基于统一强度理论的土体应变局部化预测研究
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摘要
土体剪切带的形成机理与应变局部化理论是当今国际力学界和岩土工程界广泛研究的课题，应变局部化分叉理论预测为揭示岩土材料的破坏机理提供了有力依据。统一强度理论具有统一的力学模型、统一的理论和统一的数学表达式，可以有规律地变化以适用于各类工程材料，形成了一系列有序的破坏准则，可广泛适用于各种工程领域。但统一强度理论在剪切带形成机理以及非共轴本构模型和应变局部化分叉判别等方面还缺乏深入细致的系统应用研究，而且以往应变局部化没有考虑三维应力空间下混合硬化模型的影响。本文将混合硬化模型和统一强度理论用于应变局部化应力应变关系，应变局部化分叉点位置和剪切带倾角等预测研究。主要研究内容与结论如下：
（1）建立了以压应力为正的统一强度理论公式，进而推导了新的加载函数和相应的塑性势函数及本构方程，并结合修正Euler积分方法编制了率型本构方程的积分程序对粘性土平面应变试验和密砂真三轴试验进行了模拟和验证，得出：当参数b取合适值时，预测值比已有文献结果更接近试验结果。对于所选的粘性土材料和密砂材料，可分别选用参数b=1和b=0.9所对应的强度理论进行应力应变关系预测。
（2）在三维非共轴应力空间内，考虑第三应力不变量对塑性变形非共轴性的影响，基于非共轴混合硬化法则，建立了更加符合土体实际受力性状的非共轴本构新模型、变形局部化分叉点判别准则和剪切带倾角公式，并对所得结果进行退化必要性验证；同时，结合修正Euler积分的基本步骤进行模拟，与已有成果和试验数据进行比较，验证了所得分叉点判别准则的初步合理性。
（3）建立了基于统一强度理论和混合硬化法则的新的加载函数、塑性势函数、统一非共轴本构模型、应变局部化分叉点判别准则和剪切带倾角公式，并对粘性土平面应变试验和密砂真三轴试验进行了模拟和试验验证，得出：非共轴项的引入并不改变土体应力应变关系特性；对于所选的粘性土材料和密砂材料，可分别选用参数b=1和b=0.9所对应的强度理论来分析预测应变局部化分叉点和剪切带倾角。
The formation of shear band and the theory of progressive failure of soils are key topicsfocused greatly both in solid mechanics and geomechanics around the world. Softeningproperties of soil is the structurally reflection of localized deformation. Strain localizationbifurcation theory predicts to reveal the failure mechanism of rock and soil materials providedstrong basis. The unified strength theory which has be widely used in various engineeringfields has a unified mechanical model, a unified theory and a unified mathematical expression,that can be applicable to more than one kind of material and establishing the relationshipamong different theories. But unified strength theory that has be used in the shear bandformation mechanism, non-coaxiality constitutive model and strain localization bifurcationdiscriminant is still lack of intensive study, and have not considered the effects of mixedhardening model in three-dimensional stress space when in the study of strain localization inthe past. In this paper, the unified strength theory and the mixed hardening model are used tostudy the stress strain relationship and bifurcation point position of strain localization, and theangle of shear band. The main contents in this dissertation can be summarized as follows:
(1) We deduce the unified strength theory when compressive stress is positive, the yieldfunction, the plastic potential function and the constitutive equation. Based on the revisedEuler integral, the constitutive equation of rate type integral program to simulate and verifydense sand true triaxial test and the clay plane strain tests was prepared, we obtain that when bis right value, the predicted results is closer to the experimental results than the existingliterature. For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the relations of stress and strain.
(2) In three-dimensional stress space, considering the effect of the third stress invarianton the non-coaxality of plastic deformation, based on the non-coaxial mixed hardening modeland non-coaxial elastoplastic constitutive model, the criterion of deformation localizationbifurcation in the true triaxial state and the shear band angle were deduced, then verify theresults by degradation. At the same time, combining with the basic steps of the revised Euler integral to simulate and comparing with existing results and test data, we verified thepreliminary rationality of the obtained bifurcation point criterion.
(3) Based on the unified strength theory and the mixed hardening rule, the new loadingfunction, the plastic potential function, non-coaxiality constitutive model, strain localizationbifurcation point criterion and the angle of shear band were established, then the dense sandtrue triaxial test and the clay plane strain tests were simulated and verified. We concluded thatthe introduction of non-coaxiality does not change the stress-strain relationship of soilproperties, For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the bifurcation point and the angle of shear band.
（1）建立了以压应力为正的统一强度理论公式，进而推导了新的加载函数和相应的塑性势函数及本构方程，并结合修正Euler积分方法编制了率型本构方程的积分程序对粘性土平面应变试验和密砂真三轴试验进行了模拟和验证，得出：当参数b取合适值时，预测值比已有文献结果更接近试验结果。对于所选的粘性土材料和密砂材料，可分别选用参数b=1和b=0.9所对应的强度理论进行应力应变关系预测。
（2）在三维非共轴应力空间内，考虑第三应力不变量对塑性变形非共轴性的影响，基于非共轴混合硬化法则，建立了更加符合土体实际受力性状的非共轴本构新模型、变形局部化分叉点判别准则和剪切带倾角公式，并对所得结果进行退化必要性验证；同时，结合修正Euler积分的基本步骤进行模拟，与已有成果和试验数据进行比较，验证了所得分叉点判别准则的初步合理性。
（3）建立了基于统一强度理论和混合硬化法则的新的加载函数、塑性势函数、统一非共轴本构模型、应变局部化分叉点判别准则和剪切带倾角公式，并对粘性土平面应变试验和密砂真三轴试验进行了模拟和试验验证，得出：非共轴项的引入并不改变土体应力应变关系特性；对于所选的粘性土材料和密砂材料，可分别选用参数b=1和b=0.9所对应的强度理论来分析预测应变局部化分叉点和剪切带倾角。
The formation of shear band and the theory of progressive failure of soils are key topicsfocused greatly both in solid mechanics and geomechanics around the world. Softeningproperties of soil is the structurally reflection of localized deformation. Strain localizationbifurcation theory predicts to reveal the failure mechanism of rock and soil materials providedstrong basis. The unified strength theory which has be widely used in various engineeringfields has a unified mechanical model, a unified theory and a unified mathematical expression,that can be applicable to more than one kind of material and establishing the relationshipamong different theories. But unified strength theory that has be used in the shear bandformation mechanism, non-coaxiality constitutive model and strain localization bifurcationdiscriminant is still lack of intensive study, and have not considered the effects of mixedhardening model in three-dimensional stress space when in the study of strain localization inthe past. In this paper, the unified strength theory and the mixed hardening model are used tostudy the stress strain relationship and bifurcation point position of strain localization, and theangle of shear band. The main contents in this dissertation can be summarized as follows:
(1) We deduce the unified strength theory when compressive stress is positive, the yieldfunction, the plastic potential function and the constitutive equation. Based on the revisedEuler integral, the constitutive equation of rate type integral program to simulate and verifydense sand true triaxial test and the clay plane strain tests was prepared, we obtain that when bis right value, the predicted results is closer to the experimental results than the existingliterature. For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the relations of stress and strain.
(2) In three-dimensional stress space, considering the effect of the third stress invarianton the non-coaxality of plastic deformation, based on the non-coaxial mixed hardening modeland non-coaxial elastoplastic constitutive model, the criterion of deformation localizationbifurcation in the true triaxial state and the shear band angle were deduced, then verify theresults by degradation. At the same time, combining with the basic steps of the revised Euler integral to simulate and comparing with existing results and test data, we verified thepreliminary rationality of the obtained bifurcation point criterion.
(3) Based on the unified strength theory and the mixed hardening rule, the new loadingfunction, the plastic potential function, non-coaxiality constitutive model, strain localizationbifurcation point criterion and the angle of shear band were established, then the dense sandtrue triaxial test and the clay plane strain tests were simulated and verified. We concluded thatthe introduction of non-coaxiality does not change the stress-strain relationship of soilproperties, For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the bifurcation point and the angle of shear band.
引文
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