Abstract
New developments of an in-house hybrid code, named Modified Discrete Element Method (MDEM) are presented in the paper. The new developments are on the treatment of pre-existing and propagating fractures in quasi-brittle materials. These developments are the embedment of Linear Elastic Fracture Mechanics (LEFM) and elastic-softening crack band model -based methodologies in the MDEM and their application in lab and reservoir scale. Using the first methodology, MDEM can calculate stress intensity factors, K^{text{I}} and K^{text{II}} using the internal contact forces of particles. K^{text{I}} and K^{text{II}} are calculated independent of boundary conditions and geometrical configuration with acceptable accuracy level. The methodology has been also used in reservoir scale to study the rupture likelihood of faults and fractures due to fluid injection. This methodology enables the code to model mode I and mode II failures and propagation direction based on the fracturing model proposed by Rao et al. (Int J Rock Mech Min Sci 40(3): 355–375, 2003). Using the second methodology, the MDEM can model nonlinear behavior of quasi-brittle materials including or excluding preexisting cracks based on fracture energy. A model was verified against an experiment of a three point bend test with a notch. The numerically obtained force-crack mouth opening curve was reasonably comparable to the experimental test. The analysis was repeated for three other mesh sizes and the results are less mesh size dependent. Finally, it was shown that MDEM has the potential in studying fracture mechanics of quasi-brittle materials both in lab and large-scale investigations.
Highlights
Failure of quasi-brittle materials such as rocks is associated with the localization of strain into a finite band forming macroscopic fracture
The main difference between Modified Discrete Element Method (MDEM) and the regular discrete element method is that the material behaves like a continuum before failure, where the conventional elastic properties are given as input values (Eq (6))
Modified Discrete Element Method (MDEM) and its new developments in fracture problem were presented in the paper
Summary
Failure of quasi-brittle materials such as rocks is associated with the localization of strain into a finite band forming macroscopic fracture. Moon et al (2007) developed a general approach to measure fracture toughness under random packing of non-uniform size particles They used the energy balance approach which is based on the equilibrium state between strain, friction, and kinetic energy as the internal and the total accumulated work done by the loaded boundaries as the external energies. For details about ELFEN the readers are referred to Klerck (2000) and Profit et al (2015) Another known hybrid method is the combined finite-discrete element method developed by Munjiza (2004) and extended by Mahabadi et al (2012) named Y-Geo by improving the limitation of Munjiza’s FDEM such as including a quasi-static friction law, Mohr–Coulomb and rock joints shear failure criterion etc.
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