基于广义位势理论的土的本构模型的研究
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摘要
本构理论是岩土工程中的关键部分,至今仍存在一些问题：基于虎克定律的弹性及非线性弹性模型不能反映土的剪胀这一重要特性；非关联模型不符合Drucker塑性公设；塑性应变增量方向不具有唯一性；传统弹塑性模型本构矩阵非正定性等,因而传统理论不足以表述岩土的本构特性。杨光华根据岩土的变形特性提出了广义弹塑性本构理论的思想,传统的弹性位势理论和塑性位势理论都可归结为数学上的势函数问题,因而可以用广义位势理论来表达和统一,这给岩土材料的本构关系研究指出了更开阔的数学背景。从广义位势理论出发来建立土的本构模型突破了传统理论中以塑性公设为前提的限制,可以无需推求塑性势函数和屈服函数,且其所能表述的本构关系比通常的塑性位势理论更为广泛,因而具有更广阔的前景。
本文主要围绕广义位势理论进行进一步深入的研究。剖析了各模型族本构矩阵的特性,通过算例展示了广义位势理论多重势面模型简便优越的特点；在广义位势理论的基础上,研究了塑性应变增量的分解准则,提出了考虑拟弹性塑性变形的土体弹塑性本构模型,把传统不可恢复的塑性应变增量分解为具有弹性应变特性的拟弹性塑性变形部分和符合传统塑性理论的纯塑性部分；提出和建立了带拟弹性参数的数值弹塑性模型,并进行了相关验证；在多重势面模型基础上研究了碎石桩的机理问题。本文主要完成的具体工作如下：
首先,对土的本构理论相关文献资料进行全面回顾,针对国内外学者研究岩土本构模型的方法进行了简单归纳和分类概述,分析了岩土材料本构理论的发展和一些具体模型的特点,阐述了岩土非线性弹性本构理论和传统弹塑性本构理论以及最新的广义位势理的研究成果及其发展现状,并对各种理论的优缺点进行了比较,分析它们之间的联系与区别,找出存在的问题和有待进一步深入的方向,指出统一的数学基础和具体土类在特定假设下的本构模型是以后发展趋向。
第二,系统阐述了广义位势理论的提出和发展,从理论基础的角度讨论了广义位势理论的内在特性及重要意义。针对土的变形的特殊性,主要介绍了应力空间多重势面模型和应变空间多重势面模型,对模型特性进行了全面展示,分析了其对于邓肯-张模型和传统弹塑性模型理论上的优越性。由于不再用屈服函数,即不再区分明显的弹、塑性阶段,这也更符合工程土的实际变形特性,有更好的适应性。通过试验验证表明多重势面模型参数简单,计算可靠,计算结果与试验符合较好,能充分利用试验成果,又能反映邓肯-张模型反映不了的剪胀特性,证明其不论理论基础还是工程实用性上都比较优越。
第三,进行了弹性矩阵与弹塑性矩阵的对比剖析,从数学本质上探讨了非线性弹性模型和传统弹塑性模型以及多重势面模型的的数学基础和假设及其联系；阐明了其主要是刚度(柔度)矩阵中角占优以及正定的问题,指出邓肯模型和传统弹塑性模型以及多重势面模型的本构矩阵内在差异为：有没有反映球应力对剪应变和偏应力对体应变交叉影响的那些元素,以及这些元素之间不同的等量关系,进而建议了对几种主要土的模型使用原则。
第四,指出了邓肯-张模型和传统塑性理论关于应力计算存在的问题,即本构矩阵的不同将在反算应力时导致较大差异,邓肯模型使应力计算结果偏大,传统关联流动弹塑性模型因为假设交叉项相等也会导致与实际不符,只有满秩且上下三角元素独立的多重势面模型才能得出更符合实际的应力计算结果。通过算例比较了用不同本构模型进行应力计算所得结果的差异,分析了多重势面模型的合理性。
第五,进一步深入分析了Ottowa砂土的变形规律。为解决传统理论对塑性应变增量方向描述的不足,本文在广义位势理论的基础上,研究了塑性应变增量的分解准则,提出了考虑拟弹性塑性变形的土体弹塑性本构模型,把传统不可恢复的塑性应变增量分解为具有弹性应变特性的拟弹性塑性变形部分和纯塑性部分,这在理论上是合理的。拟弹性部分遵从弹性法则,并与应力增量有相同的方向,采用弹性模型表示；纯塑性部分遵从传统塑性理论,方向具有唯一性,采用关联流动法则进行建模。这相当于在塑性矩阵中拿出拟弹性这一部分合并到弹性矩阵部分,从理论上阐明了这一措施可改善总的弹塑性矩阵性质,也更符合土的实际变形机理。这样分解后建立的模型将更为合理和简便,又可以解决土塑性应变增量方向不具有唯一性的问题。
第六,推导了拟弹性分解方法并给出相应参数的确定准则；在广义位势理论的框架下再增加两个拟弹性参数,从而在计算中一开始就包含两项塑性应变增量：拟弹性和纯塑性,两项各自随着应力水平的变化而变化；当拟弹性系数为零时即退化为传统的关联流动模型,因而涵盖更广。通过新模型对水坠坝冲填土的计算证明了进行分解的可行性和优越性。在此基础上研究了关联和非关联流动法则产生的差异,评估了塑性应变中符合关联法则的部分和非关联法则的部分的比例；给出关联与非关联流动法则的使用建议。
第七,建立了数值弹塑性模型。首先通过直接从试验曲线求导得到多重势面本构模型增量计算所需参数,对得到的塑性系数按所提出的分解准则进行拟弹性分解；然后把多组围压下的常三轴试验结果综合来建立数据库,通过立方插值得到其他应力状态下单元的模型参数,即得到数值弹塑性模型。包含三种模型：做关联流动假设的两参数简化模型、不做关联流动假设并分解出拟弹性应变的六参数模型、直接将试验与简化模型结果差值部分归为拟弹性的四参数模型。因为真实应力路径是由σ1、σ2、σ3控制的,不同的p值也反映了三个主应力的不同变化路径,数值模型充分利用试验成果所蕴含的力学信息,可在一定程度上反映应力路径的影响；数值模型参数纳入力学基本方程,有着明确的力学概念；处理后分别用弹性准则和关联流动法则进行建模,计算稳定可靠,且能更简便、更真实地反映土的变形特性。
第八,用编入了多重势面模型的NM2001程序计算振冲碎石桩,给出了荷载作用下土中碎石桩的体积膨胀与其承载能力提高程度的关联因子；研究了碎石芯体膨胀后的受力规律；多重势面模型能更好地反映碎石桩的作用机理,为这项工程实践提供了更深入的理论依据。
Constitutive theory plays a key role in geotechnical engineering, and there are still some problems in this field:elastic and nonlinear elastic model based on Hooke's Law does not reflect the dilatancy, which is an important characteristic of soil; non-associated plastic model does not meet the Drucker postulate, the direction of plastic strain increment is not unique, the constitutive matrix of traditional plastic models is not positive definite, so the traditional theory is inadequate to describe the constitutive behavior of soil. Based on the deformation characteristics of soil, Yang Guanghua proposed the generalized elastic-plastic constitutive theory, the traditional theory of elasticity and plasticity potential theory can be ascribed to mathematic problems of the potential function, so they can be expressed by the unified theory of generalized potential theory. The corresponding multi-potential surface theory is essentially a mathematic approach to the study of the constitutive relation for soils. The model based on the multi-potential surface theory may have wider adaptability than those based on conventional plastic-potential theory, and needs no plastic potential functions or yield functions..
This thesis conducts some further study based on the generalized potential theory. The features of constitutive matrix of different theories are analyzed. The simplicity and superiority of the new model based on generalized potential theory is demonstrated by examples. On the basis of generalized potential theory, we decompose the traditional unrecoverable deformation into two parts:the quasi-elastic-plastic, which shares characteristics with elastic strain, and pure-plastic, which follows the traditional plastic theory, the decomposing criterion of plastic strain increment is studied, and a elastic-plastic constitutive model of soil considering quasi-elastic-plastic deformation is presented; a numerical elastoplastic constitutive model with quasi-elastic parameters is also established, and then relational verification work is also conducted. The mechanism of the gravel pile problem is studied using multi-potential surface theory. The main contents are as follows:
1. A comprehensive review of relevant literature of the constitutive theory of soil is conducted, methods by which scholars at home and abroad use to study the constitutive model of soil are categorized, the development and some specific features of the theories and models for the geotechnical material is analyzed. The development of nonlinear elastic and elastic-plastic constitutive theory as well as the new generalized potential theory are expounded, and the advantages and disadvantages of various theories are compared, the relations and differences between them are analyzed, problems and developing directions are identified, and point out that the unified mathematical basis and constitutive model for particular types of soil under specific assumption is the future development trend.
2. The concept of generalized potential theory and its development is systematically expounded, the inherent characteristics and significance of generalized potential theory is discussed theoretically. For the special nature of soil deformation, the multi-potential surface model in stress space and the strain space are introduced. The features of the model are comprehensively displayed comparing with Duncan-Chang model and the traditional plastic theory, and shows the theoretical advantages of the generalized potential theory. Because there is no yield function, there is no longer clear distinction between elastic and plastic stage, which agrees much well with the actual deformation characteristics of soil, so the new theory has a better adaptability. Experiments proved that the multi-potential surface model's parameters are simple, the calculation of reliable, and the computed results are in good agreement with the experimental results, it can make full use of test results, and also reflect the dilatation of soil which can't be described by Duncan-Chang model. It is proved that whether on practical or theoretical basis the new theory has evident advantages.
3. Comparison analysis of the elastic matrix and elastic-plastic matrix is conducted. The mathematical basis and associated assumption of nonlinear elastic model and the traditional plastic models as well as multi-potential surface model on the mathematical basis. It is expounded that the main problem is the stiffness matrix diagonally dominant and whether is positive definite, it is also pointed out that the internal differences of the constitutive matrix of the Duncan model and the traditional plastic model, and multi-potential surface model are whether not reflect cross affect of hydrostatic pressure on the shear strain and the partial stress on the volumetric strain, and then the different equal relationship between the cross-term effects. Then use principles for several major soils are proposed.
4. The problems on the stress calculation when use Duncan-Chang model or classical plasticity theory are pointed out, it is that the different constitutive matrix would result in large differences when calculate the stress, Duncan model would result in too large stress, the traditional plastic model assumed to follow associated flow rule would also lead to discrepancies with reality. Only multi-potential surface model, whose matrix is full rank and in which the upper and lower triangular elements are independent, can give a more realistic stress results. The differences in the results of stress calculation of the different constitutive models are studied and proved that multi-potential surface model is reasonable.
5. Further analysis on the deformation features of Ottawa sand is carried out. To address the deficiencies when people use traditional plastic theory to describe the direction of strain increment, the plastic strain increment is decomposed into quasi-elastic part and pure-plastic part, according to their fundamental characteristic. The former shares characteristics with elastic strain and has the same direction as the stress increment, thus can be described by elastic model, while the later follows the traditional plastic theory and has a unique direction, thus can be described by the model of associated flow rule. This is equivalent to assigning a certain part from the plastic matrix to the elastic matrix, which can improve the total elastic-plastic matrix properties, and is in close accordance with the actual deformation mechanism of soil. After decomposing, the model will be much more reasonable and simpler, and can solve the problem of non-uniqueness in the direction of plastic strain increment in soil.
6. Decomposition method is derived and determining criteria of the corresponding parameters is given. In the framework of generalized potential theory, with two additional quasi-elastic parameters, two kinds of plastic strain increments can be described at beginning of the deformation:quasi-elastic and pure plastic, the two parts vary with the stress level; when the quasi-elastic parameters are zero, it degenerates to the traditional associated flow model, so the new model covers a wider field. The feasibility and superiority of the new model is certificated by an example of hydraulic fill soil in a water falling dam. Based on this study, the difference induced by associated and non-associated flow rule is also studied, and then some recommendations are proposed.
7. Numerical elastic-plastic model is established. Firstly, deriving the parameters for incremental calculation in multi-potential surface model by derivation from the experimental curves, and decompositing the plastic parameters obtained using the proposed criteria; secondly, establishing a database by synthesizing the results of conventional tri-axial tests at different confining pressure, and then getting model parameters for other stress conditions by cubic interpolation, and this is numerical elastic-plastic model. Three specific models are then established:simplified model with two parameters in the assumption of associated flow rule; six-parameter model without assumption of associated flow rule but with decomposition of quasi-elastic-plastic strain; four-parameter model with quasi-elastic-plastic parameters derived from the difference between experimental results and simplified model. Because the real stress path is controlled byσ1、σ2、σ3 actually, so different p reflects the variations of stress path, numerical model makes full use of the mechanical information in the test results, can reflect the impact of stress path to a certain extent, parameters are taken into the basic mechanical equation, there is a clear mechanical sense for each; meanwhile only elastic model and the model of associated flow rule are used, the calculation can be much simpler. So the numerical model can reflect the soil's deformation properties much simply and satisfactorily.
8. A model of vibro-replacement stone column is established using FEM program of NM2001, in which the multi-potential surface model is realized, and some calculation work is conducted to study the mechanical mechanism. The correlation factor between volumetric dilatation and improvement of bearing capacity of the stone column is derived. Stress distribution law after dilatation is also studied. Multi-potential surface model can reflect the mechanism of stone columns better. Theoretical basis for the project of stone pile is provided.
本文主要围绕广义位势理论进行进一步深入的研究。剖析了各模型族本构矩阵的特性,通过算例展示了广义位势理论多重势面模型简便优越的特点；在广义位势理论的基础上,研究了塑性应变增量的分解准则,提出了考虑拟弹性塑性变形的土体弹塑性本构模型,把传统不可恢复的塑性应变增量分解为具有弹性应变特性的拟弹性塑性变形部分和符合传统塑性理论的纯塑性部分；提出和建立了带拟弹性参数的数值弹塑性模型,并进行了相关验证；在多重势面模型基础上研究了碎石桩的机理问题。本文主要完成的具体工作如下：
首先,对土的本构理论相关文献资料进行全面回顾,针对国内外学者研究岩土本构模型的方法进行了简单归纳和分类概述,分析了岩土材料本构理论的发展和一些具体模型的特点,阐述了岩土非线性弹性本构理论和传统弹塑性本构理论以及最新的广义位势理的研究成果及其发展现状,并对各种理论的优缺点进行了比较,分析它们之间的联系与区别,找出存在的问题和有待进一步深入的方向,指出统一的数学基础和具体土类在特定假设下的本构模型是以后发展趋向。
第二,系统阐述了广义位势理论的提出和发展,从理论基础的角度讨论了广义位势理论的内在特性及重要意义。针对土的变形的特殊性,主要介绍了应力空间多重势面模型和应变空间多重势面模型,对模型特性进行了全面展示,分析了其对于邓肯-张模型和传统弹塑性模型理论上的优越性。由于不再用屈服函数,即不再区分明显的弹、塑性阶段,这也更符合工程土的实际变形特性,有更好的适应性。通过试验验证表明多重势面模型参数简单,计算可靠,计算结果与试验符合较好,能充分利用试验成果,又能反映邓肯-张模型反映不了的剪胀特性,证明其不论理论基础还是工程实用性上都比较优越。
第三,进行了弹性矩阵与弹塑性矩阵的对比剖析,从数学本质上探讨了非线性弹性模型和传统弹塑性模型以及多重势面模型的的数学基础和假设及其联系；阐明了其主要是刚度(柔度)矩阵中角占优以及正定的问题,指出邓肯模型和传统弹塑性模型以及多重势面模型的本构矩阵内在差异为：有没有反映球应力对剪应变和偏应力对体应变交叉影响的那些元素,以及这些元素之间不同的等量关系,进而建议了对几种主要土的模型使用原则。
第四,指出了邓肯-张模型和传统塑性理论关于应力计算存在的问题,即本构矩阵的不同将在反算应力时导致较大差异,邓肯模型使应力计算结果偏大,传统关联流动弹塑性模型因为假设交叉项相等也会导致与实际不符,只有满秩且上下三角元素独立的多重势面模型才能得出更符合实际的应力计算结果。通过算例比较了用不同本构模型进行应力计算所得结果的差异,分析了多重势面模型的合理性。
第五,进一步深入分析了Ottowa砂土的变形规律。为解决传统理论对塑性应变增量方向描述的不足,本文在广义位势理论的基础上,研究了塑性应变增量的分解准则,提出了考虑拟弹性塑性变形的土体弹塑性本构模型,把传统不可恢复的塑性应变增量分解为具有弹性应变特性的拟弹性塑性变形部分和纯塑性部分,这在理论上是合理的。拟弹性部分遵从弹性法则,并与应力增量有相同的方向,采用弹性模型表示；纯塑性部分遵从传统塑性理论,方向具有唯一性,采用关联流动法则进行建模。这相当于在塑性矩阵中拿出拟弹性这一部分合并到弹性矩阵部分,从理论上阐明了这一措施可改善总的弹塑性矩阵性质,也更符合土的实际变形机理。这样分解后建立的模型将更为合理和简便,又可以解决土塑性应变增量方向不具有唯一性的问题。
第六,推导了拟弹性分解方法并给出相应参数的确定准则；在广义位势理论的框架下再增加两个拟弹性参数,从而在计算中一开始就包含两项塑性应变增量：拟弹性和纯塑性,两项各自随着应力水平的变化而变化；当拟弹性系数为零时即退化为传统的关联流动模型,因而涵盖更广。通过新模型对水坠坝冲填土的计算证明了进行分解的可行性和优越性。在此基础上研究了关联和非关联流动法则产生的差异,评估了塑性应变中符合关联法则的部分和非关联法则的部分的比例；给出关联与非关联流动法则的使用建议。
第七,建立了数值弹塑性模型。首先通过直接从试验曲线求导得到多重势面本构模型增量计算所需参数,对得到的塑性系数按所提出的分解准则进行拟弹性分解；然后把多组围压下的常三轴试验结果综合来建立数据库,通过立方插值得到其他应力状态下单元的模型参数,即得到数值弹塑性模型。包含三种模型：做关联流动假设的两参数简化模型、不做关联流动假设并分解出拟弹性应变的六参数模型、直接将试验与简化模型结果差值部分归为拟弹性的四参数模型。因为真实应力路径是由σ1、σ2、σ3控制的,不同的p值也反映了三个主应力的不同变化路径,数值模型充分利用试验成果所蕴含的力学信息,可在一定程度上反映应力路径的影响；数值模型参数纳入力学基本方程,有着明确的力学概念；处理后分别用弹性准则和关联流动法则进行建模,计算稳定可靠,且能更简便、更真实地反映土的变形特性。
第八,用编入了多重势面模型的NM2001程序计算振冲碎石桩,给出了荷载作用下土中碎石桩的体积膨胀与其承载能力提高程度的关联因子；研究了碎石芯体膨胀后的受力规律；多重势面模型能更好地反映碎石桩的作用机理,为这项工程实践提供了更深入的理论依据。
Constitutive theory plays a key role in geotechnical engineering, and there are still some problems in this field:elastic and nonlinear elastic model based on Hooke's Law does not reflect the dilatancy, which is an important characteristic of soil; non-associated plastic model does not meet the Drucker postulate, the direction of plastic strain increment is not unique, the constitutive matrix of traditional plastic models is not positive definite, so the traditional theory is inadequate to describe the constitutive behavior of soil. Based on the deformation characteristics of soil, Yang Guanghua proposed the generalized elastic-plastic constitutive theory, the traditional theory of elasticity and plasticity potential theory can be ascribed to mathematic problems of the potential function, so they can be expressed by the unified theory of generalized potential theory. The corresponding multi-potential surface theory is essentially a mathematic approach to the study of the constitutive relation for soils. The model based on the multi-potential surface theory may have wider adaptability than those based on conventional plastic-potential theory, and needs no plastic potential functions or yield functions..
This thesis conducts some further study based on the generalized potential theory. The features of constitutive matrix of different theories are analyzed. The simplicity and superiority of the new model based on generalized potential theory is demonstrated by examples. On the basis of generalized potential theory, we decompose the traditional unrecoverable deformation into two parts:the quasi-elastic-plastic, which shares characteristics with elastic strain, and pure-plastic, which follows the traditional plastic theory, the decomposing criterion of plastic strain increment is studied, and a elastic-plastic constitutive model of soil considering quasi-elastic-plastic deformation is presented; a numerical elastoplastic constitutive model with quasi-elastic parameters is also established, and then relational verification work is also conducted. The mechanism of the gravel pile problem is studied using multi-potential surface theory. The main contents are as follows:
1. A comprehensive review of relevant literature of the constitutive theory of soil is conducted, methods by which scholars at home and abroad use to study the constitutive model of soil are categorized, the development and some specific features of the theories and models for the geotechnical material is analyzed. The development of nonlinear elastic and elastic-plastic constitutive theory as well as the new generalized potential theory are expounded, and the advantages and disadvantages of various theories are compared, the relations and differences between them are analyzed, problems and developing directions are identified, and point out that the unified mathematical basis and constitutive model for particular types of soil under specific assumption is the future development trend.
2. The concept of generalized potential theory and its development is systematically expounded, the inherent characteristics and significance of generalized potential theory is discussed theoretically. For the special nature of soil deformation, the multi-potential surface model in stress space and the strain space are introduced. The features of the model are comprehensively displayed comparing with Duncan-Chang model and the traditional plastic theory, and shows the theoretical advantages of the generalized potential theory. Because there is no yield function, there is no longer clear distinction between elastic and plastic stage, which agrees much well with the actual deformation characteristics of soil, so the new theory has a better adaptability. Experiments proved that the multi-potential surface model's parameters are simple, the calculation of reliable, and the computed results are in good agreement with the experimental results, it can make full use of test results, and also reflect the dilatation of soil which can't be described by Duncan-Chang model. It is proved that whether on practical or theoretical basis the new theory has evident advantages.
3. Comparison analysis of the elastic matrix and elastic-plastic matrix is conducted. The mathematical basis and associated assumption of nonlinear elastic model and the traditional plastic models as well as multi-potential surface model on the mathematical basis. It is expounded that the main problem is the stiffness matrix diagonally dominant and whether is positive definite, it is also pointed out that the internal differences of the constitutive matrix of the Duncan model and the traditional plastic model, and multi-potential surface model are whether not reflect cross affect of hydrostatic pressure on the shear strain and the partial stress on the volumetric strain, and then the different equal relationship between the cross-term effects. Then use principles for several major soils are proposed.
4. The problems on the stress calculation when use Duncan-Chang model or classical plasticity theory are pointed out, it is that the different constitutive matrix would result in large differences when calculate the stress, Duncan model would result in too large stress, the traditional plastic model assumed to follow associated flow rule would also lead to discrepancies with reality. Only multi-potential surface model, whose matrix is full rank and in which the upper and lower triangular elements are independent, can give a more realistic stress results. The differences in the results of stress calculation of the different constitutive models are studied and proved that multi-potential surface model is reasonable.
5. Further analysis on the deformation features of Ottawa sand is carried out. To address the deficiencies when people use traditional plastic theory to describe the direction of strain increment, the plastic strain increment is decomposed into quasi-elastic part and pure-plastic part, according to their fundamental characteristic. The former shares characteristics with elastic strain and has the same direction as the stress increment, thus can be described by elastic model, while the later follows the traditional plastic theory and has a unique direction, thus can be described by the model of associated flow rule. This is equivalent to assigning a certain part from the plastic matrix to the elastic matrix, which can improve the total elastic-plastic matrix properties, and is in close accordance with the actual deformation mechanism of soil. After decomposing, the model will be much more reasonable and simpler, and can solve the problem of non-uniqueness in the direction of plastic strain increment in soil.
6. Decomposition method is derived and determining criteria of the corresponding parameters is given. In the framework of generalized potential theory, with two additional quasi-elastic parameters, two kinds of plastic strain increments can be described at beginning of the deformation:quasi-elastic and pure plastic, the two parts vary with the stress level; when the quasi-elastic parameters are zero, it degenerates to the traditional associated flow model, so the new model covers a wider field. The feasibility and superiority of the new model is certificated by an example of hydraulic fill soil in a water falling dam. Based on this study, the difference induced by associated and non-associated flow rule is also studied, and then some recommendations are proposed.
7. Numerical elastic-plastic model is established. Firstly, deriving the parameters for incremental calculation in multi-potential surface model by derivation from the experimental curves, and decompositing the plastic parameters obtained using the proposed criteria; secondly, establishing a database by synthesizing the results of conventional tri-axial tests at different confining pressure, and then getting model parameters for other stress conditions by cubic interpolation, and this is numerical elastic-plastic model. Three specific models are then established:simplified model with two parameters in the assumption of associated flow rule; six-parameter model without assumption of associated flow rule but with decomposition of quasi-elastic-plastic strain; four-parameter model with quasi-elastic-plastic parameters derived from the difference between experimental results and simplified model. Because the real stress path is controlled byσ1、σ2、σ3 actually, so different p reflects the variations of stress path, numerical model makes full use of the mechanical information in the test results, can reflect the impact of stress path to a certain extent, parameters are taken into the basic mechanical equation, there is a clear mechanical sense for each; meanwhile only elastic model and the model of associated flow rule are used, the calculation can be much simpler. So the numerical model can reflect the soil's deformation properties much simply and satisfactorily.
8. A model of vibro-replacement stone column is established using FEM program of NM2001, in which the multi-potential surface model is realized, and some calculation work is conducted to study the mechanical mechanism. The correlation factor between volumetric dilatation and improvement of bearing capacity of the stone column is derived. Stress distribution law after dilatation is also studied. Multi-potential surface model can reflect the mechanism of stone columns better. Theoretical basis for the project of stone pile is provided.
引文
[1]王勖成.有限单元法[M].北京：清华大学出版社,2003.7
[2]李广信.高等土力学[M].北京：清华大学出版社,2004.7
[3]杨光华.土的本构模型的广义位势理论及其应用[M].北京：中国水利水电出版社,2007,5
[4]俞茂宏.双剪理论及其应用[M].北京：科学出版社,1998.6.
[5]Shi Genhua. Block System Modeling by Discontinuous Deformation Analysis. Southampton UK and Boston USA,1993
[6]郑颖人,孔亮.塑性力学中的分量理论——广义塑性力学[J].岩土工程学报,2000,22(3)：269-274.
[7]郑颖人,沈珠江,龚晓南.广义塑性力学——岩土塑性力学基本原理[M].北京：中国建筑工业出版社,2002.
[8]郑颖人,孔亮.广义塑性力学及其运用[J].中国工程科学,2005,7(11)：21-36.
[9]杨光华.建立弹塑性本构关系的广义塑性位势理论[A].第二届全国岩土力学数值分析与解析方法会议论文集[C].珠海,1988.140-148.
[10]杨光华.岩土类工程材料本构关系的势函数模型理论.见：第四届全国岩土力学数值分析与解析方法会议论文集.武汉测绘科技大学出版社,1991.
[11]YANG Guang-hua. A new elasto-plastic coustititive madel for soils[C]//Int Conf on Soft Soil Eng, Guangzhou,1993,313-320.
[12]杨光华.土的数学本构理论的研究[A].第二届全国青年岩土力学与工程会议论文集[C].大连：大连理工大学出版社[C],1995,100-112.
[13]杨光华.岩土类材料的多重势面弹塑性本构模型理论.岩土工程学报,1997,13(5)：99-107.
[14]杨光华.21世纪应建立岩土材料的本构理论[J].岩土工程学报,1997,19(3)：116-117.
[15]杨光华.土体材料本构特性的数学分析[C]//第六届全国岩土力学数值分析与解析方法讨论会论文集.广州：广东科技出版社,1998.
[16]杨光华,李广信.岩土的本构模型的数学基础与广义位势理论[J].岩土力学,2002,23(5)：531-535.
[17]杨光华,李广信.从广义位势理论的角度看土的本构理论的研究[J].岩土工程学报,2007,29(4)：594-597
[18]杨光华.岩土类工程材料的多重势面弹塑性本构方程理论[J].岩土工程学报,1991,15(5)：100-107.
[19]杨光华.岩土类工程材料本构方程的一个张量普遍形式定律水工结构工程理论与应用[M],大连：大连海运学院出版社,1993.315-320.
[20]杨光华,土的本构模型的数学理论及其运用[博士论文D].北京：清华大学,1998.
[2l]沈珠江.科学崇尚简朴-岩土工程中引进和借鉴方法评述[J].岩土工程学报,2004,26(3)：
299-300
[22]郑颖人.当前岩土计算力学的发展动向一介绍第八届岩土力学计算机方法与进展国际会议[J].岩土力学,1995,16(1)：84-90
[23]Duncan J M, Chang C Y. Nonlinear analysis of stress-strain in soils[J]. Proc. ASCE,1970,96(SM5): 1692-1653
[24]王钊,王协群.三峡工程二期围堰低高防渗墙方案的有限元分析[J].武汉水利电力大学学报,1997,30(3)：1-6
[25]沈珠江.考虑剪胀性的土和石料的非线性应力应变模式[J].水利水运科学研究,1985,(4)：12-17
[26]罗刚,张建民.邓肯一张模型和沈珠江双屈服面模型的改进[J].岩土力学,2004,25(6)：887-890
[27]Roscoe K. H., Schofield A. N., Worth C.P. On the yielding of soils[J]. Geotechnique,1958,8(1): 22-53.
[28]Roscoe K, H., Schofield A. N., Thurarrajah A. Yielding of clays in states wetter than critical[J].Geotechnique,1963,13(1):211-240.
[29]Palmar A C. Mechanique.5.2(1966):217-222
[30]Schofield A N. Wroth C P. Critical State Soil Mechanics[M]. London:McG raw Hill,1968
[31]魏汝龙.正常压密粘土的塑性势[J].水利学报,6(1964)：9-20
[32]魏汝龙.南京水利科学研究所报告.16(1963)
[33]Prevost J H.Koeg K. Geotec,25,2(1976):279-297
[34]Lade P V. Duncan J M. JGE. ASCE,101, GT10(1975):1037-1053.
[35]Mroz Z. Xerris V. Zienkiewicz O C. Geotech.29.1(1979):1-34
[36]Valanis K C.Arch.Mech..23 (1971):517-534.
[37]Dafallias Y F, Herrman L R. Int. Symp. on Soil under Cyclic Transient Loading. Swansea(1980):335-345
[38]刘元雪.岩土本构理论的几个基本问题研究[J].岩土工程学报,2001,(1)：45-48
[39]沈珠江.土的三重屈服面应力应变模型[J].固体力学学报,1984,(2)：51-57
[40]沈珠江.土体应力应变分析中的一种新模型[A].第五届土力学及基础工程学术讨论会论文集[C].北京：中国建筑工业出版社,1990.101-105.
[41]秦理曼.基于能量耗散的土的本构关系研究[D].大连理工大学,2006,4.
[42]姚仰平,路德春,周安楠,等.广义非线性强度理论及其变换应力空间[J].中国科学(E辑),2004,34(11)：1283-1299.
[43]姚仰平,路德春,周安楠.岩土材料的变换应力空间及其应用[J].岩土工程学报,2005,27(1)：24-29.
[44]Matsuoka H, Nakai T. Stress deformation and strength characteristics of soil under three difference principal stresses[C]//Proceedings of JSCE. [S.l.]:[s.n.],1974:59-70.
[45]孙德安,姚仰平,殷宗泽.基于SMP准则的双屈服面弹塑性模型的三维化[J].岩土工程学报Vol21，No.5,1999：631-634
[46]张永光.土本构关系及数值建模[D].华中科技大学,2007,4.
[47]沈珠江.关于土力学发展前景的设想[J].岩土工程学报,1994,16(1)：100-111.
[48]赵成刚,张雪东,郭璇.土的本构方程与热力学[J].力学进展,2006,36(4)611-618.
[49]Chang, C.Y., Duncan, J.M. Analysis of soil movement around a deep excavation. Journal of the Soil Mechanics and Foundations Division,1970,96(SMS):1655-1681
[50]屈智炯.土的塑性力学[M].成都：成都科技大学出版社,1987
[51]Chen W.F., Saleeb, A.F. Constitutive equations for engineering materials. Vol.1:Elasticity and modeling. John Wiley-Inierseienee, New York,1982
[52]Domasehuk, L. Valliappan, P. Nonlinear settlement analysis by finite element. Journal of the Soil Mechanics and Foundations Division,1975,101 (GT7):601-614
[53]沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2)：11-19
[54]沈珠江.考虑剪胀性的土和石料的非线性应力应变模式.水利水运科学研究,1986,4：1-14
[55]Chen, W.F., Mizuno, E. Nonlinear analysis in soil mechanics-Theory and Implementation, Elsevier Science Publishers B.V, Amsterdam,1990
[56]张学言.土塑性力学的建立与发展[J].力学进展,1989,19(4)：485-495
[57]K.H. Roscoe, A.N. Schofield and Thurairajh. Yielding of Clays in States Wetter than Critieal. Geotechnique,13,1963.
[58]P.V.Lade and J.M.Duncan. Cubical triaxial tests on cohesionless soil. Journal of the soil mechanics foundation division, ASCE, Vol.99, No.SMIO, Oet.1975.
[59]黄文熙.土的工程性质[M].北京：水利电力出版社.1983
[60]黄文熙,淮家骆,陈愈炯.土的硬化规律和屈服函数[J].岩土工程学报,1981,3(3)：19-27
[61]Coulomb, C.A.,朱百里(译).极大极小原理在建筑静力学中的应用[J].岩土工程学报,1993,15(6)：110-121
[62]Drucker, D.C., Prager, W. Extended limit design theorems for continuous media. Quarterly of Applied Mathematics,1952,9:381-389
[63]Drucker, D.C, prager, W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematies.1952,10:157-165
[64]Drucker, D.C., Gibson, R.E., Henkel, D.J. Soil mechanics and work-hardening theories of plasticity. Transactions ASCE.1957,122:338-346
[65]Roscoe K.H, Burland J.B. On the generalized stress-strain behaviour of wet clay[M]. Cambridge: Cambridge University Press,1968:535-609.
[66]Chen, W.F. Limit analysis and soil Plasticity. Elsevier Scientific Publishing Company, Amsterdam,
1975
[67]魏汝龙.正常压密粘土的本构定律[J].岩土工程学报,1981,3(3)：10-18
[68]Chen W.F Constitutive equations for engineering materials Vol.2:Plastieity and modeling. Elsevier, Amsterdam,1994
[69]DiMaggio, F.L., Sandler, I.S. Material model for granular soils. Journal of Engineering Mechanics Division,1971,97(EM3):935-950
[70]Resende, L., Martin, J.B. Formulation of Drucker-Prager cap model. Journal of Engineering Mechanics,1985,111(7):855-881
[71]Vermeer, P.A. A double hardening model for sand. Geotechnique,1978,28(4):413-433
[72]Nova, R. On the hardening of soils. Archives of Mechanics,1977,29(3):445-458
[73]Jefferies, M.G. Nor-sand:a simple critical state model for sand. Geotechnique,1993,43(1):91-103
[74]Pastor M., Zienkiewica O.C., Chan, A.H.C. Generalized plasticity and the modeling of soil behavior. International Journal for Numerical Analytical Methods in Geomechanics,1990,14:151-190
[75]Mroz, Z. On the description of anisotropic work hardening. Journal of the Mechanics and Physics of Solids,1967,15:163-175
[76]Dafalias, Y.F., Popov, E.P. A model of nonlinearly hardening materials for complex loading. Acta Mechanica,1975,21:173-192
[77]Dafalias, Y.F. Bounding surface Plasticity(Ⅰ):Mathematical foundation and hypo-plasticity. Journal of Engineering Mechanics,1986,112(9):966-987
[78]王志良.塑性力学与土的性质模拟.塑性力学和地球动力学文集,北京：北京大学出版社,1990：23-29
[79]架茂田,吴兴征,李相裕.堆石料的亚塑性边界面模型及其验证[J].岩石力学与工程学报,2001,20(2)：164-170
[80]沈珠江.粘土的双硬化模型[J].岩土力学.1995,16(1)：1-8
[81]刘元雪.含主应力轴旋转的土体一般应变关系[D].解放军后勤工程学院.1997.
[82]沈珠江.三种硬化理论的比较[J].岩土力学,1994,15(2)：13-19.
[83]沈珠江,关于破坏准则和屈服函数的总结[J].岩土工程学报,1995,17(1)：1-8
[84]沈珠江.几种屈服函数的比较[J].岩土力学,1993(1).
[85]沈珠江.土体弹塑性变形分析中的几个基本问题[J].江苏力学论文集.河诲大学出版杜,1994.1-10.
[86]渡家骤,李广信.土的本构关系及其验证与应用[J].岩土工程学报,1986,1.8(1)：312-386.
[87]殷宗泽.一个土体的双屈服面应力-应变模型[J].岩土工程学报,1988,10(4)：64-71.
[88]郑颖人.土的多重屈服面理论与模型.塑性力学和细观力学文集,北京：北京大学出版社,1993：75-84
[89]耿黎明.混合遗传算法在初始地应力场反分析中的应用研究[M].武汉大学,2002
[90]王靖涛,杨毅,张曦映.考虑应力路径的砂土的神经网络本构关系模型[J].岩石力学与工程学报,2002,21(10)：1487-1489.
[91]任青阳,王靖涛.等主应力比路径下砂土弹塑性本构关系的数值建模[J].华中科技大学学报(市科学版).2005,22(3)：69-71.
[92]Naki T. An isotropic hardening elastoplastic model for sand considering the stress Path dependeney in the three-dimensional stress. Soils and Foundations,1989,29(1):119-137
[93]Matsuoka H, Sun DA, Konde T. A constitutive law from frictional to cohesive materials[A]. X III ICSMFE[C]. New Delhi:[s.n.].1994.403-406.
[94]Matsuoka H., et al. A constitutive equation for sands and its application to analyses of rotational stress path and liquefaction resistanee.Soils and Foundations,1985,25(1):27-42
[95]Nakata, Y, etal. Flow deformation of sands subjected to principal stress rotation. Soils and Foundations,1998,38(2):115-128
[96]刘元雪,郑颖人.考虑主应力轴旋转对土体应力应变关系影响的一种新方法[J].岩土工程学报,1998,20(2)：45-47
[97][117]刘元雪,郑颖人.含主应力轴旋转的土体本构关系研究进展[J].力学进展,2000,30(4)：597-604
[98]窦宜,段勇.主应力方向偏转条件下粘性土的变形特性[J].水利水运科学研究,1990(4)：351-366
[99]姜洪伟,赵锡宏.主应力轴旋转对软土塑性变形影响分析[J]上海力学,1997,18(2)：140-146
[100]陈生水,沈珠江，郦能惠.复杂应力路径下无粘性上的弹塑性数值模拟[J]岩土工程学报,1995,17(2)：20-28
[101]史宏彦,谢定义,汪闻韶.平面应变条件下主应力轴旋转产生的应变[J].岩土工程学报,2001,23(2)：162-166
[102]Matsuoka H. Constitutive equation and FE analysis for anisotropic soil. In:Yamada Y ed. Proc of 4th Int Conf on numerical Methods in Geomechanics.1982.223-233
[103]Hong, W. P.and Lade, P. V.. Strain increment and Stress Directions in Torsion Shear Tests. J. Geo.Eng.1989,115(10)：1388-1401
[104]Nakai T, Matsuoka H. A generalized elastoplastic constitutive model for clay in three-dimensional stresses. Soils and Foundations 1986,26(3),81-89,
[105]姚仰平,罗汀.新的变换应力空间及其应用.见：栾茂田主编.第七届全国岩土力学数值分析与解析方法会议论文集.大连：大连理工大学出版社,2001.16-20
[106]姚仰平,孙凯,路德春.岩土材料塑性应变增量方向的确定[J].力学学报,2007,39(5)692-698.
[107]向大润.土体弹塑性理论加卸载准则和计算模型探讨[J].岩土工程学报,1983,5(4)：78-91
[108]Kiousis P D. Strain space approach for softening plasticity[J].ASCE.J.Eng.Mech.l987,113(2):
210-221.
[109]Wang Zhi-liang,Yannis F D,Shen Chi-kang. Bounding surface hypoplasticity model for soil[J].ASCE.J.Eng. Mech.1990,166(5):983-1001.
[110]Zienkiewicz O C.广义塑性力学和地力学的一些模型[J].应用数学和力学,1982,3(3)：267-279.
[111]杨光华,介玉新,李广信,等.土的多重势面模型及其验证[J].岩土工程学报,1999,22(5)：578-582
[112]介玉新,胡韬,李广信,等.平面应变情况下多重势面模型与邓肯-张模型的比较[J].工程力学,2004,21(1)：148-152
[113]介玉新,刘正,杨光华,等.基于应力空间的多重势面模型及其与邓肯-张模型的比较[J].岩土力学,2004,25(增)：7-12
[114]刘正,介玉新,杨光华,等.应力型多重势面模型及其参数求取的改进[J].长江科学院院报,2006,23(1)：31-34
[115]郑颖人.岩土的多重屈服面理论与应变空间理论.岩石力学新进展,沈阳：东北工学院出版社,1989.
[116]殷有泉,曲圣年.弹塑性耦合和广义正交法则[J].力学学报,1982,(1)
[117]程展林等.围堰填料的应力应变关系试验研究.长江科学院,1995
[118]沈珠江,采百家之长、酿百花之蜜——岩土工程研究中如何创新[J].岩土工程学报,2005,27(3)：365-367
[119]沈珠江.当前土力学研究中的几个问题[J].岩土工程学报,1986,8(5)：1-8.
[120]沈珠江.从学步走向自立的岩土力学[J].岩土工程界,2003,6(12)：15-17.
[121]冯卫星,常绍东,胡万毅.北京细砂土邓肯-张模型参数试验研究[J].岩石力学与工程学报,1999,18(3)：327-330
[122]杨林德,张向霞.剑桥模型可反映剪切变形的一种修正[J].岩土力学,2007,28(1)：7-11
[123]邱斌,徐志伟.中主应力对邓肯-张模型影响的真三轴试验研究[J].岩土工程技术,2002,1：45-47
[124]Janbu,N. Soil compressibility as determined by Oedometer and triaxial tests[A], Proc. European Conf. On Soi&Mech.&Foud. Engrg. N.1963.
[125]Kulhawy F H, Dunean J M. Stresses and movements in Oroville dam. Journal of soil Meehanies and Foundation Division, ASCE.1972,98(SM7):653-665.
[126]陈正汉.岩土力学的公理化理论体系[J].应用数学和力学,1994,15(10)：901-910.
[127]殷宗泽、朱俊高、卢海华.土体弹塑性柔度矩阵与真三轴试验研究.第七届土力学与基础工程学术会议论文集,中国建筑工业出版社,北京,1994年10月,139-144
[128]沈珠江.理论土力学[M].中国水利水电出版社,北京,2000年5月
[129]殷宗泽,卢海华,朱俊高.土体的椭圆-抛物双屈服面模型及其柔度矩阵[J].水利学报,1996,12：23-28
[130]窦宜,关于塑性势问题的讨论,岩土工程学报,1981年第2期,75-76
[131]窦宜、盛树馨、施艳平,轴对称条件下饱和粘土的变形特性,水利水运科学研究,1986年第2期,l-12
[132]盛树馨、施艳平,伸长应力条件下正常固结粘土的变形特性,水利水运科学研究,1985第4期,97-104
[133]Anandarajah. Incremental Stress-Strain Behhavior of Granular Soil[J]. Journal of Geotechnical Engineering,1995, January 121 (1):57-68.
[134]李广信.土的三维本构关系的探讨与模型验证[D].清华大学,1985
[135]沈珠江.科学家不应只是解释现象——关于岩土本构理论研究方向的评述[J].岩土工程学报,2005,27(12)：1494-1495
[136]Collins IF, Houlsby GT. Application of thermomechanical principles to the modeling of geotechnical materials. ProcR Soc Lond, A,1997,453:1975-2001
[137]Lade PV, Kim MK. Single hardening constitutive model for soil, rock and concrete. International Journal of Solids and Structures,1995,32(14):1963-1978
[138]Yao YP, Sun DA. Application of Lades criterion to Cam-Clay Model. Journal of Engineering Mechanics, ASCE,2000,126(1):112-119
[139]Wbod DM. Soil Behavior and Critical State Soil Mechanic. Cambridge, UK:Cambridge University Press,1990
[140]Collins I F, Kelly P A. A thermomechanical analysis of a family of soil models[J]. Geotechnique, 2002,(7):507-518.
[141]张建民.砂土的可逆性与不可逆性剪胀规律[J].岩土工程学报,2000,22(1)：12-17.
[142]陆培炎,陈韶永,熊丽珍等.水坠坝冲填土弹塑性本构方程[J].岩土工程学报,1984,6(2)：23-39
[143]Lambe T W. A mechanistic Picture of shear strength in clay. Research conference on shear of cohesive soils,1960.
[144]Taylor D W. Fundamentals of soils mechanics.1948
[145]吴春秋.非线性有限单元法在土体稳定分析中的理论及应用研究[D].武汉大学,2004,4
[2]李广信.高等土力学[M].北京：清华大学出版社,2004.7
[3]杨光华.土的本构模型的广义位势理论及其应用[M].北京：中国水利水电出版社,2007,5
[4]俞茂宏.双剪理论及其应用[M].北京：科学出版社,1998.6.
[5]Shi Genhua. Block System Modeling by Discontinuous Deformation Analysis. Southampton UK and Boston USA,1993
[6]郑颖人,孔亮.塑性力学中的分量理论——广义塑性力学[J].岩土工程学报,2000,22(3)：269-274.
[7]郑颖人,沈珠江,龚晓南.广义塑性力学——岩土塑性力学基本原理[M].北京：中国建筑工业出版社,2002.
[8]郑颖人,孔亮.广义塑性力学及其运用[J].中国工程科学,2005,7(11)：21-36.
[9]杨光华.建立弹塑性本构关系的广义塑性位势理论[A].第二届全国岩土力学数值分析与解析方法会议论文集[C].珠海,1988.140-148.
[10]杨光华.岩土类工程材料本构关系的势函数模型理论.见：第四届全国岩土力学数值分析与解析方法会议论文集.武汉测绘科技大学出版社,1991.
[11]YANG Guang-hua. A new elasto-plastic coustititive madel for soils[C]//Int Conf on Soft Soil Eng, Guangzhou,1993,313-320.
[12]杨光华.土的数学本构理论的研究[A].第二届全国青年岩土力学与工程会议论文集[C].大连：大连理工大学出版社[C],1995,100-112.
[13]杨光华.岩土类材料的多重势面弹塑性本构模型理论.岩土工程学报,1997,13(5)：99-107.
[14]杨光华.21世纪应建立岩土材料的本构理论[J].岩土工程学报,1997,19(3)：116-117.
[15]杨光华.土体材料本构特性的数学分析[C]//第六届全国岩土力学数值分析与解析方法讨论会论文集.广州：广东科技出版社,1998.
[16]杨光华,李广信.岩土的本构模型的数学基础与广义位势理论[J].岩土力学,2002,23(5)：531-535.
[17]杨光华,李广信.从广义位势理论的角度看土的本构理论的研究[J].岩土工程学报,2007,29(4)：594-597
[18]杨光华.岩土类工程材料的多重势面弹塑性本构方程理论[J].岩土工程学报,1991,15(5)：100-107.
[19]杨光华.岩土类工程材料本构方程的一个张量普遍形式定律水工结构工程理论与应用[M],大连：大连海运学院出版社,1993.315-320.
[20]杨光华,土的本构模型的数学理论及其运用[博士论文D].北京：清华大学,1998.
[2l]沈珠江.科学崇尚简朴-岩土工程中引进和借鉴方法评述[J].岩土工程学报,2004,26(3)：
299-300
[22]郑颖人.当前岩土计算力学的发展动向一介绍第八届岩土力学计算机方法与进展国际会议[J].岩土力学,1995,16(1)：84-90
[23]Duncan J M, Chang C Y. Nonlinear analysis of stress-strain in soils[J]. Proc. ASCE,1970,96(SM5): 1692-1653
[24]王钊,王协群.三峡工程二期围堰低高防渗墙方案的有限元分析[J].武汉水利电力大学学报,1997,30(3)：1-6
[25]沈珠江.考虑剪胀性的土和石料的非线性应力应变模式[J].水利水运科学研究,1985,(4)：12-17
[26]罗刚,张建民.邓肯一张模型和沈珠江双屈服面模型的改进[J].岩土力学,2004,25(6)：887-890
[27]Roscoe K. H., Schofield A. N., Worth C.P. On the yielding of soils[J]. Geotechnique,1958,8(1): 22-53.
[28]Roscoe K, H., Schofield A. N., Thurarrajah A. Yielding of clays in states wetter than critical[J].Geotechnique,1963,13(1):211-240.
[29]Palmar A C. Mechanique.5.2(1966):217-222
[30]Schofield A N. Wroth C P. Critical State Soil Mechanics[M]. London:McG raw Hill,1968
[31]魏汝龙.正常压密粘土的塑性势[J].水利学报,6(1964)：9-20
[32]魏汝龙.南京水利科学研究所报告.16(1963)
[33]Prevost J H.Koeg K. Geotec,25,2(1976):279-297
[34]Lade P V. Duncan J M. JGE. ASCE,101, GT10(1975):1037-1053.
[35]Mroz Z. Xerris V. Zienkiewicz O C. Geotech.29.1(1979):1-34
[36]Valanis K C.Arch.Mech..23 (1971):517-534.
[37]Dafallias Y F, Herrman L R. Int. Symp. on Soil under Cyclic Transient Loading. Swansea(1980):335-345
[38]刘元雪.岩土本构理论的几个基本问题研究[J].岩土工程学报,2001,(1)：45-48
[39]沈珠江.土的三重屈服面应力应变模型[J].固体力学学报,1984,(2)：51-57
[40]沈珠江.土体应力应变分析中的一种新模型[A].第五届土力学及基础工程学术讨论会论文集[C].北京：中国建筑工业出版社,1990.101-105.
[41]秦理曼.基于能量耗散的土的本构关系研究[D].大连理工大学,2006,4.
[42]姚仰平,路德春,周安楠,等.广义非线性强度理论及其变换应力空间[J].中国科学(E辑),2004,34(11)：1283-1299.
[43]姚仰平,路德春,周安楠.岩土材料的变换应力空间及其应用[J].岩土工程学报,2005,27(1)：24-29.
[44]Matsuoka H, Nakai T. Stress deformation and strength characteristics of soil under three difference principal stresses[C]//Proceedings of JSCE. [S.l.]:[s.n.],1974:59-70.
[45]孙德安,姚仰平,殷宗泽.基于SMP准则的双屈服面弹塑性模型的三维化[J].岩土工程学报Vol21，No.5,1999：631-634
[46]张永光.土本构关系及数值建模[D].华中科技大学,2007,4.
[47]沈珠江.关于土力学发展前景的设想[J].岩土工程学报,1994,16(1)：100-111.
[48]赵成刚,张雪东,郭璇.土的本构方程与热力学[J].力学进展,2006,36(4)611-618.
[49]Chang, C.Y., Duncan, J.M. Analysis of soil movement around a deep excavation. Journal of the Soil Mechanics and Foundations Division,1970,96(SMS):1655-1681
[50]屈智炯.土的塑性力学[M].成都：成都科技大学出版社,1987
[51]Chen W.F., Saleeb, A.F. Constitutive equations for engineering materials. Vol.1:Elasticity and modeling. John Wiley-Inierseienee, New York,1982
[52]Domasehuk, L. Valliappan, P. Nonlinear settlement analysis by finite element. Journal of the Soil Mechanics and Foundations Division,1975,101 (GT7):601-614
[53]沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2)：11-19
[54]沈珠江.考虑剪胀性的土和石料的非线性应力应变模式.水利水运科学研究,1986,4：1-14
[55]Chen, W.F., Mizuno, E. Nonlinear analysis in soil mechanics-Theory and Implementation, Elsevier Science Publishers B.V, Amsterdam,1990
[56]张学言.土塑性力学的建立与发展[J].力学进展,1989,19(4)：485-495
[57]K.H. Roscoe, A.N. Schofield and Thurairajh. Yielding of Clays in States Wetter than Critieal. Geotechnique,13,1963.
[58]P.V.Lade and J.M.Duncan. Cubical triaxial tests on cohesionless soil. Journal of the soil mechanics foundation division, ASCE, Vol.99, No.SMIO, Oet.1975.
[59]黄文熙.土的工程性质[M].北京：水利电力出版社.1983
[60]黄文熙,淮家骆,陈愈炯.土的硬化规律和屈服函数[J].岩土工程学报,1981,3(3)：19-27
[61]Coulomb, C.A.,朱百里(译).极大极小原理在建筑静力学中的应用[J].岩土工程学报,1993,15(6)：110-121
[62]Drucker, D.C., Prager, W. Extended limit design theorems for continuous media. Quarterly of Applied Mathematics,1952,9:381-389
[63]Drucker, D.C, prager, W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematies.1952,10:157-165
[64]Drucker, D.C., Gibson, R.E., Henkel, D.J. Soil mechanics and work-hardening theories of plasticity. Transactions ASCE.1957,122:338-346
[65]Roscoe K.H, Burland J.B. On the generalized stress-strain behaviour of wet clay[M]. Cambridge: Cambridge University Press,1968:535-609.
[66]Chen, W.F. Limit analysis and soil Plasticity. Elsevier Scientific Publishing Company, Amsterdam,
1975
[67]魏汝龙.正常压密粘土的本构定律[J].岩土工程学报,1981,3(3)：10-18
[68]Chen W.F Constitutive equations for engineering materials Vol.2:Plastieity and modeling. Elsevier, Amsterdam,1994
[69]DiMaggio, F.L., Sandler, I.S. Material model for granular soils. Journal of Engineering Mechanics Division,1971,97(EM3):935-950
[70]Resende, L., Martin, J.B. Formulation of Drucker-Prager cap model. Journal of Engineering Mechanics,1985,111(7):855-881
[71]Vermeer, P.A. A double hardening model for sand. Geotechnique,1978,28(4):413-433
[72]Nova, R. On the hardening of soils. Archives of Mechanics,1977,29(3):445-458
[73]Jefferies, M.G. Nor-sand:a simple critical state model for sand. Geotechnique,1993,43(1):91-103
[74]Pastor M., Zienkiewica O.C., Chan, A.H.C. Generalized plasticity and the modeling of soil behavior. International Journal for Numerical Analytical Methods in Geomechanics,1990,14:151-190
[75]Mroz, Z. On the description of anisotropic work hardening. Journal of the Mechanics and Physics of Solids,1967,15:163-175
[76]Dafalias, Y.F., Popov, E.P. A model of nonlinearly hardening materials for complex loading. Acta Mechanica,1975,21:173-192
[77]Dafalias, Y.F. Bounding surface Plasticity(Ⅰ):Mathematical foundation and hypo-plasticity. Journal of Engineering Mechanics,1986,112(9):966-987
[78]王志良.塑性力学与土的性质模拟.塑性力学和地球动力学文集,北京：北京大学出版社,1990：23-29
[79]架茂田,吴兴征,李相裕.堆石料的亚塑性边界面模型及其验证[J].岩石力学与工程学报,2001,20(2)：164-170
[80]沈珠江.粘土的双硬化模型[J].岩土力学.1995,16(1)：1-8
[81]刘元雪.含主应力轴旋转的土体一般应变关系[D].解放军后勤工程学院.1997.
[82]沈珠江.三种硬化理论的比较[J].岩土力学,1994,15(2)：13-19.
[83]沈珠江,关于破坏准则和屈服函数的总结[J].岩土工程学报,1995,17(1)：1-8
[84]沈珠江.几种屈服函数的比较[J].岩土力学,1993(1).
[85]沈珠江.土体弹塑性变形分析中的几个基本问题[J].江苏力学论文集.河诲大学出版杜,1994.1-10.
[86]渡家骤,李广信.土的本构关系及其验证与应用[J].岩土工程学报,1986,1.8(1)：312-386.
[87]殷宗泽.一个土体的双屈服面应力-应变模型[J].岩土工程学报,1988,10(4)：64-71.
[88]郑颖人.土的多重屈服面理论与模型.塑性力学和细观力学文集,北京：北京大学出版社,1993：75-84
[89]耿黎明.混合遗传算法在初始地应力场反分析中的应用研究[M].武汉大学,2002
[90]王靖涛,杨毅,张曦映.考虑应力路径的砂土的神经网络本构关系模型[J].岩石力学与工程学报,2002,21(10)：1487-1489.
[91]任青阳,王靖涛.等主应力比路径下砂土弹塑性本构关系的数值建模[J].华中科技大学学报(市科学版).2005,22(3)：69-71.
[92]Naki T. An isotropic hardening elastoplastic model for sand considering the stress Path dependeney in the three-dimensional stress. Soils and Foundations,1989,29(1):119-137
[93]Matsuoka H, Sun DA, Konde T. A constitutive law from frictional to cohesive materials[A]. X III ICSMFE[C]. New Delhi:[s.n.].1994.403-406.
[94]Matsuoka H., et al. A constitutive equation for sands and its application to analyses of rotational stress path and liquefaction resistanee.Soils and Foundations,1985,25(1):27-42
[95]Nakata, Y, etal. Flow deformation of sands subjected to principal stress rotation. Soils and Foundations,1998,38(2):115-128
[96]刘元雪,郑颖人.考虑主应力轴旋转对土体应力应变关系影响的一种新方法[J].岩土工程学报,1998,20(2)：45-47
[97][117]刘元雪,郑颖人.含主应力轴旋转的土体本构关系研究进展[J].力学进展,2000,30(4)：597-604
[98]窦宜,段勇.主应力方向偏转条件下粘性土的变形特性[J].水利水运科学研究,1990(4)：351-366
[99]姜洪伟,赵锡宏.主应力轴旋转对软土塑性变形影响分析[J]上海力学,1997,18(2)：140-146
[100]陈生水,沈珠江，郦能惠.复杂应力路径下无粘性上的弹塑性数值模拟[J]岩土工程学报,1995,17(2)：20-28
[101]史宏彦,谢定义,汪闻韶.平面应变条件下主应力轴旋转产生的应变[J].岩土工程学报,2001,23(2)：162-166
[102]Matsuoka H. Constitutive equation and FE analysis for anisotropic soil. In:Yamada Y ed. Proc of 4th Int Conf on numerical Methods in Geomechanics.1982.223-233
[103]Hong, W. P.and Lade, P. V.. Strain increment and Stress Directions in Torsion Shear Tests. J. Geo.Eng.1989,115(10)：1388-1401
[104]Nakai T, Matsuoka H. A generalized elastoplastic constitutive model for clay in three-dimensional stresses. Soils and Foundations 1986,26(3),81-89,
[105]姚仰平,罗汀.新的变换应力空间及其应用.见：栾茂田主编.第七届全国岩土力学数值分析与解析方法会议论文集.大连：大连理工大学出版社,2001.16-20
[106]姚仰平,孙凯,路德春.岩土材料塑性应变增量方向的确定[J].力学学报,2007,39(5)692-698.
[107]向大润.土体弹塑性理论加卸载准则和计算模型探讨[J].岩土工程学报,1983,5(4)：78-91
[108]Kiousis P D. Strain space approach for softening plasticity[J].ASCE.J.Eng.Mech.l987,113(2):
210-221.
[109]Wang Zhi-liang,Yannis F D,Shen Chi-kang. Bounding surface hypoplasticity model for soil[J].ASCE.J.Eng. Mech.1990,166(5):983-1001.
[110]Zienkiewicz O C.广义塑性力学和地力学的一些模型[J].应用数学和力学,1982,3(3)：267-279.
[111]杨光华,介玉新,李广信,等.土的多重势面模型及其验证[J].岩土工程学报,1999,22(5)：578-582
[112]介玉新,胡韬,李广信,等.平面应变情况下多重势面模型与邓肯-张模型的比较[J].工程力学,2004,21(1)：148-152
[113]介玉新,刘正,杨光华,等.基于应力空间的多重势面模型及其与邓肯-张模型的比较[J].岩土力学,2004,25(增)：7-12
[114]刘正,介玉新,杨光华,等.应力型多重势面模型及其参数求取的改进[J].长江科学院院报,2006,23(1)：31-34
[115]郑颖人.岩土的多重屈服面理论与应变空间理论.岩石力学新进展,沈阳：东北工学院出版社,1989.
[116]殷有泉,曲圣年.弹塑性耦合和广义正交法则[J].力学学报,1982,(1)
[117]程展林等.围堰填料的应力应变关系试验研究.长江科学院,1995
[118]沈珠江,采百家之长、酿百花之蜜——岩土工程研究中如何创新[J].岩土工程学报,2005,27(3)：365-367
[119]沈珠江.当前土力学研究中的几个问题[J].岩土工程学报,1986,8(5)：1-8.
[120]沈珠江.从学步走向自立的岩土力学[J].岩土工程界,2003,6(12)：15-17.
[121]冯卫星,常绍东,胡万毅.北京细砂土邓肯-张模型参数试验研究[J].岩石力学与工程学报,1999,18(3)：327-330
[122]杨林德,张向霞.剑桥模型可反映剪切变形的一种修正[J].岩土力学,2007,28(1)：7-11
[123]邱斌,徐志伟.中主应力对邓肯-张模型影响的真三轴试验研究[J].岩土工程技术,2002,1：45-47
[124]Janbu,N. Soil compressibility as determined by Oedometer and triaxial tests[A], Proc. European Conf. On Soi&Mech.&Foud. Engrg. N.1963.
[125]Kulhawy F H, Dunean J M. Stresses and movements in Oroville dam. Journal of soil Meehanies and Foundation Division, ASCE.1972,98(SM7):653-665.
[126]陈正汉.岩土力学的公理化理论体系[J].应用数学和力学,1994,15(10)：901-910.
[127]殷宗泽、朱俊高、卢海华.土体弹塑性柔度矩阵与真三轴试验研究.第七届土力学与基础工程学术会议论文集,中国建筑工业出版社,北京,1994年10月,139-144
[128]沈珠江.理论土力学[M].中国水利水电出版社,北京,2000年5月
[129]殷宗泽,卢海华,朱俊高.土体的椭圆-抛物双屈服面模型及其柔度矩阵[J].水利学报,1996,12：23-28
[130]窦宜,关于塑性势问题的讨论,岩土工程学报,1981年第2期,75-76
[131]窦宜、盛树馨、施艳平,轴对称条件下饱和粘土的变形特性,水利水运科学研究,1986年第2期,l-12
[132]盛树馨、施艳平,伸长应力条件下正常固结粘土的变形特性,水利水运科学研究,1985第4期,97-104
[133]Anandarajah. Incremental Stress-Strain Behhavior of Granular Soil[J]. Journal of Geotechnical Engineering,1995, January 121 (1):57-68.
[134]李广信.土的三维本构关系的探讨与模型验证[D].清华大学,1985
[135]沈珠江.科学家不应只是解释现象——关于岩土本构理论研究方向的评述[J].岩土工程学报,2005,27(12)：1494-1495
[136]Collins IF, Houlsby GT. Application of thermomechanical principles to the modeling of geotechnical materials. ProcR Soc Lond, A,1997,453:1975-2001
[137]Lade PV, Kim MK. Single hardening constitutive model for soil, rock and concrete. International Journal of Solids and Structures,1995,32(14):1963-1978
[138]Yao YP, Sun DA. Application of Lades criterion to Cam-Clay Model. Journal of Engineering Mechanics, ASCE,2000,126(1):112-119
[139]Wbod DM. Soil Behavior and Critical State Soil Mechanic. Cambridge, UK:Cambridge University Press,1990
[140]Collins I F, Kelly P A. A thermomechanical analysis of a family of soil models[J]. Geotechnique, 2002,(7):507-518.
[141]张建民.砂土的可逆性与不可逆性剪胀规律[J].岩土工程学报,2000,22(1)：12-17.
[142]陆培炎,陈韶永,熊丽珍等.水坠坝冲填土弹塑性本构方程[J].岩土工程学报,1984,6(2)：23-39
[143]Lambe T W. A mechanistic Picture of shear strength in clay. Research conference on shear of cohesive soils,1960.
[144]Taylor D W. Fundamentals of soils mechanics.1948
[145]吴春秋.非线性有限单元法在土体稳定分析中的理论及应用研究[D].武汉大学,2004,4
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