基于粒子群优化算法的软土场地Davidenkov模型参数拟合与应用
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摘要
为探究Davidenkov模型在软土场地地震反应分析中的应用,推导了Davidenkov模型的非线性动力本构模型在初始加载、卸载和再加载阶段的增量剪切模量表达式,并将土体动应力-应变关系推广到三维。基于粒子群优化算法对Davidenkov模型的参数进行拟合,利用MATLAB编制了拟合程序,通过对典型砂土和黏土试验数据进行拟合并验证了方法的适用性,同时对某典型上海软土场地的参数进行了拟合。在此基础上,利用ABAQUS软件提供的二次开发平台UMAT,编制了基于Davidenkov模型的土体非线性动力本构模型计算子程序,利用复杂加载路径验证了该子程序的正确性,实现了在ABAQUS软件中软土非线性动力本构模型的二次开发。最后,以某典型上海软土场地为例,对比分析了上海软土场地基于非线性动力本构模型的计算结果和等效线性化的结果。结果表明:粒子群优化算法能很好地对Davidenkov模型的参数进行拟合;该非线性动力本构模型计算子程序能够较好地描述软土场地的动力非线性行为;在该算例中,上海软土场地基于非线性动力本构模型的加速度响应值和相对位移响应值要小于等效线性化的计算结果。
Here, to explore applications of Davidenkov model in seismic response analysis of soft soil sites, the incremental shear modulus expressions for Davidenkov model's nonlinear dynamic constitutive model in initial loading, unloading and reloading stages were derived, and the soil body's dynamic stress-strain relationship was extended to 3-D. Then, parameters of Davidenkov model were fitted using the particle swarm optimization(PSO) algorithm and the fitting program was compiled with MATLAB. The applicability of the method was verified through fitting test data of typical sand and clay. Parameters of a certain typical Shanghai soft soil site were fitted. Afterward, using the secondary development platform UMAT provided with ABAQUS, the subroutine for the nonlinear dynamic constitutive model of soft soil body based on Davidenkov model was compiled, and the correctness of the subroutine was verified through a complex loading path. Finally, taking a certain typical Shanghai soft soil site as an example, the calculation results based on the nonlinear dynamic constitutive model and those using the equivalent linearization method were contrastively analyzed. The results showed that parameters of Davidenkov model can be well fitted with the PSO algorithm; the subroutine of the nonlinear dynamic constitutive model proposed here can better describe nonlinear behaviors of soft soil sites; acceleration response values and relative displacement response ones of the typical Shanghai soft soil site based on the nonlinear dynamic constitutive model are smaller than those using the equivalent linearization method.
Here, to explore applications of Davidenkov model in seismic response analysis of soft soil sites, the incremental shear modulus expressions for Davidenkov model's nonlinear dynamic constitutive model in initial loading, unloading and reloading stages were derived, and the soil body's dynamic stress-strain relationship was extended to 3-D. Then, parameters of Davidenkov model were fitted using the particle swarm optimization(PSO) algorithm and the fitting program was compiled with MATLAB. The applicability of the method was verified through fitting test data of typical sand and clay. Parameters of a certain typical Shanghai soft soil site were fitted. Afterward, using the secondary development platform UMAT provided with ABAQUS, the subroutine for the nonlinear dynamic constitutive model of soft soil body based on Davidenkov model was compiled, and the correctness of the subroutine was verified through a complex loading path. Finally, taking a certain typical Shanghai soft soil site as an example, the calculation results based on the nonlinear dynamic constitutive model and those using the equivalent linearization method were contrastively analyzed. The results showed that parameters of Davidenkov model can be well fitted with the PSO algorithm; the subroutine of the nonlinear dynamic constitutive model proposed here can better describe nonlinear behaviors of soft soil sites; acceleration response values and relative displacement response ones of the typical Shanghai soft soil site based on the nonlinear dynamic constitutive model are smaller than those using the equivalent linearization method.
引文
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[5] 张如林,楼梦麟.基于达维坚科夫骨架曲线的软土非线性动力本构模型研究[J].岩土力学,2012,33(9):2588-2594.ZHANG Rulin,LOU Menglin.Study of nonlinear dynamic constitutive model of soft soils based on Davidenkov skeleton curve [J].Rock and Soil Mechanics,2012,33(9):2588-2594.
[6] 孙锐,李晓飞,陈龙伟,等.孔压增长下双曲线模型参数研究[J].振动与冲击,2018,37(7):1-7.SUN Rui,LI Xiaofei,CHEN Longwei,et al.Effects of increase in pore water pressure on dynamic parameters of hyperbolic model [J].Journal of Vibration and Shock,2018,37(7):1-7.
[7] 阮璠,齐文浩,薄景山,等.基于响嘡台阵的土层一维时域动力本构模型的检验[J].自然灾害学报,2015,24(5):207-215.RUAN Fan,QI Wenhao,BO Jingshan,et al.Verification of the one dimensional dynamic constitutive model of soil layers in time domain based on Xiangtang array [J].Journal of Natural Disasters,2015,24(5):207-215.
[8] 赖杰,郑颖人,李秀地.自重、渗流及地震耦合作用下人工岛动力稳定性分析[J].振动与冲击,2016,35(5):175-180.LAI Jie,ZHENG Yingren,LI Xiudi.Dynamic stability analysis on an artificial island triggered by self weight,seepage and earthquake [J].Journal of Vibration and Shock,2016,35(5):175-180.
[9] HARDIN B O,DRNEVICH V P.Shear modulus and damping in soils:design equations and curves [J].Journal of the Soil Mechanics and Foundations Division,1972,98(7):667-692.
[10] MARTIN P P,SEED H B.One dimensional dynamic ground response analysis [J].ASCE Journal of Geotechnical Engineering,1982,108(7):935-954.
[11] 庄海洋,陈国兴,梁艳仙,等.土体动非线性黏弹性模型及其ABAQUS软件的实现[J].岩土力学,2007,28(3):436-442.ZHUANG Haiyang,CHEN Guoxing,LIANG Yanxian,et al.A developed dynamic viscoelastic constitutive relations of soil and sand implemented by ABAQUS software [J].Rock and Soil Mechanics,2007,28(3):436-442.
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[14] EBERHART R C,KENNEDY J.A new optimizer using particle swarm theory [C]//Proceedings of the 6th Imitational Symposium on Micro Machine and Human Science.Nagoya,Japan,1995.
[15] LI B,YOUNG A A,COWAN B R.GPU accelerated non-rigid registration for the evaluation of cardiac function [C]//Medical Image Computing and Computer-Assisted Intervention.New York:MICCAI,2008.
[16] EBERHART R C,SHI Y,KENNEDY J.Swarm intelligence [M].San Mateo,CA:Morgan Kaufmann,2001.
[17] SEED H B,IDRISS I M.Soil moduli and damping factors for dynamic response analysis [R].Earthquake Engineering Research Center,University of California,Berkeley,Report No.EERC 70-10,1970.
[18] 费康,张建伟.ABAQUS在岩土工程中的应用[M].北京:中国水利水电出版社,2013.
[19] CUNDALL P A.A simple hysteretic damping formulation for dynamic continuum simulations [C]//Proceedings of the 4th International FLAC Symposium on Numerical Modeling in Geomechanics.Minneapolis:Itasca Consulting Group,2006.
[20] 王沿朝,陈清军.地震波反演与地下结构的动力响应分析[J].工程力学,2016,33(增刊1):227-233.WANG Yanchao,CHEN Qingjun.Seismic waves inversion and dynamic response analysis of underground structures [J].Engineering Mechanics,2016,33(Sup1):227-233.
[2] 齐文浩,薄景山.土层地震反应等效线性化方法综述[J].世界地震工程,2007,23(4):221-226.QI Wenhao,BO Jingshan.Summarization on equivalent linear method of seismic response for soil layers [J].World Earthquake Engineering,2007,23(4):221-226.
[3] WANG Z L,DAFALIAS Y F,SHEN C K.Bounding surface hypoplasticity model for sand [J].ASCE Journal of Engineering Mechanics,1990,116(5):983-1001.
[4] 陈国兴,谢君斐,韩炜,等.土体地震反应分析的简化有效应力法[J].地震工程与工程振动,1995,15(2):52-61.CHEN Guoxing,XIE Junfei,HAN Wei,et al.A simplified effective stress method of soil mass earthquake response analysis [J].Earthquake Engineering and Engineering Vibration,1995,15(2):52-61.
[5] 张如林,楼梦麟.基于达维坚科夫骨架曲线的软土非线性动力本构模型研究[J].岩土力学,2012,33(9):2588-2594.ZHANG Rulin,LOU Menglin.Study of nonlinear dynamic constitutive model of soft soils based on Davidenkov skeleton curve [J].Rock and Soil Mechanics,2012,33(9):2588-2594.
[6] 孙锐,李晓飞,陈龙伟,等.孔压增长下双曲线模型参数研究[J].振动与冲击,2018,37(7):1-7.SUN Rui,LI Xiaofei,CHEN Longwei,et al.Effects of increase in pore water pressure on dynamic parameters of hyperbolic model [J].Journal of Vibration and Shock,2018,37(7):1-7.
[7] 阮璠,齐文浩,薄景山,等.基于响嘡台阵的土层一维时域动力本构模型的检验[J].自然灾害学报,2015,24(5):207-215.RUAN Fan,QI Wenhao,BO Jingshan,et al.Verification of the one dimensional dynamic constitutive model of soil layers in time domain based on Xiangtang array [J].Journal of Natural Disasters,2015,24(5):207-215.
[8] 赖杰,郑颖人,李秀地.自重、渗流及地震耦合作用下人工岛动力稳定性分析[J].振动与冲击,2016,35(5):175-180.LAI Jie,ZHENG Yingren,LI Xiudi.Dynamic stability analysis on an artificial island triggered by self weight,seepage and earthquake [J].Journal of Vibration and Shock,2016,35(5):175-180.
[9] HARDIN B O,DRNEVICH V P.Shear modulus and damping in soils:design equations and curves [J].Journal of the Soil Mechanics and Foundations Division,1972,98(7):667-692.
[10] MARTIN P P,SEED H B.One dimensional dynamic ground response analysis [J].ASCE Journal of Geotechnical Engineering,1982,108(7):935-954.
[11] 庄海洋,陈国兴,梁艳仙,等.土体动非线性黏弹性模型及其ABAQUS软件的实现[J].岩土力学,2007,28(3):436-442.ZHUANG Haiyang,CHEN Guoxing,LIANG Yanxian,et al.A developed dynamic viscoelastic constitutive relations of soil and sand implemented by ABAQUS software [J].Rock and Soil Mechanics,2007,28(3):436-442.
[12] SHI Y,EBERHART R C.Experimental study of particle swarm optimization [C]//Proceedings of the IEEE Congress on Evolutionary Computation (CEC 1999).Piscataway,NJ,1999.
[13] KENNEDY J,EBERHART R C.Particle swarm optimization [C]//Proceedings of the 4th IEEE International Conference on Neural Networks.Piscataway:IEEE Service Center,1995.
[14] EBERHART R C,KENNEDY J.A new optimizer using particle swarm theory [C]//Proceedings of the 6th Imitational Symposium on Micro Machine and Human Science.Nagoya,Japan,1995.
[15] LI B,YOUNG A A,COWAN B R.GPU accelerated non-rigid registration for the evaluation of cardiac function [C]//Medical Image Computing and Computer-Assisted Intervention.New York:MICCAI,2008.
[16] EBERHART R C,SHI Y,KENNEDY J.Swarm intelligence [M].San Mateo,CA:Morgan Kaufmann,2001.
[17] SEED H B,IDRISS I M.Soil moduli and damping factors for dynamic response analysis [R].Earthquake Engineering Research Center,University of California,Berkeley,Report No.EERC 70-10,1970.
[18] 费康,张建伟.ABAQUS在岩土工程中的应用[M].北京:中国水利水电出版社,2013.
[19] CUNDALL P A.A simple hysteretic damping formulation for dynamic continuum simulations [C]//Proceedings of the 4th International FLAC Symposium on Numerical Modeling in Geomechanics.Minneapolis:Itasca Consulting Group,2006.
[20] 王沿朝,陈清军.地震波反演与地下结构的动力响应分析[J].工程力学,2016,33(增刊1):227-233.WANG Yanchao,CHEN Qingjun.Seismic waves inversion and dynamic response analysis of underground structures [J].Engineering Mechanics,2016,33(Sup1):227-233.
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