Large‐scale failure prediction of clay rock from small‐scale damage mechanisms of the rock medium using multiscale modelling

Abstract

Clay rocks are multiphase porous media whose complex structure is characterised by heterogeneity and possible anisotropy on a wide range of scales. The mesoscopic scale plays a particular role in deformation mechanisms under mechanical loading by cracking. The behaviour of rocks at mesoscale is characterised by the material and morphological (shape and size) properties of its components and their interactions. The accurate reproduction and influence of these mesoscale characteristics on the material behaviour and damage at large scale remain a complex issue. This question becomes crucial when investigating the underground stability during excavation works such as tunnels. In this numerical multi-scale study, the mesostructure characteristics are embedded in a Representative Elementary Area (REA) in a 2D configuration. A double-scale numerical framework, with finite element resolution at both scales (FE 2 ) and computational homogenisation, is considered. The influence of the mesostructural characteristics of a heterogeneous rock and the effect of different inter-granular properties on their macroscopic behaviour, are examined. Additionally, a predictive strategy which is based on the connection between the failure modes of the REA and the failure mechanisms of the macroscale structure is also presented. This study investigates the effect of the mesocracking on the shear banding in a rock specimen during laboratory biaxial shear test and the development of the Excavation Damaged Zone (EDZ) around tunnels. The objective of this work is to explain the failure mechanisms observed up to the engineering scale of underground structures through the morphological and material small-scale characteristics of the REA.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

“…For $${p_i} > 1.5{\sigma _0},$$ the influence of the VE is already visible as the $${\varepsilon _{VM}}$$ maps start to be slightly different; and for $${p_i} \ge 3.5{\sigma _0}$$, strains are localized and as soon as $${p_i} \ge 4.5{\sigma _0}$$, quasi‐periodic SBs are observed in R22‐simu‐b case while conjugated SBs are found in other cases ( R02‐simu‐b and R50‐simu‐b ). These two modes of strain localization (conjugated and quasi‐periodic) solutions shown are well consistent with other numerical and experimental observations on the borehole failure 18,49–52 …”

Three-invariant model and bifurcation analysis of deformation bands for a sandstone subjected to true triaxial loading paths

“…On the numerical modeling side, a few studies have reported this pre-peak localization. In the context of modeling in a continuous medium, it is generally observed if a slight material heterogeneity has been introduced into the medium [21,44]. It is also observed in the context of discrete medium modeling [14].…”

Modelling the time‐dependent mechanical behaviour of clay rocks based on meso‐ and micro‐structural viscous properties

“…Considering the complex mesostructure of clay rocks, one possibility to evaluate their impacts on mesoscale and macroscale overall mechanical responses is to use a multi‐scale approach. Such approach allows to study a statistically equivalent Representative Elementary Volume (REV for 3D case) or Representative Elementary Area (REA for 2D case) to determine the behaviour of the equivalent homogeneous medium 24–33 . In particular, computational homogenisation methods, 34–36 also known as multi‐scale analyses, have emerged.…”

“…Such approach allows to study a statistically equivalent Representative Elementary Volume (REV for 3D case) or Representative Elementary Area (REA for 2D case) to determine the behaviour of the equivalent homogeneous medium. [24][25][26][27][28][29][30][31][32][33] In particular, computational homogenisation methods, [34][35][36] also known as multi-scale analyses, have emerged. They include, among others, finite element squared (FE 2 ) 24,[37][38][39][40] and FEM-DEM 41 methods for continuous media at the large scale and heterogeneous/discrete material at the small scale.…”