Embedded discontinuity approach for coupled hydromechanical analysis of fractured porous media

Abstract

Summary In this paper, a new continuum approach for the coupled hydromechanical analysis of fractured porous media is proposed. The methodology for describing the hydraulic characteristics invokes an enriched form of Darcy's law formulated in the presence of an embedded discontinuity. The constitutive relations governing the hydromechanical response are derived by averaging the fluid pressure gradient and the discontinuous displacement fields over a selected referential volume of the material, subject to some physical constraints. The framework incorporates an internal length scale which is explicitly embedded in the definition of gradient operators. The respective field equations are derived following the general form of balance equations in interacting continua. The conventional finite element method is then employed for the spatial discretization, and the generalized Newmark scheme is used for the temporal discretization. The proposed methodology is verified by some numerical examples dealing with a steady‐state flow through fractured media as well as a time‐dependent consolidation in the presence of a discontinuity.

On Hydromechanical Interaction during Propagation of Localized Damage in Rocks

“…Most of the past developments dealt with the mechanical response of a single-phase solid and focused on modeling of discrete propagation of the damage in both brittle and frictional materials. Recently, the framework has been extended to include the description of hydro-mechanical interaction [18]. The approach involves imposing a weak discontinuity in fluid pressure as well as a strong discontinuity in the displacement field within the considered referential volume.…”

“…Within the CLED approach, the homogenized constitutive relations governing the hydromechanical response within the referential volume adjacent to the localized region, take the form (cf. [18])…”

“…The finite element mesh contains trilinear isoparametric hexahedral elements for both the displacement and pressure fields (Figure 1). The coupled FE formulation, which employs the embedded discontinuity approach, follows the framework outlined in Reference [18]. The approach is enhanced by updating the permeability tensor in each loading step, cf.…”

Effect of inherent microcrack populations on rock tensile fracture behaviour: numerical study based on embedded discontinuity finite elements

“…Due to its importance in geology and rock engineering, the effect of microcracks on rock under various loading conditions has been widely investigated both experimentally [5,14,16,29,49,52] and numerically [5,11,13,16,18,20,22,25,26,53]. The focus in numerical modelling has been on the effect of microcracks under compression as it is the natural state of bedrock.…”

“…For this reason, FEM has been enhanced or enriched during the last two decades to better describe discontinuities. This research has resulted in two classes of enrichment methods, which are the embedded discontinuity FEM [18,40,41], or EDFEM, and the extended FEM [2,3], or XFEM. EDFEM has the computational/implementational advantage over XFEM that extra degrees of freedom related to the enrichment of the displacement field can be eliminated by static condensation.…”