Effect of crack distribution on elastic properties of rocks revisited

Most models of pressure dependency of rock properties relate such a dependency to the distribution of aspect ratios of pores and cracks. This approach might not always be accurate because moderate roughness of crack boundaries has little effect on effective properties of the medium but asperities heights determine the pressure level at which partial contact between crack faces takes place. We explore how the pressure dependency could be related to distributions of crack radii and their thicknesses (or aspect ratios and thicknesses). For an idealized case of uniform distribution of aspect ratios, the bulk modulus is proportional to an expression of the form 1pα+ (until pressure p reaches a value mp where all the cracks are closed). The model can be used to derive the distribution of crack properties from pressure dependency of elastic moduli, and to take into account the effect of crack roughness.