Power-law relationship between joint spacing and bed thickness in sedimentary rocks and implications for layered rock mechanics

Abstract

Fracture spacing (s) distribution and its dependence on bed thickness (t) are investigated for opening-mode joints in sandstone interlayered with shale in the Sainte-Anne des Monts area (the Gaspé Peninsula), Quebec, Canada. The s values of cross joints, which extend across intervals between long parallel systematic joints and abut these joints at about 90° angles, are consistently larger than those of systematic joints by a mean factor of 1.81. The s-t relationship follows a power law: s = mt1-1/k, where m equals half the ratio of layer tensile strength to interface shear stress, and k is the Weibull modulus. The m value is significantly larger for cross joints than systematic joints, indicating that the interfacial shear stress was direction-dependent during the deformation. The Weibull modulus of sandstone was larger during the formation of systematic joints than that of cross joints by a factor of ~1.2, indicating that the number and size of flaws in a unit of volume of the sandstone increased during progressive deformation. Furthermore, the compilation of s-t data from the literature yields: m = 2.53 ± 2.12 and k = 3.09 ± 1.24 for sandstones, and m = 3.53 ± 3.11 and k = 3.54 ± 1.33 for carbonates. The analysis also raises doubt about the existence of real joint saturation in sedimentary rocks.