Modelling Fracture Propagation Across Layer Boundaries using Linear Elastic Fracture Mechanics

Linear Elastic Fracture Mechanics allows rapid modelling of fracture propagation, but is only valid in a homogeneous medium so cannot model fractures propagating across mechanical boundaries. We use phase field models to derive empirical expressions for the energy release rate of a fracture crossing a mechanical boundary, as a function of fracture length, layer thickness and the mechanical properties on both sides of the boundary. This is shown to be a combination of the classical LEFM formula but with Young’s Modulus averaged along the length of the fracture, and an additional term for the boundary effect. This boundary term is negligible away from the boundary, but tends to zero or infinity close to the boundary. This expression can be used to simulate fractures propagating across layer boundaries in mechanically layered rocks.