# Stress-controlled reaction pattern in the layered lower crust: Field evidence

Marie Baïsset, Loïc Labrousse, Philippe Yamato, Anaïs Cochet

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Marie Baïsset, Loïc Labrousse, Philippe Yamato, Anaïs Cochet. Stress-controlled reaction pattern in the layered lower crust: Field evidence. Earth and Planetary Science Letters, 2025, 657, pp.119270. 10.1016/j.epsl.2025.119270. insu-04977201

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# Stress-controlled reaction pattern in the layered lower crust: Field evidence

Marie Baïsset<sup>a,b,*</sup> <sup>ID</sup>, Loïc Labrousse<sup>c</sup>, Philippe Yamato<sup>b>ID</sup>, Anaïs Cochet<sup>b>ID</sup>

## ARTICLE INFO

### Keywords:

- Mechanical anisotropy

- Reaction propagation

- Finger-shaped structures

- Eclogitization

- Reactive transport

- Stress field

## ABSTRACT

Stress can strongly modify the mechanical and transport properties of rocks. This effect is particularly important for metamorphic equilibria in subduction zones where metamorphic reactions and deformation are often concomitant. However, the impact of stress on the propagation of high pressure metamorphic reactions remains largely under-explored. The island of Holsnøy (Norway) shows incipient eclogitization affecting layered continental granulites along shear zones and puzzling finger-shaped structures. While eclogite shear zones suggest that reaction progress is controlled by strain, a mechanism is still required to explain the propagation of finger-shaped reaction fronts in adjacent low-strain domains. Here, we present a detailed structural analysis of the partially eclogitized Holsnøy massif that highlights the relationship between fingers and shear zones in the anisotropic granulite. We show that these structures are not randomly distributed. Finger-shaped eclogite fronts preferentially propagate along the granulite foliation when layering is at high angle to the local maximal principal stress $\sigma_1$. This feature can be described using the Damköhler number from the theory of reactive transport. Conjunction of anisotropic eclogitization kinetics and anisotropic stress state actually controls the possible development of finger-shaped reaction fronts.

## 1. Introduction

Cutting-edge self-consistent databases allow the prediction of complex metamorphic equilibrium assemblages, involving both solid and fluid phases at given pressure, temperature and oxygen fugacity (among other intensive parameters; Berman, 1988; Holland and Powell, 2011). All these databases rely on experiments performed at hydrothermal conditions, i.e. when pressure is equal to fluid pressure. This feature has lead to recurrent debates over the past few years about the significance of natural metamorphic assemblages (e.g. Wheeler 2014, 2018; Carlson et al., 2015; Spear and Pattison, 2017; Moulas et al., 2019; Powell et al., 2018) that, with few exceptions, develop in rocks under-saturated in fluids, in non-hydrostatic conditions (e.g. Dahlen, 1992; Frolov and Mishin, 2010), and with strain rates that compare with the metamorphic reactions rates (Baxter and DePaolo, 2004). It therefore seems that anisotropic stress state, disequilibrium and incomplete reactions are the rule, rather than full hydrostatic equilibrium (Wayte et al., 1989; Rubie, 1998; Young and Kylander-Clark, 2015; Tajčmanová et al., 2015; Richter et al., 2016; Cionoiu et al., 2022).

In addition, studies focused on the relation between strain and

reaction kinetics highlight how deformation mechanisms can enhance reaction rates (Brodie and Rutter, 1985; De Ronde and Stünitz, 2007). Dissolution-precipitation creep that precisely relies on the coupling between deviatoric stress and diffusion of chemical species constitutes one of the best examples of this phenomenon (e.g. Malvoisin and Baumgartner, 2021).

Eventually, as metamorphic rocks constitute a low permeability endmember in porous media, fluid ingression constitutes one of the main limiting factors for reaction progress. It has been shown that fluid pressure not only impacts reaction kinetics but also controls reaction front topology (Jamtveit et al., 2000; Leclère et al., 2018; Roded et al., 2018). Effective reaction progress in a fluxed and strained metamorphic rock is hence expected to be controlled by (i) the average and deviatoric components of the stress ellipsoid, (ii) the reaction kinetics itself, (iii) the effective permeability and fluid pressure gradients and (iv) all the possible feedbacks between them.

However, only few natural data have actually been produced to evidence these effects, namely because transient paragenesis consecutively replace one another, and because most studies focus on cases where some equilibrium was eventually reached. In this prospect the

<footnote><sup>a</sup> Université PSL, CNRS, Laboratoire de Géologie de l'ENS, UMR8538, France</footnote>

<footnote><sup>b</sup> Univ Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France</footnote>

<footnote><sup>c</sup> Sorbonne Université, CNRS-INSU, Institut des Sciences de la Terre Paris, ISTE, UMR7193, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: marie.baisset.pro@gmail.com (M. Baïsset), loic.labrousse@sorbonne-universite.fr (L. Labrousse), philippe.yamato@univ-rennes.fr (P. Yamato), anais.cochet@univ-rennes.fr (A. Cochet).</footnote>
Caledonian partially eclogitized granulite-facies massif of Holsnøy (Norway) constitutes an emblematic example to study the link between reaction progress and the state of stress. In Holsnøy, partial eclogitization of a granulite-facies lower continental crust unit is observed either within meter to decameter-thick shear zones or within pervasive reaction patches associated to fluid ingression at high pressure (Boundy et al., 1992). These patches form finger-like patterns on outcrop surfaces in the low-strain domains preserved between shear zones (Zertani et al., 2019). Eclogite fingers and shear zones have been intensively studied independently (Austrheim and Griffin, 1985; Jamtveit et al., 2000; Kaatz et al., 2021; Bras et al., 2021; Putnis et al., 2021; Baïssel et al., 2023) but the significance of their coeval development remains untold. Geometrical relationships between shear zones and fingers do not support any unequivocal relative chronology (fingers are not offset by shear zones and shear zones are not cross-cut by fingers). Field rather exhibits fingers rooting unilaterally on shear zones. Although the pattern and intensity of finite strain has been mapped at the massif scale (Boundy et al., 1992; Raimbourg et al., 2005; Zertani et al., 2019), a detailed analysis of the spatial distribution of eclogite-facies fingers is still missing. While these fingers do not show any evidence of macroscopic deformation and develop in undeformed granulite, a recent petrological study actually showed that reactive plagioclase grains in fingers record a non-hydrostatic state of stress the orientation of which is consistent with the regional finite strain field (Baïssel et al., 2023). In addition, fingers often originate in shear zones and systematically propagate along the pre-existing granulite fabric. Although granulites in Holsnøy always exhibit a strong layering or stretching delineated by their coronae (Austrheim and Griffin, 1985), fingers are not systematically present on shear zone-bearing outcrops. So-called static eclogitization can also propagate from the shear zone into the granulite on a narrow rim along the shear zone itself. This suggests that eclogitization progresses with a finger-shaped reaction front in some specific cases only, possibly depending on (i) the regional stress field at the time of eclogitization (Jamtveit et al., 2000) and (ii) the orientation of the pre-existing granulite layering. In order to test this hypothesis from a field point of view, we here present the results of a statistical analysis of the relative orientations of eclogite-facies structures and the granulite layering in Holsnøy.

## 2. Results and interpretation

### 2.1. Structural analysis

Orientations of eclogite shear zones and granulite foliation were measured on 110 shear zone-bearing outcrops (Fig. 1). In this study, all the fingers we measured happen to lie along the granulite foliation. Eclogite-facies lineations within shear zones were also measured when visible. Outcrops are scattered throughout the island in partially eclogitized areas (Fig. 2; Table S1). Chosen areas exposed a well-defined planar granulite-facies foliation associated with dm- to cm-thick shear zones presenting offsets of the same length order ($\gamma \sim 1$). Finger-shaped eclogite-facies overprints were observed in 67 outcrops. On average, the granulite-facies foliation strikes at $\sim$ N130-N140 with a steep dip more often toward SW than NE (Fig. 3a and b). Eclogite shear zones form a conjugate set with dextral shear zones striking at $\sim$ N110 (Fig. 3c, 26 measurements) and sinistral shear zones striking at $\sim$ N40-N50 (Fig. 3d, 84 measurements) with most of the dips toward the NE and NW, respectively.

### 2.2. Are finger-shaped eclogite reaction patterns randomly distributed?

From the orientation and sense of shear of eclogite-facies shear zones we inferred: (i) the local principal shortening direction when a lineation has been measured or (ii) the position of the apparent dilatation and compression quadrants, as defined for focal mechanisms when lineation could not be measured (Figs. 1 and 4a). A clear N-S direction for the principal shortening direction is obtained by stacking the dilatation (white) and compression (shaded) quadrants inferred from the orientation of the shear zones of the 110 measured outcrops (Fig. 4a). This direction is consistent with regional kinematics (Raimbourg et al., 2005; Zertani et al., 2019; Baïssel et al., 2023). Four cases were considered with all combination of two conditions: (i) presence or absence of fingers, and (ii) position of the pole to the granulite foliation in the dilatation or compression quadrants defined by the eclogite-facies shear zone (Fig. 1). If fingers development is controlled by the relative orientation of the granulite foliation and the local principal shortening direction (Z) deduced from the nearby shear-band, two of the four aforementioned cases (i.e. one with- and one without-fingers) should be significantly more represented in the data. This is actually statistically correct: cases with fingers present and the pole to the granulite foliation

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Field photographs of two outcrops from Holsnøy, Norway. (a) Eclogite fingers originating from an eclogite shear zone (60°35′37″N, 5°01′53″E). (b) A finger-free eclogite shear zone (60°35′41″N, 5°02′06″E). Stereographic plots: shear zones in green (shear plane, shear direction and pole to shear plane $S_e$) and granulite foliation in red (pole to the foliation $S_g$). Dilatation quadrants in white, compression quadrants shaded. Quadrants are defined by the shear plane and by the vertical plane that contains $S_e$ in the absence of lineation. An approximate principal shortening direction Z is inferred from geometric considerations (arrows).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Location of all the outcrops where the orientation of eclogite shear zones and granulite foliation have been measured (see inset for the location of the island of Hoslnøy in Norway). As several measurements have sometimes been realized at a same location (black dots), enlargements of the principal analyzed areas are represented in Fig. 5.</figcaption></figure>

in the dilatation quadrant and cases with no fingers and the pole to the granulite foliation in the compression quadrant (Fig. S1) together account for 82/110 = 75 % of the measurements ('model-compatible' outcrops Fig. 5). It seems therefore that the formation of eclogite fingers is favored when the pole to the granulite foliation is located in the dilatation quadrant, i.e. close to the local shortening direction (Figs. 1a, 6a, S1a and d) while in areas where it lies in the compression quadrant, ie. at high angle to the local shortening direction, fingers do not develop (Figs. 1b, 6b, S1b and c). For each outcrop, we calculated the oriented angle ($S_g \to S_e$) between the granulite foliation and the shear sense (see Fig. S1 for details). By construction, when the pole to the granulite foliation lies in the dilatation quadrant, ($S_g \to S_e$) is small (< 90°) while ($S_g \to S_e$) is high (> 90°) when the pole to the granulite foliation lies in the compression quadrant (Fig. S1). Statistical distribution of this angle also shows that relative orientation of the structures linked to the eclogitization reaction (shear zones, fingers) is not random (Fig. 4b and c). Indeed, ($S_g \to S_e$) is lower than 90° (75° on average with a quite sharp gaussian peak) in finger-bearing outcrops (Fig. 4b) while it is higher than 90° (105° on average with a wider distribution of the values) in finger-free outcrops (Fig. 4c). These results confirm the hypothesis of an optimal configuration for the formation of eclogite fingers when the granulite foliation pole is close to Z (Fig. 6a). Assuming that strain directions deduced from the shear zone and stress direction in the adjacent low-strain granulite wall can be considered as parallel, our statistical results show that fingers preferentially develop along the anisotropy of the rock when it is close to normal to the maximal principal stress $\sigma_1$.

### 3. Discussion: effect of anisotropy and stress on the reaction pattern

Reaction front topology in fluxed porous media is a function of the reaction progress, i.e. the rate of dissolution and precipitation of reactive species, and fluid flow that allows transport of these species (Roded et al., 2018). The dimensionless Damköhler number $Da$ allows to quantify the competition between fluid consumption and diffusion through the ratio of the reaction rate constant $k$, over the diffusion coefficient, $D$. At low $Da$ (<<1), in the so-called 'reaction-controlled' domain, experiments and numerical modeling show that reaction fronts evolve cylindrically along the flow direction (Clark and Vanorio, 2016;

Roded et al., 2018). On the opposite, for large $Da$ values, in the so-called 'transport-controlled' regime, instabilities develop and the reaction front tends to form 'wormholes' in the flow direction (Daccord et al., 1993; Szymczak and Ladd, 2006). First used for isotropic porous media subject to unidirectional corrosive fluid flow, the $Da$ number has also proven to be relevant for unstable growth processes in anisotropic media (Roded et al., 2020). A tensor expression of $Da$ has even been proposed by Malvoisin and Baumgartner (2021) for the formulation of reaction-assisted pressure-solution creep:

$$Da_i = \sqrt{\frac{kL^2}{Dw} \left( \frac{1}{c_{r,i}(\sigma_i)} - \frac{1}{c_{p,i}(\sigma_i)} \right)} \quad (1)$$

with $i = 1,2,3$ the indices of the principal stress directions, $L$, the average grain size in m, $w$ the fluid film thickness in m and $c_{r,i}$, $c_{p,i}$ the stress ($\sigma_i$) dependent solute concentrations in the fluid phase of reactants $r$ and products $p$ for the considered reaction in $mol.m^{-3}$. $D$ is a function of the temperature $T$ (in K) following the equation derived by Malvoisin and Baumgartner (2021) from the diffusivity estimates of Oelkers and Helgeson (1988):

$$D = 1.2 \times 10^{-9} \exp \left( \frac{-10^4}{RT} \right) \quad (2)$$

with $R$ the gas constant ($8.314 \ J.K^{-1}.mol^{-1}$). According to this formalism, an anisotropy in $Da$ can result from (i) a difference in the $k/D$ ratio in the different directions, and/or (ii) a difference in balance between stresses and fluid pressure. An anisotropic material under stress can therefore have a low $Da$ direction along which reaction develops without reaction front instabilities, and a high $Da$ direction along which reaction front is unstable and hence fingers develop. In our case study, eclogitization of granulite-facies anorthosite is first controlled by the flow of fluid involved in the breakdown reaction of plagioclase. The first steps of this metamorphic transformation consist in the breakdown of the anorthite component of plagioclase (An) into zoisite (Zo), kyanite (Ky) and quartz (Qtz) (Wayte et al., 1989). This reaction is associated with a significant solid volume decrease (17 %, Bras et al., 2021) which may promote higher transient porosity and permeability in the former low-porosity protolith (Plümper et al., 2017; Zertani et al., 2022). On-going eclogitization hence exhibits a feed-back between reaction progress, transient porosity and fluid flow (Schmalholz et al., 2024)
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

C Poles to dextral eclogite shear zones

<figure><img src="image_7.png" /></figure>

d Poles to sinistral eclogite shear zones

<figure><img src="image_8.png" /></figure>

**Fig. 3.** Statistical representation of the 110 raw measurements. (a) Distribution of the strike of the granulite foliation $S_g$ of the 110 measured outcrops (in gray) and of the finger-bearing outcrops (in blue). Lower hemisphere equal area stereonet projections of: (b) poles to the granulite foliation with finger-bearing data represented in blue, (c) poles to dextral eclogite shear zone planes, and (d) poles to sinistral eclogite shear zone planes (d). Kamb contours for these three sets of data (all data considered) are colored and have been calculated with Stereonet 11 (Cardozo and Allmendinger, 2013).

similar to porous rocks subject to corrosive fluid flow. Similar relationships between stress field and the development of reaction fronts have been documented for other fluid-assisted reactions, such as the preferred growth of myrmekite (negative volume change reaction) that occurs orthogonal to $σ_1$ instantaneous shortening direction (Menegon et al., 2006). Other symplectic reactions in contrast, characterized by a positive volume change growth preferentially orthogonal to $σ_3$ instantaneous stretching direction (Brodie, 1995). We here calculated a Da number for the eclogitization reaction affecting a foliated (i.e. anisotropic) granulite (Fig. 7). We considered the diffusion coefficient D as an isotropic property, and hence a scalar while k, the bulk eclogitization rate constant is anisotropic, and hence a tensor. In this study, k has been chosen equal for reactants and products because reaction kinetics are very poorly constrained for the studied system (plagioclase breakdown)

but should be of the same order of magnitude for the dissolving and precipitating minerals in the case of interface-coupled dissolution-precipitation (Putnis, 2009). In Fig. 7, the value of k is varied between $3.5 \times 10^{-8}$ mol·m$^{-2}$·s$^{-1}$ (~100×D [mol]) and $3.5 \times 10^{-12}$ mol·m$^{-2}$·s$^{-1}$ (~D/100 [mol]). The high boundary value compares with the results of experiments of plagioclase dissolution in hydrothermal conditions (Hellmann and Tisserand, 2006) while the four orders magnitude range also compares with acknowledged variation range between bulk fluid hydrothermal conditions and natural metamorphic conditions (Malvoisin and Baumgartner, 2021). L in Eq. (1) has been chosen equal to 1 mm which is the mean grain size of plagioclase in the Holsøy granulite (e.g. Baïsset et al., 2023) and w, the fluid film thickness has been chosen equal to 10 nm as its value lies between 1 nm and 100 nm according to the literature (Dysthe et al., 2002). $c_{r,i}$ and $c_{p,i}$ in Eq. (1)
<figure><img src="image_9.png" /><figcaption>Fig. 4. Statistical analysis of the measurements. (a) Stereographic plot of the stacked compression and dilatation quadrants from the 110 measured outcrops. Arrows indicate the principal shortening direction Z and the principal stretching direction X inferred from the stacked beachball diagram. (b-c) Shear zone vs. granulite foliation orientation. (S_g→S_e) is the oriented angle between the granulite foliation S_g and the shear zone S_e (see Figure S1 for further explanation). Gray bars represent all the data. Blue bars in (b) represent outcrops where fingers are present and they are hatched when (S_g→S_e) is higher than 90°. Red bars in (c) represent outcrops where fingers are absent and they are hatched when (S_g→S_e) is lower than 90°. Gaussian fit of finger-bearing and finger-free data are represented by the blue (b) and red (c) curves, respectively.</figcaption></figure>

depend on the stress state of the fluid-solid interface according to the Paterson (1973) relation:

$$c_{r,p,i} = c_{r,p}^0 \exp\left(\frac{(\sigma_i - P_f)V_{r,p}}{RT}\right) \quad (3)$$

with $\sigma_i$ the principal stress normal to grain-fluid boundary i in Pa, $P_f$ the fluid pressure in Pa, $V_r$ and $V_p$ the solid molar volumes of reactants and products in $m^3.m^{-1}$ and $c_{r,p}^0$ the solute concentrations at equilibrium (i. e. when $\sigma_i = P_f$). These solute concentrations at equilibrium were computed using the Meemum script of the Perple_X suite (Connolly, 2005) with the DEW13HP622ver_oxides.dat thermodynamic data base combining the Sverjensky et al. (2014) aqueous species data base for the Deep Earth Water (DEW) and the Holland and Powell (2011, DS6.22 revision) data base for solid phases. In plagioclase-rich layers, the first and main plagioclase breakdown reaction to occur is the anorthite-out hydration reaction (Wayte et al., 1989). We therefore considered the anorthite-out reaction:

$$4 \text{An} + \text{H}_2\text{O} \rightarrow 2 \text{Zo} + \text{Ky} + \text{Qtz} \quad (4)$$

Equilibrium concentrations have been calculated at T = 700 °C and P_f = 2 GPa, using the sum of Ca²⁺ and Ca(OH)⁺ concentrations as a proxy for the solubility of reactants and products. Molality and fluid density values yielded $c_p^0 = 44 \text{mol.m}^{-3}$ and $V_p = 335.7 \text{cm}^3.\text{mol}^{-1}$ at equilibrium with zoisite, kyanite and quartz. Excluding zoisite, kyanite, quartz but also clinozoisite, sillimanite, coesite, grossular, lawsonite, margarite and prehnite allows for the calculation of solute concentrations in the presence of metastable anorthite at T = 700 °C and P_f = 2 GPa and yielded $c_r^0 = 176 \text{mol.m}^{-3}$ with $V_r = 406.6 \text{cm}^3.\text{mol}^{-1}$. As expected reactants have a higher solubility than products (Putnis, 2021; see Supplementary Materials for the complete concentrations computation). This anorthite-out reaction has a high solid volume change, suffers a large overstepping at the peak P-T conditions and also exhibits a high nucleation rate in the whole plagioclase matrix volume, at grain boundaries but also within grains (Wayte et al., 1989; Rubie, 1998; Moore et al., 2019; Zertani et al., 2022; Bäisset et al., 2023). This reaction is therefore expected to control the eclogitization progress in the layering direction. Across the layering, eclogitization also implies solid state reactions of granulite-facies pyroxene and garnet in the coronitic

layers (Raimbourg et al., 2007; Bras et al., 2021). The involved reactions have a lower solid volume change, suffer a lesser overstepping at peak conditions, and mostly develop by crystal growth around existing phases (e.g. Austrheim, 2013). Hence the effective k constant for eclogitization can be considered as significantly lower across layering than along layering (Zertani et al., 2022).

The computation of Da relations with effective stress for two end-member k/D ratios (Fig. 7) exhibits a contrasted behavior to the reacting granulite depending on the stress orientation relative to reaction anisotropy. If the minimum effective stress ($\sigma_3$) is collinear to the maximum reaction rate direction and the maximum effective stress ($\sigma_1$) is collinear to the minimum reaction rate direction (Fig. 6a), then the stress effects and the kinetics effects add up and a significant Da differential emerges between the two perpendicular directions. In the layering direction, Da is higher than 1 and fingers therefore develop. In the opposite configuration (Fig. 6b) stress and kinetics effects compensate and Da has low and comparable values along and across layering. No finger-shaped structures develop and eclogitization progresses steadily from shear zones to the pristine granulite. For Da to be substantially different between maximal and minimal stress directions, $\sigma_3$ has to be close to $P_f$ while $\sigma_1$ has to differ from $P_f$. Here $\sigma_3 - P_f$ was arbitrarily set to 1 MPa but the depicted behavior would still prevail for values from 0.1 to 10 MPa. In Fig. 7, we considered a $\sigma_1 - \sigma_3$ offset of 198 MPa computed using the dislocation creep law of Moghadam et al. (2010) for omphacite (diopside$_{50}$-jadeite$_{50}$ at a strain rate of $10^{-14} \text{s}^{-1}$) as it constitutes the more appropriate flow law for the composition of the Holsnøy eclogite (Austrheim and Griffin, 1985). The value of $\sigma_1 - \sigma_3$ is of ~ 145 MPa when considering the dislocation creep law of Boland and Tullis (1986) for wet diopside, but Fig. 7 shows that our interpretation remains valid for this lower value. A drastic strength reduction due to the activation of dissolution-precipitation processes and grain-size sensitive creep in the eclogite (Stüntitz et al., 2020; Kaatz et al., 2022) would only make the conditions in which Da contrasts between the two configurations more specific but not invalidate the model itself. Even if the strength of rocks deforming by dissolution-precipitation creep remains largely unknown, some significant differential stress is needed for the process to accommodate strain. In addition, recent studies of orientation piezometry applied to the Holsnøy eclogite (Hess and Ague, 2024) estimated differential stresses values even higher than the one we used
<figure><img src="image_10.png" /><figcaption>**Fig. 5.** Sample locations in the principal analyzed areas (a and b) shown in Fig. 2. The measurements realized at each location are represented by white dots when they are "model-compatible" (i.e. with fingers present and the pole to the granulite foliation in the dilatation quadrant or with no fingers and the pole to the granulite foliation in the compression quadrant) and by red dots when they are "model-incompatible" (i.e. with fingers present and the pole to the granulite foliation in the compression quadrant or with no fingers and the pole to the granulite foliation in the dilatation quadrant).</figcaption></figure>

for the calculation, from ~ 308 MPa to 860 MPa in static and deformed eclogite, respectively.

To estimate the relevance of our Damköhler number tensor model, we can use binary predictions metrics, comparing observed and predicted positives (fingers) and negatives (no fingers). Accuracy, defined as the ratio of correct predictions over total cases is (54+28)/110 = 75 %. Sensitivity, defined as true positives/(true positives + false negatives) is 54/(54+13) = 80 % and specificity, defined as true negatives/(true negatives + false positives) is 28/(28+15) = 65 %. These metrics highlight that our conceptual model is relevant and has a better success at predicting the presence of fingers than their absence. Fingers may not develop although the stress orientation is prone to their development, if the local kinetics anisotropy is not as high as assumed. Our model is indeed based on the assumption of a double anisotropy: a stress anisotropy, effectively evidenced by the development of shear zones, and a kinetics anisotropy that may vary with the degree of layering of the reacting granulite. Our model only aims at explaining the very incipient stages of the eclogitization process and the measurements it relies on are from very low strained and little transformed domains. Therefore, it does not reproduce the mutual evolution of eclogitization features and deformation in high strained areas (Zertani et al., 2019, their figure 2a) where static eclogitization could have been overprinted by mylonitization after rotation of granulite blocks into a more suitable orientation (Raimbourg et al., 2005). While previous studies highlighted

the effect of the state of stress on the metamorphic equilibria (Wheeler, 2018; Moore et al., 2019; Putnis et al., 2021; Cionoiu et al., 2022) or the impact of fluid pressure on reaction front topology (Leclère et al., 2018), the present contribution emphasizes the impact of stress state on reaction front patterns in low permeability rocks as modeled by Jamtveit et al. (2000) adding the contribution of anisotropic reactive properties of the medium to the stress anisotropy.

## 4. Conclusions

Our data shows that finger-shaped eclogite patches on Holsnøy develop preferentially (i) along the granulite foliation and (ii) when this layering is close to normal to local maximum principal stress. Considering that reaction rate is higher along than across the layering, the documented preferential distribution of finger-shaped reaction fronts can be explained by the conjunction of anisotropic eclogitization kinetics and anisotropic stress state. The Damköhler number proves to be a relevant formalism to explain the observed occurrences of finger-shaped reaction fronts in the Holsnøy granulite, hence emphasizing the effect of stress even in the low-strain domains of the reacting lower crust.

### CRediT authorship contribution statement

Marie Baïsset: Writing – original draft, Writing – review & editing,
<figure><img src="image_11.png" /><figcaption>**Fig. 6.** Conceptual model showing: (a) the ideal configuration for eclogite finger propagation, when the principal shortening direction Z inferred from the orientation of the shear zone S<sub>e</sub> is at high angle to the granulite foliation S<sub>g</sub> and (b) the worst configuration for finger propagation, when Z is close to the plane of the granulite foliation S<sub>g</sub>.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 7.** Damköhler number (Da) vs effective stress in the reacting granulite. Da has been calculated using Malvoisin and Baumgartner (2021) formulation (Eq. (1)-(3)) with L = 1000 µm, w = 10 nm, c₀ = 176 mol.m⁻³, V<sub>f</sub> = 406.6 cm³·mol⁻¹, c₀ = 44 mol.m⁻³ and V<sub>p</sub> = 335.7 cm³·mol⁻¹. Da is a function of k/D that has been varied from 0.01 mol to 100 mol. σ₁ – σ₃ offset (~198 MPa) is estimated from the nearby strength of the eclogite shear zone according to Moghadam et al. (2010) dislocation creep law for omphacite (diopside<sub>50</sub>-jadeite<sub>50</sub> at a strain rate of 10⁻¹⁴ s⁻¹). σ₃ – P<sub>f</sub> was set to 1 MPa (see Section 3 and Supplementary Material for computational details). a and b indices refer to Fig. 6 configurations. For σ₃ along the layering, considered here as the fastest reaction direction and σ₁ orthogonal to the layering (Fig. 6a), considered as the slowest reaction direction, Da is higher than 1 along the layering and four orders of magnitude higher than across the layering. Finger-type reaction fronts are therefore expected to develop. In the opposite configuration (Fig. 6b), Da remains low and compares in both directions. Reaction fronts are then expected to develop without any finger-type features.</figcaption></figure>

Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Loïc Labrousse:** Writing – review & editing, Validation, Methodology, Supervision, Conceptualization. **Philippe Yamato:** Writing – review & editing, Validation, Supervision, Funding acquisition, Conceptualization. **Anaïs Cochet:** Writing – review & editing, Validation, Investigation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was conducted as part of the project METROLOGY supported by the ANR (ANR-23-CE49-0008). We thank S. Zertani and L. Menegon for their constructive suggestions that contributed to improve the quality of the manuscript.

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.epsl.2025.119270.

Data availability

All data are available in the manuscript and supplementary material

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