Chemo-Mechanical Modeling of Anhydritic Claystones

This paper presents a model for the swelling of anhydritic claystones – a severe problem in tunnelling. The model incorporates the effect of the chemical process of anhydrite to gypsum transformation via a strain decomposition in a mechanical (e.g., elastoplastic) part and a reaction-induced part. The latter depends on the mass change of anhydrite and considers that the volumetric chemical strain rate is the sum of the solid and pore volume change. The former is given by the chemical reaction's stoichiometry and the molar volumes of anhydrite and gypsum; while the latter may decrease or increase depending on whether new gypsum crystals precipitate within the available pore space or expand the matrix. Laboratory observations indicate that the higher the stresses and the porosity, the less the pore volume will increase during the chemical reaction. Moreover, the model assumes that the chemical strain rate is coaxial with the stress and that the strain in every principal direction depends on all three principal stresses. The predictions of the proposed model agree well with the results of test on artificial anhydrite-kaolin specimens and a high degree of correlation is achieved (R2 = 0.92). 1. INTRODUCTION The swelling of anhydritic claystones is attributed to the water uptake by the clay minerals and the chemical process of anhydrite (CaSO4) to gypsum (CaSO4·2H2O) transformation ("AGT"). This phenomenon has caused extensive damages to a number of tunnels (e.g., tunnel floor heave, damage of the invert arch; cf., Amstad and Kovári, 2001; Anagnostou, 2007) and hence it has attracted great attention from the scientific community (e.g., Anagnostou et al., 2010; Ramon, 2014; Serafeimidis, 2014; Butscher et al., 2016; Wanninger, 2019). Nevertheless, a swelling law, capable of capturing these processes, is still missing (Anagnostou et al., 2010; Butscher et al., 2016), thus introducing uncertainties in tunnel design. Early swelling models for tunneling (e.g., Einstein et al., 1972; Wittke and Rissler, 1976; Fröhlich, 1986) were based on Grob's (1972) "semi-logarithmic swelling law" and described swelling as a purely mechanical process; the developed strains are associated only with the stress changes. However, swelling rocks might also deform under constant stress or experience a stress increase without deformation, phenomena beyond the scope of purely mechanical models.