ABSTRACT:

Fracture initiation and propagation modelling of poroelastic medium has a vast practical application such as extraction of oil and natural gas by hydraulic fracturing, dam failure due to high fluid pressure and a lot more. This has led to an increased attention among the researchers to model fracturing in geomaterials. However, modelling this process in standard FEM is a challenging task as the rock deformation and pore fluid pressures are coupled, it involves a lot more degrees of freedom per node compared to a deformation analysis of dry rock. On the other hand, fracture propagation with standard finite element method is a highly computationally expensive technique, which involves the remeshing of the fracture domain after every time increment. This paper adopts the XFEM technique to study the effects of rock stiffness on the behaviour of fracture propagation in a saturated rocks mass, and the pore pressure variation in to the crack tip region. The finding shows a negative pore pressure distribution in to the fracture process zone, and increased length of fractures for stiffer rocks.

1. Introduction

The fluid-driven fracture propagation in the saturated porous medium is being studied for a long time. This technique is mostly used in hydrocarbon extraction from subsurface rocks. Analysing the stress-deformation conditions deep underground through field and laboratory investigation is often not feasible and therefore numerical techniques preferred to be adopted. The pore fluid plays an essential role in the mechanics of geomaterials. Therefore the numerical formulation, in this case, should also consider the coupling between deformation and pore pressure. Solutions for these sort of coupling equations can be achieved possibly in four different ways namely fully coupled, iteratively coupled, explicitly coupled and loosely coupled solutions (Armero, 1999, Minkoff, 2006, Massimiliano et al., 2010, and Kim et al., 2011). Among these solutions, the fully coupled solutions technique is unconditionally stable but with a higher computational effort. The finite element is one of the most suitable and widely accepted numerical methods for solving hydromechanically coupled domain problems (Zienkiewicz et al., 1999, Khoei, 2014). The accuracy of this method depends upon the polynomial approximation for the degrees of freedom (DOF). In the case of fracture propagation problems, when there are discontinuities in the field variable (displacement) or singularities in the crack tip zone, getting an optimally accurate solution may need the re-meshing of the domain after every time step of fracture evolution in the standard finite element method, therefore, the system matrix will be reconstructed every time, which will make this a computationally expensive method to adopt. On the other hand with the extended finite element method (XFEM) this problem can be resolved by choosing an extra set of DOF which will take care of the displacement part due to discontinuity. The number of DOF will be increased for those nodes whose basic function is cut by the crack. However implementing this technique into the already written standard finite element codes (e.g. Abaqus) are not easy, as the degrees of freedom per node will be varying, some nodes with enriched DOF and some without, different element matrix will have different dimensions (Belytschko et al., 2013). To overcome this issue, the enrichment DOF are added to some additional nodes which are called phantom nodes (Song et al., 2006). Only the elements with the fracture cut will have these phantom nodes activated. In this present work, an attempt is made to study the effect of stiffness on the pore pressures at the near crack tip zone considering the cohesive zone model (CZM) with maximum principal stress criterion as the fracture propagation mechanism. It has been tried to incorporate the XFEM technique for fracture propagation in the hydromechanically coupled rock.

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