A series of numerical simulations has been done to reproduce the experimental observations made on gypsum specimens with two and three flaws, loaded in uniaxial compression. The flaws can be either open or closed (frictional flaws). The simulations are aimed at comparing the type of crack that initiates from the flaws, either tensile or shear, the direction and stress of initiation, the type of coalescence, if any, and the stress at which coalescence occurs. The code FROCK, based on the Displacement Discontinuity Method (DDM), is used for the simulations. Two initiation criteria have been implemented into the code: the maximum stress criterion and the critical energy release rate criterion. The two criteria have been expanded, from their initial formulation for tensile cracks, to incorporate initiation of shear cracks. The two initiation criteria give similar results. Predictions of initiation of wing (tensile) and secondary (shear) cracks made with the model are in good agreement with experiments. The numerical code is also capable, with some limitations, of duplicating the coalescence types and stresses observed in the experiments.
Extensive research has been done on fracturing processes on rocks and rock-model materials in compression. Although there are some differences in the crack patterns observed in compression depending on the materials used, two types of cracks are commonly found from a pre-existing fracture: wing cracks and secondary cracks. Wing cracks are tensile cracks that initiate at or near the tips of a flaw (the terms preexisting fracture and flaw will be used interchangeably) and propagate in a stable manner in the direction of maximum compression. The surface of wing cracks is characterized by a plumose structure, which is typical of tension cracks, and by the complete absence of pulverized material, which indicates the absence of shearing. Secondary cracks are shear cracks that initiate from the tips of a flaw and propagate in a stable manner. The surface of shear cracks is very rough and composed of crushed material. Shear cracks initiate in two different directions: coplanar or quasi-coplanar and oblique to the flaw [1, 2]. Crack coalescence occurs by the linkage of two flaws through a combination of tensile and/or shear cracks. Although there are numerous crack initiation criteria for mixed mode loading (i.e. both mode I, tensile, and mode II, shearing), most of them are fundamentally based on one of three theories: the maximum tangential stress theory , the maximum energy release rate theory  and the minimum energy density theory . The three theories have been used to estimate the direction of tensile cracks and give reasonable predictions for open flaws. However, they cannot reproduce shear cracks. The F-criterion  and the maximum stress criterion  have been successfully used to predict both tensile and shear cracks. However the criteria are either semiempirical  or are based on semi-empirical parameters . A new criterion is explored based on the critical energy release rate. The advantage of the new criterion is that it is based on fundamental material properties and provides a consistent formulation for both tensile and shear cracks.