ABSTRACT
Figure 1: An experimental axial stress-strain curve for dry Berea sandstone under uniaxial strain showing small-amplitude unloading cycles together with curves derived from the integration of small-strain elastic moduli derived from unloading cycles and seismic velocities. During the nucleation and growth of cracks, frictional sliding along favorably oriented grain boundaries and closed cracks constitute crack-closing tractions that resist crack displacements, thereby, reducing the energy available for extensile microcrack growth and effectively stabilizing the system. Similar frictional stabilization effects have been recognized as a toughening mechanism in brittle ceramics [23]. The magnitude of this effect is likely to be large given the amount of hysteresis typically observed during the failure of a rock, but has yet to be quantified. In porous rocks loaded with moderate confining stresses, frictional sliding plays a significant role in the process of shear-enhanced compaction which is a combination of particle crushing followed by readjustment of the subparticles by sliding and rotation. In the post-failure (localization) regime, strength and deformation characteristics of rocks are thought to be controlled by sliding along several well developed macrocracks [7, 3]. While it is clear from this discussion that there is sufficient evidence to postulate that friction across grain boundaries, microcracks and macrocracks
influences the overall deformation and strength of rocks, additional theoretical work is needed. 4 Micromechanical modeling
Because of the basic similarity in rock deformation and failure under compression in a wide variety of rock types, it is not surprising that the various micromechanical failure processes in crystalline and clastic rocks have many similarities [24]. Kemeny and Cook [25] have demonstrated that the various micromechanical models for extensile microcrack growth (sliding crack, pore squeezing, point loading, dislocation pile-up, grain bending, etc.) share the following similarities: 1. Crack growth occurs predominantly in the 61 direction. 2. KI proportional to a size parameter, such as pore or grain size, initial crack length, etc. 3. Unstable growth occurs initially when the crack length is close to the size parameter. 4. Stable crack growth occurs when the crack length is much larger than the size parameter. 5. KI decreases rapidly with increasing 62. 6. KI is linearly proportional to 61-C62, where C is a constant. 7. Non-interacting microcracks produce only strain-hardening and crack interaction is required to produce strain-softening. These similarities may explain the success of certain micromechamcal models, such as the sliding crack model, in spite of the lack of evidence for these models in laboratory studies.
