A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.
With the development of modern geotechnical engineering practices such as the construction of high level radioactive waste repositories, exploitation and utilization of geothermal resources, energy-saving buildings and underground storage of CO 2 , research into the influence of temperature on the basic mechanical properties of unsaturated soils has become an important issue internationally. By using the work expression and considering the influence of temperature on the basic properties of unsaturated soils, the average soil skeleton stress, modified suction and temperature were selected as state variables of generalized forces in thermodynamics and the soil skeleton strain, saturation and entropy were chosen as state variables of generalized flows conjugate to the variables of generalized forces. Based on the nonlinear multi-field coupled model and by using existing experimental results, an elastic-plastic constitutive model of unsaturated soils under non-isothermal conditions was developed to analyze the influence of temperature on the deformation properties of unsaturated soils. The model was used to predict and analyze the influence of suction and temperature on the deformation properties of unsaturated soils under isotropic conditions, and was successfully verified using experimental results.
The influence of gases on unsaturated soils is discussed in the paper.First,the selection of stress state variables is discussed.It is shown that gas pressure as well as generalized effective stress and modified suction are required to construct a constitutive model of an unsaturated soil.The deformation mechanisms of solid,liquid and gas phases in soils are then investigated.It is realized that the deformation of gas phase interacts with the deformations of the other two phases in soils.Gas laws are used to describe the gas behavior.Similar to the other two phases in soil,the change of gas volume can be divided into an elastic part and a plastic part, and the latter part is then introduced to the soil hardening equation to reflect the impact of the gas on the soil.Then,a simple elasto-plastic model considering the gas effect for isotropic states is developed.Finally,the model predictions are given and compared with existing experimental data.A good agreement between them is found.Comparisons of the predictions between our model and Wheeler’s model are also performed.
