A new high-pressure high-temperature deformation apparatus to study the brittle to ductile transition in rocks

Understanding the micro-mechanisms underlying the localized–ductile transition (LDT) as well as the brittle–plastic transition (BPT) has become crucial for our wider understanding of crustal processes and seismicity. Given how difficult in situ observations of these transitions are to perform, laboratory experiments might be our only way to investigate the processes active under these conditions (high T and high P). Here, we present Triaxial AppaRatus for GEoThermal energy, a new gas-based triaxial apparatus located at EPFL in Switzerland that was specifically designed to operate under conditions where both the LDT and BPT can occur in geomaterials. We show that the machine is capable of deforming rock samples at confining pressures of up to 400 MPa, temperatures of up to 800 ○ C, and pore pressures (liquid or gas) of up to 300 MPa while keeping the temperature gradient along samples of 40 mm in length and 20 mm in diameter minimal (less than 30 at 700 ○ C). Most importantly, the maximum load is 1000 kN (stresses as high as 2.2 GPa on 24 mm samples and 3 GPa on 20 mm samples), allowing for the deformation of very competent rock samples. Moreover, during deformation, the pair of syringe pore pressure pumps allow for continuous permeability or dilatancy recording. We benchmarked our machine against existing data in the literature and show that it accurately and precisely records stress, strain, permeability, pressure, and temperature.


I. INTRODUCTION
The colloquial "BDT" is a zone in the crust of extremely complex rheology, where both a transition of the mode of deformation (localized to ductile, LDT) and a transition in the type of deformation (brittle to plastic, BPT) can overlap. In this regime, both brittle and plastic micro-mechanisms interact (Fredrich et al., 1989;Paterson, 1958). Paradoxically, it marks a significant decrease in seismicity as well as the locus of some of the biggest recorded earthquakes Scholz, 1988;2002;and Sibson, 1982). Moreover, it also limits the maximum depth of hydrothermal fluid-flow in the crust (meteoric fluids; Jupp and Schultz, 2004;Weis, 2012). Lately, it has become an economical target since, at the root of hydrothermal systems, within rocks deforming in mixed localized-ductile conditions, pressure and temperature conditions allow for the extraction of supercritical water, which could increase the energy production of geothermal plants by a factor of 10 Friðleifsson et al., 2014;and Muraoka et al.,

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scitation.org/journal/rsi 2014). Given the average depth of the BDT, between 12 and 15 km (Scholz, 1988), drilling boreholes represent a tremendous engineering challenge, making in situ observation sparse and extremely costly. Therefore, laboratory replication of the high pressure and high temperature conditions found at these depths is necessary to bridge the gap in our understanding of the BDT and to potentially unlock its geothermal potential (Watanabe, et al., 2017a;2017b).
To carry out rock deformation experiments under crustal conditions, three types of triaxial apparatus are generally used with the main difference in design being the medium used to apply the confining pressure: solid, gas, or liquid. The confining medium controls the temperature range that can be investigated as well as the sensors equipping the apparatus.
Solid medium machines (often referred to as "Griggs" presses) use salt to apply confining pressures as high as 5000 MPa and an internal furnace to reach temperatures as high as 1500 ○ C (Griggs, 1967). These capabilities span the entire crust and a part of the upper mantle but require the use of rather small samples (6 mm in diameter and 12 mm in length), restricting the use of the Griggs press to homogeneous fine-grained rocks. Such extreme pressure and temperature conditions only allow for data recording outside of the pressure vessel, i.e., external differential stress and strain and (active or passive) ultrasonic wave speeds (Moarefvand et al., 2021). Additionally, it is currently impossible to control and/or monitor pore pressure within samples under confining pressure in Griggs presses.
Gas medium triaxial apparatus or "Paterson" presses use an inert gas to apply confinement (Paterson, 1970). These can generally reach up to 500 MPa and 1300 ○ C but are limited to moderate differential loads of up to 100 kN (1273 MPa vertical stress on 10 mm diameter samples). The bigger pressure vessels used in this design allow for the use of bigger samples (10 mm in diameter and 20 mm in length on average) and an internal load cell as well as pore fluid systems, allowing for the measurement of pore volume changes and permeability (Fischer and Paterson, 1992;Violay et al., 2015;and 2017). Acoustic systems can also be fitted to these machines (Khazanehdari et al., 2000;Rybacki et al., 2021). One exception to this general design is the newly refurbished Murrell press located at UCL, London, United Kingdom. While this particular gas-based triaxial apparatus can reach remarkable confining pressures and temperatures (1000 MPa and 700 ○ C), it shares some of the drawbacks of solid medium presses, most importantly, the small sample size (Harbord et al., 2022).
In a liquid-based apparatus, confining pressure is applied by the means of a liquid (e.g., silicon oil, water, and kerosene). Their capabilities are controlled by the type of liquid used to apply confinement. The difference in confining medium also necessitates that the furnace be located outside the pressure vessel, limiting the maximum range of temperatures (at 200 MPa confining pressure, 500 ○ C for a steel vessel, and 700 ○ C for Nimonic© steel; Walker et al., 1990). The most ubiquitous liquid-based triaxial apparatus is the oil-based design that can reach pressures of up to 300 MPa and temperatures of up to 200 ○ C (e.g., Cornelio and Violay, 2020;Eccles et al., 2005;Noël et al., 2019). This design accommodates the biggest samples with rock cores up to 40 mm in diameter and 100 mm in length. This allows for the use of a vast array of sensors, such as on-sample acoustic sensors (e.g., Meyer et al., 2021;Noël et al., 2021;Schub-nel et al., 2005), pore pressure sensors (Aben and Brantut, 2021;Proctor et al., 2020), or strain gauges (e.g., Passelègue et al., 2020). Despite this advantage, the most commonly used oil-based apparatus can only span the conditions of the upper crust and do not allow for the exploration of the BDT in most rocks (for a counter example, see Rutter, 1972).
Here, we present a newly designed gas type triaxial press TAR-GET (Triaxial AppaRatus for GEoThermal energy), located at EPFL in Switzerland, and specifically designed for the exploration of the BDT. Based on the original design of the Paterson press, it can accommodate larger samples than any other modern gas-based press up to 400 MPa and 800 ○ C. Moreover, it allows for continuous recording of sample dilatancy and permeability. First, we describe in detail the design of the apparatus before describing its calibration. Finally, we benchmark our machine against recent data produced on similar machines.

A. Overview
The TARGET apparatus, installed at EPFL, Switzerland, is inspired by the Paterson press designed by Mervyn Paterson in the 1970s at the Australian National University (Paterson, 1990;Paterson and Olgaard, 2000) and has been built by Wille Geotechnik (DE) in strong collaboration with EPFL and ENS Paris. For reference, the original drawings of Paterson can be found on the website put together by Mark Zimmerman. All original blueprints were personally shared by Paterson to A. Schubnel. The TARGET apparatus is based on the combination of a high-pressure, internally heated pressure chamber that is commonly used in experimental petrology (Edgar and Edgar, 1973) with an axial deformation system (Fig. 1). The confining pressure is applied with an inert gas, argon, and can reach 400 MPa. The high-pressure confining vessel houses an internal Kanthal furnace allowing it to reach temperatures of up to 800 ○ C (Fig. 1). The large inner diameter of the confining vessel also allows for the use of large samples up to 48 mm in length and 24 mm in diameter. Moreover, TARGET is equipped with an internal straingauge based force sensor located inside the high-pressure vessel. This design allows for force readings free from the contribution of the frictional forces required to move the loading piston past the high pressure seals. The axial load is applied externally using a servohydraulic actuator. The piston is compensated, i.e., the confining pressure does not exert a force on it (Griggs, 1936), and the maximum achievable axial force is 1000 kN, representing an axial stress of 2.2 GPa on 24 mm samples and 3.2 GPa on 20 mm samples (Fig. 1). Similarly, the design of the compensation chamber (based on that described in Paterson, 1990) allows for piston displacement without changes in pressure vessel volume (i.e., constant confining pressure). Two piezo-electrical sensors for active and passive seismic measurements are located at either end of the loading column. Two high precision syringe pumps for controlling gas or water pore-fluid pressure are installed and allow continuous pore-volume changes and permeability measurements during experiments (Fig. 1).
TARGET presents key advantageous features over other deformation apparatus used in rock mechanics: (1) constant confining pressure (due to compensation of the axial piston); (2) a high performance furnace with three independent heating zones ensuring a gradient of less than 0.8 ○ C/mm at 700 ○ C along the length sample; (3) a thermocouple for temperature readings directly on the sample; (4) an internal force sensor that measures the true axial load on the sample, preventing measurement pollution from parasitic friction between the loading column and the seals; (5) the ability to accommodate large samples; (6) a hemispherical seat within the loading column preventing misalignment during deformation; (7) piezo-electrical sensors for active and passive acoustics; (8), top-andbottom independent pore fluid pressure system for permeability and pore volume changes measurements at high temperature; (9) low axial strain rate system (alongside the main servo-hydraulic one) controlled by syringe hydraulic pumps to mimic more realistic strain rates (as low as 10 −9 s −1 ; (10) high axial force capacity (1000 kN), granting access to rock failure across the brittle-to-ductile regimes; and(11) a servo-controlled intensifier regulating precisely confining pressure during experiments. Nevertheless, the TARGET apparatus also has disadvantages, such as the risk of explosion arising from the large amount of energy stored in the vessel due to the high compressibility of argon and the large volume of the high-pressure chamber. To mitigate such risks, the entire high-pressure system is enclosed in a bullet-proof Kevlar cabinet to protect the user in the case of projection. However, there remains the important risk of blast noise in the case of a significant, catastrophic leak at high pressure. For this reason, TARGET must be operated while wearing personal protection equipment, i.e., ear defenders.

B. Detailed description
TARGET weighs more than 7.7 tons in total and is composed of seven main units: (1) the sample assembly' (2) the high-pressure chamber associated with a pneumatic pump and a hydraulic pressure intensifier; (3) the hydraulic-mechanical system and associated rigid frame that drives the movement of the axial piston; (4) the internal furnace and its associated control systems; (5) the pore fluid pressure system; (6) the set of sensors for measuring the deformation of the sample (in μm) and the load applied to it (in kN); and (7) the digital acquisition and control systems. The various controls of the device are gathered on its front panel including the high-pressure circuit valves, fluid pressure valves, confining and fluid pressure pump controls, temperature controls and regulations, and sensor displays (force and displacement). The user can reach all the controls of the device, allowing for enhanced reactivity.

Sample assembly
The sample assembly is composed of a rock core wrapped in an inner copper foil jacket (0.025 mm thickness) to improve contact with the outer copper jacket (0.2 mm thickness) with an internal diameter of 24 ± 0.1 mm, isolating the sample from the confining medium (see Fig. 1). The jacket is a tube cut to 285 mm and then swaged in its middle section onto a former with the diameter of the sample (i.e., between 20 and 24 mm). The Mg-stabilized zirconia pistons are conical at their ends to accommodate the change in diameter between the ample and loading columns. Sample compression is accompanied by an intense deformation of the jacket; therefore, the rheology of the latter inevitably influences the mechanical response of the assembly. To minimize this, annealed copper jackets with low mechanical strength are used during experiments at low temperatures (20-400 ○ C) on weak samples, whereas untreated copper jackets are preferred at higher temperatures (400-800 ○ C). The deviatoric stress is transmitted to the sample via a succession of pistons made of zirconia ceramics (Mg doped) selected for their mechanical strength, high stiffness, and low thermal conductivity and heat capacity as well as hardened steel for the contact with the closing screw cap and the spherical joint.

High pressure chamber and associated pumps
The total confining system is about 1400 × 730 × 2470 mm 3 in size and weighs ∼690 kg. The chamber (1.4542 X5 CrNiCuNb17-4 P1070 steel) is closed at the top by two screw caps and at its base by the main deformation piston (Fig. 1). The vessel is encased in a cooling sleeve (3.2315 AlMgSi1 steel) that comprises a water-cooled copper coil (2.0060 E-Cu 57) with an internal diameter of 12 mm. Sealing of the high-pressure chamber (also referred to as "vessel") is ensured by lip seals supported by anti-extrusion polyether ether ketone (PEEK) rings. The vessel contains the furnace, the sample assembly, and the deformation piston coupled to the internal load cell. One special feature of this design is that the movement of the deformation piston in the confining medium does not change

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scitation.org/journal/rsi the confining pressure due to a high-pressure compensation chamber that maintains the gas volume constant in the confining vessel (Fig. 1). The confining gas is drawn and pressurized from argon commercial bottles to the pressure vessel in two stages. A primary pneumatic pump (gas booster from Haskel) draws argon from the bottle and brings the pressure in the vessel up to 100 Mpa (Fig. 2). For higher confining pressure, the primary system is isolated by a valve before pressure is raised further by pumping oil into the low pressure side of a 10:1 pressure intensifier to the desired pressure of up to 400 MPa. During the experiment, the confining pressure is automatically regulated around the target value by the computer-controlled intensifier, allowing for active compensation of the pressure variations due to temperature changes. The confining pressure is measured at different points of the high-pressure circuit by two digital pressure transducers (Fig. 2). Furthermore, a mechanical Bourdon tube is used to monitor the pressure in case of an electronic failure of the sensors. The confining pressure is measured with an accuracy of ±0.1 Mpa.

Deformation piston
The axial piston (1.4112 X90CrMoV18 steel) is located under the high-pressure vessel and connected to the internal load cell (Fig. 1). Two pumps can drive the axial piston: a hydraulic one (for large displacements) and a syringe-pump volume/pressure controller (for very low strain rates and constant force experiments). The hydraulic unit generates the hydraulic oil pressure required for FIG. 2. Synoptic diagram of the confining pressure system (orange) and the pore pressure system (blue). Green denotes the oil system controlling the intensifier.
operation. The hydraulic oil is led onwards through a flow pipe connection and returned to the hydraulic oil tank via the return line. The hydraulic unit is about 780 × 550 × 1170 mm 3 in size, weighs about 350 kg, and is associated with a mechanical frame made of a bottom and top plate and four columns (total of 1987 kg). The syringepump volume/pressure controller serves to maintain the pressure generated by the hydraulic unit. It is ∼550 × 400 × 1400 mm 3 and weighs about 80 kg. All units are computer operated. To accurately control the position of the axial piston, TARGET is equipped with two independent displacement sensors (Linear Variable Differential Transformers; LVDTs) mounted in parallel that can be used in a feedback loop. The first one is located on the displacement piston and has a stroke of 15 mm with an accuracy of 0.01 mm and the second one is within the hydraulic system with a stroke of 10 mm and an accuracy of 0.005 mm.

Furnace and thermocouple
The furnace consists of a solid alumina tube wrapped in three independent resistive heating coils, forming three independent heating zones. These are powered and operated independently to limit the thermal gradient on the sample. All three of the coils are made of kanthal wire of varying lengths (resistivity of the coils ∼6 Ω). The furnace is insulated with compressed alumina fiber. The latter limits heat dissipation to the outside. The whole furnace is encased in a thin steel casing that holds the elements in place. If the furnace were to be damaged, the wool fiber could be removed, and all of the parts reused for the construction of a new furnace (i.e., reuse the machined ceramics and steel casing). Temperature monitoring is carried out with a type K thermocouple slid into the pore pressure system down to the top of the sample. The tip of the thermocouple is always placed in contact with the sample in an almost zero-temperature gradient zone. The accuracy of the measurement is ±0.1 ○ C. Additionally, a separate safety thermocouple monitors the temperature of the seal carrier.
The temperature gradient in the sample zone is calibrated before the experiments and regularly monitored over the lifespan of the furnace (Fig. 3). For this purpose, a calibration sample with a central borehole is used through which a multiple-zone thermocouple is inserted. The latter consists of 5 k-type thermocouples distributed along the axis every 20 mm. The calibration consists in adjusting the respective electrical powers of the three heating coils so that the temperature gradient is minimal at the sample location. Calibration is done for several pressure-temperature combinations as the confining fluid heat capacity is strongly dependent on pressure and temperature (see data from the National Institute of Standards and Technology and Acosta et al., 2018) and thus the heating power needed to reach a given temperature depends on the overall gas pressure. Given that the furnace has very reproducible characteristics for given pressure-temperature conditions over a large number of consecutive experiments, the settings obtained during furnace calibration for heating power are confidently repeated during experiments.

Pore pressure system
Pore pressure can be applied by means of all types of fluids be it gases, liquids, or even corrosive fluids (up to 35 g/l of NaCl), owing to the use of two Inconel 718 volume pressure controllers Scientific Instruments (VPC, maximum pressure 300 Mpa). The whole pore pressure system is about 400 × 700 × 2455 mm 3 and weighs about 380 kg. The pore pressure system connects to the sample through the top of the pressure vessel, and the upper sealing piston is designed to accommodate a high-pressure fluid feed tube with an internal diameter of 1 mm (Fig. 1). The thermocouple is slid into this supply tube. A junction T-fitting is used between the thermocouple tube and the fluid pressure piping. The thermocouple is silver-soldered to a cone fitting, which is then screwed onto the T-fitting. The bottom pore fluid line is attached to the bottom anvil within the confining pressure chamber. The pore pressure line can easily be replaced in the case of precipitation after use with corrosive fluids. The pressure controller is composed of two high precision step motor pumps (VPC) with a volume of 70 ml. A displacement sensor allows for the measurement of the pump pistons' displacement and the injected fluid volume. The accuracy of this sensor is 2 μm. Three 0-300 Mpa pressure sensors, located at different points of the circuit, allow for pressure measurements with an accuracy of 0.1 Mpa (Fig. 2). Pore pressure and volume are both computer controlled with constant pressure, time ramps, or pressure oscillations capabilities, giving access to pulse decay or oscillating pore pressure measurements (Bernabé et al., 2006;Fischer and Paterson, 1992).

The internal load-cell
The axial force applied to the sample is one of the most important parameters to be measured. The biggest challenge is discriminating the friction of the deformation piston against the seals in the high-pressure chamber during its displacement. The best solution is to use an internal load cell, which must withstand the confining pressure and transmit the information to the external measurement and control system. In TARGET, the internal load cell is composed of a hollow hardened-steel cylinder of known elastic properties fitted on its inner surface with four 1000 Ω strain gages. The strain gages are wired in full Wheatstone bridge to record resistance variations from which strain and then load are derived. The absolute precision of the internal force sensor is 0.01 kN. This sensor is calibrated against the external load cell located in the hydraulic unit, which itself has an accuracy of 0.1 kN. The total error on the measurement of differential stress is estimated to be ∼0.22 Mpa on 24 mm diameter samples and 0.32 MPa on 20 mm diameter samples. This error can be considered negligible with regard to the deviatoric stresses reached during the deformation.

A. Stiffness and load cell calibration
One critical calibration to be done when performing triaxial experiments is the machine stiffness. It consists in measuring the elastic deformation of a calibration sample of known elastic properties in order to estimate the deformation of the loading column. Here, we use a cylindrical alumina sample dummy of 42 × 20 mm 2 with Young's modulus E = 300 GPa.
We loaded this dummy at a strain rate of 10 −5 s −1 (standard in the field of rock mechanics) up to a differential load of 150 kN (Fig. 4). At a confining pressure of 100 MPa, we found machine stiffness to be 120 and 115 kN/mm when measuring with the external and internal load cells, respectively [ Fig. 4(a)]. Additionally, we show that machine stiffness is mostly pressure independent and is 127 kN/mm on the external load cell at a confining pressure of 300 MPa [ Fig. 4(b)].

B. Preliminary results on Carrara marble
In order to validate the mechanical data produced by TARGET, we compare some preliminary data against those in the extensive work of Rybacki et al. (2021). They conducted a tremendous number of experiments on cylindrical samples of Carrara marble (20 × 10 mm 2 ) at a wide variety of experimental conditions spanning brittle, semibrittle, and ductile rheologies in a Paterson-type gas apparatus.
Similarly, we conducted a series of experiments on Carrara marble samples. Cylindrical cores of 42 × 20 mm 2 were cored from a single block, and their ends were ground to ensure parallelism of the loading surfaces.
The samples were wrapped in a copper foil inner jacket before being slid into the outer copper jacket and placed in the pressure vessel. The samples were brought to an effective confining pressure of 100 MPa, before being warmed up to the target temperature (400 or 600 ○ C). Experiments were all dry to reproduce the conditions in Rybacki et al. (2021). The samples were then deformed at a constant strain rate of 10 −4 s −1 or 10 −5 s −1 until about 10% uncorrected strain was accumulated in the sample. Recorded stresses are corrected for the contribution of the copper jacket by estimating its strength with a power law (Frost and Ashby 1982). 41 Experimental results are gathered in Fig. 5. At both tested temperatures, the general mechanical behavior of Carrara marble is ductile and virtually identical in its trends in both setups. However, the absolute strength values found are ∼20% higher in TARGET compared to those reported in Rybacki et al. (2021): at 400 ○ C, the Scientific Instruments Red data are from this study while data in black are from Rybacki et al. (2021). Full lines are data gathered at a strain rate of 10 −5 s −1 , and dashed lines are data gathered at 10 −4 s −1 .
strength reached at 8% strain in TARGET is 279 and 266 MPa at 10 −4 s −1 and 10 −5 s −1 , respectively. In Rybacki et al. (2021), the authors report strength at 8% of 238 and 219 MPa at 10 −4 and 10 −5 s −1 , respectively. Similarly, at 600 ○ C, in TARGET, strength at 8% is 156 and 158 MPa at 10 −4 and 10 −5 s −1 while it is 128 and 110 MPa at similar strain rates in Rybacki et al. (2021). These differences in the absolute strength of the sample are imputable to differences in sample origin, sample geometry, machine and ensuing corrections, operators, and so on. Given the two sets of experiments were conducted on different machines, we consider them to be in excellent accordance, hence validating the mechanical data produced by TARGET.

C. Permeability calibration
We conducted experiments to estimate the permeability range in which TARGET can be used, i.e., the maximum and minimum recordable values for rock permeability. In our setup, maximum recordable permeability is controlled by the permeability of the piping used in the pore pressure system (see "pore pressure line" in Fig. 1) as well as by the permeability measurement method. The piping used here is standard high-pressure piping with an internal diameter of 1 mm. To record its permeability, we conducted an experiment with a hollow alumina sample with extremely high permeability at an effective confining pressure of 50 MPa and an argon pore pressure of 15 MPa. Pore pressure oscillations of 1.5 MPa amplitude and 180 s period were applied to the downstream end of the sample, and the resulting pressure perturbation was recorded at the upper end of the sample. Following the method described in Bernabé et al. (2006), we determined the piping permeability to be 7.21 × 10 −16 m 2 [ Fig. 6(a)]. Hence, this value is the highest recordable permeability using the oscillatory method in our setup. Different methods, such as constant flow, could yield higher values of permeability but could not be used while actively deforming a sample.
Observations of post-mortem samples showed that the copper jacketing used to isolate samples from the confining medium tends to deform when subjected to confinement, forming a vertical crease along the sample axis. Hence, we expect the jacket to be the limiting unit with regard to minimum recordable permeability. Since the copper is malleable, we posited that the permeability of the crease, if permeable at all, would be pressure and temperature dependent, with its contribution being greatest at low effective confining pressure and room temperature. To somewhat limit the Scientific Instruments ARTICLE scitation.org/journal/rsi FIG. 6. Permeability calibration data for the piping (a) and for the jacket (b). Upper and lower dashed lines represent maximum and minimum recordable permeabilities, respectively. An error bar representative for all data points is shown for the data point at 300 ○ C in (b). All data points are recorded with the oscillatory method.
contribution of the jacket to the permeability, all samples are wrapped in a copper foil (0.025 mm thickness) inner jacket that improves contact between the sample and the jacket. We conducted an experiment on a virtually impermeable steel plug, increasing the first effective confining pressure by 25 MPa steps up to 100 MPa, from which the temperature was increased by 100 ○ C steps up to 400 ○ C [ Fig. 6(b)]. At every pressure and temperature step, permeability was recorded by means of the oscillatory method with an argon pore pressure of 30 MPa, oscillations of 3 MPa in amplitude, and a period of 300 s. At every step, the oscillations were maintained for a minimum of five cycles in order to reach a satisfying confidence level in our measurement.
It appears that jacket permeability rapidly plummets from its value of 5.37 × 10 −19 m 2 at 25 MPa effective confining pressure down to 1 × 10 −19 m 2 at 75 MPa and remains below the minimum recordable value with an oscillation period of 300 s (about 2 × 10 −20 m 2 ). With further temperature increments, permeability does not reappear, and post experiment observation showed that the crease in the jacket completely disappeared at high pressure and temperature. It is important to note here that the minimum recordable value of permeability can be decreased by an order of magnitude from the value displayed here by increasing the amplitude and period of the pore pressure oscillations (Fischer and Paterson, 1992;Bernabé et al., 2006).
In conclusion, it appears from this calibration that TAR-Get allows for a wide range of permeability measurements, which makes it ideal for experimenting on both porous (10 −15 m 2 ) and extremely tight rocks (10 −22 m 2 with a longer oscillation period and greater oscillation amplitude).

D. Preliminary results on volvic trachyandesite
Volvic trachyandesite is a porous igneous rock from Volvic, Central France. It has a starting porosity of about 20%. Most importantly, it has recently been the focus of a thorough study in which permeability data were gathered during hydrostatic loading from atmospheric pressure up to 150 MPa effective pressure (Fig. 8, Heap et al., 2022). In order to benchmark the permeability data obtained with TARGET, we conducted a similar experiment. We cored cylindrical cores of 42 × 20 mm 2 from the same block used by the authors of the comparative study and ground their faces to ensure parallelism of the loading surfaces. The samples were then wrapped in a copper foil inner jacket and slid into the outer copper jacket. Effective confining pressure was increased to 200 MPa step-wise while recording permeability using the oscillatory method every step. To do so, an argon pore pressure of 30 MPa was applied to the sample as well as 3 MPa oscillations with a period of 180 s. Every effective confining pressure step was held until five pore pressure oscillations had elapsed. An example of raw pore pressure data is shown in Fig. 7.
We recorded a permeability evolution with effective pressure strikingly similar to that reported in Heap et al. (2022). In fact, while we recorded a permeability of 3.76 × 10 −16 m 2 and 2.18 × 10 −16 m 2 at 50 and 150 MPa confining pressure, respectively, Heap et al., 2022 report permeabilities of 3.98 × 10 −16 m 2 and 2.18 × 10 −16 m 2 at the same effective pressures.
Additionally, we tested the permeability recording capabilities of the apparatus under elevated temperature conditions. In this experiment, we set the effective pressure to 150 MPa and increased FIG. 8. Permeability of Volvic trachyandesite as a function of effective pressure (a) and temperature (b). Data in black are from Heap et al. (2022) while colored data are from this study. Uncorr. denotes permeability data computed without accounting for changes in pore fluid (argon) viscosity change with temperature. All data points were recorded with the oscillatory method with pore pressure oscillations of amplitude 3 MPa and period 300 s. temperature step-wise by 100 ○ C steps. At every step, we recorded permeability using the oscillatory method with a set argon pore pressure of 30 MPa and with 3 MPa and 300 s oscillations. In this configuration, permeability data have to be corrected for changes in argon viscosity with temperature. Since it increases with temperature (see data from the National Institute of Standard Technology), a failure to apply such a correction leads to a marginal but nonnegligible, underestimation of permeability. In the case shown in Fig. 8 panel (b), the experiment had to be stopped when, at 700 ○ C, the copper jacket intruded into a sample pore, leading to a puncture. In the future, this problem can be avoided by using steel jackets on porous rocks at a temperature higher than 700 ○ C, which is stronger. Overall, TARGet allows for permeability recordings in both tight and porous rocks at low or high effective pressure and temperatures of up to 800 ○ C.

IV. CONCLUSION
We designed a new gas-based triaxial apparatus to explore the hydraulic and mechanical properties of rocks at the brittle-ductile transition. TARGET can accommodate the largest samples of any modern gas-based triaxial apparatus up to effective pressures of 400 MPa and temperatures of 800 ○ C. Permeability can be readily and continuously recorded in both tight and porous rocks via the use of the oscillatory method. We benchmarked our new apparatus and showed that it yields data in accordance with the latest results in the literature.