Spacing of fractures in a multilayer at fracture saturation

Using a three-layer model with a fractured central layer, and with a top la yer and a bottom layer of the same thickness, we study the change of the cr itical fracture spacing to layer thickness ratio (i. e., the ratio at fract ure saturation) as a function of the thickness of the top and bottom layers . Results show that, with increasing thickness of these layers, the critica l spacing to layer thickness ratio decreases rapidly from infinity to a con stant value, corresponding to that for very thick top and bottom layers. Al so, we study the change of the critical spacing ratio as a function of the thickness of the top layer where the bottom layer is much thicker (5 times) than the fractured layer. In this case, the critical spacing to layer thic kness ratio decreases rapidly from the value for edge fractures to the same constant value as the thickness of the top layer increases. These results imply that if the adjacent layers are thicker than 1.5 times the thickness of the fractured layer, the multilayer can be treated approximately as a sy stem with infinitely thick top and bottom layers in terms of spacing at fra cture saturation.