【作者】 姚捷；

【导师】 杨光华； 何亚伯；

【作者基本信息】 武汉大学 ， 岩土工程， 2010， 博士

【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。更多还原

【Abstract】 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.更多还原