Although it is recognized that the peak strength of the rock is a unique function of confining stress minus pore pressure (s3 – P), examples of laboratory or numerical studies that focused on investigating the effects of pore pressure on weakening or strengthening the crack damage (CD) stress has received less attention. The objective of this study is to examine, and gain a better insight into the capability of the Grain-based Discrete Element Method (GDEM) approach in mimicking the effect of pore pressure in weakening the peak strength, crack damage threshold (CD) threshold of material. A cohesive crack-based UDEC-Voronoi code is generated considering the real mineral heterogeneity of a crystalline rock. The hydraulic and mechanical properties of the micro-constituents of the model is calibrated. The compressibility and Biot coefficient of the material is determined by applying hydrostatic stress on a square sample. The simulation results demonstrate that like the peak strength, crack damage threshold also follows the “Terzaghi's effective stress law”. The modeling approach is able to evaluate the Biot coefficient of the crystalline rock based on its derived drained and solid matrix bulk moduli.
There is a considerable body of experimental evidence which shows that the failure strength of a wide variety of rocks is a unique function of s3 – P, in which s3 is the total confining stress and P is the pore-fluid pressure. As a result, to a fairly good approximation Terzaghi's effective stress law (s3 = s3 – P) governs the failure strength of porous rocks (Serdengecti and Boozer, 1961, Handin et al., 1963; Murrell, 1965; Robinson and Holland, 1969, Dunn et al., 1973; Byerlee, 1975; Gowd and Rummel, 1977; Paterson and Wong, 2005). An example is given in Fig. 1. That is, in general, the differential stress for fracture strength of a particular rock is approximately the same at the same “effective confining pressure” when the latter is taken to be the total confining pressure minus the pore pressure. In addition to that, according to a series of triaxial compression tests, Brace and Martin (1968) concluded that the law of effective stress holds for fracture strength of crystalline rocks of low porosity (0.1-3 %) such as Westerly granite as long as loading rates are kept below certain critical values in order to maintain the drained loading condition during the test. It should be noted that most experiments support the conclusion that the Biot's coefficient (a) for failure of rocks is unity. And that, the Biot's coefficient for failure processes has no particular connection to the effective stress coefficient (Biot's coefficient) that appears in the theory of linear poroelasticity (Jaeger et al., 2009). As a result, the concept of effective stress coefficient in which the effective stress is equal to difference between the total stress (s3) and effective pore pressure (s.P) only applies for linear elastic deformation of the porous material, not to the non-linear part of the axial stress-axial strain curve. However, the peak strength of materials are governed by Terzaghi's effective stress law in which the Biot's coefficient is considered to be unity.