Micromechanical constitutive models of geomaterials

Geomaterials" is the generic term for the main civil engineering materials: soil, rock and concrete. Geomaterials have a microstructure formed by elementary particles or aggregates (the grains of a sand, or the crystalline assemblies of a rock, for example). Describing the mechanical behavior of geomaterials can therefore be approached at several levels:

• from a large scale with respect to the characteristic size of the heterogeneities forming the microstructure, they are then seen as continuous media and their behaviour can be described by elasto-visco-plastic phenomenological models within the framework of the mechanics of continuous media;

• or by describing the physical (or even physico-chemical) interactions at play at the microstructural scale, such as contact interactions between two grains of sand, which are responsible for large-scale deformations. These small-scale interactions are described within the framework of micromechanics, and it is possible to build models of the mechanical behavior of geomaterials based in whole or in part on these micromechanical elements.

This article presents developments relating to this second level of description. The behavioral models that emerge from it are enjoying a boom in the context of research and development activities for civil engineering. These models are based in particular on a numerical method known as the "discrete element method", which will be presented in this article. This method is based on "Molecular Dynamics", one of the most powerful numerical methodologies in contemporary physical chemistry. The numerical modeling tools derived from this approach, capable of taking into account each individual soil grain, rock or concrete element, open up new perspectives for engineers. These prospects are currently being extended by the possibility of coupling these tools with CFD (Computational Fluid Dynamics) methods to describe the dynamics of the interstitial liquid and its interaction with the solid granular phase during internal flows.

We'll also be looking at analytical models, known as "micromechanical constitutive relations", which are an alternative to numerical models based on the discrete element method, and which can be implemented instead of phenomenological models in conventional calculation codes using the finite element or finite difference methods.

Finally, it is also possible to enrich existing phenomenological models by integrating micromechanical elements describing the anisotropy of the geomaterial.