Wave propagation in rocks with elastic-plastic deformations

Wave propagation in rocks subject to elastic-plastic deformations can be described by the equations of motion for small dynamic fields superposed on a static bias. The static bias refers to the statically deformed state of the material with large deformations. Referred to this statically deformed state, the Piola-Kirchhoff stress equations of motion describe wave propagation in terms of second- and third-order elastic constants, static stresses, and finite deformation gradients. Plane wave propagation along the principal stress directions can be described in terms of principal stretches, total static strains, and plastic strains. The elastic strains are differences between the total and plastic strains. Calculations are performed for the plane wave speeds in the absence and presence of plastic strains. Theoretical predictions agree very well with the laboratory measurements made on dry Castlegate sandstone samples subject to multiple uniaxial load cycles up to 70% of the unconfined compressive strength of 16 MPa. The difference between the plane wave speeds in these two cases can be calibrated as function of a certain measure of plastic strain. This analysis also provides a framework for the estimation of plastic strain as a measure of mechanical damage in the material from the acoustic wave velocity measurements. Estimation of near-wellbore damage influences perforation strategy that would avoid sanding during hydrocarbon production.