# Decrease in the Permeability of Microcracked and Macrocracked Granite at Elevated Pressure and Temperature

Lucille Carbillet, Michael J Heap, Patrick Baud, Jamie Farquharson

► To cite this version:

Lucille Carbillet, Michael J Heap, Patrick Baud, Jamie Farquharson. Decrease in the Permeability of Microcracked and Macrocracked Granite at Elevated Pressure and Temperature. Geophysical Research Letters, 2025, 52 (7), pp.e2024GL112970. 10.1029/2024GL112970. hal-05022221

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL112970

**Key Points:**

* Increasing temperature to 150°C at constant pressure reduces permeability by up to an order of magnitude by thermally closing microcracks

* Up to our maximum confining pressure (50 MPa), reductions in permeability are observed at high temperature (150°C)

* High-temperature (150°C) does not appear to influence the permeability of a tortuous macrocrack

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

L. Carbillet and M. J. Heap,
lucille.carbillet@univ-lorraine.fr;
heap@unistra.fr

**Citation:**

Carbillet, L., Heap, M. J., Baud, P., & Farquharson, J. I. (2025). Decrease in the permeability of microcracked and macrocracked granite at elevated pressure and temperature. *Geophysical Research Letters*, 52, e2024GL112970. https://doi.org/10.1029/2024GL112970

Received 14 OCT 2024
Accepted 1 FEB 2025

**Author Contributions:**

**Data curation:** L. Carbillet,
J. I. Farquharson

**Formal analysis:** L. Carbillet, P. Baud

**Investigation:** L. Carbillet

**Methodology:** L. Carbillet, P. Baud,
J. I. Farquharson

**Resources:** P. Baud

**Software:** J. I. Farquharson

**Validation:** L. Carbillet

**Visualization:** L. Carbillet

**Writing – original draft:** L. Carbillet

**Writing – review & editing:** L. Carbillet,
P. Baud, J. I. Farquharson

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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# Decrease in the Permeability of Microcracked and Macrocracked Granite at Elevated Pressure and Temperature

L. Carbillet¹,² ID, M. J. Heap¹,³ ID, P. Baud¹, and J. I. Farquharson⁴,⁵ ID

¹Institut Terre et Environnement de Strasbourg, Université de Strasbourg, CNRS UMR, Strasbourg, France, ²Laboratoire GéoRessources, Université de Lorraine, CNRS UMR 7359, Vandoeuvre-lés-Nancy, France, ³Institut Universitaire Français, Paris, France, ⁴Institute for Research Administration, Niigata University, Niigata, Japan, ⁵Research Institute for Natural Hazards and Disaster Recovery, Niigata University, Niigata, Japan

**Abstract** Pressure and temperature increase with depth, modifying the microstructure of crustal rocks. The opening or closing of micro- and macrocracks resulting from variations in the *in-situ* conditions influences the permeability of crustal rocks. While confining pressure is known to close pre-existing cracks, reducing permeability, the influence of temperature has received less attention. Here, we measured the permeability of micro- and macrocracked granite at confining pressures and temperatures up to 50 MPa and 150°C, respectively. We find that the permeability of micro- and macrocracked granite decreases with confining pressure. At constant pressure, increasing temperature reduces permeability by up to an order of magnitude, interpreted as the closure of microcracks due to mineral thermal expansion. Using a simplified microstructural model, we show that microcrack aperture is reduced by up to 50% at 150°C compared to room temperature. However, temperature does not appear to influence the permeability of a tortuous macrocrack.

**Plain Language Summary** From the Earth's surface to the lower crust, pressure and temperature conditions change significantly. These variations lead to changes in the internal structure of crustal rocks by the opening or closing of cracks between and within the crystals forming the rock. When open, these cracks provide pathways for fluids to flow through the rock. In this experimental study, we specifically examine how temperature affects the permeability—defined as the ease with which fluids flow through a rock—of a granite initially populated with numerous cracks, representative of rocks commonly found in fault zones. Our experiments show that as temperature increases up to 150°C, permeability decreases due to the closure of cracks caused by the thermal expansion of adjacent mineral crystals. These findings have important implications for understanding fluid dynamics in geothermal reservoirs, fault zones, and other subsurface environments where temperature variations are expected.

## 1. Introduction

Temperature variations within the Earth's crust, caused by natural processes like volcanism, or by anthropogenic activities like geothermal energy extraction, can induce substantial crack damage (Collins et al., 2018; Merrien-Soukatchoff & Gasc-Barbier, 2023). Laboratory studies have shown that, when exposed to a heating-cooling cycle to high temperature, the strength, Young's modulus, and P-wave velocity of crystalline rocks are decreased (Griffiths et al., 2018; Reuschlé et al., 2006; Xu et al., 2023), a consequence of the increase in number, length, and connectivity of thermal cracks (Griffiths et al., 2017). In polymineralic rocks, at high temperature, anisotropic thermal expansion coefficients and thermal expansion mismatches between different minerals cause deformation heterogeneities, inducing intra- and intercrystalline thermal stresses that result in microcracking (Meredith et al., 2001). However, rocks have been shown to develop different patterns of microcracking under repeated heating-cooling cycles (Browning et al., 2016, 2022; Fredrich & Wong, 1986; Griffiths et al., 2024; Simmons & Cooper, 1978). Moreover, depending on the mineralogy and microstructure, especially the crystal size and arrangement, different amounts of thermal microcrack damage can be generated either during heating or cooling (Browning et al., 2022; Griffiths et al., 2024; Li et al., 2020). Previous studies have also demonstrated the importance of the maximum temperature that rocks have previously been exposed to, introducing the notion of a temperature-memory effect (Daoud et al., 2020; Griffiths et al., 2018, 2024; Yong & Wang, 1980), analogous to the Kaiser stress-memory effect observed during mechanical loading, where a rock does not undergo further damage when subject to stresses it has already experienced (Holcomb, 1981; Lavrov, 2003).
Thermally induced microcracks influence the transport properties of crustal rocks, where they provide pathways for fluid flow, if they are connected in a percolating network (David, 1993; David et al., 1999). Because of their importance in many processes from hazardous natural phenomena like earthquake ruptures, and potentially hazardous geoengineering projects like the sub-surface storage of radioactive waste, the influence of micro- and macrocracks on permeability has received much attention in the recent decades. In initially crack-free crystalline rocks, thermal stressing increases permeability due to the formation and propagation of microcracks (Darot & Reuschlé, 2000; Darot et al., 1992; Faoro et al., 2013). While macrocracks can provide efficient fluid pathways and drastically increase permeability if they are dilatant, un-filled, and oriented in the fluid flow direction (Y. Chen et al., 2014; Kluge et al., 2021; Mitchell & Faulkner, 2008), they can also act as barriers to fluid flow if they are compressional, filled with fragmental material, or oriented in the opposite direction to fluid flow (Moore et al., 1994; Morrow et al., 2001). For example, Nara et al. (2018) reported that the permeability of granite increases due to the existence of an open macrocrack, but decreases upon filling it with fine-grained material.

To investigate the evolution of micro- and macrocracks under in-situ conditions, that is, conditions representative of those found at depth in the crust, the permeability of microcracked and macrocracked rocks has been measured across various pressure conditions. Walsh (1981) showed that the antagonist effects of confining pressure, which acts to close cracks and reduce permeability, and pore fluid pressure, which acts to open cracks and increase permeability, are captured by a pressure law, expressed as $P_e = P_c - \alpha P_p$, where permeability is linearly related to $\ln(P_e)$ and $\alpha$ is a rock-dependant constant. The exponential decrease of permeability with effective pressure was also shown for rocks initially containing crack-type voids such as gabbro and granite (Darot et al., 1992; David, 1993; Morrow et al., 1981; Trimmer et al., 1980) and for “tight” sandstones (Bernabe, 1986; Keaney et al., 1998; Xiao et al., 2019). Previous experimental studies measured permeability during triaxial deformation and reported a large increase in permeability for samples that initially contained very few microcracks loaded up to brittle failure (Y. Chen et al., 2014; Kluge et al., 2021; Mitchell & Faulkner, 2012; Oda et al., 2002). By contrast, for crystalline rocks that initially contain numerous thermal microcracks, the permeability immediately prior to failure was found to be less than the initial permeability (S. Chen et al., 2017). Experimental studies on rocks initially containing single or multiple macrocracks also reported permeability decreases with confining pressure due to a stress-induced reduction of macrocrack aperture (Lamur et al., 2017; Nara et al., 2011; Stanton-Yonge et al., 2023).

Previous efforts to understand the influence of temperature on permeability have primarily focused on measuring the permeability of initially intact samples at high temperature (Darot & Reuschlé, 2000; Darot et al., 1992; Faoro et al., 2013). However, it is not possible during these experiments to distinguish between changes resulting from thermal microcracking and those resulting from measuring the permeability at high temperature. As a result, changes to the permeability of rock that do not result from thermal microcracking remain poorly understood. Experiments have also typically been performed on intact rocks while, in many crustal settings, such as fault zones (Mitchell & Faulkner, 2012) and geothermal reservoirs (Genter & Traineau, 1996), rocks often contain abundant micro- and macrocracks. In this study, we aim to characterize the evolution of permeability at elevated pressure and temperature in micro- and macrocracked granite samples. Our approach allows us to (a) analyze the effect of pressure and temperature on permeability independently and (b) evaluate how pre-existing microcracks evolve at elevated temperature.

## 2. Materials and Methods

### 2.1. Lanhélin Granite

Lanhélin granite, a granodiorite from Brittany, France, was used. It consists of quartz, feldspar, and mica, with an average crystal diameter of approximately 1 mm (Figure 1). Six cylindrical samples were cored to a diameter of 25 mm. Four of these samples were cut and precision-ground to a length of 50 mm (Figure 1a), while the other two were prepared to a length of 25 mm. All samples were washed and dried at 40°C for 48 hr. We thermally stressed the samples to create a network of microcracks (Figures 1c and 1d): samples were heated to 700°C at a rate of 1°C/min, maintained at that temperature for 2 hours, and cooled back to room temperature (RT) at 1°C/min. Above the $\alpha/\beta$ quartz transition (573°C), the difference in thermal expansion between quartz and feldspar results in intense thermal cracking (Glover et al., 1995). We stressed our samples to 700°C to ensure that no new microcracks would form during our high-temperature (up to 150°C) permeability measurements (temperature-memory effect). The connected porosity of each thermally stressed sample was calculated using the bulk sample volume and the
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Photograph and microstructure of (a, b) an intact Lanhélin granite sample, (c, d) a sample thermally stressed to 700°C, showing inter- and intracrystalline thermally induced microcracks, and (e) a thermally stressed sample deformed in tension, showing a cross-cutting tortuous macrocrack.</figcaption></figure>

solid sample volume measured using a helium pycnometer (AccuPyc II by Micromeritics®). Post thermal stressing, samples have a connected porosity of approximately $\phi = 3.7 \pm 1.2\%$.

In addition to thermal stressing, the two 25 × 25 mm samples were subjected to tensile deformation. Samples were wrapped in tape to preserve bulk cohesion during deformation. The tensile experiments were performed at RT and pressure in a uniaxial loading frame (LoadTrac II load frame by Geocomp®) (Griffiths et al., 2018) using the Brazil disc technique (Heap et al., 2022; Perras & Diederichs, 2014). Samples were deformed at a constant displacement rate of 0.025 mm/s until the first macrocrack formed (Figure 1e). The formed macrocracks were throughgoing (they connected the sample endfaces) and tortuous in cross-section (Figure 1e).

## 2.2. Permeability Measurements at Elevated Pressure and Temperature

The permeability of microcracked Lanhélin granite samples (with and without macrocracks) was measured using a custom-designed permeameter (Figure 2). The permeameter comprises three circuits: a confining pressure circuit (Figure 2(4,6,11)), a heating system (Figure 2(12,13)), and a pore pressure circuit (Figure 2(1,2,5,7–10)).

For each measurement, a sample (Figure 2(3)) is placed between the up- and downstream platens (1,5), into an annular Viton jacket (2) which is secured within the pressure vessel (4). Temperature can be raised from room-temperature to up to 150°C using a heating mantle (12) wrapped around the pressure vessel and connected to a control box (13). Confining pressure can be applied by filling the void space between the vessel and jacket through the inlet (6) with high-temperature oil (Thermofluid DW-Therm from Huber®). Confining pressure can be increased up to 70 MPa using a high-pressure ENERPAC® hand pump (11). To ensure microstructural equilibration at the experimental conditions, each measured sample is left at the target temperature for a minimum of 1 hr before increasing confining pressure (Figure S1 in Supporting Information S1) and then for a minimum of 1 hr after each pressure step prior to measuring permeability.

After the confining pressure and temperature have been applied to the system, permeability is measured by flowing nitrogen (the permeant gas) through the sample. The setup monitors the pressure differential between the upstream pressure transducer and atmospheric pressure downstream using a KELLER® pressure transducer, and the volumetric flow of gas through the sample using a downstream Bronkhorst® gas flowmeter (Figure 2). The imposed confining pressure ensures the pore fluid does not navigate the pore pressure circuit by flowing along the sample sides.

The permeability of all Lanhélin granite samples was measured at confining pressures of 2, 5, 10, 15, 20, 30, 40, and 50 MPa. Two of the four microcracked samples were measured at RT, one was measured at 75°C, and the other at 150°C. One of the two micro- and macrocracked samples was measured at RT, and the other at 150°C. During these latter experiments, samples were positioned so that the plane of the tensile macrocrack was parallel to the direction of fluid flow. To estimate and account for sample-to-sample variability, permeability measurements on microcracked samples at RT were repeated and the permeability of 4 different micro- and macrocracked samples was measured at RT at 2 MPa.

The higher permeability ($k > 10^{-17} m^2$) measurements were performed using the steady-state method, by measuring volumetric flow rate $Q_v$ for several different pore pressure gradients $\Delta P$ (up to a maximum of 0.2 MPa). For lower permeability ($k \le 10^{-17} m^2$) measurements, the transient pulse method was used (Brace
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Schematics of the high-pressure, high-temperature permeameter. Not to scale.</figcaption></figure>

et al., 1968). For the pulse method, we monitored the decay of pore fluid pressure (0.2 MPa) from an upstream reservoir of constant, and known, volume to near-ambient conditions. Permeability $k_D$ for the steady-state and pulse methods were calculated using Equations 1 and 2, respectively.

$$k_D = \frac{Q_v \mu LP_d}{P_m \Delta P A} \qquad (1)$$
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Evolution of permeability with confining pressure at room temperature (light and dark blue), 75°C (orange) and 150°C (red). Open symbols represent measurements on samples containing both microcracks and a macrocrack, while solid symbols are for samples with microcracks only. The permeability of the intact granite is approximately $10^{-20}$ m$^2$ (Carbillet et al., 2024). Representative photographs of the samples are provided near their respective data sets. Sample temperature is given in the legend; RT: room temperature. (b) Trendlines obtained using an empirical exponential law. The fitting parameters used are written on each corresponding trendline.</figcaption></figure>

$$k_D = \frac{2L\mu}{A} \frac{V_u}{P_u^2 - P_d^2} \frac{dP_u}{dt} \quad (2)$$

where $P_u$ and $P_d$ are the upstream and downstream pore pressure, respectively, $P_m$ the mean pore fluid pressure (where $P_m = \frac{1}{2}(P_u + P_d)$), $\mu$ the pore fluid viscosity, $t$ time, and $L$ and $A$ the length and cross-sectional area of the sample, respectively.

Data obtained at elevated temperature were corrected to account for changes in pore fluid volume induced by the temperature gradient between the sample (elevated temperature) and where volumetric flow is measured (RT). The volumetric flow rate of the pore fluid was corrected using the ratio between the density of the pore fluid (nitrogen) at ambient temperature and at the sample temperature. The derivation of this correction can be found in Morrow et al. (1981) and Kushnir et al. (2017). Additionally, permeability data were corrected for the effect of fluid flow-related artifacts, turbulent flow (i.e., Forchheimer effect) and/or gas slip along flow channel walls (i.e., Klinkenberg effect) following the procedure and calculations detailed in Kushnir et al. (2018).

### 3. Results

The permeability measured at different temperatures is presented as a function of confining pressure in Figure 3. The permeability of microcracked Lanhélin samples (Figures 1c and 1d) decreases exponentially with confining pressure. The experimental data can be fitted using an empirical exponential law of the form $k = k_0 e^{-aP_c}$, where $a$ is a constant. The exponential trendlines obtained are presented in Figure 3b. At RT, permeability decreases from $1 \times 10^{-15}$ m$^2$ at 2 MPa to $2.6 \times 10^{-18}$ m$^2$ at 50 MPa. In addition, at a fixed confining pressure, increasing temperature from RT to 150°C decreases the permeability of the microcracked samples by up to one order of magnitude. For example, at 2 MPa, permeability decreases from $1 \times 10^{-15}$ m$^2$ at RT to $4.9 \times 10^{-16}$ m$^2$ at 75°C
and to $3.2 \times 10^{-16}$ m$^2$ at 150°C. We repeated the permeability measurements at RT and results show that the variation in permeability between samples is smaller than those resulting from pressure and temperature changes. In detail, the variance in permeability is $\sigma^2 = 3.82 \times 10^{-31}$ m$^2$.

Figure 3 shows the evolution of permeability as a function of confining pressure for samples that contain both microcracks and a macrocrack (Figure 1e) at RT and 150°C. Figure 3 also shows permeability values obtained at RT and 2 MPa on 4 different micro- and macrocrack samples to illustrate the natural sample-to-sample variability. The variance in permeability derived from these permeability values is $\sigma^2 = 6.52 \times 10^{-25}$ m$^2$. The permeability of micro- and microcracked granite is about three orders of magnitude higher than the permeability of granite that only contains microcracks. Similar to the microcracked granite, the permeability of the micro- and macrocracked granite decreases exponentially with increasing pressure, and decreases as temperature is increased from RT to 150°C. Our results demonstrate that, at constant temperature, an increase in confining pressure from 2 to 50 MPa leads to a decrease in permeability by more than two orders of magnitude. At RT, permeability decreases from $1.9 \times 10^{-12}$ m$^2$ at 2 MPa to $2.7 \times 10^{-14}$ m$^2$ at 50 MPa. At constant pressure, an increase in temperature from RT to 150°C results in a decrease in permeability by more-or-less one order of magnitude, modulo natural sample variability. At 50 MPa, permeability decreases from $2.7 \times 10^{-14}$ m$^2$ at RT to $1.7 \times 10^{-15}$ m$^2$ at 150°C.

Compared to the microcracked samples, larger decreases in permeability are observed for samples containing both micro- and macrocracks at low pressure (<20 MPa; Figure 3). Specifically, the permeability decrease observed between 5 and 15 MPa is larger than that between 30 and 40 MPa. We note that the decrease in permeability due to an increase in confining pressure is slightly more pronounced at higher temperature for microcracked samples than for samples containing both micro- and macrocracks (Figure 3b).

## 4. Discussion

Rocks found in crustal fault zones are often characterized by a high crack density, inherited from a complex stress-pressure-temperature history (Mitchell & Faulkner, 2009). Here, we consider granite samples thermally stressed to 700°C, that is, microcracked granite, as our starting material and we examine how an increase in temperature affects permeability, while remaining at temperatures well below 700°C to avoid the creation of new microcracks and the growth of pre-existing microcracks (temperature-memory effect). The experiments of Griffiths et al. (2018) show that we should not expect new microcracks in Lanhélin granite at 75 or 150°C. This allows us to study how temperature fluctuations, at different confining pressures, can influence the permeability of granite.

The microcrack network formed by thermally stressing the granite samples (Figures 1c and 1d) serves as an efficient fluid pathway, ensuring a permeability of approximately $10^{-15}$ m$^2$ at 2 MPa of confining pressure at RT (Figure 3). As a reference, the permeability of intact Lanhélin granite is about $10^{-20}$ m$^2$ (Carbillet et al., 2024). A large increase in permeability following thermal stressing has previously been observed in granite (e.g., Darot et al., 1992; Darot & Reuschlé, 2000; Faoro et al., 2013). As confining pressure increases, we observe an exponential reduction in the permeability of the microcracked samples (Figure 3). Confining pressure acts to close the thermal microcracks that initially populate the samples, thereby diminishing the efficiency of fluid flow through the microcrack network (Walsh & Brace, 1984). A permeability reduction during hydrostatic pressurization has been consistently observed in rocks with microstructures featuring “fracture-type” voids such as granite and gabbro (Bernabe, 1986; Skoczylas et al., 1994; Trimmer et al., 1980), basalt (Fortin et al., 2011), or tight sandstone (Keaney et al., 1998; Xiao et al., 2019).

In addition to thermal microcracks, the cross-cutting macrocrack increases the initial permeability: the micro- and macrocracked sample is about three orders of magnitude more permeable than the microcracked sample at RT (Figure 3b). For dilatant open macrocracks oriented in the fluid flow direction, like in our micro- and macrocracked granite samples, large increases in permeability have previously been reported for granite (Darot et al., 1992; Morrow et al., 1981; Nara et al., 2018; Pérez-Flores et al., 2017; Trimmer et al., 1980), and other rock types such as sandstone (Kushnir et al., 2018), basalt (Nara et al., 2011), and andesite (Heap & Kennedy, 2016; Pérez-Flores et al., 2017). A decrease in permeability with pressure is also observed in the microcracked and macrocracked Lanhélin granite samples (Figure 3), as reported by Nara et al. (2011) for basalt. However, while the rate at which permeability decreases with pressure is more-or-less constant for microcracked granite, the permeability of micro- and macrocracked granite decreases rapidly up to 20 MPa and then more slowly (Figure 3b). We interpret this change in slope as the result of the closure, or partial closure, of the macrocrack at
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Pressure and temperature dependency of the microcrack aperture. Relative microcrack aperture between room temperature and 75°C (light and dark orange dots) or 150°C (pink and red dots) are calculated using Equation 4. Estimations of the mean microcrack aperture are given next to the corresponding data point.</figcaption></figure>

low pressure (i.e., <20 MPa), as also observed and discussed by Nara et al. (2011). In detail, low aspect ratio and oriented macrocracks are easier to close with pressure than high aspect ratio and isotropically distributed microcracks (Nara et al., 2011).

In addition to the applied confining pressure, the microcracked samples were subjected to a temperature change. Our results show that, at constant confining pressure, an increase in temperature leads to a decrease in permeability (Figure 3). We interpret this as a result of the thermal expansion of minerals when temperature increases at a given confining pressure, where pre-existing intra- and intercrystal microcracks serve as free space for individual crystals to expand into. In other words, because confining pressure prevents the free expansion of the bulk granite sample, the thermal expansion of minerals is accommodated by the closure of pre-existing microcracks which, in turn, reduces permeability. As crystals can expand into the pore space without contributing to the bulk expansion of the crystal aggregate, the thermal expansion of highly microcracked crystalline rocks is significantly lower than that for intact rocks, as reported by Richter and Simmons (1974). Recent results of Griffiths et al. (2024) on cyclic heating-cooling of low-porosity basalts show an increase in P-wave velocity during the second and third heating cycles, which they also attribute to the closure of microcracks with increasing temperature. Finally, as the pressure at which cracks close is a function of their aspect ratio (Walsh, 1965), a decrease in crack aperture with temperature explains why the rate of decrease in permeability per unit confining pressure is higher at 150°C than at RT (Figure 3). However, our data show that not all microcracks are fully closed at 50 MPa (given that the permeability of intact Lanhélin granite is $10^{-20}$ m²), and increasing temperature to 150°C can still reduce the aperture of microcracks further or close

additional microcracks. We speculate that, at a given higher pressure, all microcracks would become closed and increasing temperature would not decrease permeability further. Given that the rate of permeability decrease per unit pressure is higher at higher temperature, the confining pressure for complete microcrack closure would be expected to be lower at 150°C than at 20°C.

However, an increase in temperature does not appear to influence the permeability of a macrocrack: the change in slope in the permeability data as a function of confining pressure (Figure 3), thought to be a consequence of the partial closure of the macrocrack, occurs at about 20 MPa at RT and at 150°C. We note that macrocrack formation in microcracked granite samples likely exploits the inter- and intracrystalline microcracks present within the samples (Figure 1d), producing tortuous, rough-walled macrocracks (see Figure 1e) and therefore complex and tortuous fluid flow paths. We speculate that the thermal expansion of minerals may reduce the aperture of the macrocrack in certain locations but, because the tortuous macrocrack has created a complex flow path, the passage of the pore fluid is ultimately not restricted and permeability is not reduced. Indeed, well-matched low-tortuosity macrocracks—the formation of which is favored in homogenous rocks with a low initial porosity (Heap & Kennedy, 2016)—close at lower stress than rough, tortuous macrocracks (Tsang & Witherspoon, 1983).

To further explore, and quantify, the influence of temperature on pre-existing microcracks, we consider the relationship between permeability and the geometrical attributes of an isotropic population of microcracks proposed by Guéguen and Dienes (1989):

$$k = \frac{4\pi}{15} f \frac{\overline{w^3 c^2}}{\overline{l^3}} \quad (3)$$

where f is the percolation factor, and the three parameters $\overline{w}$, $\overline{c}$, and $\overline{l}$ are the average crack aperture, radius, and spacing, respectively. Given that samples were thermally stressed to 700°C, we assume that the increase in temperature does not change the radius or spacing of microcracks (temperature-memory effect, i.e., Lanhélin granite does not undergo further damage when subject to temperatures it has already experienced). Therefore, the relative average crack aperture under diverse pressure-temperature conditions can be estimated using:
$$ \Delta w = \frac{w_T}{w_{T0}} = \sqrt[3]{\frac{k_T}{k_{T0}}} \quad (4) $$

We use Equation 4 to estimate the relative microcrack aperture between RT (T0) and either 75°C or 150°C (T) at different confining pressures (Figure 4). Using optical microscope image analysis (Figure S2 in Supporting Information S1), initial microcrack aperture (post thermal stressing) was estimated to be 4.27 ± 2.08 µm and absolute aperture values were estimated using the aperture change (Equation 4). We found that, at 2 MPa, increasing temperature to 75°C results in the closure of microcracks to a residual aperture of about 3.76 µm (Figure 4). At 50 MPa, an increase in temperature from RT to 150°C reduces aperture to 2.37 µm. A comparable reduction is anticipated as a result of a 10 MPa increase in confining pressure for microcracked Lanhélin granite. We propose that future studies evaluate if the changes in crack aperture we report can be fitted using a thermal expansion model. Temperature changes of this magnitude may be expected to occur in tectonically active fault zones, where the circulation of fluids can trigger seismicity (Violay et al., 2014), in volcanic systems, where permeable outgassing reduces the propensity for explosive behavior (Farquharson et al., 2017; Okumura & Sasaki, 2014), or in geo-engineering sites targeted for geothermal energy production (Duwiquet et al., 2021). Our results have implications for settings where rocks are constrained to varying extents and temperature variations are expected. At a given depth, in microcracked rocks, increases and decreases in temperature can decrease and increase permeability, respectively.

## Data Availability Statement

The experimental data presented in this study are available at Carbillet (2025).

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## Acknowledgments

The authors wish to acknowledge the funding received from the ANR project GERESFAULT (ANR-19-CE05-0043). Additionally, this research conducted at the Interdisciplinary Thematic Institute GeoT, as part of the ITI 2021-2028 program at the University of Strasbourg, CNRS, and Inserm, received support from IdEx Unistra (ANR-10-IDEX-0002) and the SFRI-STRAT'US project (ANR-20-SFRI-0012) under the framework of the French Investments for the Future Program. M.J. Heap acknowledges the support provided by the Institut Universitaire de France (IUF). The authors thank John Browning and an anonymous reviewer for providing comments that helped improved the manuscript. This paper benefitted from discussions with Alexandra Kushnir. Finally, the authors also thank Bertrand Renaudie for sample preparation and Laurent Rihouey for machining fittings for the permeameter.
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