Hydro-chemo-mechanical modelling of tunnels in sulfated rocks A. RAMON à , E. E. ALONSO à and S. OLIVELLA à A modelling procedure to address the tunnel–anhydritic rock interaction is described in this paper. The model incorporates the basic physico-chemical phenomena involved in rock swelling, often observed during excavation and subsequent operation of tunnels. It includes (a) a provision for rock damage during tunnel excavation, (b) the precipitation of gypsum crystals in discontinuities and (c) a stress- dependent relationship between swelling strains and mass of gypsum precipitation. The model includes hydro-mechanical coupling and the transport of sulfate salts dissolved in the massif water. Rock damage is described by the development of a network of fractures that increases permeability and allows gypsum crystal growth. Field information, laboratory data and monitoring records available for Lilla tunnel, located in the province of Tarragona, Spain and excavated in Tertiary anhydritic claystone, were selected as a convenient benchmark case to test model capabilities. Predictions and measurements (swelling records of the unlined tunnel floor and swelling pressures against a structural invert) were found to agree reasonably well. KEYWORDS: finite-element modelling; monitoring; soft rocks; tunnels & tunnelling INTRODUCTION AND BACKGROUND Geological formations rich in anhydrite, when crossed by tunnels, may experience severe heave displacements, which usually manifest at floor level. Later, when lining is in place, recorded swelling pressures on load cells are often high or very high (one to several MPa). Case histories have been reported for many decades (Grob, 1972, 1976; Henke, 1976; Einstein, 1979, 1996; Wittke & Pierau, 1979; Kovári et al., 1988; Wittke, 1990, 2006; Steiner, 1993; Madsen et al., 1995; Amstad & Kovári, 2001; Kovári & Descoeudres, 2001; Wittke-Gattermann & Wittke, 2004; Anagnostou, 2007; Alonso et al., 2013). Anhydrite formations belonging to the Triassic Keuper period are frequent in central Europe. The rock massif excavated in Lilla tunnel located in the province of Tarragona, Spain, which will be analysed in this paper, is a recent Tertiary deposit that exhibits a number of features (a clay matrix, variable proportions of anhydrite and gypsum and a history of tectonic deformations) found in Keuper rocks. Early attempts to introduce ground swelling into tunnel design relied on the determination of a ‘swelling law’. A classic example is the Huder–Amberg procedure to determine, under oedometric conditions, a relationship between confining stress and swelling deformation (Huder & Amberg, 1970; Grob, 1972; Einstein et al., 1972; Kovári et al., 1988). Madsen (1999) and ISRM (1989) describe similar procedures to determine the swelling law. Kovári et al. (1988) derived a simple and clever procedure to find a tunnel characteristic curve in the case of swelling ground, which incorporates a swelling law. This contribution opens up the possibility of designing tunnel linings by requiring compat- ibility between lining deformations and the ‘swelling charac- teristic curve’. Historically, the next step was to introduce the swelling law as an imposed ‘external deformation’ into numerical analyses, typically using finite elements; contributions in this regard are provided by Wittke & Rißler (1976), Gysel (1977, 1987), Fröhlich (1986) and Anagnostou (1992, 1995). Some researches describe coupled flow–deformation procedures (Anagnostou, 1993; Wittke-Gattermann, 1998; Heidkamp & Katz, 2002, 2004; Wittke, 2003; Wahlen & Wittke, 2009; Schädlich et al., 2013). Swelling laws may include time, refer to anisotropic conditions and reproduce stress paths expected by tunnel excavations (Barla, 2008). Kramer & Moore (2005) describe swelling rock behaviour by means of viscoelastic models. The calculation procedures developed for swelling non- sulfated clay rocks experience significant difficulties in anhydrite-related swelling. In sulfated rocks, swelling strains are mainly a consequence of gypsum crystal precipitation in aqueous solutions (Ramon & Alonso, 2013; Alonso et al., 2013). This chemical reaction is described by kinetic equations, which require information on the exposed anhy- drite and gypsum surfaces to water, the mass rates of anhydrite dissolution and gypsum precipitation, the current sulfate and ionic concentration of the massif water and the saturation concentration of gypsum and anhydrite. The exposed surfaces of sulfate minerals in a real environment depend on the structural arrangement of the rock constitu- ents and also on fissuring, which is, in part, a response to tunnelling-induced stress changes. These interactions are representative at the scale of field problems and can hardly be reproduced by a ‘point’ estimation, which is the concept behind the formulation of constitutive models. From a laboratory perspective, the ‘point’ is reproduced by a small sample and its representativeness is therefore very limited. Mass rates of dissolution/precipitation require information that is sometimes derived from tests involving the direct interaction of crystals and water – a circumstance far from the physics of clayey sulfated rocks. Saturation concen- trations depend on the pressure acting on crystals, tempera- ture and on the remaining salts dissolved in pore water. Reproducing all these cross-effects in small ‘representative’ samples therefore appears to be a daunting task. The ‘swelling laws’ proposed for expansive clay rocks are not à Division of Geotechnical Engineering and Geosciences, Department of Civil and Environmental Engineering, Universitat Politecnica de Catalunya, Barcelona, Spain. Manuscript received 27 February 2017; revised manuscript accepted 10 July 2017. Published online ahead of print 22 August 2017. Discussion on this paper closes on 1 April 2018, for further details see p. ii. Ramon, A. et al. (2017). Géotechnique 67, No. 11, 968–982 [http://dx.doi.org/10.1680/jgeot.SiP17.P.252] 968 Downloaded by [ UNIV POLITEC CAT - BIBLIOTECA RECTOR G FERRATE] on [19/10/17]. Copyright © ICE Publishing, all rights reserved.