Abstract:
Compressional waves velocity VP was measured during long-term experiments in a high-pressure vessel (in the range [10-75] MPa for confining and pore pressures). Experiments were carried out on a granite specimen prepared by a controlled heating treatment at 510 °C, which generated thermal cracks.Data analysis is proposed by using an effective medium approach based on Kachanov's [Appl. Mech. Rev. 45 (1992)304] model. The elastic behaviour of the cracked rock is controlled by the crack density parameter which varies with confining and pore pressures due to crack closure. In order to model the progressive closure of cracks, we assume elliptical cracks with major axis 2c and aspect ratio α. By using a conformal mapping technique, we derive the variation of the crack aspect ratio as a function of effective pressure, the effective pressure coefficient η depending on α and Poisson's ratio ν0. As a result, we compute the crack density parameter and the elastic moduli of the cracked rock as a function of confining and pore pressures. To take into account the heterogeneity of the rock sample, a peak-like distribution of crack aspect ratios is introduced, which allows us to calculate the acoustic velocity VP for various effective pressures.Comparison is made between theoretical and experimental values and shows that this simple model captures the essential features of the acoustic velocity variation: an increase of VP when pore pressure is decreased followed by a plateau for a threshold pore pressure. Best consistency between theoretical and experimental velocity values is obtained by introducing a second crack population with a higher mean aspect ratio and an irreversible closure mechanism as effective pressure is cycled.
