Effects of overburden on joint spacing in layered rocks

When a layered system of rock beds is subjected to a sufficiently large extensional strain, joints form in the competent layers. Previous analyses have shown that the ratio between joint spacing and competent layer thickness decreases as the applied strain increases. Further, if the entire interface between the competent layer and the matrix fails in shear (slip), no new joints can form and a lower bound on the joint spacing is reached. In this paper, a joint spacing analysis is developed to explicitly account for the effects of overburden depth. The resulting model is a pair of non-linear equations that can be solved for the characteristic joint spacing as a function of layer thickness, applied strain, and overburden depth. The model results show that, for a given applied strain, the joint spacing first decreases and then increases with depth. This behavior is controlled by the opposing effects of depth-increasing shear strength along the competent layer-matrix interface and depth-increasing compressive prestress. The analysis also reveals that the lower bound (saturation) joint spacing is strongly dependent on depth. Within the choice of realistic physical parameters, predicted values of the saturation-spacing-to-layer-thickness ratio span the range of values observed in the field.