Study On Constitutive Model Of Soil Based On Generalized Potential Theory

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.