A Constitutive Model For Soils Considering Complex Stress Paths Based On The Generalized Nonlinear Strength Theory

Complex stress states widely exist both in nature and in engineering. Recently, the stress-strain relationship and the strength of materials under complex stress states have been pushed into spotlight. Based on the test data of various materials obtained by many scholars in their researches, a Generalized Non-linear Strength Theory (GNST) is proposed; meanwhile, the application of GNST into the transformed stress spaces is also given. A viewpoint that the stress-strain relationship of soils under two sufficiently close loading stress paths are approximately same with each other is proposed during the research of soil under complex loading conditions. Based on the above ideas, a constitutive model for soils which takes complex stress paths into account is established and this model can be used successfully into cyclic loading condition by defining a new loading/unloading criterion.The main achievement in this dissertation: (1) A theory, namely the Generalized Non-linear Strength Theory (GNST). (2) A model, namely the constitutive model for soils considering complex stress paths.Generalized Non-linear Strength Theory (GNST): The basic properties of GNST are listed as follows. (1) GNST has a unified mathematical form and relevantly fewer material parameters (only four parameters are needed in above theory), all of which have obvious physic significance. (2) GNST can be applied to describe the general strength behavior of materials like soils, concrete and rocks, including different extended and compressive strength and effect of hydrostatic pressure, intermediate principal stress and cohesion. (3) GNST could evolve back to some famous failure criteria and strength theories, such as SMP and Mises criterion which can be regarded as special cases of GNST. (4) Its validity can be confirmed by some existing well-known experimental data. (5) GNST owns continuous smooth failure plane in the principal stress space and can be conveniently applied into numerical analysis when it is combined with the transformed stress method.GNST should have a broad perspective for application, compared with other present criteria, because of its powerful function and theoretical significance. On the one hand, GNST could describe the failure behavior of materials like soils, rocks, concrete and metal as a failure criterion; on the other hand, GNST could be used to research the behavior of deformation for soils and concrete as a yield criterion. GNST has a continuous and smooth failure plane in the principal stress space, which results in a better convergence in numericalsolution.Constitutive model for soils considering complex stress paths: According to the mechanics behavior of sands, a constitutive model is established, which takes the following points into consideration. The first, this model, as a tool for solving engineering problems, is assumed that the principal purpose is to model the basic constitutive behavior of soils. So, simplicity will be of overriding importance. The second, the major requirement of the model is that it should, to large extent, reflect the underlying physical processes of the mechanics of soils. In particular, the parameters describing the soil should have an identifiable physical significance.The main features of this model are shown as follows. (1) This model has eight conventional material parameters in the general cases; especially, to normal consolidated clay, has only five material parameters, which can be defined by some ordinary experiments. (2) This model can reflect the general stress-strain behavior of sands including the non-linear stress-strain relationship, hardening behavior, positive/negative dilatancy, influence of intermediate principal stress on the deformation and strength, and the plastic strain coupled with hydrostatic and shear stress. (3) The stress-strain behavior influenced by complex stress paths can be well predicted. (4) This model can be used in simple loading as well as in cyclic loading. (5) This model can be simplified and used for clays, of which the Modified Cam-Clay (MCC) model can be viewed as a special case. (6) This model can be used to describe three-dimensional stress-strain behavior by combining transformed stress space in the framework of GNST.The stress-strain behavior influenced by complex stress paths is one aspect of compressive hardening features, which can be reckoned as the basic mechanics characteristic of soils. Based on test data, the presented model considering complex stress paths can well predict the stress-strain behavior depended on different stress paths.The relationship among principal stresses of soil under plane strain condition is proposed in appendix.