The Signature of Deformation Bands in Porous Sandstones

Accurate identification and differentiation of various deformation bands in porous sandstone constitute a critical first step towards thorough understanding of these failure patterns. Two conventional ways prevail on band identification for sandstone, one based on a kinematic definition of shear offset (the ratio between shear and compaction displacement S/C) and the other according to a geometric inclination angle between band orientation and the principal stress direction. The two methods are not always consistent with each other, frequently leading to confusions or false identification of band patterns, especially when a deformation pattern is in transition. Employing an advanced multiscale modeling approach, we have reproduced a complete kinematic spectrum of deformation bands in porous sandstone. Enlightened by an exponential relation between \(|\epsilon _v/\epsilon _q|\) and \(|S/C |\) observed in the results, a new, accurate classifier, \(B_i=\epsilon _v/\epsilon _q\), is proposed in this study, where \(\epsilon _v\) and \(\epsilon _q\) denote, respectively, the volumetric and deviatoric strains inside a band. The validity and robustness of \(B_i\) are examined with rigorous mechanical analyses in conjunction with insights drawn from multiscale modeling of localized deformation. Instead of decomposing the displacements, we further propose splitting the deformation gradient into four distinct kinematic components: (1) deviatoric compaction, (2) lateral extension, (3) simple shear, and (4) rigid rotation. As an end member of the kinematic spectrum, a pure dilation band (PDB) is found dominated by lateral extension without apparent compaction, shear, or rotation; a pure compaction band (PCB) is dominated by deviatoric compaction without apparent extension, shear, or rotation; a simple shear band (SSB) distinguishes itself from the previous two with the presence of substantial, proportional compaction, extension, shear, and rotation. As transitional patterns, shear-enhanced dilation band (SEDB), and shear-enhanced compaction band (SECB) are closer to pure volumetric deformation bands (PDB and PCB), while dilatant shear band (DSB) and compactive shear band (CSB) are more similar to simple shear band. In addition, \(B_i\) shows advantages in characterizing spatial variation and temporal transition of band patterns in complex boundary-value problems of sandstone.