Notes:

The elastically coupled plane strain models treat fracture propagation like a wedge being driven into a log. All the pressure applied to the walls of the fracture is transmitted through the elastic deformation of the rock to the crack tip where it is concentrated. So, the larger the fracture gets the more stress is concentrated at the tip and the faster the frac tends to grow. As the height increases the width also increases because the fracture opening is directly proportional to its characteristic height. All this behavior is rooted in the assumed boundary conditions used to derive the simple closed-form equation.