r - The Hong Kong Polytechnic University

The distance between clay platelets constitutes nanoscopic porosity and significant controls water sensitivity and
time dependent behaviour of argillite. Further, the poromechanical properties are also influenced by interaction
between nanoscopic and microscopic pores.
Figure 1 Micrograph of a typical argillite structure:
calcite grains (C), quartz grains (tectosilicates) (T)
and clay matrix (MA)
Figure 2 Nucleation and propagation of microcrack
around mineral grains under applied stress
All these experimental data and microscopic investigations clearly show that the macroscopic properties of
argillite are inherently related to the evolution of microstructure at different scales. A number of constitutive
models have been proposed for geomaterials, elastoplastic models, damage models, coupled plastic damage
models. Most models are based on phenomenological approaches using the framework of thermodynamics of
irreversible process. In practice, these models can capture main features of mechanical behaviours of
geomaterials and used for engineering analysis and design. However, the phenomenological models fail in
linking macroscopic responses to microscopic mechanisms. For example, they are not able to properly describe
influences of mineral compositions. Some micromechanical models have been proposed for modelling induced
damage in brittle geomaterials. They are so far generally based on linear fracture mechanics without using
rigorous up-scaling methods. With the rapid use of new composite materials, significant advances have been
realised in homogenization methods for determination of effective properties of linear and heterogeneous
materials. The application of such techniques to geomaterials represents an interesting challenge in constitutive
modelling of such complex materials. In this short review paper, we intend to present the general framework of
multi-scale modelling of geomaterials using proper homogenization methods. Two typical cases will be
considered. In the first case, a micromechanical model for anisotropic damage in brittle rocks will be presented.
In the second one, we will show the application of a nonlinear homogenization method to plastic damage
modelling of the Callovo-Oxfordian argillite.
LINEAR HOMOGENIZATION
Consider a component of structure in geomaterials (Figure 3). Each material point constituting the structure
component is seen as homogeneous medium at the macroscopic scale ( L ). However, at smaller scales, the
material point contains various heterogeneities as above mentioned. The macroscopic properties of the material
point depend on the mineral composition and microstructure at this position, and can be estimated by different
homogenization schemes. The homogenization methods are based on the proper definition of a representative
volume element (RVE). The definition of RVE must verify the principle of scale separation. The seize of the
RVE ( l ) must be large enough compared with the characteristic length of heterogeneities (noted as a ) to be
studied such as average grains size, and at the same time smaller enough compared with the characteristic length
of structure component ( L ). Thus the scale separation implies a ≤ l ≤ L.
x i
L
l
x j
Figure 3 From macroscopic to microscopic scale: definition of representative volume element (RVE)
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