Constitutive models for unsaturated soils. A thermodynamic approach
(English) Unsaturated soils are particular instances of porous materials, which are characterized by a solid skeleton and a number of fluids that can move through the skeleton. At the microscale, a porous material is made of interacting entities of various dimensions (3D phases, 2D interfaces, 1D co...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/692241 |
| Acceso en línea: | http://hdl.handle.net/10803/692241 https://dx.doi.org/10.5821/dissertation-2117-415063 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Enginyeria civil 624 |
| Sumario: | (English) Unsaturated soils are particular instances of porous materials, which are characterized by a solid skeleton and a number of fluids that can move through the skeleton. At the microscale, a porous material is made of interacting entities of various dimensions (3D phases, 2D interfaces, 1D common lines, 0D common points), which contain various species (mineral, water, air, …). If representative volume elements (REV) can be defined, averaging yields a set of macroscale interacting continua, which can be modeled using mixture theory. After averaging, the microscale geometric features of the entities and the microscale distributions of thermodynamic properties within the entities are lost. In order to recover part of this information, macroscale geometric variables (e.g. volume, area, length or number of points of each entity in the REV) and macroscale density variables (e.g. mass of each species in each entity in the REV) are defined. Additional macroscale variables can be defined in order to characterize the anisotropy of the porous material (e.g. structure tensors). The state of a porous material is assumed to be given by the deformation of the solid skeleton, the measure (volume, area, length, number of points) of each microscale entity in the REV, the mass of each species in each microscale entity in the REV, the temperature and a set of internal variables. The number of state variables can be significantly reduced by assuming that the evolution of the porous material is along local equilibrium states. These states are such that, for prescribed values of the strain tensor of the solid skeleton, the total mass of each species per unit reference volume, the temperature and the internal variables, the measure of each microscale entity in the REV and of the mass of each species in each microscale entity in the REV take unique values, such that the total free energy per unit reference volume is minimum. As a result, the state of a porous material is given by the strain tensor of the solid skeleton, the total mass of each species per unit reference volume, the temperature and the internal variables. The constitutive model of a porous material is derived using the framework of thermodynamics with internal variables, in which the porous material is considered to be an open thermodynamic system. The state equations are derived from the free energy and the evolution equations of the internal variables are derived from the dissipation or a dissipation potential. For unsaturated soils, additional simplifying assumptions are made: (1) small strains of the solid skeleton; (2) isothermal atmospheric conditions; (3) three species: solid mineral, water and gas; and (4) elastoplastic response of the deformation of the solid skeleton and of the water mass content. In some soils short-range interaction forces bond water to the solid skeleton. Vicinal water is bond to the solid skeleton, whereas free water is not. The behavior of free water is as if it were outside the soil, so that microscale pressure distributions are uniform (neglecting gravity), so that chemical potentials and temperature allow to define a macroscale pressure. In contrast, the behavior of vicinal water depends on the interaction forces, so that microscale pressure distributions are not uniform. The behavior of a soil is assumed to be given by three different regimes: (1) saturated (fixed vicinal water, variable free water, no gas phase); (2) capillary (fixed vicinal water, variable free water, gas phase), with an hysteretic water retention curve; and (3) dry (variable vicinal water, no free water, gas phase). At each of these regimes a different constitutive model for the soil is used. Generic examples of these models are given: elastoplastic for the saturated regime, elastoplastic with water content hysteresis for the capillary regime and elastoplastic for the dry regime. |
|---|