NON-RIEMANNIAN AND FRACTAL GEOMETRIES OF FRACTURING IN GEOMATERIALS

The mechanism of earthquakes is presented by use of the elastic disloc ation theory. With consideration of the continuous dislocation field, the general problem of medium deformation requires analysis based on n on-Riemannian geometry with the concept of the continuum with a discon tinuity (''no-more continuum''). Here we derive the equilibrium equati on (Navier equation) for the continuous dislocation field by introduci ng the relation between the concepts of the continuous dislocation the ory and non-Riemannian geometry. This equation is a generalization of the Laplace equation, which can describe fractal processes like diffus ion limited aggregation (DLA) and dielectric breakdown (DB). Moreover, the kinematic compatibility equations derived from Navier equation ar e the Laplace equations and the solution of Navier equation can be put in terms of functions which satisfy the biharmonic equation, suggesti ng a close formal connection with fractal processes. Therefore, the re lationship between the non-Riemannian geometry and the fractal geometr y of fracturing (damage) in geomaterials as earthquakes can be underst ood by using the Navier equation. Moreover, the continuous dislocation theory can be applied to the problem of the earthquake formation with active folding related with faulting (active flexural-slip folding re lated to the continuous dislocation field).