Linear elastic fracture mechanics is widely used to describe fracture behavior in hard rock, and fracture toughness values for many such rocks are in the literature. The main application has been in hydraulic fracturing. However, hydraulic fracturing operations are now widely performed in unconsolidated and weakly-cemented sandstones or "soft rocks." Soft rocks can have significantly different mechanical behavior than hard rocks, but typically linear elastic models are still applied in these rocks for fracture design purposes. Because of the difficulty of coring and preparing of samples, fracture toughness testing of soft sandstone samples from the subsurface is very challenging. In the study reported here, we assess the fracture mechanics behavior of weakly cemented sandstone numerically with the Discrete Element Method (DEM), in which input parameters are evaluated by comparison with selected elastic and fracture properties. The first step in the study was to carry out the assessment for well cemented Berea sandstone. Mode I fracture toughness was determined using the semi-circular specimen under three-point bending (SCB) test. Further DEM simulations were then run by progressively weakening the bond strength from the reference values determined for Berea sandstone in order to estimate the behavior of weakly-cemented sandstones. The variation of fracture toughness with particle size, notch length, and specimen size is presented and discussed. The assessments of fracture behavior in this study provide a framework of guidelines for fracture mechanics testing and characterization in weakly cemented sandstones.
In hard rock, Linear Elastic Fracture Mechanics (LEFM) is generally used for the analysis fracture propagation. In weakly cemented and poorly consolidated rocks, fracture propagation mechanisms may be complex, including inelastic deformation, disaggregation, and near-tip shear failure. The mechanical behavior of weakly cemented granular materials is strongly influenced by the amount or characteristic of the cement between particles, and several studies have been conducted on the effect of cement on the deformation and failure behavior of sandstones 2].
BernabÃ¨ et al.  created well-consolidated artificial sandpacks using sand and cement material, and measured the variations in strength, dilation and stress-strain behavior with cement content. They observed that small amounts of cement deposited at grain-to-grain contacts had a significant effect on mechanical behavior and strength. Nakagawa and Myer  showed that load-displacement paths for samples with constant porosity were identical for different cement saturation ratios until the grains achieved a certain level of intergranular cohesion. After the critical cohesion was achieved, deformation due to intergranular slip decreased and the deformation behavior became more rock-like than soil-like.
Continuum modeling of inelastic deformation and brittle fracturing of rocks can be classified as an indirect method, where damage is represented by its effect on constitutive relations . The present study employs the Discrete Element Method (DEM), which can be categorized as a direct method, where deformation is represented by explicitly introducing cracks and tracking grain motion. DEM has several advantages over continuum based numerical methods. Instead of the complex constitutive relationships that must be characterized to use continuum methods, DEM traces the motion and interactions of individual particles based on the direct application of Newtonâ??s second law. Particles interact through contacts and bonds with other particles.