准塑性的黏弹性模型在黏土中的应用
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摘要
在内变量准热力学的框架内分析黏性理论和塑性理论之间的关系。从殷建华–Graham的一维EVP模型出发,假定参考等效时间线上的参考点为加载初始点,分析了黏土骤然施加有效应力后等时间线上的一些性质,获得了新假设A和假设B相互近似等价的条件,并指出原假设A的缺陷。当加载后的有效应力大于1.1倍初始有效应力且持续时间大于参考绝对等效时间时,绝对等效时间近似地等于持续时间,黏土的变形可分为弹塑性变形与分项蠕变变形之和,其中弹塑性变形只与有效应力有关,而与时间无关;分项蠕变变形只与持续时间有关,而与有效应力无关。利用内变量准热力学理论,揭示了一维EVP模型的Lagrange耗散率函数与纯塑性模型的Lagrange耗散率函数的内在联系,阐明一维EVP模型具有准塑性的黏弹性性质的原因。参照一维EVP模型的Lagrange耗散率函数所呈现出来的规律,把一维EVP模型推广到三维EVP模型,并与三轴不排水剪切蠕变试验数据相比较,验证了本文三维EVP模型的合理性。
On the basis of the framework of internal variable quasi-thermodynamics,the relationship between viscosity theory and plasticity theory is studied.Assuming that the reference point at the reference equivalent time line is an initial loading point and the effective stress is abruptly loaded on clay,some behaviors of the iso-time lines derived from Yin-Graham’s 1-D elastic visco-plastic model are analyzed.The scope that new Hypothesis A is approximately equivalent to Hypothesis B is obtained and the flaws of the original Hypothesis A are pointed out.When the loading effective stress is 1.1 times larger than the initial effective stress and the duration time is larger than the reference absolute equivalent time,the absolute equivalent time is approximately equal to the duration time.The strain of clay is the sum of plasto-elastic strain and fractional creep strain,in which the plasto-elastic strain depends on effective stress and is independent of time,while the fractional creep strain depends on time,but not on effective stress.By means of the theory of internal variable quasi-thermodynamics,the internal relation of Lagrange’s dissipative rate function between the 1-D EVP model and a pure plastic model is demonstrated and the reason why the 1-D EVP model has quasi-plastic visco-elastic characteristics is revealed.A 3-D EVP model is generalized from the 1-D EVP model according to the rule of Lagrange’s dissipative rate function occurring in the 1-D EVP model.Compared with experimental data obtained from consolidation-undrained triaxial shear creep test,the present 3-D EVP model is verified to be valid.
On the basis of the framework of internal variable quasi-thermodynamics,the relationship between viscosity theory and plasticity theory is studied.Assuming that the reference point at the reference equivalent time line is an initial loading point and the effective stress is abruptly loaded on clay,some behaviors of the iso-time lines derived from Yin-Graham’s 1-D elastic visco-plastic model are analyzed.The scope that new Hypothesis A is approximately equivalent to Hypothesis B is obtained and the flaws of the original Hypothesis A are pointed out.When the loading effective stress is 1.1 times larger than the initial effective stress and the duration time is larger than the reference absolute equivalent time,the absolute equivalent time is approximately equal to the duration time.The strain of clay is the sum of plasto-elastic strain and fractional creep strain,in which the plasto-elastic strain depends on effective stress and is independent of time,while the fractional creep strain depends on time,but not on effective stress.By means of the theory of internal variable quasi-thermodynamics,the internal relation of Lagrange’s dissipative rate function between the 1-D EVP model and a pure plastic model is demonstrated and the reason why the 1-D EVP model has quasi-plastic visco-elastic characteristics is revealed.A 3-D EVP model is generalized from the 1-D EVP model according to the rule of Lagrange’s dissipative rate function occurring in the 1-D EVP model.Compared with experimental data obtained from consolidation-undrained triaxial shear creep test,the present 3-D EVP model is verified to be valid.
引文
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[3]殷建华,JACK I C.土体与时间相关的一维应力–应变形状、弹黏塑性模型和固结分析[J].岩土力学,1994,15(3):65–80;15(4):65–75.(YIN Jian-hua,JACK I C.One-dimensional time dependent stress-stress behaviour of soil,elastic visco-plastic modeling and consolidation analysis[J].Rock and Soil mechanics,1994,15(3):65–80;15(4):65–75.(in Chinese)
[4]YIN Jian-hua.Nonlinear elastic visco-plastic modeling and a simplified method for calculating settlement of soil with creep[C]//Proc Int Workshop on Constitutive Modeling-Development,Implementation,Evaluation&Application.Hong Kong,2007:718–725.
[5]殷宗泽,张海波,朱俊高,等.软土的次固结[J].岩土工程学报,2003,25(5):521–526.(YIN Zong-ze,ZHANG Hai-bo,ZHU Jun-gao,et al.Secondary consolidation of soft soils[J].Chinese Journal of Geotechnical Engineering,2003,25(5):521–526.(in Chinese))
[6]ADACHI T,OKA F.Constitutive equations for normally consolidated clay based on elasto-viscoplasticity[J].Soils and Foundation,1982,22(4):57–70.
[7]ZHOU C,YIN J H,ZHU J G,CHENG C M.Elastic anisotropic viscoplastic modeling of the strain-rate-dependent stress-train behavior of K0-consolidated natural marine clays in triaxial shear tests[J].Internation Journal of Geomechanics,2005,5(3):218–232.
[8]王立忠,但汉波.K0固结软黏土的弹黏塑性本构模型[J].岩土工程学报,2007,29(9):1344–1354.(WANG Li-zhong,DAN Han-bo.Elastic viscoplastic constitutive model for K0-consolidation soft clays[J].Chinese Journal of Geotechnical Engineering,2007,29(9):1344–1354.
[9]COLLINS I F,HOULSBY G T.Application of thermomechanical principles to the modeling of geotechnical materials[J].Proceedings of the Royal Society of London A,1997,45(3):1975–2001.
[10]COLLINS I F.The concept of stored plastic work or frozen elastic energy in soil mechanics[J].Geotechnique,2005,55(5):373–382.
[11]HOULSBY G T.PUZRIN A M.Rate-dependent plasticity models derived from potential functions[J].Journal of Rheology,2002,46(1):113–126.
[12]ERLICHER S,POINT N.Endochronic theory,non-linear kinematic hardening rule and generalized plasticity:a new interpretation based on generalized normality assumption[J].Journal of Solids and Structure,2006(43):4175–4200.
[13]POINT N,ERLICHER S.Application of the orthogonality principle to the endochronic and Mroz models of plasticity[J].Materials Science and Engineering,2007.in press.
[14]胡亚元.从耗散率函数看黏性与塑性的内在联系[J].浙江大学学报(工学报),待刊.(HU Ya-yuan.Interrelationship between viscosity and plasticity based on dissipative rate function[J].Journal of Zhejiang University(Engineering Science),in Press.(in Chinese))
[15]赵彭年.松散介质力学[M].北京:地震出版社,1995:32–35.(ZHAO Peng-nian.Mechanics of media[M].Beijing:China Seismic Press,1995:32–35.(in Chinese))
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