Two of the major joint-driving mechanisms are joint-normal stretching and poroelastic shrinkage, and these lead to joint sets commonly associated with structural bending and natural hydraulic fracturing, respectively. Regardless of joint-driving mechanism, joint infilling is a nonhomogeneous Poisson process in the presence of stress shadows. Through probability modeling, we show that in all cases joint spacing is best fit with gamma distributions. The shape parameter of the best-fit gamma distribution to joint-spacing data is a quantitative means to assess the extent of saturation, which is represented in a new parameter, the joint-saturation ratio (JSR). To test the utility of JSR, we call upon published structural bending joint data (Elk Basin, Lilstock, and Rives plate-bending experiment). The shape parameters for these well-developed structural bending joints are equal to around three, corresponding to a JSR of approximately 30%. Using the same analysis on the spacing of natural hydraulic fractures collected from outcrops in the gas-prone Devonian sections of the Appalachian Basin, we find that natural hydraulic fractures differ in two aspects from structural bending joints. First, the joint spacing is proportional to bed thickness in bedded rocks but not in gas shale sections. Second, the joint saturation of natural hydraulic fractures is generally lower than in well-developed structural bending joints. Thus, the JSR is a means to distinguish the joint-driving mechanism and to represent joint-saturation level independent of bed thickness effects. It can be used to distinguish natural fractures from drilling-induced fractures and to improve the fracture-network modeling.

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