Variational modeling of drying induced complex fracture initiation in granular geomaterials
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The driving mechanism behind fracture initiation in granular geomaterials is of great interest in various contexts including desiccation cracking of drying soils, methane gas venting through hydrate stability zones, and cap-rock integrity in carbon dioxide sequestration. When it comes to weakly cohesive granular media, saturated with a wetting fluid and subject to invasion by a non-wetting fluid, it has been evidenced in the case of drying soils [1] that initiation of opening mode fractures occurs due to the action of the fluid-fluid interface in rearranging the grain structure at the drying boundary. Similar observations have also been noted in the context of forced invasion of non-wetting fluid [2, 3, 4]. Quite recently in [5] a continuum-scale model has been proposed that allows to investigate the above mechanism which is in contrast to purely mechanistic tensile stress state-driven fracture opening. In this model the macro-scale energetic counterpart of the pore-scale fluid interfaces, that is the capillary energy, is invoked to drive the dissipation due to the evolution of a scalar damage variable. In the current work, the capillary energy-driven fracturing mechanism is investigated by performing a numerical bifurcation analysis of homogeneous solutions associated with a drying-induced water loss in an a priori saturated soil sample. While homogeneous damage evolution starting at the drying surface represents a diffused zone of degraded porous media, fracture initiation is akin to localization of damage evolution in narrow regions controlled by an internal length. The bifurcation analysis revealed that this possibility is higher with more closely spaced and earlier fracture initiation for relatively shallower sample sizes and for intense drying fluxes, which is qualitatively similar to what has been observed in experiments [6]. To investigate a similar driving mechanism in the case of forced invasion of non-wetting fluid the current model needs to be extended to describe a compressible non-wetting fluid phase, which is one of our future perspectives.