Previous research on the interaction and evolution of stress, permeability, strength, and reaction kinetics in this chemical system has concentrated on the dehydration reaction of gypsum (Olgaard et al., 1995; Ko et al., 1995; 1997; Wang and Wong 2003; Milsch and Scholz, 2005; Milsch et al., 2011; Llana-Fúnez et al., 2012; Leclère et al., 2016; Marti et al., 2021; Schrank et al., 2021). Hydration of anhydrite to gypsum has been studied mainly with powders of sieved natural and synthetic anhydrite under hydrostatic conditions (e.g. Leininger et al., 1957; Hardie, 1967; Sievert et al., 2005). Hardie (1967) studied the influence of temperature on pure anhydrite powders with different grain sizes in experiments lasting about 8 months at different temperatures between 25–60 ∘C without recording hydration. Only the addition of gypsum “seeds” under similar conditions induced relatively rapid hydration. A 1:1 mixture of polycrystalline anhydrite and gypsum produced 3 % more gypsum after 83 d (Hardie, 1967).

Evolution of strength, stress–strain behaviour, permeability as well as the role of grain size and fabric without any hydration or dehydration reaction in gypsum and anhydrite has been studied by Bell (1994) and De Paola et al. (2009). Bell (1994) found that anhydrite has a “strong” unconfined compressive strength (102.9 and 97.5 MPa for two types of anhydrites), whereas gypsum is ranked as having “medium” properties (average ranges between 24.1 and 34.8 MPa, depending on the pressure). Based on the stress vs. strain behaviour, Bell (1994) found that the onset of plastic deformation occurs at an earlier stage during axial loading for gypsum compared to anhydrite. Effective pressure has a significant effect on the permeability evolution under confined-stress conditions and controls the brittle-to-ductile transition of pure polycrystalline anhydrite during deformation (De Paola et al., 2009). During brittle failure, permeability increased dynamically by about 2 to 3 orders of magnitude. The dynamic permeability and porosity evolution during the triaxial-loading tests can be summarized in three stages: (i) permeability and volume reduction through compaction in progress, (ii) permeability increase due to the onset of intra-granular micro-cracking, and (iii) volume increase (dilation) and brittle failure (De Paola et al., 2009). The strength of dry anhydrite cap rock during triaxial tests increased with increasing confining pressure and slightly weakened with increasing temperature, whereas fluid contact prior to failure changed the effective pressure and lowered the strength, but not the volumetric (permeability) behaviour (Hangx et al., 2010, 2011).

Petrographic observations from natural rocks and experimental studies indicate that the mechanisms behind hydration (and dehydration) are (dis)solution–precipitation and direct replacement with additional water available (Hardie, 1967; Sievert et al., 2005; Jaworska and Nowak, 2013; Bedford, 2017). Secondary gypsum is produced initially in the most fractured areas of anhydrite rocks and forms along cracks and grain boundaries (Jaworska, 2012; Warren, 2016). Leininger et al. (1957) studied the effect of acids, bases, and salts, particularly alkali sulfates, and showed that cations serve as activators and accelerate the hydration of gypsum, whereas anions decelerate the reaction. Activator solutions speed up the time for the appearance of maximum specific surface area and the rate of formation of maximum gypsum.

Sievert et al. (2005) developed a conceptual model for solution–precipitation that is now widely accepted (Pina, 2009; Jaworska and Nowak, 2013; Lebedev and Avilina, 2019). Hydration experiments of natural anhydrite in a ball mill with water and activator solutions, such as H2SO4 (pH 1), 5 % MgSO4 ⚫ 7H2O, and a solution of calcium hydroxide, show that the maximum specific surface area develops quickly and does not coincide with the formation rate of the maximum amount of gypsum, which takes rather longer to achieve. There is a time lag between adsorption of ions on the surface of anhydrite, which increases the specific surface area, and the formation of gypsum. Sievert et al. (2005) proposed a five-step mechanism of hydration via solution–precipitation: (i) rapid initial partial dissolution of CaSO4 and adsorption of hydrated Ca2+ and SO42- ions at the surface of anhydrite, (ii) slow increase in thickness of the adsorbed layer, (iii) crack formation in the adsorbed layer and counter-migration of H2O (in) and Ca2+ and SO42- ions (out), (iv) formation of gypsum nuclei at the surface of anhydrite, and (v) formation of nuclei followed by rapid gypsum crystallization.

A total of eight natural-anhydrite core plugs were used for the triaxial experiments. Six samples were run with water present, and two were run without the presence of water. The core plugs were extracted from two anhydrite-dominated surface outcrop field samples of the Òdena Gypsum Formation. This is the marginal equivalent of the salt deposits of the Cardona Saline Formation (upper Eocene) in the southern Pyrenean foreland basin in Spain (Ortí Cabo et al., 1985).

Macroscopically, the Òdena samples are of a pale beige colour with discrete centimetre-scale domains that contain light-brown clay or mud inclusions (Fig. 2a). The anhydrite rocks have minor natural-gypsum content of approximately 10 % to 15 %. All samples show fibro-radiate crystals of anhydrite (Fig. 2b, c). These spherulites appear either isolated or arranged in centimetre-long bands. Microscopically, gypsum is located in between the anhydrite blades of the spherulites in veins (up to 10 µm in aperture), in the spherulite centres, and in between spherulites in broader fractures (up to 50 µm in aperture) and in the centre of the band structures. Electron backscatter diffraction (EBSD) analysis shows that the crystal orientation in the spherulite “blades” changes successively with radial rotation, with lattice orientation being mirrored from the centre (Fig. 2d). The statistical description of the intensity of the fabric based on clustering of poles on pole figures, known as the “multiple of uniform density” (m.u.d.), was calculated. A crystallographic preferred orientation, or CPO, exists where m.u.d. > 1.

One additional core of pure gypsum was taken from an outcrop from Volterra, Italy, to compare the stress–strain behaviour and strength of anhydrite-dominated vs. gypsum-dominated rocks. Volterra gypsum is a well-studied polycrystalline material (Heard and Rubey, 1966; Ko et al., 1997; Llana-Fúnez et al., 2012) and has been used in many experiments (e.g. Olgaard et al., 1995; Hildyard et al., 2011b; Brantut et al., 2012). As required for the triaxial apparatus, cores with a length (x axis) of 60 mm and a diameter of 25 mm (y and z dimension) were drilled out of sample blocks. Given that the sample material does not display any preferred orientation fabric at the macroscale and was collected from an outcrop, cores were drilled perpendicular to the bedding. The Volterra gypsum is homogeneous with no foliation; thus the orientation of the core from this material is arbitrary.

Core plugs were drilled in the presence of water and were air-dried for 24 h immediately afterward to mitigate any potential alteration effects. It was presumed that the time of exposure to water under ambient laboratory conditions did not permit hydration of the anhydrite before deformation experiments. Pre- and post-experiment analysis of thin sections validates this assumption. A hole was then drilled (dry) into the centre of the anhydrite cores along the x axis using a drill head with a diameter of 1.5 mm through the axis of each core to increase fluid flow and sample surface to facilitate faster and more intense hydration. All core plugs intended to be used in the experiment with fluid pressure were immersed in water and left to soak 10 min before starting experimental runs. Core plugs were prepared for triaxial experiments by encapsulation in Viton™ elastomer jackets to ensure a seal is formed during the experiments that shields the sample from the oil used to generate confining pressure in the cell.

All samples were analysed before and, where possible, after triaxial-loading tests under confining pressure via scanning electron microscopy using backscattered electron (BSE) imaging, energy-dispersive X-ray spectroscopy (EDS), and EBSD. Grain and fracture characteristics and mineral content were analysed via a range of software, including FracPaQ (Healy and Rizzo, 2017; Healy et al., 2017), ImageJ (Rasband, 1997; Schneider et al., 2012), and Oxford Instruments Channel 5 for EBSD data processing.

Surplus material sourced directly adjacent to the core plugs was used to prepare polished thin sections in the core plug reference frame x–y, z and x= y, z–y, and z directions before starting any experiment. Thin sections of the samples taken after experiments were cut approximately parallel to the x axis (i.e. parallel to σ1). Thin sections were prepared for scanning electron microscopy (SEM) by polishing with alumina, followed by a final polish with 0.6 µm colloidal silica in NaOH using a Buehler VibroMet II polisher for 2 to 4 h. An evaporative carbon coating was applied to prevent charging during SEM. BSE imaging was conducted with a Zeiss EVO MA10 SEM fitted with an Oxford Instruments INCA X-ray microanalysis system. A Tescan MIRA3 field emission scanning electron microscope (FE-SEM) at the John de Laeter Centre at Curtin University with an Oxford Instruments EBSD acquisition system, including a Symmetry EBSD detector, was used to quantify crystallographic microstructures.

Secondary electron (SE) and BSE images were acquired, and EBSD maps with step sizes ranging from 1.7 to 50 µm were collected. Data acquisition and processing settings as well as processing procedures (Table 1) followed those of Vargas-Meleza et al. (2015) and Timms et al. (2017, 2019). Isolated, erroneous EBSD data points were removed using a “wild spike” correction in Channel 5, and a zero-solution infill to six nearest-neighbour extrapolations was applied routinely. Mis-indexing of anhydrite with a range of systematic-crystallographic-orientation relationships was identified, and data were corrected using the function in the Tango module of Channel 5.

For phase quantification, BSE images were combined with energy dispersive spectroscopy (EDS) phase identification data and analysed with ImageJ software (Rasband, 1997; Schneider et al., 2012) using a greyscale threshold to determine phase abundance. Minor uncertainties of this approach include greyscale variation at phase boundaries and/or due to the topography of the polished surface. Additionally, fracture patterns in post-experiment sample material were quantified by manual digital tracing of gypsum-filled fractures and veins in BSE images followed by FracPaQ analysis of orientation and length of the mapped linear-fracture trace segments (Healy and Rizzo, 2017; Healy et al., 2017).

All testing was conducted with the high-pressure, high-temperature (HP–HT) triaxial-rock-deformation apparatus (TRI-X 250 MPa/200 ∘C) from Sanchez Technologies at the University of Aberdeen (Fig. 1b). The parameters chosen for testing are listed in Table 2. The experiments followed three different testing modes: (i) dry, (ii) “wet”, and (iii) constant-stress differential compaction (CSDC) (Fig. 1c). The principal stress configuration was σ1>σ2=σ3 throughout runs in modes (i) and (ii) and achieved through the application of an axial load (“active” deformation). The (i) dry and (ii) wet modes were created to evaluate material strength and stress vs. strain behaviour for the sample material with different axial-load and pressure settings.

During wet-mode tests, fluid pressure was applied before initiating the axial load. In the case of constant-stress differential compaction, the axial load (i.e. displacement rate) was put on hold after achieving ∼ 100 MPa differential stress (75 % yield stress of the wet experiments W3 and W4) to achieve micro-cracking, and before coalescing shear fractures are supposed to have formed. Only then was water flooded into the sample chamber and fluid pressure applied. The principal stress configuration was hydrostatic, i.e. σ1=σ2= σ3. If failure was not achieved within 6 h of starting CSDC, the same axial load was reapplied, which reinstated the respective differential-stress field. At the end of each experiment of modes (ii) and (iii) the Viton™ jackets were opened, and the samples were placed in an oven at 50 ∘C for ∼ 30 min to prevent any further hydration from proceeding.

The strongest evidence for successful hydration and formation of gypsum is represented by the breccia vein shown in Fig. 6. The main vein has an orientation of 37.5∘ to x (σ1), which is consistent with a shear fracture caused by the CSDC-mode experiment. Optical assessment and greyscale threshold analysis shows that the gypsum content in and around the shear fracture is significantly higher compared to the initial sample material (Fig. 2b). The higher abundance of gypsum and the presence of rounded, rotated anhydrite grains in the margins (domains B and D) of the breccia vein are evidence for active (syn-experiment) gypsification. The centre of the breccia vein (Fig. 6, domain C) contains >100 µm gypsum clasts, which is orders of magnitude larger than any observed pre-experiment gypsum, located in centres of anhydrite spherulites and short, narrow (< 50 µm) veins (Fig. 2b). These clasts can contain small anhydrite inclusions and are derived from newly formed gypsum (Fig. 6a). Based on the distribution of the anhydrite inclusions at the margins of the gypsum clasts, the gypsum was part of a shear interface with active gypsification before brecciation occurred.

The formation of the gypsum vein system from sample W1, documented after a wet-mode experiment (Fig. 4a, b), is consistent with syn-experiment gypsification and deformation. The wide vein apertures (≫50 µm) in combination with the systematic orientation and length of the gypsum-filled vein system of > 2.5 cm were not present in the primary sample material. These are strong indicators for experimentally induced extension and formation of new gypsum. The wide gypsum-filled vein system formed by linked extensional fractures with a minor shear component that progressively coalesced to result in a stepped shear fracture. (Fig. 4). Additionally, the crystallographic orientation of the vein gypsum is such that poles to {010} generally coincide with the direction of maximum shear stress during the experiments. This geometric link between gypsum growth and stress during an experiment and independent of the surrounding anhydrite has not been described before and requires further discussion.

The spatial link between newly formed gypsum and fractures shows that hydration predominantly progressed through the fracture network rather than a front that progressed through the sample, similar to that reported for gypsum dehydration and anhydritization (Wang and Wong, 2003; Llana-Fúnez et al., 2012). A concept for the hydration mechanism of anhydrite particles developed by Sievert et al. (2005) involves dissolution and precipitation, which was adapted here to explain hydration of the Òdena anhydrite under stress (Fig. 8). The wet-mode experiments make H2O groups available to new mineral interfaces during the initial intra-granular fracturing. Upon the contact of anhydrite surfaces with water, the CaSO4 solution and the surface absorption layer of hydrated Ca2+ and SO42- ions formed (Fig. 8) (Sievert et al., 2005). The increase in thickness of the absorbed layer is reportedly a slow process and needs to be followed by the crack formation in the absorbed layer and counter-migration of H2O and Ca2+ as well as SO42- ions (Sievert et al., 2005).

Pre-existing gypsum in the samples acted as a natural seeding material, which has been demonstrated elsewhere to enable (or speed up) the hydration reaction process because the kinetically challenging process of forming nuclei (e.g. Hardie, 1967; Wheeler, 1991; Sievert et al., 2005) is skipped. The enhancement of mineral replacement reactions by the presence of seeds is also a common phenomenon in other diagenetic processes, such as dolomitization (e.g. Whitaker and Xiao, 2010). Therefore, hydration was possible as soon as the samples had water contact and more likely in CSDC experiments due to the amount of time of contact with H2O. However, the importance of this process is difficult to reconcile with the distinct microstructural location of new gypsum in newly formed veins or the lack of gypsum in hydrostatic experiments. Rounded anhydrite inclusions in gypsum margins of shear fractures and as clasts in brecciated veins (Fig. 6a) are specific indicators for the dissolution of anhydrite.

The role of fractures is threefold: firstly, they provide new surface area available for reaction. Secondly, they facilitate fluid flow to enable a readily available medium (H2O) for solution transfer of Ca2+ and SO42- ions. Thirdly, locally variable stresses associated with fracture propagation give rise to spatial variations in chemical potential and, as a consequence, chemical disequilibrium (Llana-Fúnez et al., 2012; Wheeler, 2018). Solid–fluid contacts will be at the pressure of the fluids (Pf), whilst solid–solid contacts will have a higher average normal stress, depending on the bulk effective pressure and contact area (Llana-Fúnez et al., 2012). That provides different pathways of Ca2+ and SO42- ions during the reaction. Therefore, the anhydrite solution was preferentially formed in the stressed anhydrite at fracture tips, grain boundaries, and gypsum–anhydrite contacts. Once gypsum nuclei were established, growth was likely to be rapid, following the findings of Sievert et al. (2005).

The transformation of anhydrite to gypsum requires a significant change in volume of solid material (i. e. swelling). Upon contact with water, gypsum is no longer solid but partly dissolved and starts to moderately swell (Fig. 8b). Simultaneously, anhydrite dissolution occurs, and Ca2+ and SO42- ions and H2O molecules permeate through the gypsum (Fig. 8b, c). The consumption of water acts to lower local fluid pressure, whereas replacement of anhydrite by gypsum causes swelling, counteracting the decrease in local fluid pressure. Recall that the tests were conducted at a constant bulk fluid pressure (held 10 MPa lower than confining pressure) without any induced sample-scale fluid flow. Nevertheless, fresh supply of H2O at the scale of grains, pores, and cracks was facilitated by the opening of a connective network of new inter-granular fractures (Fig. 7aiii). Fracturing, combined with the availability of water for the formation of gypsum, facilitates dilatancy, which is seen as bulging of the jacketed sample charges (Fig. 7aiii). Swelling (volume increase) and water loss through H2O groups being bound into the gypsum impact activity of hydration in places. Swelling can seal up cracks and trap free water. This potentially stops the hydration reaction in places, while the water migrates into other, harder-to-reach environments, like grain boundaries, facilitating hydration there with fewer H2O groups available.

Cataclastic flow and the full development of major shear fractures (Fig. 7a, biv) occurred after the peak stress was reached. The wet tests show that these major shear fractures with thin interconnected parallel fractures and areas of wide fractures are all filled with gypsum. These form planar zones of weakness for catastrophic shear failure. For the phase after peak stress is achieved, De Paola et al. (2009) recorded a rapid increase in permeability that becomes “chaotic” in the final stage of failure. This is likely to be coupled with a rapid increase in the area of available reaction surfaces. The macroscopic observations show that the sample cores after experiments with applied fluid pressure, if they do not fail catastrophically, comprise fragmented debris of centimetre to millimetre size, covered with a white slurry. This indicates that rapid gypsum formation may occur during the last stage (only seconds long) and upon failure. The lower peak stress of sample H2 after re-initiation of the axial-displacement rate can be explained by the development of weakening zones due to the appearance of mechanically weaker gypsum and dynamic opening and filling of cracks. Only sample H1 failed during CSDC. This could be due to a favourable orientation of pre-existing zones of weakness. There is gypsum in the initial sample in short (< 1 cm) veins with an aperture of < 50 µm. The formation of new gypsum is linked to sample failure.

The magnitude and significance of differential stresses that may be induced through hydration reactions of mineral systems accompanied by a solid-volume increase are poorly understood. However, hydration reactions are commonly associated with deformation reactions like dilatant fracturing, which increases the fluid permeability. Plümper et al. (2022) showed that the hydration reaction MgO + H2O = Mg(OH)2 can induce stresses of several hundred megapascals in nature, with maximum local stresses up to ∼ 1.5 GPa. This is in agreement with the findings of this study, based on which stress, as opposed to pressure, influences the hydration reaction specifically through micro-cracking and faulting, providing pathways for fluids and surface area for the reaction.

There are two different stress–material interactions to consider for understanding the impact of stress on chemical reactions (Wheeler, 2018). Normal stress (anisotropy) along grain interfaces and between interfaces with different orientations has the main impact on chemical reactions in the Earth and thus plays a key role in quantifying stress-related chemical processes (Wheeler, 2014, 2018). Chemical potential depends on a “weighted” mean stress, which means that the magnitude and orientation of stress have an impact (Wheeler, 2018). Experiments show that narrow aqueous fluid or other fluid films along (grain) boundaries may persist, even if normal stress is greater than fluid pressure (Hickman and Evans, 1995; Israelachvili, 2011). They are regarded as stressed solids rather than fluids (e.g. Israelachvili, 1992; Wheeler, 2018), which provide fast diffusion pathways (Rutter, 1976). Integral parameters for models are the grain boundary structure, assumptions about the mobility of specific components, and reaction activity (Wheeler, 2018). These include grain boundary film properties like the connection between surface and interface energies and film structure (Hickman and Evans, 1995) as well as the relationship of fluid film thickness to normal stress (Israelachvili, 2011). The basic concept is that grain boundaries, representing a small-scale volume, are locally buffered by (i.e. are in local equilibrium with) the adjacent solids (Wheeler, 2018). Wheeler (2018) states that diffusion is the main mechanism of stress-related chemical processes and is active along long-range chemical reaction pathways that are provided by interconnected interfaces under crustal conditions. It is established that diffusion rates along interfaces such as grain boundaries are several orders of magnitude faster compared to intracrystalline diffusion (Dohmen and Milke, 2010).

Further, segregation of (incompatible) elements and their enrichment in grain interfaces are considered to have a significant impact on the physical and chemical properties of mantle rocks (Hiraga et al., 2007). Interfacial segregation linked with grain boundary character distribution (GBCD) may lead to grain boundary energy minimization (Tacchetto et al., 2021). It follows that interfacial segregation potentially influences if and where diffusion is active or accelerated in natural samples during hydration.

Macroscopically, the difference between the wet- and CSDC-mode samples is that the main shear faults after CSDC are characterized by an area of intense fracturing, filled with brecciated material. The resulting lateral chips are either not faulted or extremely faulted compared to the dry- and wet-test samples. Altogether, the pieces resulting from fracturing seem smaller in size and are coated by a pale-grey, soft, viscous layer. Combined with the relative mechanical weakness of samples after CSDC compared to dry and especially wet tests, it is possible to conclude that there is a difference between reaction rates and mechanisms for hydrostatic and non-hydrostatic loadings. The possible relationship between the spatial distribution and crystallographic orientation of the new gypsum in veins with orientations of 45∘ from the maximum shear stress presented by this study is a start to understanding hydration processes on the grain–pore–crack scale and how they are linked to mechanic, thermodynamic, and kinetic processes.

The main implication of this study of hydration under stress in the crystalline CaSO4–H2O system is that mechanical–chemical coupling of deformation and hydration is central to permitting water to reach the reaction zone and cause significant mechanical weakening. The stability of natural evaporites is of major interest in various settings, especially in contexts of underground structures with a variety of purposes, including road and tunnel construction and monitoring as well as mining of evaporites, and where caverns in evaporites are used as geo-energy storage facilities. In general, evaporitic rock salt deposits are anything but homogeneous or monomineralic (Stewart, 1963), with gypsum and anhydrite being two of the nine most important minerals. Organizations in Germany and the United States of America are already storing low- and intermediate-level nuclear waste in repositories within rock salt deposits. The basic assumptions are that rock salt functions as a seal, with halokinesis “healing” potential leaks. The need for more studies to determine the safety and efficiency of rock salt deposits is widely recognized.

The findings of this study, mechanical–chemical weakening through hydration of anhydrite along stressed fractures, show how rapidly mechanical weaknesses may form and threaten the stability of caverns in natural evaporite deposits. This needs to be included in future stability models. Anhydrite-bearing evaporite sequences are commonly the weakest horizons in sedimentary basins and form detachment horizons in foreland fold-and-thrust belts (e.g. Heard and Rubey, 1966; Hildyard et al., 2011a). Hydration of the anhydrite through stressed fractures must further weaken the mechanical strength of such sequences and make the formation of detachment horizons easier.

The findings of this study also have implications for hydration in a wider variety of geological settings. The CaSO4–H2O system could be seen as an analogue for other rock systems that are controlled by hydration, dehydration, and stress. Common fluid pathways in the Earth include faults, shear zones, and stratigraphic aquifers. The study suggests that hydration along such pathways can be rapid and generate planes of significant weakness under differential stress. Deep crustal earthquakes are often associated with local weakening of the generally dry, mechanically strong deep crust through fluid-driven metamorphic reactions (Jamtveit et al., 2019). Studies from the Bergen Arcs in western Norway show that fluid migration through shear zones facilitates highly localized eclogitization of anhydrous (granulite) crust along these zones (e.g. Austrheim and Griffin, 1985; Austrheim, 1987; Jamtveit et al., 1990; Jamtveit et al., 2019) and can result in transient mechanical weakening, brittle deformation, and earthquakes (e.g. Jamtveit et al., 2019; Bras et al., 2021). However, weakening in the case of granulite is the consequence of fracturing, not necessarily of hydration, unless the eclogites were deformed. At an early stage, eclogite facies mineralogy is even known to be found as veins in extension fractures (Jamtveit et al., 1990), although the difference in strength between granulite and eclogite is not as significant as that of anhydrite and gypsum. Subduction of oceanic and continental crust (Pérez-Gussinyé and Reston, 2001; Ranero et al., 2003; Bayrakci et al., 2016) even transports water to the deep mantle and creates local water-rich horizons.