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

Hobbs' model [Hobbs, D. W. (1967) The formation of tension joints in sedime ntary rocks: on explanation. Geological Magazine 101, 550-556.] has been ci ted as one of the theories for interpretation of the linear relationship be tween saturated joint spacing (s) and bed thickness (t) in interbedded sedi mentary rocks. However, this model is based on an assumption that the shear stress in the bounding non-jointing layers decreases linearly from the max imum value at the layer-matrix interface to zero at a distance exactly equa l 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 = eta root td for the competent beds bounded by two incompetent layers n early identical in thickness. The constant eta depends on both material pro perties of rocks (i.e. the Young's modulus, tensile strength and fracture s aturation strain of the competent bed, and the shear modulus of the incompe tent 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 linea r. If d is constant, the joint spacing increases as a function of the squar e 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, howeve r, result in a statistically linear relationship between s and t. (C) 1998 Elsevier Science Ltd. All rights reserved.