Numerical investigations for hydraulic fracturing in heterogeneous geomaterials

Predicting the load bearing capacity of solid rock masses and their failure behaviour due to fracture growth under mechanical loading is an important subject in a wide range of geotechnical problems. Sometimes fractures can also initiate and develop because of an increase in pore pressure inside porous media, and this is known as hydraulic fracturing. This phenomenon is of high significance for its diverse applications in geoengineering problems. Experiments have been conducted to investigate the problem of fracture propagations in rocks. Closed-form solutions based on the theories of elasticity and plasticity have also been offered for some simple problems of rock fracturing. However, both analytical solutions and experiments have limitations in various aspects. The experimental set-up may be restricted by complex boundary/loading conditions, or the opaqueness of rocks may not allow the observation of the internal details of fracture evolution. Furthermore, due to the heterogeneity of rock masses, it is not easy to obtain a closed-form analytical solution for fracture initiation and propagation when the rock specimen is subjected to complicated boundary/loading conditions. In recent decades, numerical simulation has become popular as an alternative/complementary method to experimental tests, empirical relations or exact analytical solutions for the evaluation of fracture behaviour in rock masses. Incorporating the principals of damage mechanics into the framework of the finite element method (FEM) is one of the numerical algorithms adopted for such an assessment. Unlike fracture-mechanics-based FEM, this approach does not require the remeshing of the model geometry. The fracture propagation route does not need to be pre-known, as is the case for many finite element models involving cohesive elements. Furthermore, the mutual effects of fracture branches on each other can be captured at any moment by using this method. Nevertheless, most of the works following this approach are limited to 2D problems, and in many cases simplifying assumptions have been made, which restricts their applications to specific circumstances. The first objective of this study is the development of a finite element algorithm that is capable of simulating fracture initiation and propagation in heterogeneous rock masses. A FORTRAN code is written in the UMAT user-subroutine interface of ABAQUS, as powerful, finite-element-based commercial software. The performance of the proposed numerical model is then validated against experimental results in the literature, followed by conducting parametric studies on the fracture propagation and coalescence in numerical samples containing one or two pre-existing fissure(s) in a 2D space. Afterwards, this FORTRAN code is upgraded to suit the simulation of 3D fracture propagation. The reliability of the 3D numerical algorithm is discussed in terms of the calibration of the material model parameters by performing parallel executions for the reproduction of the previously experimental results for 3D rock fracturing in the literature. Further numerical simulations for 3D fracture propagation and coalescence in cylindrical models containing two parallel fissures are also undertaken and discussed. Meanwhile, both the effect of the heterogeneity level and the confining stress on the load bearing capacity of models and fracture growth are numerically investigated in 2D and 3D spaces. In addition, the simulation of fracture propagation in a coupled fluid/solid medium is a sophisticated problem in geomechanics. The numerical codes developed for the analysis of pure solid rock masses serves as a basis for the numerical modelling of hydraulic fracturing, which is the second objective of this study. To achieve this objective, the evolution of the permeability of rock with the stress and damage states is incorporated into the FORTRAN codes using the USDFLD user-subroutine of ABAQUS. Coupled analyses are undertaken by solving the equilibrium and transient fluid conservation equations simultaneously. In the meantime, the change in the saturation degree of the medium with a negative pore pressure can be considered. The transient fluid and partially-saturated conditions are together shown to play key roles in the realistic simulation of hydraulically-driven fractures under a high ratio of pressurisation rate to hydraulic conductivity of the medium. The problem of hydraulic fracturing is numerically investigated with respect to several input parameters in 2D and 3D spaces. The numerical results show good agreement with those of the available experimental results in the literature, both quantitatively and qualitatively.