软土动应力-应变曲线复合指数-正弦模型
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摘要
软土动应力-应变曲线(DSSC)模型是土动力学研究中的一个重要课题。结合软土DSSC的试验规律,分析了其数学模型应具有的基本性质。以最终动强度和初始切线模量为基本参数,对传统双曲线模型和指数模型进行了数学分析。引入动强度因子的概念,揭示了两传统DSSC模型的缺陷。提出了一个软土DSSC复合指数-正弦模型,该模型是一个单调递增、外凸且有极限值的函数。数学分析表明,新模型克服了传统模型的不足,两传统模型均是新模型对应的特例。最后,给出了模型参数的确定方法,通过实测数据拟合验证了新模型的正确性。
Mathematical modeling of dynamic stress-strain curve(DSSC)is important to the study of dynamic behavior of soft soil.Based on an analysis of measured data,the required primary behaviors of DSSC model are analyzed.Ultimate dynamic strength and initial tangent modulus are used to analytically examine the conventional DSSC models,hyperbolic model and exponential model,and a dynamical stress index is proposed and adopted to show the shortcomings of these two models.A composite exponential-sine model of three parameters,or a monotonically increasing and convex function with an upper bound,is developed,and an approach for determinination of model parameters is presented.Mathematical analysis shows that this model can overcome the shortcomings of the two conventional models that are two special cases of the new model,and the modeling results agree with the measured data.
Mathematical modeling of dynamic stress-strain curve(DSSC)is important to the study of dynamic behavior of soft soil.Based on an analysis of measured data,the required primary behaviors of DSSC model are analyzed.Ultimate dynamic strength and initial tangent modulus are used to analytically examine the conventional DSSC models,hyperbolic model and exponential model,and a dynamical stress index is proposed and adopted to show the shortcomings of these two models.A composite exponential-sine model of three parameters,or a monotonically increasing and convex function with an upper bound,is developed,and an approach for determinination of model parameters is presented.Mathematical analysis shows that this model can overcome the shortcomings of the two conventional models that are two special cases of the new model,and the modeling results agree with the measured data.
引文
[1]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)
[2]高玉峰,黎冰.黏土与EPS颗粒混合轻质土的动力变形特性试验研究[J].岩土工程学报,2007,29(7):1042～1047.GAO Yufeng,LI Bing.Experimental study on dynamic deformation characteristics of lightweight clay-EPS beads soil[J].ChineseJournal of Geotechnical Engineering,2007,29(7):1042～1047.(in Chinese)
[3]王军,蔡袁强,潘林有.双向激振下饱和软黏土应变软化现象试验研究[J].岩土工程学报,2009,31(2):178～185.WANG Jun,CAI Yuanqiang,PAN Linyou.Degradation of stiffness of soft clay under bidirectional cyclic loading[J].Chinese Journalof Geotechnical Engineering,2009,31(2):178～185.(in Chinese)
[4]迟世春,郭晓霞,杨峻,等.土的动力Hardin-Drnevich模型小应变特性[J].岩土工程学报,2008,30(2):243～249.CHI Shichun,GUO Xiaoxia,YANG Jun,et al.Small strain characteristics and threshold strain of dynamic Hardin～Drnevich modelfor soils[J].Chinese Journal of Geotechnical Engineering,2008,30(2):243～249.(in Chinese)
[5]王伟,卢廷浩.滨海软土动孔压发展模型核心函数研究[J].自然灾害学报,2009,18(5):192～196.WANG Wei,LU Tinghao.Study on core function for dynamic pore water pressure developing process of seashore soft soil[J].Journalof Nature Disasters,2009,18(5):192～196.(in Chinese)
[6]梅国雄,宰金珉,殷宗泽,等.沉降时间曲线呈“S”型的证明[J].岩土力学,2004,25(1):20～22.MEI Guoxiong,ZAI Jinmin,YIN Zongze,et al.Proof of s～t curve appearing“S”shape based on one dimensional consolidation theory[J].Rock and soil mechanics,2004,25(1):20～22.(in Chinese)
[7]Duncan J M,Chang C Y.Nonlinear analysis of stress and strain in soils[J].Journal of the Soil Mechanics and Foundations Division,1970,96(5):1629～1653.
[8]Lee K-H,Ju Y T,Shin D S,et al.Development of a Modified Duncan-Chang model for soils[C]//Proceedings of the10thInternational Symposium on Numerical Models in Geomechanics NUMOG 10.2007:93～98.
[9]魏海斌,刘寒冰,高一平,等.循环荷载下粉质中液限黏土和粉煤灰土的动剪强度研究[J].岩土力学,2007,28(9):1927～1930.WEI Haibin,LIU Hanbing,GAO Yiping,et al.Study on dynamic shear strength of middle-liquidity limit silty clay and fly ash soilsunder cyclic loading[J].Rock and soil mechanics,2007,28(9):1927～1930.(in Chinese)
[10]黎冰,高玉峰,丰土根.振动频率对LCES动力特性的影响分析及其机理初探[J].岩土力学,2008,29(10):2731～2735.LI Bing,GAO Yufeng,Feng Tugen.Cyclic loading frequency efect and mechanism of lightweight clay-EPS beads soil[J].Rock andsoil mechanics,2008,29(10):2731～2735.(in Chinese)
[11]廖红建,李涛,马宗源,等黄土骨干曲线模型比较分析[J].岩土力学,2009,30(2):17～22.LIAO Hongjian,LI Tao,MA Zongyuan,et al.Comparative analysis of backbone curve models for loess soils[J].Rock and SoilMechanics,2009,30(2):17～22.(in Chinese)
[12]WANG Wei,LING Hua,XU Shunde,et al.Composite tangent-exponent model for skeleton stress-strain curve of soft soil underdynamic loading[J].Advanced Materials Research,2010,(108-111):1092～1096.
[13]殷德顺,王保田.负乘幂本构模型的切线模量[J].岩土力学,2009,30(7):2168～2173.YIN Deshun,WANG Baotian.Tangent modulus of negative-power constitutive model[J].Rock and Soil Mechanics,2009,30(7):2168～2173.(in Chinese)
[14]齐文浩,薄景山.一种新的土体动力本构模型[J].地震工程与工程振动,2009,29(1):169～174.QI Wenhao,BO Jingshan.A new soil dynamic constitutive model[J].Journal of Earthquake and Engineering Vibration,2009,29(1):169～174.(in Chinese)
[15]王伟,宋新江,凌华,等.滨海相软土应力–应变曲线复合指数–双曲线模型[J].岩土工程学报,2010,32(9):1455～1459.WANG Wei,SONG Xin-iang,LING Hua,et al.Composite exponential-hyperbolic model for stress-strain curve of seashore soft soil[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1455～1459.(in Chinese)
[2]高玉峰,黎冰.黏土与EPS颗粒混合轻质土的动力变形特性试验研究[J].岩土工程学报,2007,29(7):1042～1047.GAO Yufeng,LI Bing.Experimental study on dynamic deformation characteristics of lightweight clay-EPS beads soil[J].ChineseJournal of Geotechnical Engineering,2007,29(7):1042～1047.(in Chinese)
[3]王军,蔡袁强,潘林有.双向激振下饱和软黏土应变软化现象试验研究[J].岩土工程学报,2009,31(2):178～185.WANG Jun,CAI Yuanqiang,PAN Linyou.Degradation of stiffness of soft clay under bidirectional cyclic loading[J].Chinese Journalof Geotechnical Engineering,2009,31(2):178～185.(in Chinese)
[4]迟世春,郭晓霞,杨峻,等.土的动力Hardin-Drnevich模型小应变特性[J].岩土工程学报,2008,30(2):243～249.CHI Shichun,GUO Xiaoxia,YANG Jun,et al.Small strain characteristics and threshold strain of dynamic Hardin～Drnevich modelfor soils[J].Chinese Journal of Geotechnical Engineering,2008,30(2):243～249.(in Chinese)
[5]王伟,卢廷浩.滨海软土动孔压发展模型核心函数研究[J].自然灾害学报,2009,18(5):192～196.WANG Wei,LU Tinghao.Study on core function for dynamic pore water pressure developing process of seashore soft soil[J].Journalof Nature Disasters,2009,18(5):192～196.(in Chinese)
[6]梅国雄,宰金珉,殷宗泽,等.沉降时间曲线呈“S”型的证明[J].岩土力学,2004,25(1):20～22.MEI Guoxiong,ZAI Jinmin,YIN Zongze,et al.Proof of s～t curve appearing“S”shape based on one dimensional consolidation theory[J].Rock and soil mechanics,2004,25(1):20～22.(in Chinese)
[7]Duncan J M,Chang C Y.Nonlinear analysis of stress and strain in soils[J].Journal of the Soil Mechanics and Foundations Division,1970,96(5):1629～1653.
[8]Lee K-H,Ju Y T,Shin D S,et al.Development of a Modified Duncan-Chang model for soils[C]//Proceedings of the10thInternational Symposium on Numerical Models in Geomechanics NUMOG 10.2007:93～98.
[9]魏海斌,刘寒冰,高一平,等.循环荷载下粉质中液限黏土和粉煤灰土的动剪强度研究[J].岩土力学,2007,28(9):1927～1930.WEI Haibin,LIU Hanbing,GAO Yiping,et al.Study on dynamic shear strength of middle-liquidity limit silty clay and fly ash soilsunder cyclic loading[J].Rock and soil mechanics,2007,28(9):1927～1930.(in Chinese)
[10]黎冰,高玉峰,丰土根.振动频率对LCES动力特性的影响分析及其机理初探[J].岩土力学,2008,29(10):2731～2735.LI Bing,GAO Yufeng,Feng Tugen.Cyclic loading frequency efect and mechanism of lightweight clay-EPS beads soil[J].Rock andsoil mechanics,2008,29(10):2731～2735.(in Chinese)
[11]廖红建,李涛,马宗源,等黄土骨干曲线模型比较分析[J].岩土力学,2009,30(2):17～22.LIAO Hongjian,LI Tao,MA Zongyuan,et al.Comparative analysis of backbone curve models for loess soils[J].Rock and SoilMechanics,2009,30(2):17～22.(in Chinese)
[12]WANG Wei,LING Hua,XU Shunde,et al.Composite tangent-exponent model for skeleton stress-strain curve of soft soil underdynamic loading[J].Advanced Materials Research,2010,(108-111):1092～1096.
[13]殷德顺,王保田.负乘幂本构模型的切线模量[J].岩土力学,2009,30(7):2168～2173.YIN Deshun,WANG Baotian.Tangent modulus of negative-power constitutive model[J].Rock and Soil Mechanics,2009,30(7):2168～2173.(in Chinese)
[14]齐文浩,薄景山.一种新的土体动力本构模型[J].地震工程与工程振动,2009,29(1):169～174.QI Wenhao,BO Jingshan.A new soil dynamic constitutive model[J].Journal of Earthquake and Engineering Vibration,2009,29(1):169～174.(in Chinese)
[15]王伟,宋新江,凌华,等.滨海相软土应力–应变曲线复合指数–双曲线模型[J].岩土工程学报,2010,32(9):1455～1459.WANG Wei,SONG Xin-iang,LING Hua,et al.Composite exponential-hyperbolic model for stress-strain curve of seashore soft soil[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1455～1459.(in Chinese)
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