基于能量耗散的土的本构关系研究
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摘要
传统岩土本构模型包括两类,一类是拟合试验数据得到的经验模型,这种模型以提高拟合精度为目标,缺乏对岩土材料应力应变本质特性的把握。另一类是理论模型,以Drucker公设和塑性位势理论为基础,由经典塑性力学本构的几个要素(屈服条件、流动法则、硬化规律)组合而成。但这些要素一般都是单独确定,有时会相互矛盾,导致传统岩土理论模型在某些应力路径上,有可能违反热力学基本定律。针对这一问题,本文从热力学基本定律出发,讨论了基于能量耗散的土体本构关系模型及其应用。
论文介绍了基于热力学原理建立本构模型的基本理论和一般过程;研究了能量耗散函数的合理表达形式,并以此为基础讨论了耗散应力空间的屈服函数;根据Ziegler正交假定,确定耗散应力空间的流动法则;根据自由能函数确定迁移应力和弹性关系;再通过迁移应力确定真实应力空间的屈服函数和流动法则;最后结合硬化规律,建立完整的本构关系。
以Collins提出的各向同性模型(isotropic model)耗散函数为出发点,建立了各向同性本构模型。根据屈服面的几何形状,分析了模型参数的取值范围。通过拟合某筑坝土料三轴试验曲线,提供了确定模型参数的方法。将计算的应力应变曲线及体变曲线与试验结果比较,验证了各向同性模型的有效性。对比计算结果说明各向同性模型优于修正剑桥模型。
在各向同性模型基础上,修改耗散函数,增加表征屈服面倾斜程度的变量,建立各向异性模型(anisotropic model)。引入旋转硬化规律,描述屈服面随着加载过程在应力空间旋转,模拟土的各向异性。类比各向同性模型,讨论了不同参数对屈服面的影响,参数之间的关系和参数的取值范围。利用试验数据确定模型参数,计算三轴曲线。与各向同性模型的计算结果对比表明,各向异性模型优于各向同性模型。
在三轴试验中,排水条件下松砂体缩,密砂剪胀;不排水条件下松砂和密砂的有效应力路径不相同。考虑剪胀对材料状态的依赖,尝试了用两种统一模型描述松砂和密砂的变形特性。采用Li建议的e-p′平面的临界状态线,定义当前孔隙比与当前应力对应的临界孔隙比之差作为状态参量。
一种方法是修正各向同性模型的耗散函数,将描述砂土松密的状态参量引入到屈服面函数中,并结合相应的硬化规律,建立基于能量耗散的修正各向同性统一本构模型,体现材料状态对应力应变关系的影响。给定模型参数,计算不同初始状态和加载条件下的三轴试验,验证了这种方法能够模拟松砂和密砂的不同应力路径。
另一种方法是在各向同性、各向异性模型的基础上,引入初始状态参量,修正旋转硬化规律,建立基于能量耗散的联合统一本构模型。分析控制方程,可以定性说明并用
Traditional constitutive models of soils may be divided into two groups. One is experiential models obtained by fitting experimental data, which aim at improving fitting precision, and are short of holding the essential characters of strain-stress relations for geomatenals. The other is theoretic models, which comprise several elementary factors (yield condition, flow rule and hardening law) of classical plastic, and base on Drucker Postulate and the theory of plastic potential. Generally, these factors are determined independently and contradict each other sometimes, which results there is probability of violating thermomechanics laws under some stress paths. To avoid these differences, soils constitutive models based on energy dissipation and its applications are discussed in this paper, which starts from the thermomechanics laws directly.The elementary theories and general procedure of constituting models based on thermomechanics laws are introduced. A proper energy dissipation function is studied and the yield function in dissipation stress space is deduced. The flow rule in dissipation space is determined in terms of Ziegler orthogonality principle. Shift stress and elastic rule come from free energy function. Then the yield function and the flow rule in true stress space are deduced by the shift stress. Combined the hardening law, a complete constitutive model is built.Referring the isotropic dissipation function presented by Collins, an isotropic constitutive model is established. The spans of model parameter are analyzed in terms of reasonable shape of yield locus. The parameters can be determined by fitting the triaxial test data, and the genetic algorithm is adopted in the fitting process. According to the obtained parameters, a group of drained triaxial tests are computed, and then the relation curves of shear stress invariant, shear strain and volumetric strain are plotted and compared with the experimental results to verify the validity of the model. The results of the isotropic model are better than that of modified Cam-clay.The anisotropic model is set up by extending the isotropic model. Dissipation function of the isotropic model is modified and added a variable to denote the inclination of yield locus. The rotation of yield locus in true stress space is described via the rotational hardening law to embody the anisotropy. Similar to the isotropic model, the effects of variable model parameters on yield locus, the relations among parameters, and the spans of parameter are discussed. Employing the genetic algorithm, the model parameters are identified by fitting the data of triaxial drained test. Then the parameters obtained were used to calculate the drained
test curves for other consolidated pressures conditions, and these curves were compared with observed data in corresponding cases. It shows that the results are satisfying and the anisotropic model is better than the isotropic model.In drained triaxial test, loose sands contract while dense sands dilate. In undrained triaxial test, the effective stress paths of loose sands and dense sands are different The different deformation curves of loose sands and dense sands can be simulated in unified ways by introducing the dependence of dilatancy on material state, and two feasible methods are presented. The critical state line in e-p' plane suggested by Li is used to define state parameter as the difference of current void ratio and corresponding critical void ratio.The first method is modifying the dissipation function of isotropic model, and the state parameter distinguishing loose sands and dense sands is introduced to yield equation to set up the modified isotropic unified constitutive model, which covers the effect of material state on stress-strain relations. The simulative capability is shown by computing different features under various initial densities and confining pressures in triaxial undrained shear test, using the modified isotropic unified constitutive model with a unified set of model parameters and the hardening law suggested.The second method is introducing the initial state parameter into the anisotropic rotational hardening law to build the combined unified constitutive model. Analyzed the constitutive relations and stress paths, it is proved qualitatively and validated by samples that the deformation characteristics of loose sands are described properly by the isotropic model, while the anisotropic model is suit for the deformation curves of dense sands. They are incorporated by the rotational hardening law involving initial state parameter to simulate the two types of deformations for the sands. The parameters can be determined by fitting a part of triaxial test data of Toyoura sand, and then the residual triaxial curves are computed. The results tally with the experimental data. The developments of shear friction angle and dilation with deformations accord with the common trend of loose sands and dense sands, and the relation between peak friction angle and initial state parameter consist with the test data reported by Been and Jefferies.Based on the isotropic model, an approach aiming at unloading and reloading response is discussed. The general curves of unloading and reloading can be computed by modified hardening laws in unloading and reloading stage.
论文介绍了基于热力学原理建立本构模型的基本理论和一般过程;研究了能量耗散函数的合理表达形式,并以此为基础讨论了耗散应力空间的屈服函数;根据Ziegler正交假定,确定耗散应力空间的流动法则;根据自由能函数确定迁移应力和弹性关系;再通过迁移应力确定真实应力空间的屈服函数和流动法则;最后结合硬化规律,建立完整的本构关系。
以Collins提出的各向同性模型(isotropic model)耗散函数为出发点,建立了各向同性本构模型。根据屈服面的几何形状,分析了模型参数的取值范围。通过拟合某筑坝土料三轴试验曲线,提供了确定模型参数的方法。将计算的应力应变曲线及体变曲线与试验结果比较,验证了各向同性模型的有效性。对比计算结果说明各向同性模型优于修正剑桥模型。
在各向同性模型基础上,修改耗散函数,增加表征屈服面倾斜程度的变量,建立各向异性模型(anisotropic model)。引入旋转硬化规律,描述屈服面随着加载过程在应力空间旋转,模拟土的各向异性。类比各向同性模型,讨论了不同参数对屈服面的影响,参数之间的关系和参数的取值范围。利用试验数据确定模型参数,计算三轴曲线。与各向同性模型的计算结果对比表明,各向异性模型优于各向同性模型。
在三轴试验中,排水条件下松砂体缩,密砂剪胀;不排水条件下松砂和密砂的有效应力路径不相同。考虑剪胀对材料状态的依赖,尝试了用两种统一模型描述松砂和密砂的变形特性。采用Li建议的e-p′平面的临界状态线,定义当前孔隙比与当前应力对应的临界孔隙比之差作为状态参量。
一种方法是修正各向同性模型的耗散函数,将描述砂土松密的状态参量引入到屈服面函数中,并结合相应的硬化规律,建立基于能量耗散的修正各向同性统一本构模型,体现材料状态对应力应变关系的影响。给定模型参数,计算不同初始状态和加载条件下的三轴试验,验证了这种方法能够模拟松砂和密砂的不同应力路径。
另一种方法是在各向同性、各向异性模型的基础上,引入初始状态参量,修正旋转硬化规律,建立基于能量耗散的联合统一本构模型。分析控制方程,可以定性说明并用
Traditional constitutive models of soils may be divided into two groups. One is experiential models obtained by fitting experimental data, which aim at improving fitting precision, and are short of holding the essential characters of strain-stress relations for geomatenals. The other is theoretic models, which comprise several elementary factors (yield condition, flow rule and hardening law) of classical plastic, and base on Drucker Postulate and the theory of plastic potential. Generally, these factors are determined independently and contradict each other sometimes, which results there is probability of violating thermomechanics laws under some stress paths. To avoid these differences, soils constitutive models based on energy dissipation and its applications are discussed in this paper, which starts from the thermomechanics laws directly.The elementary theories and general procedure of constituting models based on thermomechanics laws are introduced. A proper energy dissipation function is studied and the yield function in dissipation stress space is deduced. The flow rule in dissipation space is determined in terms of Ziegler orthogonality principle. Shift stress and elastic rule come from free energy function. Then the yield function and the flow rule in true stress space are deduced by the shift stress. Combined the hardening law, a complete constitutive model is built.Referring the isotropic dissipation function presented by Collins, an isotropic constitutive model is established. The spans of model parameter are analyzed in terms of reasonable shape of yield locus. The parameters can be determined by fitting the triaxial test data, and the genetic algorithm is adopted in the fitting process. According to the obtained parameters, a group of drained triaxial tests are computed, and then the relation curves of shear stress invariant, shear strain and volumetric strain are plotted and compared with the experimental results to verify the validity of the model. The results of the isotropic model are better than that of modified Cam-clay.The anisotropic model is set up by extending the isotropic model. Dissipation function of the isotropic model is modified and added a variable to denote the inclination of yield locus. The rotation of yield locus in true stress space is described via the rotational hardening law to embody the anisotropy. Similar to the isotropic model, the effects of variable model parameters on yield locus, the relations among parameters, and the spans of parameter are discussed. Employing the genetic algorithm, the model parameters are identified by fitting the data of triaxial drained test. Then the parameters obtained were used to calculate the drained
test curves for other consolidated pressures conditions, and these curves were compared with observed data in corresponding cases. It shows that the results are satisfying and the anisotropic model is better than the isotropic model.In drained triaxial test, loose sands contract while dense sands dilate. In undrained triaxial test, the effective stress paths of loose sands and dense sands are different The different deformation curves of loose sands and dense sands can be simulated in unified ways by introducing the dependence of dilatancy on material state, and two feasible methods are presented. The critical state line in e-p' plane suggested by Li is used to define state parameter as the difference of current void ratio and corresponding critical void ratio.The first method is modifying the dissipation function of isotropic model, and the state parameter distinguishing loose sands and dense sands is introduced to yield equation to set up the modified isotropic unified constitutive model, which covers the effect of material state on stress-strain relations. The simulative capability is shown by computing different features under various initial densities and confining pressures in triaxial undrained shear test, using the modified isotropic unified constitutive model with a unified set of model parameters and the hardening law suggested.The second method is introducing the initial state parameter into the anisotropic rotational hardening law to build the combined unified constitutive model. Analyzed the constitutive relations and stress paths, it is proved qualitatively and validated by samples that the deformation characteristics of loose sands are described properly by the isotropic model, while the anisotropic model is suit for the deformation curves of dense sands. They are incorporated by the rotational hardening law involving initial state parameter to simulate the two types of deformations for the sands. The parameters can be determined by fitting a part of triaxial test data of Toyoura sand, and then the residual triaxial curves are computed. The results tally with the experimental data. The developments of shear friction angle and dilation with deformations accord with the common trend of loose sands and dense sands, and the relation between peak friction angle and initial state parameter consist with the test data reported by Been and Jefferies.Based on the isotropic model, an approach aiming at unloading and reloading response is discussed. The general curves of unloading and reloading can be computed by modified hardening laws in unloading and reloading stage.
引文
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