Multiphysics modelling of desaturation cracks in non-isothermal multiphase porous media

The presented work aims at the development and validation of a general Thermo-Hydro-Mechanical crack phase-field numerical model able to study the nucleation and propagation of cracks induced by thermo-hydro-mechanical effects in multiphase porous materials. Earlier research ([1], [2], [3]) proposed a computational u-p w -d model (displacements, u; water pressure, p w ; crack phase-field, d) for the simulation of liquid water flow, deformation and cracking in isothermal variably saturated porous media. That model assumed the passive gas phase assumption. However, a gaseous phase can play a role in the development of deforming porous materials, e.g. [5], as well as the non-isothermal processes, needing also to consider the phase change of the liquid water in water vapour and vice versa [5]. Hence, a non-isothermal multiphase and multiphysics porous media model including a gas phase composed by dry air and water vapour needs to be formulated and coupled with a fracture model for the solid skeleton. In this work, a new model to describe cracking in variably saturated deformable porous media including heat flow, flows of liquid water and gas and water evaporation/condensation is developed. The porous media model is based on the Hybrid Mixture Theory developed in [5] implemented in [4]. This model is sequentially coupled with the brittle crack phase-field model developed in [1], [2], [3] and is named as u-p c -p g -T-d model in the following (with p c and p g the capillary and gas pressure). The staggered algorithm adopted is summarised in Figure 1. This model is validated by simulating test cases from the literature, including two numerical benchmark tests: (i) a free desaturation test and (ii) the corresponding restrained desaturation one [1], whose results are now presented. (i) is a u-p c -p g problem, known in literature as Liakopoulos test, which is the desaturation of an initially water saturated vertical column of sand. Figure 2(a) presents the comparison between the vertical displacements obtained with the Comes-Geo u-p c -p g -T finite element code [5], [4] and the u-p c -p g -T-d model of Figure 1. The coincidence of the two numerical solutions is displayed. The numerical results obtained by solving the corresponding restrained desaturation test (ii) are presented in Figures 2(b) and 2(c). In this case the vertical displacement of the upper horizonal surface is prevented, to induce traction in the desaturating upper part of the column [1]. Figure 2(b) shows the development of cracks in the upper part of the column within the zone where capillary pressures are formed, Figure 2(c). The u-p c -p g -T-d model of Figure 1 is going to be applied to the simulation of a restrained desiccation test of an initially water saturated clay sample applying a convective thermal boundary condition [4], to simulate more realistically the experimental desiccation test solved in [1] (in which an outgoing water flux boundary condition was applied to simulate the evaporation of the liquid water from the clay sample).