Accounting for Small-Scale Heterogeneity and Variability of Clay Rock in Homogenised Numerical Micromechanical Response and Microcracking

Abstract

Clayey rocks have a complex microstructure with multiple characteristic lengths. Deformation under mechanical loading generally induces damage by microcracking, which essentially concerns the scale of mineral inclusions embedded in the clay matrix. The modelling of these materials is considered within the framework of a double scale approach, by numerical homogenisation, of the squared finite element method type. This allows a heterogeneous microstructure of the material to be taken into account and a distribution of morphological properties to be introduced. Emphasis is placed on the generation of microstructures satisfying experimental observations, and keeping a certain simplicity to fit into the framework of double scale modelling. The material characteristics and behaviour are defined at the grain scale: the mineralogical properties include the mineral phase proportions and the grain morphology, while the material constituents are represented by elastic grains separated by damageable cohesive crack models. Then, the overall microscale behaviour of the material under solicitation is derived from equilibrated elementary area (EA) configuration and computational homogenisation. The variability of the material response is studied with regard to small-scale aspects as microstructure variability, microstructure size, grain angularity, and properties of grain contacts. Deformation anal-

Micro-cracking and incipient shear microstructures at low-strain deformation of Opalinus Clay: Insights from triaxial testing and broad-ion-beam scanning-electron-microscopy (BIB-SEM)

“…The results of this study support more recent efforts (e.g. Pardoen et al, 2020;Jameei and Pietruszczak, 2021) to implement damage in constitutive models for modelling OPA or similar clay shales, which allow reproducing local porosity and permeability changes due to crack formation, crack coalescence, and the development of shear zones. Further studies on samples tested to larger axial strains on consolidated-undrained samples will test our model of strain localisation and pore space reduction.…”

Effect of Claystone Small-Scale Characteristics on the Variability of Micromechanical Response and on Microcracking Modelling

“…1a). The generation method is adapted from van den Eijnden et al 2017to enrich the mineralogical characteristics (Pardoen et al, 2020). A variability of the latter is also considered to reproduce the observed distribution of clay and mineral contents, orientation, and elongation.…”

“…The micromechanical properties of the heterogeneous EAs are chosen to reproduce the clay rock behaviour (Table 2). Each mineral constituent is assigned linear elastic properties (Ahrens, 1995;Robinet et al, 2012;van den Eijnden et al, 2017) and homogeneous interface properties are assumed (van den Eijnden et al, 2017;Pardoen et al, 2020). The clay rock micromechanical behaviour is analysed through the responses of EAs subjected to loading.…”

Bounding the Multi-Scale Domain in Numerical Modelling and Meta-Heuristics Optimization: Application to Poroelastic Media with Damageable Cracks

“…An asymptotic homogenization and the related double-scale model for poroelastic media with damageable cracks were previously developed [ 41 ]. Compared to numerical homogenization approaches such as direct micro–macro-techniques [ 39 , 42 ], the asymptotic homogenization theory permits equivalent properties to be obtained and allows an analytic and a numerical approach to be combined. The homogenized problem can be solved on a generic micro-structural cell (solved using, e.g., finite elements) so that the homogenized macroscopic properties are finally obtained.…”