From discrete to continuum modelling of Boundary Value Problems in Geomechanics: an integrated FEM-DEM approach

Double-scale numerical methods constitute an effective tool for simultaneously
representing the complex nature of geomaterials and treating real-scale engineering
problems such as a tunnel excavation or a pressuremetre at a reasonable
numerical cost. This paper presents an approach coupling discrete elements
(DEM) at the microscale with finite elements (FEM) at the macroscale. In this
approach, a DEM-based numerical constitutive law is embedded into a standard
FEM formulation. In this regard, an exhaustive discussion is presented on
how a 2D/3D granular assembly can be used to generate, step by step along the
overall computation process, a consistent Numerically Homogenised Law. The
paper also focuses on some recent developments including a comprehensive
discussion of the efficiency of Newton-like operators, the introduction of a regularisation
technique at the macroscale by means of a second gradient framework,
and the development of parallelisation techniques to alleviate the computational
cost of the proposed approach. Some real-scale problems taking into account
the material spatial variability are illustrated, proving the numerical efficiency
of the proposed approach and the benefit of a particle-based strategy.