Evidence for a non-linear relationship between fracture spacing and layer thickness

In experiments, extension fractures were generated in rigid layers of Plaster of Paris resting on a viscous substratum (pitch). The experimental results predict a non-linear relationship between the spacing of fractures in uniform brittle layers and layer thickness for fractures generated by the tractional force of embeddins weak rocks. We derive an equation which relates the critical fracture spacing (λc) with layer thickness (b), tensile strength of the layer material/viscosity of the embedding medium ratio (τo/η) and bulk strain rate (εb). The equation shows that the spacing increases as a function of the square root of the layer thickness. The theory also predicts that the fracture spacing depends on the strain rate when the embedding weak medium is viscous