Grady’s model of the dynamic fragmentation process, in which the average fragment size is determined by balancing the local kinetic energy and the surface energy, is modified to include the stored elastic (strain) energy. The revised model predicts that the strain energy should dominate for brittle materials, with low fracture toughness and high fracture-initiation stress. This conclusion is not borne out, however, by limited experimental data on brittle steels, even when the kinetic-energy density is small compared with the strain-energy density.

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[1] Many applications in geophysics require good estimates of permeability evolution in response to deformation, pore collapse, dilatancy, and microfracturing. Simulations of the upper crust, oil well completion, and nuclear waste repositories depend upon reliable predictions of changes in rock permeability. For some applications, permeability can affect the strength of rock by influencing the pore pressure and effective stress. For example, the pore pressure during production from an oil bearing formation is controlled by the evolving permeability field. The rock strength, however, depends upon the effective stress which is influenced by the pore pressure. Accurate prediction of possible failure in such formations requires reliable estimates of permeability change. Ideally, such estimates could be obtained by directly simulating the changes in pore space connectivity at the microscale. In practice the system being studied is sufficiently large that constitutive models must be developed which address permeability evolution macroscopically. We develop a model for predicting porosity and permeability changes in Berea sandstone. The model has been kept as simple as possible in order to facilitate incorporation of the model into existing mechanics codes. For this reason we assume the existence of a separate material model capable of predicting the stress-strain response of the rock. In addition, the model assumes that the original pores and pores created by microfracturing can be treated separately with respect to permeability and porosity evolution. Despite these simplifying assumptions, the model is able to reproduce most of the key features observed in previously reported triaxial experiments performed on Berea sandstone. INDEX TERMS:5114 Physical Properties of Rocks: Permeability and porosity; 3230 Mathematical Geophysics: Numerical solutions; 3210 Mathematical Geophysics: Modeling; KEYWORDS: berea sandstone, rocks, model, permeability, porosity, deformation Citation: Morris, J. P., I. N. Lomov, and L. A. Glenn, A constitutive model for stress-induced permeability and porosity evolution of Berea sandstone,