Soil Constitutive Models Based On Energy Dissipation

Traditional constitutive models of soils may be divided into two groups. One is experiential models obtained by fitting experimental data, which aim at improving fitting precision, and are short of holding the essential characters of strain-stress relations for geomatenals. The other is theoretic models, which comprise several elementary factors (yield condition, flow rule and hardening law) of classical plastic, and base on Drucker Postulate and the theory of plastic potential. Generally, these factors are determined independently and contradict each other sometimes, which results there is probability of violating thermomechanics laws under some stress paths. To avoid these differences, soils constitutive models based on energy dissipation and its applications are discussed in this paper, which starts from the thermomechanics laws directly.The elementary theories and general procedure of constituting models based on thermomechanics laws are introduced. A proper energy dissipation function is studied and the yield function in dissipation stress space is deduced. The flow rule in dissipation space is determined in terms of Ziegler orthogonality principle. Shift stress and elastic rule come from free energy function. Then the yield function and the flow rule in true stress space are deduced by the shift stress. Combined the hardening law, a complete constitutive model is built.Referring the isotropic dissipation function presented by Collins, an isotropic constitutive model is established. The spans of model parameter are analyzed in terms of reasonable shape of yield locus. The parameters can be determined by fitting the triaxial test data, and the genetic algorithm is adopted in the fitting process. According to the obtained parameters, a group of drained triaxial tests are computed, and then the relation curves of shear stress invariant, shear strain and volumetric strain are plotted and compared with the experimental results to verify the validity of the model. The results of the isotropic model are better than that of modified Cam-clay.The anisotropic model is set up by extending the isotropic model. Dissipation function of the isotropic model is modified and added a variable to denote the inclination of yield locus. The rotation of yield locus in true stress space is described via the rotational hardening law to embody the anisotropy. Similar to the isotropic model, the effects of variable model parameters on yield locus, the relations among parameters, and the spans of parameter are discussed. Employing the genetic algorithm, the model parameters are identified by fitting the data of triaxial drained test. Then the parameters obtained were used to calculate the drainedtest curves for other consolidated pressures conditions, and these curves were compared with observed data in corresponding cases. It shows that the results are satisfying and the anisotropic model is better than the isotropic model.In drained triaxial test, loose sands contract while dense sands dilate. In undrained triaxial test, the effective stress paths of loose sands and dense sands are different The different deformation curves of loose sands and dense sands can be simulated in unified ways by introducing the dependence of dilatancy on material state, and two feasible methods are presented. The critical state line in e-p' plane suggested by Li is used to define state parameter as the difference of current void ratio and corresponding critical void ratio.The first method is modifying the dissipation function of isotropic model, and the state parameter distinguishing loose sands and dense sands is introduced to yield equation to set up the modified isotropic unified constitutive model, which covers the effect of material state on stress-strain relations. The simulative capability is shown by computing different features under various initial densities and confining pressures in triaxial undrained shear test, using the modified isotropic unified constitutive model with a unified set of model parameters and the hardening law suggested.The second method is introducing the initial state parameter into the anisotropic rotational hardening law to build the combined unified constitutive model. Analyzed the constitutive relations and stress paths, it is proved qualitatively and validated by samples that the deformation characteristics of loose sands are described properly by the isotropic model, while the anisotropic model is suit for the deformation curves of dense sands. They are incorporated by the rotational hardening law involving initial state parameter to simulate the two types of deformations for the sands. The parameters can be determined by fitting a part of triaxial test data of Toyoura sand, and then the residual triaxial curves are computed. The results tally with the experimental data. The developments of shear friction angle and dilation with deformations accord with the common trend of loose sands and dense sands, and the relation between peak friction angle and initial state parameter consist with the test data reported by Been and Jefferies.Based on the isotropic model, an approach aiming at unloading and reloading response is discussed. The general curves of unloading and reloading can be computed by modified hardening laws in unloading and reloading stage.