Thibault

Cindy Luisier
email: cindy.luisier@gmail.com

Michel Ballèvre

Thibault Duretz

The role of H2O on metamorphism and deformation at high pressure: A combined petrological and thermo-mechanical study based on the Gran Paradiso Unit, Western Alps

Keywords: high-pressure metamorphism, Gran Paradiso Unit, fluids, kinetics, rheology, thermomechanical modelling, thermodynamic modelling

The role of H2O on metamorphism and deformation at high pressure: A combined petrological and thermo-mechanical study based on the Gran Paradiso Unit, Western Alps

Introduction

Metamorphic transformations in rocks occur due to spatial-temporal variations in environmental factors such as pressure (P), temperature (T), fluid availability and composition [START_REF] Fyfe | Fluids in the Earth's crust. Their significance in metamorphic, tectonic and chemical transport mechanisms[END_REF]. In regional metamorphic environments, a change of these intensive (P, T) and extensive (fluid availability and rock composition) variables takes place due to the burial of the subducting lithosphere during ongoing convergence and triggers changes in metamorphic mineral parageneses. Along with mineral transformations, fluids may be released, through destabilization of hydrous minerals [START_REF] Schmidt | Experimentally based water budgets for dehydrating slabs and consequences for arc magma generation[END_REF] and percolate along lithological interfaces and areas of enhanced permeability (e.g., [START_REF] Connolly | A Hydromechanical Model for Lower Crustal Fluid Flow[END_REF]. Fluid-rock interactions may in turn lead to further modifications of the original rock composition through metasomatism. The mechanical behavior of rocks under stress depends on their rheology, mainly because minerals have different responses to deviatoric stress. Witnesses of the effect on deviatoric stress is recorded in rocks by deformation patterns, such as foliation, lineation, strain shadows around minerals, etc., as well as deformation mechanisms in minerals (fracturing, twinning, diverse types of recrystallisation; e.g., Passchier and Trouw, 2005). Although it is commonly accepted that the presence of a deviatoric component of stress implies that the stress state is not hydrostatic, the magnitude of the deviation from the hydrostatic stress and hence from the lithostatic P (i.e., the vertical stress component) is difficult to quantify.

Although the large-scale burial of rock units in convergent systems can be seen as a continuous process in time and space, P and T can be locally heterogeneous [START_REF] Schenker | Current challenges for explaining (ultra)high-pressure tectonism in the Pennine domain of the Central and Western Alps[END_REF]. Disturbances of the P and T values are mainly controlled by the ability of rocks to deform under tectonic stress [START_REF] Mancktelow | Tectonic pressure: Theoretical concepts and modelled examples. Lithos, Rocks Generated under Extreme Pressure and Temperature Conditions: Mechanisms, J o u r n a l P r e -p r o o f Journal Pre-proof Concepts[END_REF][START_REF] Schmalholz | Metamorphism under stress: The problem of relating minerals to depth[END_REF]. For example, shear deformation induces shear heating, which can locally increase the temperature J o u r n a l P r e -p r o o f by up 50 to 150 °C [START_REF] Kiss | Spontaneous generation of ductile shear zones by thermal softening: Localization criterion, 1D to 3D modelling and application to the lithosphere[END_REF]. As rocks are heterogeneous from the sample scale to the nappe scale, deformation induces stress perturbations, which, in turn, can result in local P deviations from the lithostatic value (e. g., [START_REF] Jamtveit | High Pressure Metamorphism Caused by Fluid Induced Weakening of Deep Continental Crust[END_REF][START_REF] Luisier | Pressure variations in the Monte Rosa nappe[END_REF][START_REF] Mancktelow | Nonlithostatic pressure during sediment subduction and the development and exhumation of high pressure metamorphic rocks[END_REF][START_REF] Moulas | The problem of depth in geology: When pressure does not translate into depth[END_REF]. Evidences are based on field observations, structural reconstructions and petrological studies in orogenic systems worldwide (e. g., [START_REF] Chu | Ultrafast eclogite formation via melting-induced overpressure[END_REF][START_REF] Vaughan-Hammon | Peak Alpine metamorphic conditions from staurolite-bearing metapelites in the Monte Rosa nappe (Central European Alps) and geodynamic implications[END_REF][START_REF] Vrijmoed | An alternative model for ultra-high pressure in the Svartberget Fe-Ti garnet-peridotite, Western Gneiss Region, Norway[END_REF]. However, on the other hand, it has been suggested that metamorphic transformations do not occur in H 2 O deficient rocks because of the slow reaction kinetics under H 2 O deficient conditions (i.e., metastability with respect to the new P-T conditions; e.g., [START_REF] Austrheim | Eclogitization of lower crustal granulites by fluid migration through shear zones[END_REF][START_REF] Rubie | The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamorphism[END_REF][START_REF] Wayte | A TEM study of disequilibrium plagioclase breakdown at high pressure: the role of infiltrating fluid[END_REF].

Fluids are known to play a major role in enhancing reaction rates [START_REF] Pattison | Petrological consequences of variations in metamorphic reaction affinity[END_REF][START_REF] Rubie | The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamorphism[END_REF]. It is relatively difficult to assess the validity of the equilibrium versus disequilibrium hypotheses in fluid-undersaturated environments (see [START_REF] Putnis | Fluid-mineral interactions: Controlling coupled mechanisms of reaction, mass transfer and deformation[END_REF], for a thorough discussion), as reaction kinetics cannot be quantified easily based on natural samples. Moreover, estimating H 2 O activity is difficult due to restricted equilibrium domains in dry rocks. Preliminary experiments designed at quantifying this effect have validated this inference [START_REF] Joachim | The effect of H2O fluid on relative component mobilities in a bimineralic reaction rim in the system CaO-MgO-SiO2[END_REF][START_REF] Remmert | Synthesis of monticellite-forsterite and merwinite-forsterite symplectites in the CaO-MgO-SiO2 model system: influence of temperature and water content on microstructure evolution[END_REF], although we are still far from a complete view due to the difficulty of experimentally controlling H 2 O activity during metamorphic transformations.

However, the effects of H 2 O on the mechanical properties of rocks and on rheology has received only limited attention in the metamorphic petrology community. [START_REF] Rybacki | Deformation mechanism maps for feldspar rocks[END_REF] have shown, based on laboratory experiments, that the presence of H 2 O in trace amounts in feldspar aggregates dramatically affects the effective strength, with up to 2-3 orders of magnitude difference in strength compared to dry rocks. Feldspar is by far the most abundant mineral constituent of the middle and lower crust [START_REF] Deer | An Introduction to the Rock Forming Minerals[END_REF] and it is commonly accompanied by either stronger (e. g., garnet) or weaker (e. g., mica, quartz)

J o u r n a l P r e -p r o o f phases. Therefore, variations in the H 2 O content, as well as the bulk mineralogy, can lead to effective strength contrasts that could affect the stress field and result in locally marked mechanical response to stress, such as localized deformation, formation of shear zones, or even the development of heterogeneous P. However, the effect of strength variations caused by gradients in H 2 O content has not been investigated. Therefore, in this contribution, we explore the role of fluids on the deformation and metamorphic record in a polymetamorphic unit of the Western Alps that underwent eclogite-facies conditions during Alpine orogeny.

Based on petrological arguments and thermodynamic as well as thermo-mechanical numerical modelling, we suggest that H 2 O-undersaturated rocks may have been sufficiently strong to remain undeformed and develop large differential stress associated with a lower peak P during Alpine orogeny.

Geological setting

The Gran Paradiso Nappe

The Gran Paradiso Nappe belongs to the Internal Crystalline Massifs, together with the Monte Rosa and the Dora Maira nappes (e.g., [START_REF] Le Bayon | Evolution structurale et métamorphique d'une croûte continentale subductée (Grand Paradis, Alpes occidentales)[END_REF]. It corresponds to the middle Penninic Unit of the Western Alps (Fig. 1a) and was part of the former European-derived Briançonnais microcontinent, a ribbon of continental crust lying between the European and Adriatic plates [START_REF] Michard | The Maira-Sampeyre and Val Grana Allochthons (south Western Alps): review and new data on the tectonometamorphic evolution of the Briançonnais distal margin[END_REF]. During Alpine orogeny, the closure of the Piemonte-Liguria oceanic domain was followed by the subduction of the Briançonnais microcontinent, leading to the formation of a tectonic nappe that was successively backfolded and exhumed along with the Penninic nappe stack [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF][START_REF] Manzotti | Exhumation rates in the Gran Paradiso Massif (Western Alps) constrained by in situ U-Th-Pb dating of accessory phases (monazite, allanite and xenotime)[END_REF].

The Gran Paradiso Nappe consists of a polymetamorphic Variscan basement, made up of paragneisses and micaschists, that locally contain amphibolite boudins (Fig. 1b; Biino and J o u r n a l P r e -p r o o f [START_REF] Biino | Palaeozoic continental-type gabbros in the Gran Paradiso nappe (Western Alps, Italy): Early-Alpine eclogitization and geochemistry[END_REF]Compagnoni et al., 1974;[START_REF] Compagnoni | Paramorfosi di cianite su sillimanite in scisti pregranitici del massicio del Gran Paradiso[END_REF][START_REF] Manzotti | Petro-structural map of the Money Unit (Gran Paradiso Massif, Valnontey valley, Western Alps)[END_REF]. The basement metasediments were intruded by porphyritic granitoids in the Late Paleozoic, dated at 277 to 264 Ma by U/Pb on zircon [START_REF] Bertrand | Permian zircon U-Pb ages in the Gran Paradiso massif: revisiting post-Variscan events in the Western Alps[END_REF][START_REF] Ring | U-Pb SHRIMP data on the crystallization age of the Gran Paradiso augengneiss, Italian Western Alps: Further evidence for Permian magmatic activity in the Alps during break-up of Pangea[END_REF]. They are now mostly outcropping as undeformed metagranites to strongly foliated augen-gneisses [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF].

Tectono-metamorphic evolution

The metamorphic evolution of the nappe is characterized by a first equilibration under amphibolite-facies conditions during the Variscan orogeny, estimated at 0-5-0.9 GPa and 600-650 °C [START_REF] Gasco | Metamorphic evolution of the Gran Paradiso Massif: A case study of an eclogitic metagabbro and a polymetamorphic glaucophane-garnet micaschist[END_REF]Le Bayon et al., 2006), based on the chemical composition of pre-Alpine garnets in polymetamorphic paragneisses. Evidence of this metamorphic event is scarce and locally restricted to the presence of relict garnet porphyroclasts and the preservation of low-pressure, high-temperature accessory minerals, such as ilmenite, in inclusions in garnet. The intrusion of granitic bodies in the Late Palaeozoic lead to the formation of a thin contact aureole in the paragneiss surrounding the granites, which resulted in the development of hornfelses at conditions of 0.25 to 0.35 GPa and 670-700 °C [START_REF] Gabudianu Radulescu | Polymetamorphic history of a relict Permian hornfels from the central Gran Paradiso Massif (Western Alps, Italy): a microstructural and thermodynamic modelling study: Polymetamorphic History of Relict Permian Hornfels[END_REF]. Locally, pegmatites have been observed, that crosscut the pre-Alpine, Variscan foliation [START_REF] Le Bayon | Evolution structurale et métamorphique d'une croûte continentale subductée (Grand Paradis, Alpes occidentales)[END_REF]. The pre-Alpine foliation associated with the Variscan orogeny is mainly recorded in the low-strain areas of the nappe, whereas it is overprinted by the younger deformation and Alpine metamorphic mineral assemblages in most places throughout the nappe [START_REF] Le Bayon | Evolution structurale et métamorphique d'une croûte continentale subductée (Grand Paradis, Alpes occidentales)[END_REF][START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF].

Alpine metamorphism in the Gran Paradiso nappe was extensively studied [START_REF] Ballèvre | Collision continentale et chemins P-T. L'unité pennique du Grand Paradis (Alpes occidentales)[END_REF][START_REF] Borghi | Composite P-T paths in the internal Penninic massifs of the western Alps: Petrological constraints to their thermo-mechanical evolution[END_REF][START_REF] Brouwer | Structure and metamorphism of the Gran Paradiso massif, western Alps, Italy[END_REF]Compagnoni and Lombardo, 1974;[START_REF] Compagnoni | Paramorfosi di cianite su sillimanite in scisti pregranitici del massicio del Gran Paradiso[END_REF][START_REF] Dal Piaz | Early Alpine eclogite metamorphism in the Penninic Monte Rosa-Gran Paradiso basement nappes of the northwestern Alps[END_REF][START_REF] Gabudianu Radulescu | Polymetamorphic history of a relict Permian hornfels from the central Gran Paradiso Massif (Western Alps, Italy): a microstructural and thermodynamic modelling study: Polymetamorphic History of Relict Permian Hornfels[END_REF][START_REF] Gasco | Metamorphic evolution of the Gran Paradiso Massif: A case study of an eclogitic metagabbro and a polymetamorphic glaucophane-garnet micaschist[END_REF]Le Bayon et al., 2006;[START_REF] Manzotti | Exhumation rates in the Gran Paradiso Massif (Western Alps) constrained by in situ U-Th-Pb dating of accessory phases (monazite, allanite and xenotime)[END_REF][START_REF] Manzotti | Constraining P-T conditions during thrusting of a higher pressure unit over a lower pressure one (Gran Paradiso, Western Alps)[END_REF][START_REF] Massonne | Derivation of P-T paths from high-pressure metagranites -Examples from the Gran Paradiso Massif, western Alps[END_REF] and estimates J o u r n a l P r e -p r o o f of the peak Alpine P and T conditions vary between 1.4 -2.7 GPa and 490 -600 °C, depending on the studies. The Alpine peak stage was dated at 41.5 ± 0.3 Ma by in situ U-Th/Pb LA-ICP-MS technique on monazite by [START_REF] Manzotti | Exhumation rates in the Gran Paradiso Massif (Western Alps) constrained by in situ U-Th-Pb dating of accessory phases (monazite, allanite and xenotime)[END_REF]. A HP deformation event was characterized, mainly based on structural data from mafic eclogites, that show a N-S stretching lineation [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF]. The whole nappe underwent a younger deformation event, coeval with an albite-epidote-amphibolite facies stage. This younger deformation phase is associated with nappe stacking, exhumation and backfolding. It almost pervasively affected the nappe and partially overprinted the high-pressure stage [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF]. The main foliation developed during this event defines the broad regional dome-shape of the nappe and is characterized by an E-W stretching lineation and a sub-horizontal foliation, moderately dipping to the north in the northern part of the nappe, with top to the west sense of shear [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF].

Field observations

The studied area is located in the Valeille valley, in the northern part of the Gran Paradiso massif, south of the Aosta valley in north-western Italy. There, previous glaciation events deeply dug the valley along a N-S orientation. On both sides of the valley, a large body (ca. 200 m x 100 m) of Alpine low strain paragneisses crops out, surrounded by Alpine high strain paragneisses [START_REF] Le Bayon | Evolution structurale et métamorphique d'une croûte continentale subductée (Grand Paradis, Alpes occidentales)[END_REF][START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF]. The Alpine low strain body is delimited in the South by a sub-vertical shear zone and in the North by a northward dipping foliation (Fig. 2a). The foliation in the North and South wraps around the low strain paragneisses. Both are essentially parallel and belong to the same deformation event. The overall shape of the Alpine low strain paragneisses mimics the shape of a boudin, with the swell region on the bottom of the valley and the necking zone on the top (Fig. 2b). The foliation within the Alpine low strain paragneisses is sub-horizontal. The prolongation of J o u r n a l P r e -p r o o f these structures, i.e., the shear zone and northward dipping foliation, including the Alpine low strain volume, are also visible in the Bardoney valley, on the East of the Valeille. Both volumes of low strain paragneisses were interpreted by Le Bayon and [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF] as a unique volume, cropping out laterally in the two valleys and delimited by the same shear zone. In the Bardoney valley, undeformed pre-Alpine pegmatites crosscut the sub-horizontal foliation, attesting for the pre-Alpine age of the foliation within the Alpine low strain body.

Eclogitic boudins are also found, embedded within the paragneiss of the sub-vertical Alpine shear zone, that preserved the Alpine high-pressure foliation, hence indicating that the activity of the shear zone had already started during the high-pressure history (Le Bayon and [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF]. The structural data that support this interpretation can be found in Le Bayon and [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF] as well as in Le Bayon (2005), along with petrographic argument that support eclogite facies conditions for the mafic rocks. Two samples from the Valeille valley were selected for detailed investigation. Sample 20GP10 was collected in the Alpine shear zone, South of the Alpine low strain paragneiss and sample 20GP07 was collected in the Alpine low strain paragneiss body (Fig. 2b).

Methods

Optical microscopy and electron probe microanalysis (EPMA)

Thin sections were studied using optical microscopy and back-scattered electron microscopy prior to quantitative analysis by electron probe microanalysis (EPMA). Mineral spot analyses and X-ray element maps were performed using a Cameca SX100 electron microprobe at the Microsonde Ouest facility in Brest, France. 1 µm spot analyses of garnet and 3 µm spots analyses of plagioclase were acquired with operating conditions set to 15 kV, 20 nA and 10 s counting time on the peak, except for Ti, 30 s. Standards used are natural minerals:

J o u r n a l P r e -p r o o f wollastonite (Si, Ca), corundum (Al), andradite (Fe), forsterite (Mg), MnTiO 3 (Mn, Ti), albite (Na), orthoclase (K), apatite (P), and Cr 2 O 3 (Cr). 5 µm spot analyses of mica and chlorite were acquired with operating conditions set to 15 kV, 20 nA and 10 s counting time on the peak, except for Ti and F, 30 s. Standards used are natural minerals: wollastonite (Si, Ca), corundum (Al), andradite (Fe), forsterite (Mg), MnTiO 3 (Mn, Ti), albite (Na), orthoclase (K), apatite (F), and pyromorphite (Cl). Structural formulae were calculated based on 8 cations for garnet, 11 oxygens for mica, 8 oxygens for feldspar and 23 oxygens for amphibole. The X Mg is calculated as the ionic ratio of Mg/(Mg+Fe) in mica and X an is calculated as Ca/(Ca+Na) in plagioclase. Mineral abbreviations follow the system of [START_REF] Warr | IMA-CNMNC approved mineral symbols[END_REF].

Thermodynamic modelling

Equilibrium phase diagrams were calculated using the software suite Theriak-Domino (de [START_REF] De Capitani | The computation of chemical equilibrium in complex systems containing non-ideal solutions[END_REF]. P-T pseudosections for sample 20GP10 were calculated using the 6.2 dataset of [START_REF] Holland | An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids[END_REF] and the following solution models: garnet, phengite, biotite, chlorite, chloritoid, staurolite, and ilmenite [START_REF] White | New mineral activity-composition relations for thermodynamic calculations in metapelitic systems[END_REF]; clinoamphibole, clinopyroxene [START_REF] Green | Activity-composition relations for the calculation of partial melting equilibria in metabasic rocks[END_REF]; epidote [START_REF] Holland | An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids[END_REF]; and feldspar [START_REF] Baldwin | Modelling of mineral equilibria in ultrahigh-temperature metamorphic rocks from the Anápolis-Itauçu Complex, central Brazil[END_REF]. The reactive bulk composition of both samples was calculated by combining mineral compositions with the modal amounts (in %) of phases from a selected area, determined based on image analysis of the grey-scale levels of the backscattered electron images. Garnet cores interpreted as pre-Alpine (2 vol%; see below) were removed from the reactive bulk composition. H 2 O-saturated conditions were assumed. The reactive bulk composition of the shear zone sample 20GP10 used for calculations is the following (in moles): Si(58.75), Ti(0.87), Al(20.43), Fe(5.94), Mn(0.16), Mg(3.85), Na(1.87), Ca(2.51), K(5.63), H(30).

J o u r n a l P r e -p r o o f

A P-T diagram showing the colormap and isopleths of total H 2 O content of solids (in mol%) was drawn for the pre-Alpine paragneiss, sample 20GP07. Given that these rocks were neither deformed nor totally transformed during Alpine orogeny (see below), it is difficult to assess the area to take into account for a reactive bulk composition estimate. However, slight changes in the reactive bulk composition do not significantly affect the general trend shown by the results and hence we use the reactive bulk composition of sample 20GP07 of (in moles): Si(62.27), Al(20.34), Fe(4.48), Mg(3.08), Na(4.10), Ca(0.72), K(4.77), H(30).

Thermo-mechanical modelling

The numerical models were designed using the 2D thermo-mechanical code MDoodz [START_REF] Duretz | Modeling Lithospheric Deformation Using a Compressible Visco-Elasto-Viscoplastic Rheology and the Effective Viscosity Approach[END_REF]. The code is based on the finite difference method/marker-in-cell approach and allows studying large strain deformation of heterogenous materials. A rectangular model domain of 2 × 1 km was designed, consisting of a homogeneous matrix with an oblique layer in the center, to study the effects of shearing on a competent dry rock layer embedded in a weaker hydrated rock matrix. The rheological model is visco-elasto-plastic and material parameters are based on rock deformation data. In order to investigate the effect of H 2 O on the viscous rheology of the matrix and layer, we prescribed laboratory-derived flow laws of anorthite wet (An100, 0.07 wt% H 2 O; [START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF] and anorthite dry (An100, 0.004 wt% H 2 O; [START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF] in the matrix and layer respectively. The plagioclase viscous flow laws were used, because they are representative of crustal rocks and these laws were derived consistently for different H 2 O contents, which is precisely the parameter of interest of this study. The plastic rheological model is frictional and is based on the Drucker-Prager model. An initial background P of 1.6 GPa is applied. The model setup consists of a 2×1 km wide box, containing a strong layer inside a weak matrix. The strong layer has an initial angle of 85° from horizontal direction. Top to the right shear deformation J o u r n a l P r e -p r o o f is applied at the top and bottom boundaries inducing a bulk strain rate of 10 -14 s -1 . Periodic boundary conditions are applied to the lateral sides. Flow laws of dry (0.004 wt% H 2 O) and wet feldspar (0.07 wt% H 2 O) are attributed to the strong and weak materials, respectively [START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF]. A seed with the similar properties as the matrix (weak hydrated) is placed in the middle of the competent layer. This heterogeneity induces a stress perturbation, which promotes necking in the middle domain rather than along the top and bottom boundaries. The model parameters are summarized in Table 3.

Results

Petrography, structures and mineral chemistry

Shear zone paragneiss 20GP10

Sample 20GP10 is a polymetamorphic schistose garnet metagrauwacke (Fig. 3a). It consists of a fine-grained assemblage of garnet (18 vol%), phengite (35%), plagioclase (10%), quartz (25%), biotite (5%), chlorite (3%), titanite (2%), epidote (1%) and minor amounts of the accessory minerals rutile, ilmenite, apatite and zircon (together 1%). The foliation is spaced, with mica-chlorite rich layers separating quartzofeldspathic rich layers (Fig. 3). The foliation can be characterized as a disjunctive foliation, according to the nomenclature of Passchier and Trouw (2005, p. 78). In the quartzofeldspathic layers, micas are aligned obliquely to the mica-chlorite layers. The latter form the cleavage layers and are parallel. The spacing occurs over a millimeter scale distance and is hence better visible at the thin section scale. In the quartzofeldspathic layers, the foliation is essentially defined by white mica and elongated quartz aggregates, which wrap around garnet porphyroblasts. Garnets occur either as few large subhedral porphyroblasts (up to 800 µm in size), or mostly as small subhedral to euhedral garnets (50 -100 µm in size). Pre-Alpine, supposedly Variscan (see Nosenzo et al., J o u r n a l P r e -p r o o f 2022 for a discussion on pre-Alpine garnet ages) garnet cores (Grt V ) are often found both within the Alpine large and small garnets. Grt V are identifiable in thin section because they are usually rimmed by early Alpine garnets (Grt A ) that are rich in inclusion, with mostly rutile. In some Grt A , small rutile inclusion trails also follow the schistosity. The transition between the Grt V and the Grt A is irregular, suggesting that the Grt V were resorbed before the growth of Grt A . Apatite, zircon and ilmenite are other relic minerals from the Variscan stage, that were not completely resorbed. The irregular external outline of most garnets suggests partial resorption on a late stage as well. Garnet is also fractured, and the fractures are mostly filled with chlorite. Rutile is found either as inclusion within garnet and plagioclase, or in the matrix. Two types of plagioclases were observed. The first one consists of poikiloblastic plagioclase riddled with inclusions of garnet, phengite, rutile, and quartz. The schistosity defined by phengite is preserved in the plagioclase, indicating that plagioclase grew during the Alpine history, and is post-kinematic with respect to the earlier Alpine deformation. The second consists of equant, often elongated euhedral plagioclase, found in aggregates with chlorite and quartz, suggesting that they could represent breakdown products of glaucophane.

Biotite is an Alpine post-kinematic phase, growing at the expense of white mica, mainly at its extremities, or where it is in contact with garnet (Fig. 3b). Titanite is mainly found as rims overgrowing rutile in the matrix. In the quartzofeldspathic rich layers, chlorite is the youngest post-kinematic phase, found either as large individual crystals in the plagioclase-chloritequartz aggregates, or as minor amounts of very fine-grained crystals replacing biotite and phengite. Chlorite in the mica-chlorite rich domains is parallel to the foliation, suggesting that the deformation was probably continuous from the Alpine peak conditions (at HP) to greenschist-facies conditions.

Large garnet porphyroblasts have cores of the Grt V generation, hence an area devoid of those large garnets was selected as a representative area in order to estimate the reactive bulk J o u r n a l P r e -p r o o f composition and conduct quantitative phase petrology analysis. Among the small subhedral garnets, a few of them show cores of pre-Alpine Grt V , that are identifiable by their chemical composition, with in particular low Ca content (5 to 7 mol% grossular) and high Mn content (up to 32 mol% spessartine; Fig. 4a ande). Alpine Grt A display an irregular growth zoning, with first an increase in Ca (grossular content up to 28 mol% -locally up to 32 mol%), and a subsequent decrease to 15 mol% (Fig. 4b), which is compensated by a first decrease in almandine content to 60 mol% and then an increase to 68 mol% towards the rim (Fig. 4c).

Pyrope content in Grt A is rather constant in the core (Fig. 4d andf), with 7.8 to 8.0 mol%, and slightly increases up to 12 mol% towards the rim (Fig. 4f). Spessartine content in Grt A is 3 mol% and increases to 6-8 mol% towards the rim. Based on the zoning characteristics, an Alpine peak composition can be deduced, with 28 -32 mol% grossular, 7.8 to 8.0 mol.% pyrope, 60 mol% almandine and 3 mol% spessartine.

White micas are zoned and their chemical composition corresponds to the phengite series (Supplementary Material S3). They show aluminum contents that are lower in the cores than in the rims (Fig. 5a). Silicon contents range between 3.25 to 3.53 atoms per formula unit (a.p.f.u), with one outlier at 3.16 a.p.f.u. The trend in silicon content correlates with the Tschermak exchange vector (Fig. 5b). The increase in silicon content is also correlated with a decrease in titanium (Fig. 5d). No relics of pre-Alpine, low-Si compositions have been found in this sample.

Chlorite can be separated into two groups, based on their chemistry. The large individual crystals found in aggregates with plagioclase and quartz are magnesium-rich (X Mg = 0.56) and small crystals in the matrix and in the fractures of garnet are magnesium-poor (X Mg = 0.35).

The EPMA data confirmed the presence of two types of feldspars: poikiloblastic feldspars are nearly pure albite in composition (X an = 0.00 to 0.05), whereas feldspars in the chloritequartz-feldspar aggregates have a X an ranging from 0.29 to 0.33.

J o u r n a l P r e -p r o o f

Low Alpine strain paragneiss 20GP07 Sample 20GP07 is a foliated paragneiss, consisting of white mica (35%), plagioclase pseudomorphs (17%), quartz (30%), biotite (3%), garnet (10%), chlorite (5%) and amphibole (~ 1%). Accessory minerals are clinozoisite, tourmaline, apatite, zircon, titanite, ilmenite and rutile. The foliation is defined by alternating quartz and white mica layers, wrapping around plagioclase porphyroblasts. White micas (hereafter all called phengite whatever their silica content, according to the classification of [START_REF] Rieder | Nomenclature of the micas[END_REF] appear mainly as elongated coarse-grained phengite flakes, which are oriented parallel to the foliation, or set in randomly oriented packages (Fig. 3c). As the coarse-grained phengites define the foliation of the sample, they are interpreted as belonging to the pre-Alpine, Variscan generation (Ph V ). A younger, Alpine generation of phengite is characterized by randomly oriented, fine-grained phengite crystals (Ph A ), found locally in association with garnet, rutile, ilmenite, amphibole, ± quartz, or as overgrowth on Ph V . Garnets are small subhedral crystals (20 -100 µm) and usually found in clusters, associated with fine-grained phengite (± biotite, chlorite, amphibole, ilmenite, rutile) between Ph V and the former plagioclase domains (Fig. 3d). The inclusions in garnet are mostly rutile. The plagioclase domains consist of an assemblage of albite and very fine-grained phengite, clinozoisite and chlorite. Biotite is found as a late replacement of Ph A , as replacement of phengites that are in contact with garnet, or as individual small crystals in the plagioclase domains. Indication of the presence of pre-Alpine biotite that has been pseudomorphosed is seen in areas where Ph A flakes are included with sagenite needles. These Ph A are usually also partially rimmed with garnet. Chlorite is found essentially in the plagioclase pseudomorphs, as individual crystals, or as replacement of biotite. A few amphibole grains were found, in association with the clusters of fine-grained Ph A , garnet, biotite and chlorite. They show a brownish-green pleochroism, similar to the one J o u r n a l P r e -p r o o f of biotite and can only be confidently distinguished from biotite based on the extinction angle. Amphibole occurs as small individual crystals, in very low modal amounts (ca. 1 vol%) and there is no textural indication that could suggest that it replaces former glaucophane.

The overall microtextures as well as the evidence that the foliation is pre-Alpine show that the rock was neither completely transformed, nor deformed during Alpine orogeny. This is also supported by the large chemical range of phengite (Fig. 5c), with high aluminum Ph V (up to 0.05 a.p.f.u.) and low aluminum Ph A (0.01-0.02 Al a.p.f.u.). The correlation between silicon content and the Tschermack exchange vector forms a continuous compositional trend from 3.05 to 3.49 Si a.p.f.u (Fig. 5b). The high titanium content of the low-silicon Ph V suggests a formation under high-temperature conditions [START_REF] Auzanneau | Titanium in phengite: a geobarometer for high temperature eclogites[END_REF], which is another argument in favor of a Variscan age for the Ph V generation. Finer-grained randomlyoriented phengite clusters surrounding coarse-grained phengites also have high Al cores, similar to the coarse-grained Ph V and are therefore also interpreted as Variscan. Garnets show irregular growth zoning. Most garnet cores are almandine rich (70 -76 mol%), grossular poor (1 -10 mol%), have low pyrope contents (10 -20 mol%) and variable spessartine content (3 -15 mol%). A decrease in almandine (60 -70 mol%), and pyrope (6 -16 mol%) as well as an increase in grossular content (10 -23 mol%) is often observed towards the garnet rims, whereas spessartine content is variable and does not show a spatial trend.

Overall, the zonation patterns are usually neither regular nor symmetric, as shown by the variable spessartine content. Plagioclase is mostly albitic in composition, with X an ranging from 0.00 to 0.07. A few outliers have X an of 0.19 to 0.23. The amphibole compositions correspond to the sodic-calcic group, and more specifically match the compositional range of barroisite.

J o u r n a l P r e -p r o o f P-T estimates

Alpine peak P-T estimates were undertaken on sample 20GP10 using phase equilibria modelling. This method could not be applied to sample 20GP07 due to the too large disequilibrium. Hence, only an estimate of the maximum value of the peak P will be assessed based on its mineralogy and assuming a temperature of 500-520 °C, as determined for the peak conditions of sample 20GP10.

Sample 20GP10

The P-T pseudosection was calculated in the system MnNCKFMASHT for a reactive bulk composition including the mapped area of Fig. 4 (see methods for details). The isopleths of pyrope and grossular mole fractions in garnet have been calculated and compared to the composition of the garnets in order to constrain the peak P-T conditions (Fig. 6). The isopleths of pyrope and grossular crosscut in the stability field of garnet, phengite, glaucophane, chloritoid, lawsonite, quartz and rutile, with peak P -T conditions inferred at 1.80 -1.95 GPa and 500 -520 °C. Note that the silica in phengite barometer of [START_REF] Massonne | Phengite geobarometry based on the limiting assemblage with K-feldspar, phlogopite, and quartz[END_REF] cannot be applied to this rock because it lacks the buffering assemblage K-feldspar, biotite and quartz at the peak conditions. The modelled mineral mode corresponds to the observed mode for garnet (11%, taking into account only the vol% of the observed Alpine garnet cores) and quartz (28%). Phengite is slightly overestimated in the calculations (42%, in comparison with 35% observed), however part of the potassium attributed to phengite would be compensated by biotite growth upon decompression, which explains such high values for the modelled amount of phengite. According to the pseudosection of Fig. 6, the HP sodic phase is glaucophane (11 vol%). Although glaucophane is not observed in the mineral assemblage, its former presence is suggested by the occurrence of Mg-rich chlorite, plagioclase and quartz aggregates. Lawsonite and chloritoid have not J o u r n a l P r e -p r o o f been identified in the sample, however their calculated modal abundances are 4 and 1 vol%, respectively. Both phases could account for the Ca and Mg-Fe contained in the plagioclase and chlorite now occurring as retrograde phases. They could have been dissolved during the post-peak retrogression during the late stages of deformation associated with the activity of the shear zone. Chlorite and biotite are late phases and are interpreted as not being part of the peak assemblage. The stability field of chlorite reaches relatively high P at T of 500 to 520 °C and the biotite breakdown reaction is reached at P of 1.3 -1.4 GPa over this temperature range. The absence of both phases from the peak assemblage hence supports the estimated high value of P. Moreover, the P-T conditions estimated agree with estimates from the literature for similar rock types in the northern part of the Gran Paradiso Unit (Le Bayon et al., 2006;[START_REF] Manzotti | Constraining P-T conditions during thrusting of a higher pressure unit over a lower pressure one (Gran Paradiso, Western Alps)[END_REF][START_REF] Manzotti | Exhumation rates in the Gran Paradiso Massif (Western Alps) constrained by in situ U-Th-Pb dating of accessory phases (monazite, allanite and xenotime)[END_REF].

Sample 20GP07

Due to the large apparent disequilibrium over the mm scale, as shown by microtextural/microchemical observations, the preservation of pre-Alpine mineral phases (such as the white mica Ph V ), as well as the large compositional range of phengite, a paleoequilibrium domain could not be reliably defined. Garnet zonation is not regular, with intraand inter-grain chemical inhomogeneities, so they cannot be used to determine the Alpine peak P composition. Moreover, the isopleths of the silicon in phengite are sub-vertical in the pressure and temperature range of interest, which does not provide a reliable pressure indication (see Supplementary Material, Fig. S1). Therefore, phase equilibrium modelling cannot be applied reliably to this rock. However, an attempt to determine the peak P range can be made, based on petrographic observations. First, it is important to note here that thermodynamic disequilibrium at the thin section scale does not imply a lack of reaction at the grain scale. It is evident that the rock has been partially affected by Alpine J o u r n a l P r e -p r o o f metamorphism, as attested by the occurrence of high silica phengite, garnet and rutile. Along with barroisite, plagioclase is the only sodium-bearing phase present in the rock. The stability limit of plagioclase is expected to end at P around 1.4 GPa for temperature of 500 to 520 °C [START_REF] J O U R N A L P R E -P R O O F Holland | The reaction albite = jadeite+quartz determined experimentally in the range 600-1200 degrees C[END_REF]. Above that P, the expected stable sodium-bearing phases are paragonite, glaucophane and sodic pyroxene. However, paragonite, glaucophane, or sodic pyroxene are not observed in the sample, neither were any indications of their former presence found.

Barroisite occurs as a minor phase, representing ca. 1 vol% of the sample, and is observed as dispersed crystals. It does not occur as pseudomorph after glaucophane, neither as a reaction rim around former glaucophane, despite the absence of deformation. Moreover, it is found in association with Alpine garnet and phengite in the plagioclase domains and hence, it seems to be stable along with plagioclase.

With respect to plagioclase, the reaction history within sample 20GP10 may have followed different paths.

1. The pre-Alpine plagioclase may have remained metastable at peak P-T conditions, and may have been transformed into an albite-bearing aggregate during decompression. This hypothesis would be consistent with the lack of jadeite, or products of replacement of jadeite (provided we are able to identify them).

Metastability of plagioclase would have been favored by the lack of strain energy (this sample is in the undeformed volume) associated to the lack of additional H 2 O entering the system and allowing the growth of a Ca-bearing, hydrated, phase (zoïsite) necessary to account for the anorthite component.

2. The pre-Alpine plagioclase may have been replaced by albite and zoisite during the late-Variscan history, or during the prograde Alpine history. In such a hypothesis, albite was still stable at peak P-T conditions in the undeformed volume, thus limiting the peak P range for sample 20GP07 to a maximum value of 1.4 GPa.

J o u r n a l P r e -p r o o f 3. Last, the pre-Alpine plagioclase may have been replaced by a fine -grained aggregate consisting of jadeite and zoïsite, as described in some HP metagranites (for a recent summary, see [START_REF] Schorn | Self-induced incipient 'eclogitization' of metagranitoids at closed-system J o u r n a l P r e -p r o o f Journal Pre-proof conditions[END_REF], later replaced by albite during decompression. We lack unambiguous textural and mineralogical evidence in favor of this hypothesis.

In the light of the results presented for the two samples, there are two points in which the samples differ strikingly. First, from a petrological perspective, sample 20GP10 equilibrated to the evolving P-T conditions during the Alpine orogeny, whereas in sample 20GP07 a large proportion of the low P pre-Alpine minerals were preserved during Alpine orogeny. Second, from a structural perspective, the sample 20GP10 was pervasively deformed during the formation of the shear zone, whereas the sample 20GP07 remained mostly unaffected by Alpine deformation. There is hence an apparent relationship between the extent of deformation and the extent of Alpine metamorphic equilibration between the two samples, suggesting that in this case, fluids played a major role in the establishment of the structural and petrological characteristics of the samples.

Discussion

Geological significance

Based on our results, there is a discordance in apparent peak P between the sample 20GP07 (P <1.4 GPa, according to hypothesis 2 above) and the shear zone paragneiss 20GP10 (ca. 1.8 -1.9 GPa) of at least 0.4 GPa. Compared to the previous peak P estimates for the Gran Paradiso nappe, both peak P fit into the estimated range from the literature (from 1.2 to 2.7 GPa, see introduction). Although the geothermobarometric methods have constantly evolved [START_REF] Lanari | Metamorphic geology: progress and perspectives[END_REF] since the first Alpine peak P estimates in the Gran Paradiso by Dal Piaz and [START_REF] Dal Piaz | Early Alpine eclogite metamorphism in the Penninic Monte Rosa-Gran Paradiso basement nappes of the northwestern Alps[END_REF], it is unlikely that the methodology can solely explain the discrepancy J o u r n a l P r e -p r o o f in peak P. It is therefore evident that we are facing a problem, which relates to the interpretation of such P variation at the outcrop scale. Here, the rocks that did record the highest peak P are also the rocks that are deformed and, in the opposite, the rocks that seem to record a large thermodynamic disequilibrium are the least deformed. The relationships between deformation and metamorphism are usually tightly related to the conditions of access to fluids and fluid-rock interactions (e.g., [START_REF] Rubie | The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamorphism[END_REF]). In the next section, we discuss independently the role of H 2 O on the progress of metamorphic reactions and on the mechanical behavior of rocks under stress.

The role of H 2 O in metamorphism

Fluids involved in subduction and continental collision settings at the pressures and temperatures considered in this study are likely aqueous solutions, essentially made of H 2 O in the form of supercritical vapor. Minor constituents, such as CO 2 , N 2 and ions in solution may be found as well (e.g., [START_REF] Ferry | Characterization of metamorphic fluid composition through mineral equilibria[END_REF], but for simplicity we will generalize the nature of fluids to pure H 2 O in the following discussion. H 2 O is found under different forms in rocks (see [START_REF] Putnis | Fluid-mineral interactions: Controlling coupled mechanisms of reaction, mass transfer and deformation[END_REF], for a review). In non-deforming fluid saturated rocks, hydrous species are present in the grain boundary region, either in isolated pores or as interconnected fluid-filled porosity, so that at equilibrium the fluid pressure equals the total pressure. In fluid undersaturated rocks, either aqueous species are present in the grain boundary region in the form of isolated H 2 O molecules, or dissolved OH -and H + , forming disconnected fluid films and then the rock is nearly anhydrous. The latter situation is often found in high-grade rocks, such as granulites, in which not even hydrous minerals are stable. Note that nominally anhydrous minerals can also contain H 2 O in the form of structurally bonded hydrogen or fluid inclusions. The H 2 O saturation conditions are susceptible to evolve through time, especially

J o u r n a l P r e -p r o o f

Journal Pre-proof during metamorphism, with for example dehydration reactions, or fluid infiltration events [START_REF] Thompson | Fluid-absent metamorphism[END_REF].

Even if H 2 O does not participate to metamorphic reactions as a thermodynamic component, its presence in the grain boundary region has a significant catalytic effect on reactions (e. g., [START_REF] Rubie | The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamorphism[END_REF][START_REF] Wayte | A TEM study of disequilibrium plagioclase breakdown at high pressure: the role of infiltrating fluid[END_REF]. H 2 O acts as a transport medium, in which ions migrate by diffusion from the reactant site to the product site. Reaction rates are enhanced by several orders of magnitude in the presence of a free intergranular fluid [START_REF] Carlson | Dependence of reaction kinetics on H2O activity as inferred from rates of intergranular diffusion of aluminium[END_REF][START_REF] Rubie | The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamorphism[END_REF]. Under H 2 O undersaturated conditions and at T such as those estimated here, timescales for intergranular diffusion of most ions are longer that the geological timescales under interest [START_REF] Ahrens | Gabbro-eclogite reaction rate and its geophysical significance[END_REF]. The kinetics of metamorphic reactions in dry rocks is therefore expected to be very slow, thus limiting the extent of reaction product formation or even prohibiting the formation of the expected paragenesis at high P conditions, which leads to the occurrence of mineral assemblages, that are outside of their stability field as long as there is no deformation or fluid input [START_REF] Rubie | Disequilibrium during metamorphism: the role of nucleation kinetics[END_REF]. Many examples from tectonic units where portions recorded lower peak P than the neighboring rocks are interpreted as metastable based on the apparent lack of reaction products. However, according to experiments of reaction rim growth, the minimum amount of H 2 O necessary to qualify a system as "hydrous" is very low, in the order of a few tens of ppm of H 2 O [START_REF] Milke | Very little water is necessary to make a dry solid silicate system wet[END_REF]. Beyond this threshold, even minute amount of H 2 O is sufficient to trigger metamorphic reactions under geologically realistic timescales. Hence, totally inhibited reactions in presumably metastable rocks imply extremely dry conditions.

Reaction pathways in the Gran Paradiso samples

Timing and degree of equilibration in the shear zone sample 20GP10

J o u r n a l P r e -p r o o f

The deformed paragneiss 20GP10 has been almost completely equilibrated during the Alpine orogeny, with garnet cores Grt V being the only remnants of the former Variscan amphibolitefacies mineral assemblage (excluding other relict accessory minerals). Grt V cores occur everywhere in the sample. They are highly resorbed, suggesting that the rock was almost pervasively altered by fluids after the Variscan orogeny and before the Alpine peak P event.

Garnet probably acted as a refractory mineral during this alteration event. One hypothetical scenario that could explain the partial resorption of the garnet could be that the paragneisses from this location were affected by an external fluid infiltration before Alpine orogeny. Such fluid-rock interaction could have occurred very locally, along with a deformation event (e.g., a fault zone), which would have acted as a structural heterogeneity and would have preferentially enhanced further ductile strain localization during Alpine deformation. In this case, local external fluid infiltration would have occurred only in the vicinity of the shear zone and would not have affected the low-strain paragneiss. This interpretation is supported by the observation that Variscan minerals are preserved in the low-strain paragneiss and only locally re-equilibrated under Alpine HP conditions.

Microstructural observations in sample 20GP10 show that the Alpine deformation related to the formation of the shear zone precedes the growth of albite poikiloblasts, biotite and chlorite. Therefore, it is inferred to have occurred at HP conditions. The schistosity defined by high-silica phengite also supports this interpretation. Overall, the petrographic and microtextural observations suggest that the prograde to peak metamorphism occurred under fluid saturated conditions. Therefore, the use of fluid saturated conditions for pseudosection modelling seems justified, as prograde increase in P and T conditions would essentially lead to dehydration and further fluid supply. Then, fluids must have been available sporadically during the retrograde part of the metamorphic history, in order to provide the H 2 O necessary to form the low-silica phengite rims as well as the late chlorite.

J o u r n a l P r e -p r o o f

Timing and degree of disequilibrium in the low strain paragneiss 20GP07.

The observation of extensive disequilibrium textures in the low-strain paragneiss 20GP07 would indicate that thermodynamic equilibrium was not reached at the sample scale, or even at the grain scale, during the Alpine orogeny. Such interpretation involving sluggish kinetics has already been invoked to explain the apparent lack of reaction and significant pressure overstepping in various metamorphic rocks in the Alps and worldwide (e. g., [START_REF] Austrheim | Shear deformation and eclogite formation within granulite-facies anorthosites of the Bergen Arcs, western Norway[END_REF][START_REF] Proyer | The preservation of high-pressure rocks during exhumation: metagranites and metapelites[END_REF]. [START_REF] Proyer | The preservation of high-pressure rocks during exhumation: metagranites and metapelites[END_REF] as well as Schorn ( 2018) discuss the role of H 2 O on the preservation of mineral assemblages during prograde and retrograde metamorphic conditions. In particular, [START_REF] Proyer | The preservation of high-pressure rocks during exhumation: metagranites and metapelites[END_REF] shows, based on phase equilibria modelling, that orthogneisses require a significant amount of H 2 O addition from external sources on the prograde path in order to equilibrate to high pressure conditions. In order to test the applicability of this scenario to the Gran Paradiso low-strain paragneiss, a P-T pseudosection showing the H 2 O content (in mol%) of the mineral assemblage was calculated, based on the reactive bulk composition of sample 20GP07 (Fig. 7). The peak P-T conditions of the shear zone paragneiss 20GP10 are represented with the red star, as well as the corresponding prograde P-T path, according to Le Bayon et al. (2006). Three grey arrows show typical geothermal gradients for subduction zone environments (6, 10 and 15 °/km). The black dashed line shows the position of the albite breakdown reactions: albite = jadeite + quartz [START_REF] J O U R N A L P R E -P R O O F Holland | The reaction albite = jadeite+quartz determined experimentally in the range 600-1200 degrees C[END_REF]. The blue star at 600 °C and 0.5 GPa indicates the P-T conditions inferred for the pre-Alpine amphibolite facies conditions reached by the Gran Paradiso basement rocks (Le Bayon et al., 2006). The white dashed lines represent the total H 2 O content in the mineral assemblage, in mol% (meaning the sum of all H 2 O content in mineral phaseswithout adding a fluid phase in an unspecified porosity). The H 2 O content isopleths have a positive slope in the P-T diagram, with an increasing amount towards higher P and lower T.

J o u r n a l P r e -p r o o f

Journal Pre-proof

The isopleths on Fig. 7 show that under normal prograde increase in P and T along either of the geothermal gradients, the total H 2 O content decreases, hence the rock should dehydrate.

Metamorphic reactions under such conditions are normally favored, since H 2 O is progressively being released and can hence contribute to the catalysis of metamorphic reactions. However, this is true for a rock, whose protolith has a high initial H 2 O content (i.e., above ca. 8 mol%, corresponding to the H 2 O content at similar peak conditions as the shear zone paragneiss; red star on Fig. 7), such as marine sedimentary rocks saturated in H 2 O during their deposition, and constantly evolving across/through dehydration reactions.

In the case of a polymetamorphic rock, such as sample 20GP07, the H 2 O content of the rock before Alpine metamorphism may be the one acquired at amphibolite facies conditions, during the pre-Alpine Variscan metamorphism. In this case, the paragneiss has a H 2 O content of ca. 5.7 mol% (blue star on Fig. 7). Even if the sample has been affected by retrograde hydration after Variscan amphibolite facies during its cooling history, it would only result in a final H 2 O content < 6 mol%, according to the H 2 O isopleths for a constant P of 0.5 GPa.

Therefore, a fluid input from an external source is required in order to allow for equilibration of the mineral assemblage at P-T conditions higher than those allowed at the corresponding total H 2 O content. If no external fluid is added to the rock, it will remain untransformed during a prograde increase in ambient P and T conditions. In such a case, the persistence of low P parageneses are not necessarily attributed to metastability, as long as fluid-absent reactions are not overtaken, because the stability limits in terms of P and T of a H 2 O-free assemblage delimit a greater field than for the same rock with free H 2 O. Nevertheless, crossing the albite breakdown reaction without producing jadeite and quartz because of a lack of catalytic H 2 O would lead to metastability. In the case of 20GP07, glaucophane would be expected to form at the peak conditions inferred for the shear zone paragneiss 20GP10. The lack of a HP sodic phase in the rock could then suggest that the rock persisted to metastable J o u r n a l P r e -p r o o f conditions at high P-T conditions. However, this interpretation is not unique. Although this is not straightforward at the first sight, there are examples in the literature demonstrating that apparent disequilibrium textures, such as zoned reaction rims or orientation dependent reaction products can be explained by equilibrium processes in systems under high differential stress (e.g., [START_REF] Cionoiu | Impact of interseismic deformation on phase transformations and rock properties in subduction zones[END_REF][START_REF] Tajčmanová | Grain-scale pressure variations and chemical equilibrium in high-grade metamorphic rocks[END_REF]. Therefore, the metastable state of a rock cannot be inferred purely based on phase equilibria considerations, and the effect of the stress state on mineral compositions is similarly important, and must not be overlooked [START_REF] Tajčmanová | Grain-scale Pressure Variations in Metamorphic Rocks: Implications for the Interpretation of Petrographic Observations[END_REF].

In the framework of our study, an alternative mechanism to metastability may be considered, that could explain the discrepant peak P record between samples 20GP10 and 20GP07. This interpretation, investigated below, involves a mechanical analysis of strength contrasts between hydrous and H 2 O undersaturated rocks, that would produce a heterogeneous stress field during deformation, leading to local pressure variations. Here, we refer to hydrous rocks for rocks with a free fluid phase.

The role of H 2 O on stress and pressure

Although the slow diffusion rates in H 2 O undersaturated rocks are not put into question here, an alternative interpretation of the lack of reaction and deformation of the Gran Paradiso dry rocks in our case could be that dry rocks are stronger and the mechanical behavior would lead to the generation of tectonic under-pressure. The generation of heterogeneous stress conditions in inclusion -host systems has been shown by [START_REF] Moulas | Stress field associated with elliptical inclusions in a deforming matrix: Mathematical model and implications for tectonic overpressure in the lithosphere[END_REF] to be a valid explanation for pressure variations. The analytical solution derived by [START_REF] Moulas | Stress field associated with elliptical inclusions in a deforming matrix: Mathematical model and implications for tectonic overpressure in the lithosphere[END_REF] has later been applied to the high pressure whiteschists of the Monte Rosa nappe (Luisier et al., 2019a) and to an eclogite facies shear zone in the Bergen Arcs in western Norway [START_REF] Jamtveit | High Pressure Metamorphism Caused by Fluid Induced Weakening of Deep Continental Crust[END_REF]. Both studies use a rheological contrast between a strong host rock and

J o u r n a l P r e -p r o o f

Journal Pre-proof a weak inclusion and depending on the orientation and aspect ratio of the weak inclusions, pressure locally rises. The difference in pressure is explained by the force balance between a strong material which has a large differential stress and a weak material that has a small differential stress (see Fig. 4a in [START_REF] Jamtveit | High Pressure Metamorphism Caused by Fluid Induced Weakening of Deep Continental Crust[END_REF] for an explanation on the stress state).

The maximum differential stress that rocks can sustain without breaking depends on several factors, such as temperature and strain rate. The H 2 O content is also an important factor controlling the strength of rocks (see Wong et al., 2016, and references therein). From experiments, it is well established that increasing H 2 O content in a material at constant confining pressure causes a decrease in the material strength in comparison to H 2 O absent conditions. This weakening mechanism was attributed to the hydrolysis of O-Si-O bonds in quartz in the presence of traces of H 2 O, and is termed " hydrolytic weakening" [START_REF] Griggs | Hydrolytic Weakening of Quartz and Other Silicates*[END_REF]. As an example, the difference in flow strength between dry and wet samples is up to a factor of 2.5 for quartz [START_REF] Koch | Effect of water on the rheology of experimentally deformed quartzite[END_REF]. [START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF] determined flow laws for dry and wet feldspar aggregates, with total H 2 O contents of 0.004 and 0.07 wt%, respectively (i.e., the total H 2 O, including molecular H 2 O or hydroxyl, fluid inclusions as well as the H 2 O in the sample porosity of less than 1%). They show that the hydrolytic weakening effect causes a strength decrease up to a factor of 3 [START_REF] Rybacki | Influence of water fugacity and activation volume on the flow properties of fine-grained anorthite aggregates[END_REF][START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF].

The effect of H 2 O content in rocks on the rheology during deformation was tested by designing a regional scale deformation simulation using a thermo-mechanical numerical code (see method section for details). Fig. 8 shows the temporal evolution of the P field (GPa) and accumulated strain during ongoing shear deformation. The strong layer is sheared and a pinch and swell structure starts forming after ca. 1 Ma of deformation, leading to the formation of distinct boudins and necking zones after 1.8 Ma. With increasing strain, the matrix behaves in a visco-elastically while the dry strong layer behaves dominantly in a plastic manner, as

J o u r n a l P r e -p r o o f

Journal Pre-proof witnessed by the occurrence of shear bands. The pressure field is heterogeneous both in the matrix and in the strong layer, with overall higher P in the matrix (1.6 to 1.9 GPa) and lower P in the strong layer (0.8 to 1.4 GPa). The first order distribution of the P agrees well with previous results of numerical models [START_REF] Mancktelow | Tectonic pressure: Theoretical concepts and modelled examples. Lithos, Rocks Generated under Extreme Pressure and Temperature Conditions: Mechanisms, J o u r n a l P r e -p r o o f Journal Pre-proof Concepts[END_REF]. The accumulated strain is the lowest in the boudins and highest in the necking zones, with additional fringes of high strain areas developing from the necking zone towards the boudin swells, progressively wrapping around the boudins. One of such areas is highlighted by a red square on Fig. 8. Notably, these high strain areas are associated to higher P in the matrix, and could therefore be interpreted as a representative numerical equivalent area to the natural study area, with high strain and high P paragneiss surrounding the low strain and low P paragneiss boudin (see Fig. 2b for a sketch of the field area). In the red square, the P in the high strain matrix is similar to the P recorded by the shear zone paragneiss 20GP10 (1.9 GPa).

The effect of strain rate and background P on the P field were assessed through a parametric study, with the main results plotted in Fig. 9. Strain rates of 10 -15 , 10 -14 and 10 -13 s -1 were compared, along with background P of 1.4, 1.6 and 1.8 GPa. The strain rate has a strong impact on the structure development, with slower strain rates enhancing the formation of thick boudins with more homogeneous P distribution. Larger strain rates result in large P perturbations in the strong layer along with a more pronounced shear effect, resulting in thinner, more elongated boudins. Larger strain rates also increase the P contrast between the strong layer and the weak matrix. Additionally, a slow strain rate of 10 -15 s -1 results in the formation of distinct boudins and necking zones after ca. 17 Ma, whereas at large strain rates of 10 -13 s -1 , pinch and swell structures already form after ca. 200 ka. Therefore, a low to intermediate strain rate of 10 -15 to 10 -14 s -1 seems more appropriate compared to the burial and exhumation rates derived from combined microtextural, petrological and geochronological data in the Gran Paradiso Unit (see [START_REF] Manzotti | Exhumation rates in the Gran Paradiso Massif (Western Alps) constrained by in situ U-Th-Pb dating of accessory phases (monazite, allanite and xenotime)[END_REF] for a synthesis).

J o u r n a l P r e -p r o o f

Varying the background P does not strongly influence the overall shape of the boudins, neither has it an effect on the pressure distribution between boudins and matrix. However, the absolute P values shift with the same amount as the background P is varied. In order to reach the peak P of 1.8 to 1.9 GPa determined based on sample 20GP10, a background P of 1.6 to 1.8 is required.

Other parameters that influence the stress and pressure field include the angle between the long axis of the strong layer and the orientation of the principal stress applied (see Moulas et al., 2014) as well as the aspect ratio of the strong layer (Luisier et al., 2019b). Over-pressure would be generated for a strong layer set at angle 0° < 𝛼 < 45° to the principal stress, whereas under-pressure is generated for the same strong layer if set at angle 45° < 𝛼 < 90° to the principal stress. In our case, the pre-Alpine foliation in the low-strain paragneiss is subhorizontal and the Alpine foliation in the high-strain paragneiss is sub-vertical. Moreover, the regional foliation southward of the shear zone dips between 70° and 80°. Consequently, the angle 𝛼 was close to 70° -90° (Le Bayon and [START_REF] Le Bayon | Deformation history of a subducted continenta l crust (Gran Paradiso, Western Alps): continuing crustal shortening during exhumation[END_REF], which is coherent with the numerical models showing the development of under-pressure in the strong layer. As long as the aspect ratio of the layer is larger than 2, this parameter does not affect the modelled pressure (Luisier et al., 2019a). Furthermore, the rheological contrast, i.e., the viscosity contrast, between the layer and the matrix is also a parameter that influences the magnitude of the pressure variation in the domain [START_REF] Moulas | Stress field associated with elliptical inclusions in a deforming matrix: Mathematical model and implications for tectonic overpressure in the lithosphere[END_REF].

Overall, both the first order shape of the outcrop and metamorphic P distribution determined based on quantitative phase petrology can be reproduced by the model. Therefore, the results of the modelling show that a small difference in H 2 O content between two materials of the same composition (here, anorthite dry and wet) results in a significant rheological perturbation, that can locally lead to variations in the tectonic P and strain, under otherwise normal geological background conditions. Moreover, the results confirm that the deformation J o u r n a l P r e -p r o o f and metamorphic evolution of the low Alpine strain paragneiss 20GP07 was constrained by an exceptionally strong rheology and therefore, the results agree with these rocks being H 2 O undersaturated.

Consequently, the traditional interpretation that the slow kinetics due to H 2 O undersaturated conditions inhibits the formation of high P mineral assemblage is here not required anymore, as the exact same argument of H 2 O undersaturation can be used to demonstrate that P in the unstrained area did potentially never reach the 1.9 GPa as in the shear zone paragneiss, and potentially never even passed the albite breakdown reaction at 1.4 GPa. This relies on the assumption that albite is a secondary product in the deformed paragneiss (where all Nabearing phases predicted to be stable at HP have been lost during decompression), while albite was still stable at peak P in the undeformed domain.

The effect of contrasting H 2 O saturation conditions on petrology and mechanical behavior of deforming adjacent rocks can be illustrated using a simple sketch (Fig. 10), that displays the main cause to effect relationships. Two simplified rocks are considered, with rock A (Fig. 10A) depicting a H 2 O saturated rock, such as the shear zone paragneiss, and rock B (Fig. 10B) a H 2 O undersaturated rock, such as the low-strain paragneiss. For the rock A, a schematic phase diagram is drawn, with one dehydration reaction, that separates a field with a hydrous assemblage on the left side from a field with an anhydrous assemblage on the right side. The dehydration reactions is of a type A (hydrous) = B (anhydrous) + H 2 O (aq.). For the purpose of the discussion, it is assumed that the fluid produced by the reaction either leaves the system after the reaction has occurred, for example during the deformation, or is present in the rock in a very small volume of pores. In the hydrous field, reactions are kinetically enhanced and symbolized by solid arrows, whereas in the anhydrous field, they are kinetically hindered and symbolized by the dashed arrows. The previous studies that have explained outcrop scale metamorphic P variations with stressinduced P perturbations were based on similar assumptions that the coexisting rocks have strength contrasts sufficiently large to generate measurable metamorphic P variations. For example, the strength contrast in the study of [START_REF] Jamtveit | High Pressure Metamorphism Caused by Fluid Induced Weakening of Deep Continental Crust[END_REF] corresponds to a viscosity ratio of 10 between the host granulite and the eclogitic shear zone. Luisier et al. (2019) use a viscosity ratio of 100 between the strong metagranite and the weak whiteschists. Here, the strength contrast between the strong layer and the matrix corresponds to an effective viscosity ratio of 10 at the beginning of the simulation and it increases up to a ratio of 1000 during the formation of the boudins (Supplementary Material S2). Consequently, simulating deformation of materials of variable viscosities, such as weak whiteschist or eclogite versus strong granite or granulite, leads to P deviations of the same order of magnitude as for deformation of materials of fixed composition but with different H 2 O content.

Finally, the methodology used in this study could be applied to other potentially H 2 O deficient parts of the nappe, such as the metagranites, that were locally also not strongly deformed and in which the assemblage jadeite + quartz has never been reported.

Conclusion

This study emphasizes the importance of considering mechanical stresses when nonequilibrium processes are suspected in metamorphic rocks. Quantitative phase petrology allowed to recognize the key role of H 2 O in explaining the variation in peak metamorphic conditions between the shear zone paragneiss and the low Alpine strain paragneiss from the Gran Paradiso Unit. Under closed system conditions, the initial H 2 O content of the protolith as well as the slope of the H 2 O isopleths in the P-T space determine the ability of the rock to J o u r n a l P r e -p r o o f Journal Pre-proof react on the prograde path and equilibrate to HP conditions in continental collision settings. This combined thermodynamic and numerical modelling study confirms that besides its role on reaction kinetics, H 2 O has a strong impact on the mechanical behavior of rocks under stress. Our large-scale model results corroborate the previously experimentally determined behavior of dry versus wet rocks subjected to deformation. Our models highlight the fact that local differences in H 2 O saturation conditions in rocks of an otherwise same composition lead to significant strain and P variations over geological timescales, such that metamorphic rocks can record this difference in peak conditions. We show that kinetics is not necessarily the limiting factor to the development of HP mineral parageneses and that HP conditions may not even be generated in portions of nappes that evolve under H 2 O undersaturated conditions.

Past metamorphic events and more generally the tectono-metamorphic heritage has a strong impact on the H 2 O budget of rocks, hence these portions of tectonic nappes have an inherited history that influences their metamorphic and mechanical evolution during further metamorphic events. The knowledge of the past metamorphic history of HP units is thus important when considering local variations in strain and metamorphic conditions. necking localizes at the level of the soft inclusion, and progresses until a pinch-and-swell structure is formed. P field shows local deviations from the background P, with a lower P in the boudinaged layer than in the matrix. The accumulated strain is the lowest within the boudin cores and the largest in the necking zones. A square illustrates an area of the model that could be representative of the studied field area, where P is 0.4 to 0.6 GPa higher in the matrix than in the boudin, and the accumulated strain is high in the matrix and low in the boudin.

Tables and Figures

J o u r n a l P r e -p r o o f

  J o u r n a l P r e -p r o o f data and structural observations from the Gran Paradiso adjacent H 2 O (under)-saturated paragneisses.

Figure 1

 1 Figure 1 (a) Simplified tectonic map of the Western Alps (modified after Steck et al., 2015). The study area is located in the North of the Gran Paradiso nappe (GP) and outlined on the map by a square. (b) Simplified geological map of the study area, modified after Le Bayon (2005). The location of the two samples studied (20GP07 and 20GP10) are indicated by stars. 20GP07 was sampled in the low strain paragneiss and 20GP10 in the paragneiss with Alpine schistosity.

Figure 2 Figure 3

 23 Figure 2 (a) Field picture of the studied outcrops, on the left bank of the Valeille valley in the northern Gran Paradiso massif. (b) Corresponding sketch of the main structural characteristics deduced from the field observations. The straight lines represent the Alpine schistosity in the paragneiss, whereas the dashed lines show the pre-Alpine foliation and represent the Alpine low-strain paragneiss represented in the geological map of Fig. 1b. The sample 20GP07 was taken in the pre-Alpine paragneiss and sample 20GP10 was taken in the Alpine shear zone.

Figure 4 XFigure 5

 45 Figure 4 X-ray maps of garnets in sample 20GP10. (a) Mn (cps). High-Mn garnet cores are resorbed and correspond to pre-Alpine garnets (Grt V ), which served as nuclei for low-Mn Alpine garnets. (b) Similar straight boundary in X-ray intensity between Grt V cores and Alpine garnet overgrowths can be seen on the Ca signal. Alpine garnets show a high-Ca mantle and a decreasing Ca towards the rims. (c) Fe map also shows an increase in signal from mantle to rim in Alpine garnets. (d) Mg map shows an increase in Mg from mantle to rim in Alpine garnet. Two garnets were selected for profile measurements, one in a garnet enclosing a pre-Alpine core (profile A-B) and one in an Alpine garnet without pre-Alpine core (profile C-D). Profile locations are shown with white traces in (c). (e) and (f) Mole % of the four components along profiles A-B and C-D, respectively. J o u r n a l P r e -p r o o f

Figure 6 Figure 8

 68 Figure6P-T pseudosection calculated for a local bulk composition in the shear zone paragneiss 20GP10, using H 2 O saturated conditions. Red and blue dashed lines show the grossular (grs), pyrope (prp), spessartine (sps) and almandine (alm) content (in mol%), respectively. The blue field indicates the peak P-T conditions at 500 -520 °C and 1.80 -1.95 GPa, based on the garnet chemical composition. Mineral assemblages are written by order of decreasing abundance, with capital letters for phases with variable composition, and lowercase letters for phases considered as pure end-members in the calculation.J o u r n a l P r e -p r o o f

Table 1

 1 Representative mineral compositions and modes for major phases in 20GP10 and calculated local bulk rock composition

			J o u r n a l P r e -p r o o f
		Garn	Garnet A	Garnet A	Plagioclas	Phengit	Phengite	Biotit	Chlorit	Bulk
		et V	mantle	rim	e	e	max Si	e	e	rock*
	SiO 2	37.04 38.08	37.15	60.80	50.42	53.59	37.48	25.60	60.28
	TiO 2	0.16	0.16	0.03		0.32	0.24	1.93	0.07	1.18

Table 2

 2 Representative mineral compositions and modes for major phases in 20GP07 and calculated local bulk rock composition

		Phengite	Phengite max Si M uscovite	Garnet	Plagioclase Biotite Chlorite Bulk rock*
	SiO2	50.39	52.22	46.52	36.29	68.21	49.73	26.49	50.29
	TiO2	0.18	0.17	0.37	0.86		0.48	0.01	0.33
	Al2O3 27.38	25.20	32.82	20.39	19.91	27.58	21.17	26.94
	FeO	3.41	3.70	3.26	32.37	0.16	5.96	19.48	6.98
	Fe2O3								0.00
	M nO	0.00	0.00	0.00	1.10		0.02	0.23	0.15
	M gO	3.17	3.67	1.20	3.32		3.96	19.88	2.02
	CaO	0.01	0.01	0.00	6.43	0.27	0.19	0.03	0.92
	Na2O	0.38	0.33	0.94	0.01	11.44	0.33	0.00	2.51
	K2O	10.48	9.86	10.17	0.00	0.02	9.33	0.01	6.62
	H2O** 4.60	4.71	4.74			2.42	12.71	3.24
	Total	100.00	10.00	100.00	100.77	100.01	100.00 100.00	100.00
	M ode	15		20	10	17	3	5
		* Local bulk rock calculated with additional 30% quartz
		** H2O calculated as the difference between 100 and the sum of oxydes

Table 3

 3 Parameters used in the reference 2D thermo-mechanical model

	J o u r n a l P r e -p r o o f
	Parameter	Symbol	Units	Whole model
	Temperature	T	K	793.15
	Cohesion	C	Pa	2e7
	Friction angle	φ	°	30
	Shear modulus	G	Pa	1e10
	Thermal conductivity	k	W⋅m -1 ⋅K -	2.3
			1
	Heat capacity	C p	J⋅kg -1 ⋅K -1	1050
	Dislocation creep*			Matrix (An100, 0.07 %	Layer (An100, 0.004 %

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Acknowledgements

C. Luisier thanks Paola Manzotti for assistance during field work, Pavel Pitra for the interesting discussions and advice regarding the thermodynamic modelling part, Philippe Yamato for discussions on the thermo-mechanical modelling, Xavier Le Coz for sample preparation, and Martin Robyr and Jessica Langlade for assistance during EPMA acquisition.

We thank Simon Schorn, Pierre Lanari and one anonymous reviewer for their detailed and constructive reviews, as well as Nadia Malaspina for the editorial handling of the manuscript.

The dashed stars represent the LP-HT conditions reached during the Variscan orogeny. In both cases, it lies in the anhydrous field. During post-Variscan cooling, they reach LP-LT conditions (empty solid stars), where rock A is hydrated during interaction with externallyderived fluids, whereas rock B remains dry. During the Alpine prograde increase in P and T, rock A dehydrates along the black arrow going from the blue star to the black star, until it crosses the reaction and reaches the Alpine peak P-T conditions, labelled P A . From there, any reaction on the retrograde path during the exhumation would require H 2 O addition from an external source in order to allow for equilibration at lower P-T conditions. In the H 2 O saturated rock, the activity of the component H 2 O in the fluid phase, 𝑎 𝐻 2 𝑂 , is equal to 1.

Under high 𝑎 𝐻 2 𝑂 , the hydrolytic weakening effect leads to a reduction of the differential stress of the rock (i.e., the difference between the largest and the smallest principal stress), as illustrated on the Mohr circle by the black circle (Fig. 10). For rock B, the same dehydration reaction as in the case A is shown on the schematic phase diagram for a H 2 O undersaturated rock (the reaction separating the blue and grey field), however it is shifted towards lower T, as we now have 𝑎 𝐻 2 𝑂 < 1 [START_REF] Thompson | Fluid-absent metamorphism[END_REF]. Hence, the stability field of the dry assemblage is larger. At conditions of 𝑎 𝐻 2 𝑂 < 1, the hydrolytic weakening effect is reduced or absent and rock B is mechanically stronger than rock A. Therefore, the differential stress of rock B is larger than of rock A. In order to satisfy the force balance, as rocks A and B are in contact, under compression, both circles touch on the side of the maximal principal stress, such that the mean stress in rock B, corresponding to the P of rock B, P B , is lower than that of rock A, P A . From this graphical illustration, we see that units that have adjacent, mechanically heterogeneous, rocks experience different stress states, leading to different P. In turn, this strength contrast controls the strain localization, with weaker domains preferentially affected by deformation. Therefore, this schematic sketch can be used to explain both the petrological The authors declare no competing interests.

Figure 9

Effect of strain rate (10 -15 to 10 -13 s -1 ) and background P (1.4 to 1.8 GPa) on the development of the pinch-and-swell structure and P field. For lower strain rates, deformation localizes mostly in the necking zones and boudins cores remain essentially undeformed, whereas for larger strain rates, shear bands develop inside the strong layer prior to necking. A variation of the background P does not significantly affect the shape of the structures but shifts the overall P field.

J o u r n a l P r e -p r o o f

Journal Pre-proof ), such as the low strain paragneiss. In both cases, the same dehydration reaction separates a hydrous field on the left (blue field), from an anhydrous field on the right side (gray field). The P-T trajectories are shown, starting from the Variscan stage (dashed star) at HT-LP conditions. Both rocks first cool down at the end of the Variscan orogeny, where they equilibrate to the pre-Alpine LT-LP condition (empty solid star). Mohr circle illustrate the differential stress in both rocks. Due to the contrasting stress state between rock A and B, at HP conditions, P A , the P of rock A, corresponding to its mean stress, is higher than P B , the P of rock B, leading to a P difference of ∆P = P A -P B . Strain localizes in the weak rock and the strong rock remains mostly undeformed.

J o u r n a l P r e -p r o o f

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Competing interest declaration

The authors declare no competing interests.

J o u r n a l P r e -p r o o f