Micromechanical formulation of first‐ and second‐order works in unsaturated granular media

Abstract

AbstractThe current work provides a micromechanical formulation of the first‐ and second‐order works for unsaturated granular media. For this purpose, a Representative Elementary Volume (REV) of a triphasic medium is considered, which consists of a collection of particles with the pore space in between them occupied by wetting and non‐wetting fluids. By assigning a kinematics to the REV at the micro‐scale, the first‐ and second‐order works of internal forces associated with the solid phase, fluids, and the interfaces between them are derived. The formulations are presented in the most general case considering large deformations within both Eulerian and Lagrangian formalisms, while the special case of infinitesimal deformation and rotation is also investigated. With respect to classical formulations, the obtained expressions for the first‐ and second‐order works include additional contributions related to the deformation of the interface of the two fluids, and in case of the first‐order work, the change in geometry of the intersection line of the three phases. Next, we consider a special case of pendular regime at low wetting saturation, where the wetting fluid appears as a set of isolated liquid bridges formed between particle pairs. Such condition has been previously simulated via Discrete Element Method (DEM) numerical framework where the distributed capillary forces are replaced with a resultant capillary force that is added as a new contact force. We show here that using the resultant capillary force, the generated first‐ and second‐order works in the REV are generally different from the ones produced by the distributed capillary forces, unless under special conditions.