The Relation Between Recovery Deformation and In-Situ Stress Magnitudes

Abstract

ABSTRACT In this paper a theoretical basis is developed for calculating in situ stress magnitudes from recovery deformations measured in rock. The constitutive theory used assumes that the rock is linearly viscoelastic, homogeneous, and non-aging. These assumptions yield explicit integral equations relating strain as a function of time to stress history, which is taken to be instantaneous unloading of the rock. Solutions are obtained for recovery of isotropic and transversely isotropic core in which time-dependent behavior is contained in creep compliance terms and Poisson's ratio terms are constant. The main results for both cases are equations that allow calculation of horizontal principal stresses from vertical stress, principal recovery strains, and material properties that do not depend on time. For the isotropic case, the only material property required is Poisson's ratio. For the transversely isotropic case, two Poisson's ratio terms as well as the ratio of creep compliances are required. This last solution assumes that the vertical stress is parallel to the axis of material property symmetry.