The Effect of Rotational and Isotropic Hardening on the Onset of Compaction Bands

Abstract

Compaction bands are localized failure patterns that appear in highly porous rock material under the effect of relatively high confining pressure. Being affected mainly by volumetric compression, these bands appear to be almost perpendicular to the most compressive principal stress at a stress state at the so-called “cap” of the yield surface (Issen and Rudnicki, J Geoph Res 105:21529–21536 (2000) [4]). In this study we focus on the mechanism that leads to the onset of compaction bands by using a viscoplasticity model able to describe the post-localization response of these materials. The proposed constitutive framework is based on the overstress theory of Perzyna (Adv Appl Mech 9:243–377 (1966) [7]) and the anisotropic clay plasticity model of Dafalias (Mech Res Commun 13(6):341–347 (1986) [1]) as modified by Dafalias and Taiebat (Geotechnique 63(16):1406–1418 (2013) [2]) which provides not only the necessary “cap” of the yield surface, but introduces a rotational hardening mechanism thus taking into account possible anisotropic phenomena. Following the analysis of Veveakis and Regenauer-Lieb (J Mech Phys Solids 78:231–248 (2015) [8]) we identify the compaction bands as “static” cnoidal wave formations in the medium that occur at a post-yield regime and we study the effect of rotational and isotropic hardening on their onset. Moreover, we determine a theoretical lower limit of confining pressure in triaxial compression tests for the compaction bands to develop.