Constitutive Model Of Soil Based On Generalized Potential Theory And Its Preliminary Application

The constitutive model of soils is the basic equation of the modern soil mechanics, and the study on it has important significance for the development of the modern soil mechanics. At present, most of the theories which used to establish the constitutive model of soils are based on the traditional theories for metal materials. However, the mechanical properties of soils and metal materials are very different, which makes the direct application of the traditional theories on the constitutive model of soils exist great limitation. Even though making some modifications based on the traditional theories, the limitations also exist due to some basic assumptions in the traditional theories.The generalized potential theory, in wihch the constitutive model of soils is created directly by mathematical methods, and the deficiencies in the traditional theories for metal materials can be overcomed and the traditional theories can be regarded as its special cases. It gives a new theory to the study of constitutive model of soils. Meanwhile, due to the complexity of the mechanical properties of soils, many problems need further study. Therefore, according to the major problems in the present study of constitutive model of soils, some research works are carried out based on the generalized potential theory in this paper, and several constitutive models of soil are established and applied. The main contents and conclusions are summarized as follows:(1) The ansysis of mathematical essential of the traditional potential theories based on the generalized potential theory shows that the traditional potential theories are actually coordinate transformation under certain assumptions, and they can be regarded as special cases of the generalized potential theory. What is more, further analysis shows that the traditional potential theories can not describe the non-uniqueness of the direction of plastic strain increment and the non-coaxiality of soils, while the generalized potential theory can give a new theory to the study on these problems.(2) Aiming at the fuzziness brought by the energy equation hypothesis in the Cam-clay model, a similar Cam-clay model was established by mathematical methods base on the generalized potential theory. Parameters of the similar Cam-clay model can be determined as conveniently as the Cam-clay model, and the mathematical principle of similar Cam-clay model is more clear. Meanwhile, by introducing a new parameter, the similar Cam-clay model can describe the dilatancy of soil. The results of test verification show that the calculated results of the similar Cam-clay model agree well with test ones and the dilatancy of sand can also be described, which are better than the calculated results of Cam-clay model and the modified Cam-clay model.(3) Aiming at the limitations of the traditional potential theories on describing the non-uniqueness of the direction of plastic strain increment and the non-coaxiality of soils, solutions were proposed acrroding to the quasi-elastic-plastic constitutive model based on the generalized potential theory, in which the traditional plastic strain increment was decomposed into quasi-elastic part and pure-plastic part. The quasi-elastic part obeys elastic rule and the pure-plastic part obeys the traditional plasticity theory, which is reasonable and convenient, and it can also reflect the non-uniqueness of the direction of plastic strain increment and the non-coaxiality of soils. The results of test verification show that the quasi-elastic-plastic constitutive model based on the generalized potential theory can reflect the uniqueness (in high stress level) and the non-uniqueness (in low stress level) of the direction of plastic strain increment of soil simultaneously, and the non-coaxiality of soil during the rotation of principal stress axis can also be reflected, which agree with the actual.(4) Aiming at the limitations of Duncan-Chang model which is based on the generalized Hooke’s law and adopts hyperbola hypothesis, solutions were proposed acrroding to the numerical elastic-plastic constitutive model based on the generalized potential theory, in which parameters can be determined as conveniently as Duncan-Chang model and the dilatancy of soils can also be described. The results of test verification show that the calculated results of the numerieal elastic-plastic constitutive model based on the generalized potential theory agree well with test ones and the dilatancy of soils can also be described, which proves the rationality of the numerieal elastic-plastic constitutive model.(5) Based on FLAC3D, the secondary developments of the similar Cam-clay model and the quasi-elastic-plastic constitutive model and the numerieal elastic-plastic constitutive model based on the generalized potential theory were implemented, and then they were applied to the ansysis of the second stage cofferdam of three gorges project etc. The results of numerical simulation show that, compared to the coaxial model, the quasi-elastic-plastic constitutive model based on the generalized potential theory can reflect the influence of the rotation of principal stresses axis to the deformation of soil. While compared to Duncan-Chang model, the numerieal elastic-plastic constitutive model based on the generalized potential theory can describe the dilatancy of soil and the calculated results of it are more agree with the measured results, which furtherly proves the rationality of the proposed model.