r - The Hong Kong Polytechnic University

The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5)
Hong Kong, China, 13-15 July 2011
ON THE MULTI-SCALE MODELING OF HETEROGENEOUS GEOMATERIALS
J.F. Shao 1,2 , A. Guery 1 , T. Jiang 2 , Q.Z. Zhu 1 , D. Kondo 3
1
LML, UMR8107 CNRS, Email: jian-fu.shao@polytech-lille.fr
University of Lille, Villeneuve d’Ascq, France
2
Faculty of Civil and Transportation Engineering,
Hohai University, Nanjing, China
3
IJLRA, UMR7190 CNRS
University of Paris 6, Paris, France
ABSTRACT
Most geomaterials are characterized by multi-scale heterogeneous structures such as pores, mineral grains,
bedding planes, microcracks, interfaces etc. The macroscopic behaviour of such materials inherently depends on
the mineral composition and the evolution of microstructure at various scales such as microcrack propagation,
pore expansion or collapse. The macroscopic properties of such heterogeneous materials are also governed by
physical mechanisms at relevant scales. Constitutive modelling of geomaterials should take into account such
physical mechanisms. In this paper, we present a general framework for multi-scale modelling of geomaterials.
Two specific situations will be in particular discussed. Firstly, based on linear homogenization technique, we
present a micromechanics-based formulation for damage modelling in brittle rocks, by taking into account
coupling between crack growth and frictional sliding. Secondly, the micromechanical modelling is extended to
heterogeneous geomaterials containing non linear mineral phases. A non-linear homogenization method is
presented to describe coupled plastic damage behaviour in semi-brittle rocks.
KEYWORDS
Micromechanics, damage, homogenization, multi-scale modelling, heterogeneous rocks
INTRODUCTION
In many engineering applications such as stability and failure analysis of underground structures, the knowledge
of mechanical behaviours of geomaterials is required, together with other properties such permeability and heat
conductivity. Extensive experimental investigations have shown that the mechanical behaviours of geomaterials
are general complex and inherently related to their microstructure and mineral compositions. For instance, the
anisotropic properties of sedimentary rocks are due to existence of bedding planes and other weakness planes.
Damage due to nucleation and propagation of microcracks is an essential mechanism of inelastic deformation
and failure in many brittle rocks. On the other hand, for a given class of rocks, the macroscopic behaviour is
strongly affected by the variation of mineral compositions. For instance, in clayey rocks, the macroscopic
swelling capacity is directly depending on the clay content. In Figure 1, we show the microscopic image of
mineral compositions of a clayed rock. This rock called Callovo-Oxfordian argillite has been extensively studied
in France in the context of feasibility studies for geological disposal of nuclear waste. Due to its low
permeability and high mechanical strength, the Callovo-Oxfordian argillite is considered as potential host
formation for underground storage of high level radioactive wastes. It is seen that the mechanical behaviour of
the argillite varies with layer depth due to variation of mineral composition. At the macroscopic scale, the
mechanical response of the argillite can be characterized by significant plastic deformation coupled with
induced damage, strong sensitivity to confining pressure and water content, transition from volumetric
compressibility and dilatancy as well as slight anisotropy (Chiarelli et al. 2003; Shao et al. 2006; Jia et al. 2010).
A series of microscopic investigations have also been conducted in order to identify physical mechanisms at
relevant scales involved in macroscopic mechanical responses (ANDAR 2005). It is found that the argillite is
composed of three principal phases: clay matrix, quartz and calcite grains. The macroscopic deformation seems
to mainly be related to distortion of clay matrix, similar to dislocation of crystal structures. Microcracks are
observed both at interfaces between mineral grains and clay matrix and inside clay matrix. Such microcracks are
responsible to mechanical damage of argillite such as deterioration of elastic modulus. More importantly, the
macroscopic permeability can significantly change due to nucleation and propagation of microcracks. The
porosity of argillite is mainly due to voids between clay particles which is an assembly of parallel clay platelets.
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