Third Invariant Dependent Single Yield Surface Model and Localization Conditions for High Porosity Sandstone

Abstract

High porosity sandstones are observed to fail by the formation of localized bands in field and laboratory settings. Compaction bands form perpendicular to the direction of maximum compression, with pure compactant strain, while shear bands form at an angle to the direction of maximum compression, with shear strain accompanied by either compactant or dilatant strain normal to the band. Recent experimental evidence indicates that mechanical behavior of some high porosity sandstones depends on the third invariant of deviatoric stress (J 3). In this work, a J 3 dependent single yield surface constitutive model was developed, and band orientation predictions determined using the Rudnicki and Rice bifurcation theory. While in the laboratory, high porosity sandstones are typically tested under axisymmetric compression (ASC; intermediate principal stress equal to the least compressive principal stress), stress states in the field are often non-axisymmetric. Therefore, localization conditions were determined under P 1, a stress state perturbed from ASC. For ASC, the localization conditions resulting from the J 3 dependent model are identical to those from the J 3 independent model. The most favorable conditions for compaction band formation occur under ASC, while under P 1, localization conditions favor shear band formation. Mild to moderate J 3 dependence favors formation of shear bands over compaction bands, and a strong J 3 dependence prohibits localized deformation band formation. These results provide one possible expla-nation for relatively few field observations of compaction bands versus more commonly observed shear bands.