NONLINEAR ELASTIC BEHAVIOR OF DAMAGED ROCKS

The pervasive damage of rocks by microcracks and voids strongly affect s their macroscopic elastic properties. To evaluate the damage effects , we derive here the macroscopic stress-strain relations for a 3-D ela stic solid with non-interacting cracks embedded inside a homogeneous m atrix. 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 ene rgy of this rock following the self-consistent scheme of Budiansky & O 'Connell (1976). The solution describes the stress-strain relations in terms of lambda d and mu d, which are the modified Lame constants, an d an additional parameter gamma. The latter accounts for the non-linea r behaviour of the solid and is related to crack density. The solution predicts a non-linear elastic rheology even for an infinitesimal stra in of epsilon<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 b eams of Indiana limestone were deformed under four-point loading. This configuration provides simultaneously the apparent tensile and compre ssive moduli for small strains. The apparent moduli fit the effective elastic moduli calculated with the present damage model well, includin g the differences between tensile and compressive moduli.