On Porous Soil Materials Saturated with a Compressible Pore‐fluid Mixture

Abstract

AbstractGeomaterials can be understood as consisting of a porous solid skeleton, with the pores saturated by a fluid. The fluid may be water, air or, a water‐air mixture. The mechanical behaviour of the whole soil body, consisting of the soil skeleton and the pore‐fluid, is governed by the properties of its constituents. Since the exact structure of the pore‐space is not known, a homogenization over a representative elementary volume is required in order to obtain a macroscopic approach. The description of the motion of a multiphase‐mixture of immiscible constituents can be performed by the Theory of Porous Media (TPM). Based on the classical mixture theory, the TPM deals with superimposed continua. Additionally, the information of the structure is included via the concept of volume fractions [1–3].Here, the soil skeleton material is assumed to be incompressible, whereas the pore‐fluid mixture is compressible according to its composition of water and air by variable volume fractions. The pressure‐density‐function of the pore‐fluid is derived within the framework of the TPM. Furthermore, the viscous pore‐fluid allows for a linear momentum exchange (interaction force) between the constituents, which, under special assumptions, leads to the well‐known Darcy law.