturated soils are considered respectively and the influence of nonlinearity on the response of saturated soil, foundation and structure is analyzed through comparison between the results of linear elastic case and nonlinear case.
Under strong earthquakes, soil nonlinearity and pore water pressure have a great influence on the seismic response of soils. It is necessary to consider the seismic response of nonlinear saturated soils and the nonlinear saturated soil-structure interaction problem. In this paper, the soil is modeled by the Biot porous medium model. The Davidenkov model and the modified Masing rule is used to describe the nonlinear characteristics of the saturated soil skeleton in the near-field region which is analyzed by the lumped-mass explicit finite element method. Far-field region is assumed to be saturated poroelastic media, which is simulated by transmitting artificial boundaries. The structure is analyzed by Newmark implicit time integral method. The foundation is assumed to be rigid and the explicit time integral scheme is used to solve it. The corresponding code is programmed. Numerical examples for three-dimensional analysis of saturated half space and saturated soil-foudation-frame structure system under earthquake are presented. The linear elastic and nonlinear saturated soils are considered respectively and the influence of nonlinearity on the response of saturated soil, foundation and structure is analyzed through comparison between the results of linear elastic case and nonlinear case.
引文
[1] Byrne P M. A cyclic shear-volume coupling and pore pressure model for sand[M]. Mssouri, USA: 1991:47-56.
[2] Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid[J]. AcoustSoc Am, 1956, 28: 168-191.
[3] 张季, 梁建文, 巴振宁. 水平层状饱和场地地震响应分析的等效线性化方法[J].工程力学, 2016, 33(10):52-61.ZHANG Ji, LIANG Jianwen, BA Zhenning. Equivalent Linear Analysis of Seismic Response of Horizontally Layered Fluid-Saturated Poroelastic Half-Space[J]. Engineering Mechanics, 2016, 33(10):52-61(in Chinese)
[4] Prevost J H. Mechanics of continuous porous media[J]. International Journal of Engineering Science, 1980, 18(6):787-800.
[5] Prevost J H. Nonlinear transient phenomena in saturated porous media[J]. Computer Methods in Applied Mechanics and Engineering, 1982, 30(1):3-18.
[6] Prevost J H. Wave propagation in fluid-saturated porous media: an efficient finite element procedure[J]. International Journal of Soil Dynamics and Earthquake Engineering, 1985, 4(4):183-202.
[7] Yiagos A N., Prevost J H. Two-phase elasto-plastic seismic response of earth dams: Applications[J]. Soil Dynamics and Earthquake Engineering, 1991, 10(7):371-381.
[8] Aubry D, Modaressi H. A model for the nonlinear dynamic analysis of saturated soils[J]. Rev. Franc. Geoteeh., 1989, 46:43-75.
[9] Diebels S A micropolar theory of porous media: constitutive modeling[J]. Transport in Porous Media, 1999, 34(1/2/3):193-208.
[10] 李永强, 景立平, 单振东, 等. 基于两相介质理论之土层弹塑性大变形地震反应分析[J]. 岩土工程学报, 2015, 37(11):1986-1991.LI Yongqiang, JING Liping, SHAN Zhendong, et al. Nonlinear ground response based on the theory of wave propagation in two-phase media[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(11):1986-1991.(in Chinese)
[11] 杜修力, 路德春. 土动力学与岩土地震工程研究进展[J]. 岩土力学, 2011, 32(增刊2):10-20.DU Xiuli, Lu Dechun. Advances in soil dynamics and geotechnical earthquake engineering[J]. Rock and Soil Mechanics. 2011, 32(S2):10-20.(in Chinese)
[12] 蔡袁强, 于玉贞, 袁晓铭, 等. 土动力学与岩土地震工程[J]. 土木工程学报, 2016, 49(5):9-29.CAI Yuan, YU Yunzhen, YUAN Xiaoming. Soil dynamics and geotechnical earthquake engineering[J]. China Civil Engineer Journal, 2016, 49(5):9-29.(in Chinese)
[13] Idriss I M, Seed H B. Seismic response of horizontal soil layers[J]. Journal of the Soil Mechanics and Foundation Division, ASCE, 1968, 94(SM4):1003-1031.
[14] 李小军. 一维土层地震反应线性化计算程序. 廖振鹏. 地震小区化-理论与实践[M]. 北京: 地震出版社, 1989: 250-265.LI Xiaojun. A computer program for calculating earthquake response of ground layered soil. Liao Zhenpeng. Seismic microzonation (theory and practice)[M]. Beijing: Seismological Press, 1989: 250-265. (in Chinese)
[15] Schnabel P B. SHAKE a computer program for earthquake response analysis of horizontally layered sites[R]. University of California, Berkeley (USA). Report No. EERC-72/12, 1972.
[16] Bardet J P, Ichii K, Lin C H. EERA: a computer program for equivalent-linear earthquake site response analyses of layered soil deposits[R]. University of Southern California, Los Angeles (USA). A Report to Department of Civil Engineering, 2000.
[17] 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.LI Xiaojun, LIAO Zhenpeng, ZHANG Kexu. A functional formula of dynamic skeletion curve taking account of damping effect[J]. Earthquake Engineering and Engineering Dynamics, 1994, 14(1):30-35.(in Chinese)
[18] 张克绪, 李明宰, 王治琨. 基于非曼辛准则的土体弹塑性模型[J]. 地震工程与工程振动, 1997, 17(2):74-81.ZHANG Kexu, LI Mingzai, WANG Zhikun. Dynamic elastic-plastic models of soils basing on non-mansing'srule[J]. Earthquake Engineering and Engineering Vibration, 1997, 17(2):74-81.(in Chinese)
[19] 陈国兴, 庄海洋. 基于Davidenkov骨架曲线的土体动力本构关系及其参数研究[J]. 岩土工程学报, 2005, 27(8):860-864.CHEN Guoxing, ZHUANG Haiyang. Developed nonlinear dynamic constitutive relations of soils based on Davidenkov skeleton curve[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(8):860-864.(in Chinese)
[20] Lee M K W, Finn W. DESRA-2: Dynamic Effective Stress Response Analysis of Soil Deposits with Energy Transmitting Boundary Including Assessment of Liquefaction Potential[R]. The University of British Columbia, Faculty of Applied Science, Vancouver, British Columbia, 1978.
[21] Matasovic N. MOD_2: A Computer Program for Seismic Response Analysis of Horizontally Layered Soil Deposits[R]. Earthfill Dams and Solid Waste Landfills .Geomotions, LLC, Lacey, WA, 2006.
[22] Martin P P, Seed H B. One-dimensional dynamic ground response analyses[J]. Journal of Geotechnical Engineering, ASCE, 1982, 108(7): 935-952.
[23] Pyke R M. TESS users' manual[Z]. TAGA Engineering Software Services, Lafayette, California, 2000.
[24] Hashash Y M A, Groholski, D R, Phillips, C. A., et al. DEEPSOIL 5.0 user manual and tutorial[Z]. 2011.
[25] Provest J H. A simple plasticity theory for frictional cohesionlesssoils[J]. International Journal of Soil Dynamics and Earthquake Engineering, 1985, 4(85):9-17.
[26] Mroz Z. On the description of anisotropic work hardening[J]. Journal of the Mechanics and Physics of Solids, 1967, 15(3):163-175.
[27] Prevost J H. Anisotropic undrained stress-strain behavior of clays[J]. Journal of Geotechnical Engineering Division, 2014, 104(8):1075-1090.
[28] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic critical state model for soils subject to cyclic loading[J]. Geotechnique, 1981, 31(4):451-469.
[29] Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading[J]. Acta Mechanica, 1975, 21(3):173-192.
[30] Krieg R D. A practical two surface plasticity theory[J]. Journal of Applied Mechanics, 1975, 42(3):641-646.
[31] Zienkiewicz O C, Mroz Z. Generalized plasticity formulation and applications to geomechanics[J]. Mechanics of Engineering Materials, 1984:655-679.
[32] Mroz Z, Zienkiewicz O C. Uniform formulation of constitutive equations for clays and sand[J]. Mechanics of Engineering Materials, 1984: 415-450.
[33] Pastor M, Zienkiewicz O C, Chan A H C. Generalized plasticity and the modelling of soil behavior[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1990, 14(3):151-190.
[34] 赵丁凤, 阮滨, 陈国兴, 等. 基于Davidenkov骨架曲线模型的修正不规则加卸载准则与等效剪应变算法及其验证[J].岩土工程学报,2017, 39(5):888-895.ZHAO Dingfeng, RUAN Bin, CHEN Guoxing, et al. Validation of the modified irregular loading-reloading rules based on Davidenkov skeleton curve and its equivalent shear strain algorithm implemented in ABAQUS[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(5):888-895. (in Chinese)
[35] 赵宇昕, 陈少林. 关于传递矩阵法分析饱和成层介质响应问题的讨论[J]. 力学学报, 2016, 48(5):1145-1158.ZHAO Yuxin, CHEN Shaolin. Discussion on the matrix propagator method to analyze the response of saturated layered media[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5):1145-1158(in Chinese)
[2] Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid[J]. AcoustSoc Am, 1956, 28: 168-191.
[3] 张季, 梁建文, 巴振宁. 水平层状饱和场地地震响应分析的等效线性化方法[J].工程力学, 2016, 33(10):52-61.ZHANG Ji, LIANG Jianwen, BA Zhenning. Equivalent Linear Analysis of Seismic Response of Horizontally Layered Fluid-Saturated Poroelastic Half-Space[J]. Engineering Mechanics, 2016, 33(10):52-61(in Chinese)
[4] Prevost J H. Mechanics of continuous porous media[J]. International Journal of Engineering Science, 1980, 18(6):787-800.
[5] Prevost J H. Nonlinear transient phenomena in saturated porous media[J]. Computer Methods in Applied Mechanics and Engineering, 1982, 30(1):3-18.
[6] Prevost J H. Wave propagation in fluid-saturated porous media: an efficient finite element procedure[J]. International Journal of Soil Dynamics and Earthquake Engineering, 1985, 4(4):183-202.
[7] Yiagos A N., Prevost J H. Two-phase elasto-plastic seismic response of earth dams: Applications[J]. Soil Dynamics and Earthquake Engineering, 1991, 10(7):371-381.
[8] Aubry D, Modaressi H. A model for the nonlinear dynamic analysis of saturated soils[J]. Rev. Franc. Geoteeh., 1989, 46:43-75.
[9] Diebels S A micropolar theory of porous media: constitutive modeling[J]. Transport in Porous Media, 1999, 34(1/2/3):193-208.
[10] 李永强, 景立平, 单振东, 等. 基于两相介质理论之土层弹塑性大变形地震反应分析[J]. 岩土工程学报, 2015, 37(11):1986-1991.LI Yongqiang, JING Liping, SHAN Zhendong, et al. Nonlinear ground response based on the theory of wave propagation in two-phase media[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(11):1986-1991.(in Chinese)
[11] 杜修力, 路德春. 土动力学与岩土地震工程研究进展[J]. 岩土力学, 2011, 32(增刊2):10-20.DU Xiuli, Lu Dechun. Advances in soil dynamics and geotechnical earthquake engineering[J]. Rock and Soil Mechanics. 2011, 32(S2):10-20.(in Chinese)
[12] 蔡袁强, 于玉贞, 袁晓铭, 等. 土动力学与岩土地震工程[J]. 土木工程学报, 2016, 49(5):9-29.CAI Yuan, YU Yunzhen, YUAN Xiaoming. Soil dynamics and geotechnical earthquake engineering[J]. China Civil Engineer Journal, 2016, 49(5):9-29.(in Chinese)
[13] Idriss I M, Seed H B. Seismic response of horizontal soil layers[J]. Journal of the Soil Mechanics and Foundation Division, ASCE, 1968, 94(SM4):1003-1031.
[14] 李小军. 一维土层地震反应线性化计算程序. 廖振鹏. 地震小区化-理论与实践[M]. 北京: 地震出版社, 1989: 250-265.LI Xiaojun. A computer program for calculating earthquake response of ground layered soil. Liao Zhenpeng. Seismic microzonation (theory and practice)[M]. Beijing: Seismological Press, 1989: 250-265. (in Chinese)
[15] Schnabel P B. SHAKE a computer program for earthquake response analysis of horizontally layered sites[R]. University of California, Berkeley (USA). Report No. EERC-72/12, 1972.
[16] Bardet J P, Ichii K, Lin C H. EERA: a computer program for equivalent-linear earthquake site response analyses of layered soil deposits[R]. University of Southern California, Los Angeles (USA). A Report to Department of Civil Engineering, 2000.
[17] 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.LI Xiaojun, LIAO Zhenpeng, ZHANG Kexu. A functional formula of dynamic skeletion curve taking account of damping effect[J]. Earthquake Engineering and Engineering Dynamics, 1994, 14(1):30-35.(in Chinese)
[18] 张克绪, 李明宰, 王治琨. 基于非曼辛准则的土体弹塑性模型[J]. 地震工程与工程振动, 1997, 17(2):74-81.ZHANG Kexu, LI Mingzai, WANG Zhikun. Dynamic elastic-plastic models of soils basing on non-mansing'srule[J]. Earthquake Engineering and Engineering Vibration, 1997, 17(2):74-81.(in Chinese)
[19] 陈国兴, 庄海洋. 基于Davidenkov骨架曲线的土体动力本构关系及其参数研究[J]. 岩土工程学报, 2005, 27(8):860-864.CHEN Guoxing, ZHUANG Haiyang. Developed nonlinear dynamic constitutive relations of soils based on Davidenkov skeleton curve[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(8):860-864.(in Chinese)
[20] Lee M K W, Finn W. DESRA-2: Dynamic Effective Stress Response Analysis of Soil Deposits with Energy Transmitting Boundary Including Assessment of Liquefaction Potential[R]. The University of British Columbia, Faculty of Applied Science, Vancouver, British Columbia, 1978.
[21] Matasovic N. MOD_2: A Computer Program for Seismic Response Analysis of Horizontally Layered Soil Deposits[R]. Earthfill Dams and Solid Waste Landfills .Geomotions, LLC, Lacey, WA, 2006.
[22] Martin P P, Seed H B. One-dimensional dynamic ground response analyses[J]. Journal of Geotechnical Engineering, ASCE, 1982, 108(7): 935-952.
[23] Pyke R M. TESS users' manual[Z]. TAGA Engineering Software Services, Lafayette, California, 2000.
[24] Hashash Y M A, Groholski, D R, Phillips, C. A., et al. DEEPSOIL 5.0 user manual and tutorial[Z]. 2011.
[25] Provest J H. A simple plasticity theory for frictional cohesionlesssoils[J]. International Journal of Soil Dynamics and Earthquake Engineering, 1985, 4(85):9-17.
[26] Mroz Z. On the description of anisotropic work hardening[J]. Journal of the Mechanics and Physics of Solids, 1967, 15(3):163-175.
[27] Prevost J H. Anisotropic undrained stress-strain behavior of clays[J]. Journal of Geotechnical Engineering Division, 2014, 104(8):1075-1090.
[28] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic critical state model for soils subject to cyclic loading[J]. Geotechnique, 1981, 31(4):451-469.
[29] Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading[J]. Acta Mechanica, 1975, 21(3):173-192.
[30] Krieg R D. A practical two surface plasticity theory[J]. Journal of Applied Mechanics, 1975, 42(3):641-646.
[31] Zienkiewicz O C, Mroz Z. Generalized plasticity formulation and applications to geomechanics[J]. Mechanics of Engineering Materials, 1984:655-679.
[32] Mroz Z, Zienkiewicz O C. Uniform formulation of constitutive equations for clays and sand[J]. Mechanics of Engineering Materials, 1984: 415-450.
[33] Pastor M, Zienkiewicz O C, Chan A H C. Generalized plasticity and the modelling of soil behavior[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1990, 14(3):151-190.
[34] 赵丁凤, 阮滨, 陈国兴, 等. 基于Davidenkov骨架曲线模型的修正不规则加卸载准则与等效剪应变算法及其验证[J].岩土工程学报,2017, 39(5):888-895.ZHAO Dingfeng, RUAN Bin, CHEN Guoxing, et al. Validation of the modified irregular loading-reloading rules based on Davidenkov skeleton curve and its equivalent shear strain algorithm implemented in ABAQUS[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(5):888-895. (in Chinese)
[35] 赵宇昕, 陈少林. 关于传递矩阵法分析饱和成层介质响应问题的讨论[J]. 力学学报, 2016, 48(5):1145-1158.ZHAO Yuxin, CHEN Shaolin. Discussion on the matrix propagator method to analyze the response of saturated layered media[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5):1145-1158(in Chinese)