Regular spacing of deformation bands in sandstone: Layer-thickness control or constitutive instability?

Abstract

We examine whether bedding thickness or constitutive properties correlate with the spacing of equally spaced shear-enhanced compaction bands and compactional shear bands in Miocene sandstones of the Whakataki Formation, North Island, New Zealand. Quantitative spacing analysis reveals a positive correlation between bedding thickness and the spacing of strata-bound deformation bands, as is commonly observed for veins, joints, and normal faults. The observed spacing to thickness ratio (STR) ranges from 0.02 to 0.14 and is considerably smaller than observed for veins, joints, and normal faults (usually ≥ 1). Modelling compaction bands as stiff tabular inclusions in a layered sequence, simple elastostatic numerical simulations show that they act as stress amplifiers, which may explain STR ≪ 1. Additionally, we obtained laboratory estimates of rock permeability and strength to test if the constant band spacing can be explained with a constitutive instability proposed for compaction bands: the stationary cnoidal wave. The results from this study indicate that this model fails to explain the observed spacing if we use the material properties obtained in the laboratory. This discrepancy likely arises from the following: [1] laboratory estimates of host-rock properties are not the same as those at depth; [2] the used semi-analytical solution for the stationary cnoidal wave employs an incorrect value (m = 3) of the stress exponent; and [3] the equation does not account for coupled layered media. While we cannot conclusively falsify the cnoidal-wave model for compaction band spacing per se, it appears likely that the existing solution should not be used for predicting band spacing in layered porous sandstones.