This paper has extended modified mixture theory with consideration of hydration swelling in unsaturated rock. By using non-equilibrium thermodynamics and Biot elasticity, a fully coupled formulation including hydration swelling term is derived. Standard arguments of non-equilibrium thermodynamics are used to derive the Darcy’s law for unsaturated flow. Helmholtz free energy has been used to give the relationship between the stress and pore pressure. The chemical potential of water in pore space and clay platelets has been included in the analysis of water sensitive materials such as shale. Finally, a simple numerical example has been presented for illustrative purpose, the results show that the swelling parameter has a strong influence on stress and strain.
- Modified mixture theory
- Non-equilibrium thermodynamics