Path dependence of the potential for compaction banding: Theoretical predictions based on a plasticity model for porous rocks

Abstract

The paper presents a theoretical investigation of compaction banding based on a plasticity model for high-porosity rocks. The selected model is featured by a nonassociated flow rule and two internal variables simulating the competition between softening and hardening in the brittle-ductile transition. The parameters have been calibrated for two extensively studied rocks that exhibited localized compaction under laboratory conditions. In particular, the constants that control the compaction banding domain are defined by matching the stresses at which localized compaction was found in the experiments. The resulting parameters are used to simulate the stress-strain response for two loading modes (i.e., triaxial compression and radially constrained deformation), thus exploring the role of stress paths and kinematic constraints on the evolution of the compaction banding potential. The analyses suggest that the loading paths able to mobilize the plastic resources of the rock alter the potential for compaction banding through irreversible effects. A notable example is oedometric compression, for which the potential to generate localized compaction tends to vanish during the initial stages of inelastic loading. These predictions suggest that constraints to the mode of deformation can hinder the occurrence of compaction bands in the field. Moreover, they suggest that the interplay between kinematic constraints and evolution of the compaction banding potential can be used for experimental characterization purposes. As a consequence, these results emphasize the importance of complementing stress-controlled experiments with other tests able to explore different stress paths, thus providing additional data for an accurate characterization of rheological properties and strain-localization characteristics.

Extension of plasticity theory to debonding, grain dissolution, and chemical damage of calcarenites

“…To validate both the mechanical hardening and plastic potential parameters, a series of oedometric compression test results on dry and wet Gravina calcarenite samples were employed (Figure ). As is evident, the experimentally observed post yielding plateau is not captured in a satisfactory way by the model because in this phase of the test, compaction bands develop within the specimen , while the simulations implicitly assume the sample not to localize. Nevertheless, the mechanical hardening and plastic potential parameters already calibrated in the previous section fit quite well the mechanical behavior of the calcarenite when loaded under oedometric conditions.…”

“…Sometimes, owing to the particular microstructure of the material, axial strains localize along horizontal layers. This phenomenon is known as compaction banding . As the formation of a compaction band is a dynamic process, the jumps in vertical strains and the associated discontinuities in the radial stress are justified.…”

Viscoplastic Interpretation of Localized Compaction Creep in Porous Rock

“…This is simple for pure compaction bands, in that they involve a local strain jump characterized by uniaxial deformation (i.e., orthogonal to the band and characterized by lack of lateral extension/contraction; Issen & Rudnicki, ). These conditions resemble the kinematic constraints applied during oedometric (radially constrained) compression (Arroyo et al, ; Buscarnera & Laverack, ) and can be readily inspected at a material point level by considering axisymmetric stress conditions. Specifically, a potential compaction band during creep would involve a constant axial stress (i.e., ), as well as a constrained radial strain (i.e., ) as controlled variables.…”

“…For this multivariable system, the kinematics of the strain jump in the active zone of localized compaction can be described through a system of ODE compatible with equation in which the axial strain and the radial stress define the vector of the response variable X (i.e., X =[ , ]). As a result, the underlying system of ODEs governing this particular uniaxial deformation process can be written as follows: where E and ν indicate the Young's modulus and Poisson's ratio, respectively, while H CB represents the instability index for the selected controlled conditions, defined as: where H σε is a term dependent on the loading rate, H is the hardening modulus, and H χ represents the controllability index derived by Buscarnera and Laverack () in the framework of rate‐independent plasticity by enforcing the kinematic conditions typical of a pure compaction band: …”

“…Hereafter, it will be shown how this formalism can be generalized to compaction creep in porous rocks, especially for problems characterized by a marked potential for compaction localization. For this purpose, a strain‐hardening elastoplastic model (Gens & Nova, ; Lagioia et al, ; Nova et al, ), previously used to reproduce compaction localization in porous rocks (Buscarnera & Laverack, ; Das & Buscarnera, ), will be augmented to viscoplastic form (Perzyna, ) to simulate compaction creep. Material point analyses will be used to illustrate from a mathematical standpoint the differences between stable and unstable creep.…”