Chemo-thermal Stresses Analysis Of Saturated Poroelastic Media With A Cylindrical Hole Or Spherical Cavity

In the framework of Biot’s theory, a weighted average of temperatures for solid and fluid phases is used to establish a chemo-thermo-elastic mathematical model for fluid saturated transversely isotropic poroelastic media. The temperatures for solid and fluid phases, pore pressure and chemo-thermal stress around a cylindrical hole or a spherical cavity in an infinite fluid saturated porous medium under the variations of temperature and solute mole fraction are investigated by employing Laplace transform technique and numerical method. The work is mainly on:First, assumed that the pore fluid comprises of two chemical species including solute and solvent, a chemo-thermo-elastic model for fluid saturated transversely isotropic poroelastic media undergoing local thermal non-equilibrium (LTNE) is established.The decoupling governing equations of pore pressure, variation of the solute mole fraction and solid displacement are deduced under the irrotational displacement field for plane strain deformation problems. For two typical engineering problems, namely a cylindrical hole or a spherical cavity in an infinite fluid saturated poroelastic medium, the solutions of temperature field, variation of the solute mole fraction and pore pressure are obtained by using the Laplace transform technique for the case of different boundary conditions. Finally, Numerical results for two porous materials (clay and sandstone) are presented to examine the influence of variation of the solute mole fraction and material anisotropy parameters effects on the pore pressure and solid stresses around the hole, and the difference between chemical effects.chemo-thermal effects and LTNE effects.The results show that:1) For the case of a saturated medium (transversely isotropic sandstone) with a long cylindrical hole, the ratio of the thermal expansion in the transverse direction to that in the isotropic plane has a more pronounced effect than the corresponding modulus ratio on the thermally induced pore pressure and stresses. When the Sparrow number Sp is small (≈0.35) and Biot number Bi is moderate (≈1.0). The normalized peak of LTNE pressure and radial stress (magnitude) is about two times higher than the peak of the corresponding classical one.2) For the case of a saturated medium (isotropic sandstone) with a long cylindrical hole, the pore pressure and stresses are dominantly affected by chemical effects rather than thermal effects when the temperature and variation of the solute mole fraction change together. The pore pressure and stresses by considering chemical or chemo-thermal effects are same order of magnitude, which is different from that by only considering thermal effect. When Sp is small (≈0.35) and Bi is moderate (≈1.0), the normalized peak of LTNE radial stress (magnitude) is about40-50%higher than the peak of the corresponding classical one.3) For the case of a saturated medium (isotropic clay) with a spherical cavity, the pore pressure and stresses are dominantly affected by chemical effects rather than thermal effects when the temperature and variation of the solute mole fraction change together. The LTNE effects on radial stress (magnitude) become very pronounced when Sp is small (≈0.35) and Bi is moderate (≈1.0). In addition, the pore pressure and stresses whether considering chemical effect or thermal effect or chemo-thermal effect are alway same order of magnitude.