SUMMARYThis paper describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

Modeling hydraulic fracturing in the presence of a natural fracture network is a challenging task, owing to the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and existing natural interfaces. Understanding these complex interactions through numerical modeling is critical to the design of optimum stimulation strategies. In this paper, we present an explicitly integrated, fully coupled discrete-finite element approach for the simulation of hydraulic fracturing in arbitrary fracture networks. The individual physical processes involved in hydraulic fracturing are identified and addressed as separate modules: a finite element approach for geomechanics in the rock matrix, a finite volume approach for resolving hydrodynamics, a geomechanical joint model for interfacial resolution, and an adaptive remeshing module. The model is verified against the Khristianovich-Geertsma-DeKlerk closed-form solution for the propagation of a single hydraulic fracture and validated against laboratory testing results on the interaction between a propagating hydraulic fracture and an existing fracture. Preliminary results of simulating hydraulic fracturing in a natural fracture system consisting of multiple fractures are also presented. Figure 3. Typical mesh arrangement around a fracture tip. A polar coordinate system is established with its origin at the tip. The reference points used in Equations (13) and (14) are denoted as small circles, whereas alternative reference points shown as diamonds can also be used with modified formulations as elaborated in [24].

SUMMARYIn an effort to study the relation of fabrics to the critical states of granular aggregates, the discrete element method (DEM) is used to investigate the evolution of fabrics of virtual granular materials consisting of 2D elongated particles. Specimens with a great variety of initial fabrics in terms of void ratios, preferred particle orientations, and intensities of fabric anisotropy were fabricated and tested with direct shear and biaxial compression tests. During loading of a typical specimen, deformation naturally localizes within shear bands while the remaining of the sample stops deforming. Thus, studying the evolution of fabric requires performing continuous local fabric measurements inside these bands, a suitable task for the proposed DEM methodology. It is found that a common ultimate/critical state is eventually reached by all specimens regardless of their initial states. The ultimate/critical state is characterized by a critical void ratio e which depends on the mean stress p, while the other critical state fabric variables related to particle orientations are largely independent of p. These findings confirm the uniqueness of the critical state line in the e − p space, and show that the critical state itself is necessarily anisotropic. Additional findings include the following: (1) shear bands are highly heterogeneous and critical states exist only in a statistical sense; (2) critical states can only be reached at very large local shear deformations, which are not always obtained by biaxial compression tests (both physical and numerical); (3) the fabric evolution processes are very complex and highly dependent on the initial fabrics.

SUMMARYThis paper investigates shear strength of granular materials with inherent fabric anisotropy. Most previous studies have described strength of these materials in the principal stress space, and the orientation of the bedding plane with respect to the principal stress directions was used as the reference geometrical descriptor of inherent fabric. The present study has found that it is theoretically more convenient and practically more useful to use instead the inclination angle of the bedding plane with respect to the shear plane for the same purpose. Direct shear tests and biaxial compression tests with different loading directions with respect to the bedding planes were simulated with discrete element method (DEM) models consisting of ellipse-shaped particles. Key mechanical behaviors of natural sands reported in the literature were successfully captured in the numerical simulation. A shear failure criterion was determined as a function of the inclination angle based on the direct shear simulation results, and was used to successfully predict the results of the biaxial compression simulations. Microstructural inspection of deformation and strain localization of the biaxial compression simulations found that the proposed shear failure criterion can reasonably predict the orientations of the initial failure planes. It was also discovered that shear bands in directions conjugate to the initial failure plane orientations can develop and dominate specimen deformation at larger strain levels. Considering the availability of biaxial compression test equipment and historical data, two methods for back-calculating inclination angle-dependent shear strength from biaxial compression results were proposed, and validated using DEM simulation results.

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SUMMARYThis study focuses on non-coaxial flow behavior of cohesionless soil undergoing cyclic rotational shear, with a special interest in the effects of particle-scale characteristics. To this end, we perform a series of 2D discrete element simulations with various particle shapes, inter-particle coefficient of friction, initial density, and stress ratios. The validity and efficacy of the numerical model is established by systematically comparing numerical simulation results with existing laboratory testing results. Such comparison shows that the numerical simulations are capable of capturing mechanical behavior observed in laboratory testing under rotational shear. We further demonstrate and quantify a strong yet simple relationship between the deviatoric part of the normalized strain increment and the non-coaxial angle, denoted by Δε ð Þ R q and ψ, respectively. This quantitative correlation between ψ and Δε ð Þ R q is independent of applied stress ratio, initial and current void ratio, and the number of cycles applied, but dependent on the principal stress orientation and particle-scale characteristics. At the same Δε ð Þ R q , specimens with higher inter-particle friction angle or smaller particle aspect ratio show greater non-coaxial angles. A simple model ψ ¼ 45 ∘ m Δε ð Þ R q is able to fit this ψ-Δε ð Þ R q relationship well, which provides a useful relationship that can be exploited in developing constitutive models for rotational shearing.

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