Linear-elastic crack models of jointing and faulting

To gain insight into the formation and distribution of joints and faults and to illuminate the origin of associated secondary structures, we have developed methods for the interactive calculation and visualization of the stresses and displacements around these features. We assume that joints and faults can be idealized as cracks in homogeneous elastic bodies. Linear elastic fracture mechanics (LEFM) provides analytical expressions for the stress and displacement fields around cracks of various geometries for various loading conditions. We use a widely available symbolic math program to solve the general equations for a crack under uniform remote load and to display the results in two and three dimensions. Fracture mechanics has wide application in structural geology. The linked graphics and mathematics capabilities of symbolic math packages make LEFM accessible to a wide audience for both analytical and heuristic applications. We offer several geologic examples to demonstrate the power of visualizing the analytical solutions to linear elastic fracture problems. By examining the stress pattern around a modeled strike-slip fault we can predict the expression of secondary structures around the fault, including basins and ridges, or splay cracks and pressure solution surfaces. An analysis of variation in tensile stress away from an existing joint can be used to predict where the next parallel joint might initiate, defining the relationship between bed thickness and joint spacing. The crack model of a simple strike-slip fault also yields displacement vectors comparable in direction and relative magnitude to measured displacements produced by the 1989 Loma Prieta (California) earthquake.