Theoretical analysis of fluid inclusions for in situ soil stress and deformation measurements

In situ determination of stress, strength, and deformation of soils for direct assessment of trafficability and susceptibility to compaction has been a long-standing problem in soil mechanics and agricultural engineering. Despite considerable progress in development of sophisticated probes, data interpretation remains in its infancy due to incomplete understanding of soil-probe interaction. In this study we developed a novel theoretical framework for describing pressure and deformation of fluid inclusions within an elasto-plastic soil matrix subject to anisotropic remote stresses that provides the basis for development of in situ probes for stress and deformation measurement. Results showed that for a compressible fluid inclusion (e.g., air) embedded in an elastic matrix, inclusion pressure is determined primarily by the matrix mean stress, Poisson's ratio, and the product of matrix bulk modulus and fluid compressibility. For incompressible fluids (e.g., water), inclusion pressure becomes independent of matrix stiffness. Differences in remote stress affect inclusion shape and influence probe pressure for large deformation due to increasing stress concentration. The solution for an elastic matrix also provides upper and lower bounds for inclusion pressure in an elasto-plastic matrix under isotropic stress. For the more common anisotropic remote stress, inclusion pressure and deformation differ considerably for elastic and elasto-plastic soil matrix. We found that elastic rubber membranes, often used to separate the fluid inclusion from the matrix, do not influence inclusion pressure or shape as long as membrane and soil stiffness are of similar magnitude. Pressure measurements from laboratory and field experiments using the so-called Boiling probe agreed well with inclusion pressures predicted by the proposed model.