The Eshelby like approach is used to successfully model the stress and strain fields associated with a fault subject to evolving remote stresses. A modified Cam-Clay material model is implemented as the constitutive equations for the fault material. The exterior of the fault is modeled as an infinite homogeneous linear elastic material and body forces are not considered. These assumptions allow a semi-analytical approach to be applied. The stresses exterior to the fault are induced by evolving either the vertical or horizontal remote stresses. The fault is represented as an elastic-plastic (modified Cam-Clay) high aspect ratio ellipsoidal inclusion loaded by the calculated exterior stress field. Two mechanisms are discussed as criteria for fault activation, runaway instability and negative rate of work of plastic strains. Two initial conditions are considered for the fault material model. First where the parameters for the material model are supplied by the user. Second where the initial effective mean stress and shear stress are assumed to be in the immediate vicinity of the intersection of the critical state line and yield surface. The differing predictions that follow from these two assumptions are discussed.
Commonly used methods to investigate fault stability do not account for the stress and strain field inside the fault. They equate the stresses and strains inside and outside and use a simple failure criteria such as Mohr-Coulomb to assess when faults activate. A typical approach is to assume two frictional surfaces with cohesion. This level of approximation becomes questionable, particularly for sharp material contrasts between the host and fault material.
We propose in the following work a more sophisticated model for fault activation. The approach taken here is to represent the fault as a thin ellipsoidal inclusion in an infinite elastic host. The constitutive behavior of the interior of the ellipsoidal is modeled by a Cam-Clay material. Homogeneous material properties are assumed in the interior of the fault, and therefore, due to ellipsoidal geometry, the stress-strain fields in the fault will be uniform. These fields are calculated using the Eshelby approach (Eshelby 1957). This allows a material properties mismatch between the host rock and the fault to be taken into account.
The exterior of the fault is modeled as an infinite homogeneous linear elastic material and body forces are not considered. The stresses exterior to the fault are produced by varying the remote external stresses.
This approach leads to a system of differential equations for the evolution of the internal stress and strain fields interior to the fault due to these varying external stresses. Continuous traction and displacements are assumed at the interface between the fault and the host rock.