Finite-element analysis of the stress distribution around a pressurized crack in a layered elastic medium: implications for the spacing of fluid-driven joints in bedded sedimentary rock

Abstract

Bedding-perpendicular joints confined to individual beds in interbedded sedimentary rocks commonly exhibit spacings which are proportional to the thickness of the jointed bed, and which vary according to lithology or structural position. The mechanical explanation for this relationship is well understood when the joints are driven by far-field crack-normal tensile stresses, but poorly understood for cracks driven by elevated fluid pressures, where the crack-driving stress is the difference between the crack-normal compression and the fluid pressure in the crack. Through a series of finite-element numerical models, we investigate how various parameters influence the driving-stress distribution around pressurized cracks in layered media, and thereby identify factors influencing the spacing of fluid-driven joints. For the situation we modeled, we observe that: (1) crack-driving stress is reduced in the vicinity of pressurized joints, and that the extent of the stress reduction depends on the contrast in elastic properties between the layers; and (2) crack-driving stress distribution depends on the ambient pore pressure during jointing. These results indicate the spacing of fluid-driven joints should depend on lithology and pore pressure.