S U M M A R YThe pervasive damage of rocks by microcracks and voids stron ly affects their macroscopic elastic properties. To evaluate the damage effects, w d derive here the macroscopic stress-strain relations for a 3-D elastic solid with nohinteracting cracks embedded inside a homogeneous matrix. The cracks considered are oriented either perpendicular to the maximum tension axis, or perpendicular to the maximum compression axis. In the first case they dilate during loading and in the second case they contract during loading. We derive a solution for the elastic energy of this rock following the self-consistent scheme of Budiansky & O'Connell ( 1976). The solution describes the stress-strain relations in terms of Ad and pd, which are the modified Lame constants, and an additional parameter y. The latter accounts for the non-linear behaviour of the solid and is related to crack density. The solution predicts a non-linear elastic rheology even for an infinitesimal strain of ~<0.001, and abrupt change in the elastic moduli when the loading reverses from uniaxial compression to uniaxial tension.We use the derived solution to analyse rock-mechanics experiments in which beams of Indiana limestone were deformed under four-point loading. This configuration provides simultaneously the apparent tensile and compressive moduli for small strains. The apparent moduli fit the effective elastic moduli calculated with the present damage model well, including the differences between tensile and compressive moduli.

The slip instability of an earthquake and its abrupt energy release depend primarily on the intensity of strength drop during accelerated fault slip. This process is typically attributed to changes of frictional resistance between two sliding blocks. Here we show that friction changes alone cannot explain observed strength variations of artificial fault zones. Sandstone samples with saw-cut faults and gypsum gouge zones were subjected to many cycles of hold-slide loading. Samples with water-saturated gouge display (1) systematic, time-dependent increase of gouge strength; (2) unstable failure of gouge with large stress drops; and (3) lithification of gouge by crack sealing, recrystallization, porosity reduction, and grain bonding. All these features are absent in identical tests with dry gouge. These observations indicate that gouge particles are cemented by chemical processes during hold periods and suggest that the cyclical strength variations are controlled by cohesion strengthening rather than by friction changes. We further hypothesize that crustal fault zones could be lithified during the interseismic stage, and this lithification would control earthquake-slip instability.

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