Analysis of small temperature oscillation in a deformable solid matrix containing a spherical cavity filled with a compressible liquid – Analytical solutions for damage initiation induced by pore pressure variation

Abstract

This paper analyzes the possibility of damage initiation induced by a very small temperature variation near a liquid-filled spherical cavity inside a deformable solid matrix. Experiments confirm that small temperature variations in a (compressible) liquid-filled cavity can induce high pressure peaks, depending on the initial temperature and pressures. The main motivation of the study is to verify the possibility of damage initiation induced by a very small temperature variation in a saturated liquid-filled porous medium with ultra-low permeability. Depending on the interaction between micro-cracks and pores, this damage may significantly affect the permeability conditions. The study of a single water-filled pore in an infinite matrix is quite a convenient preliminary step, since the stress field in the solid matrix is independent of its constitutive behavior (a statically determinate problem) what allows simplifying the complex coupled non-linear analysis. An abstract thermodynamic framework is used to present constitutive theories for generalized compressible Newtonian fluids and for elastic and elasto-plastic solid matrix behaviors. Both theories encompass a wide variety of constitutive models for solids and fluids found in the literature and can be applied in many engineering problems involving liquid-filled porous media. Using an adequate equation of state for the thermodynamic pressure proposed for liquid water at high pressures, it is possible to predict analytically if a very small liquid temperature variation (maximum of 5 K) can induce the matrix failure. Two examples of matrix behaviors are analyzed: brittle-elastic and elasto-plastic. Adequate failure criteria are used in each case to predict analytically the critical pressure required for the damage initiation. Once this pressure is determined, the temperature variation necessary to the damage initiation can also be obtained using the state law proposed for the thermodynamic pressure.