Multiscale modeling of localized deformation in high-porosity granular rocks

Abstract

High-porosity granular rocks are critical hosts worldwide for oils and gases, underground water storage, carbon-dioxide sequestration and radioactive waste disposal. Localized deformation bands, in particular compaction bands featuring significant compactive deformation that causes substantial reduction of hydraulic conductivity of these rock formations, may impede the operation and performance of relevant applications. Key microstructural mechanisms that control the formation of deformation bands in high-porosity rocks remain poorly understood. In this thesis, a hierarchical multiscale approach is employed to simulate and analyze localized deformation bands in high-porosity rocks, with a particular focus being placed on compaction bands. A coupled Finite Element Method (FEM) and Discrete Element Method (DEM) scheme is adopted for the multiscale modeling, where the FEM is used to treat a macro-scale boundary value problem (BVP) and the DEM is employed to derive the constitutive material responses necessary for FEM based on direct particle-scale simulations. The coupled FEM/DEM scheme offers a convenient pathway to bridge the macroscopic observations (such as deformation bands) with their underlying microscopic characteristics, while avoiding phenomenological constitutive assumptions commonly needed in conventional continuum modeling. Based on the proposed multiscale modeling approach, a wide range of localized deformation bands are simulated under different boundary conditions, ranging from biaxial compression to isotropic/anisotropic borehole expansion as well as under hydro-mechanical coupling conditions and three-dimensional loadings. Emphases are placed upon exploring the possible occurrence mechanisms of compaction band without grain crushing. Key findings from the thesis study are summarized below. (i) Various deformation bands have been reproduced successfully based on a high-porosity Representative Volume Element (RVE). In the absence of particle crushing, it is possible for compaction bands to occur where debonding and pore collapse are two dominant mechanisms. High confining pressure and high porosity are identified as two major favoring factors for the occurrence of compaction bands. Decrease in either the confining pressure and/or porosity may lead to a transition of localization pattern from a compaction band to a shear-enhanced compaction band or a compactive shear band. Discrete compaction bands are likely to develop in heterogeneous specimens initiating from the local weak points, whereas compaction fronts are likely to occur in a homogeneous specimen. The cross-scale analyses confirm that shear enhanced compaction bands and pure compaction bands share great similarities, while both differ essentially from compactive shear bands in terms of shear strain, fabric anisotropy and particle rotation. (ii) A wide spectrum of localization patterns is identified around a borehole. A compaction band may initiate due to stress concentration, and in-band stress relaxation further propels its propagation with intensified stress concentration at the band tip. The stress path analyses reveal an alteration of localization pattern from compaction-dominated to shear-dominated may occur with the decrease in mean stress. A decrease in porosity may result in a positively sloped linear yield locus and an increase in cohesion strength may cause expansion of the yield locus and increase of the critical mean stress between different localization patterns. Both processes favor the alteration of localization pattern from compaction-dominated to shear-dominated. Diametrically opposite localization patterns are usually an effective indicator for identifying the σ₀ direction, but may also take place under hydrostatic far-field stress due to material anisotropy. (iii) The microscopic deformation features of compaction band (CB), shear-enhanced compaction band (SCB) and compactive shear band (CSB) can be uniquely, quantitatively characterized by decomposing the deformation gradient of in-band RVEs into vertical compaction, horizontal extension, simple shear, and rigid rotation. CB features with pure vertical compaction and SCB is similar to CB but with marginal extension, shear and rotation. CSB displays apparent differences with significant compaction, extension, shear and rotation. A new band index B_i = ln ∈_q/│∈_v│is proposed as a microscale classification index. It is demonstrated that B_i is effective in characterizing the spatial variation and the historical transition of localization pattern in complex BVPs. (iv) The coupling effects of induced pore pressure p and the formation of compaction bands have been explored under undrained biaxial compression condition. With the accumulation of p, the initial localization pattern may change from a CB in the dry (drained) case to a SCB in the undrained case. CB is reproducible under undrained condition with sufficiently large total confining pressure. Instead of showing a continuous thickening in width in a dry case, a CB in the undrained case may transit to a SB through a transition stage. The initial localization patterns and their evolutions can be analyzed based on B_i of in-band RVEs. The effective stress path analyses indicate the dominance of effective means tress p' on the localization patterns. (v) A high-porosity RVE has been prepared in an attempt to reproduce similar macropores and mechanical responses of Tuffeau de Maastricht for examination of compaction bands in 3D. The multiscale predictions show a surprising consistency in localization patterns and a qualitative similarity in mechanical responses as compared to the experimental observations. Microscale analyses demonstrate the steady propagation of compaction-dominated localization at the plateau stage and the transition to shear-dominated localization at re-hardening stage. Local porosity analyses support early conclusions that the collapse of macropores as a major mechanism of compaction bands.

Date of Award	2018
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology