Multiscale modeling of unsaturated granular materials based on thermodynamic principles

The effect of water on the hydromechanical behavior of unsaturated granular materials has been studied with a micromechanical model based on thermodynamic principles. A general framework based on the theory of thermodynamics with internal variables for constructing thermodynamically consistent multiscale constitutive relations for unsaturated granular materials has been developed. Within this framework, the microscopic total Helmholtz free energy has been separated between a mechanical and a hydraulic part, each of which is a function of either the elastic displacement or the capillary bridge volume and the distance between particles at the microscale. The inter-particle dissipation of energy, assumed to be frictional in origin, is a function of the incremental plastic displacements at the microscale. Both the microscale Helmholtz free energy and the dissipative energy have been volumetrically averaged to obtain the homogenized energy functions at the macroscale. In accordance with the suggested multiscale thermomechanical framework, a micromechanical model has been constructed to describe the behavior of partially saturated granular soils. This model has considered the deformation of soil skeleton by applying a Coulomb-type criterion at the inter-particle contacts. The hydraulic potential is made to be dependent on the size of the particles and is derived through use of the expression for the water retention curve by assuming that liquid bridges are isotropically distributed within the specimen. The performance of the suggested model has been demonstrated through numerical simulations of the behavior of sand under various degrees of saturation and a wide range of mechanical loadings.