A revised model for the relationship between joint spacing and layer thickness

Hobbsʹ model [Hobbs, D. W. (1967) The formation of tension joints in sedimentary rocks: on explanation. Geological Magazine 104, 550–556.] has been cited as one of the theories for interpretation of the linear relationship between saturated joint spacing (s) and bed thickness (t) in interbedded sedimentary rocks. However, this model is based on an assumption that the shear stress in the bounding non-jointing layers decreases linearly from the maximum value at the layer matrix interface to zero at a distance exactly equal to the jointing layer thickness from the interface. We provide a revised analytical model which takes into account the non-linear decay of the shear stress and the effects of bounding bed thickness (d). The model shows that s− η√ td for the competent beds bounded by two incompetent layers nearly identical in thickness. The constant η depends on both material properties of rocks (i.e. the Youngʹs modulus, tensile strength and fracture saturation strain of the competent bed, and the shear modulus of the incompetent layers) and decay modes of the shear stress in the bounding layers. If the ratio of d to t is constant, the relationship between s and t is linear. If d is constant, the joint spacing increases as a function of the square root of t. Complex t d variations from Cambrian flysch sediments at Plage Victor in the Saint-Jean Port-Joli area of the Quebec Appalachians, however, result in a statistically linear relationship between s and t.