A chemo-mechanical model of the swelling of anhydritic claystones

Abstract

Anhydritic claystones are widely distributed in the Gypsum Keuper formation. Their swelling is associated with the chemical process of anhydrite to gypsum transformation and has caused extensive damages in tunnels. Even though this problem has attracted great scientific interest, an adequate mathematical description of the swelling of anhydritic rocks is still missing. The present paper contributes towards closing this gap by formulating a coupled chemo-mechanical constitutive model, which considers anhydritic rock as an elastoplastic porous medium according to the principle of effective stresses, with a Mohr–Coulomb yield criterion, a non-associated flow rule and an additional, chemically induced strain component. The volumetric chemical strain is equal to the sum of the changes of the volume of the solids and of the pore volume. The change of the volume of the solids depends on the stoichiometry of the chemical reaction and is proportional to the mass of the transformed anhydrite. The pore volume may increase or decrease during the anhydrite to gypsum transformation, depending on how gypsum grows. The pore volume increases if the gypsum crystals crack and expand the matrix, and decreases if the gypsum crystals precipitate within the available pore space. The proposed model considers experimental results according to which the higher the stresses and porosity, the lower the increase in pore volume. In addition, the model assumes that the chemical strains are coaxial with the principal stresses and that the volumetric chemical strain in each principal direction is inversely proportional to the corresponding principal stress. The model is calibrated with results of tests on artificial anhydrite-kaolin specimens and achieves a very high correlation degree (R² = 0.92).