P K Gilg

F B Byrne

T Wadsworth

Reuschlé

Michael J Heap
email: heap@unistra.fr

H Albert Gilg

Paul K Byrne

Fabian B Wadsworth

Thierry Reuschlé

Petrophysical properties, mechanical behaviour, and failure modes of impact melt-bearing breccia (suevite) from the Ries impact crater (Germany)

Keywords: suevite, porosity, strength, permeability, alteration, Young's modulus

Petrophysical properties, mechanical behaviour, and failure modes of impact melt-bearing breccia (suevite) from the Ries impact crater (Germany)

Introduction

Impact craters are a geological feature ubiquitous to the solid-surface planetary bodies of our Solar System (e.g., [START_REF] Neukum | A study of lunar impact crater sizedistributions[END_REF][START_REF] Melosh | Impact cratering: A geologic process[END_REF][START_REF] Phillips | Impact craters and Venus resurfacing history[END_REF][START_REF] Wood | Impact craters on Titan[END_REF][START_REF] Barnouin | The morphology of craters on Mercury: Results from MESSENGER flybys[END_REF][START_REF] Robbins | A new global database of Mars impact craters≥ 1 km: 1. Database creation, properties, and parameters[END_REF][START_REF] Robbins | Craters of the Pluto-Charon system[END_REF]. The preservation of impact craters on Earth is rare, largely due to erosion and tectonic activity (e.g., [START_REF] Grieve | The record of past impacts on Earth[END_REF]. However, impact bombardment of bodies in the inner Solar System is all but certain; for example, nearly 400,000 >1 km-diameter craters have been identified on Mars, a few hundred of which are >100 km in diameter [START_REF] Robbins | A new global database of Mars impact craters≥ 1 km: 1. Database creation, properties, and parameters[END_REF], and Mercury is similarly marked (e.g., Fassett et al., 2012a). Well-preserved craters on the terrestrial planets and the Moon are associated with impactites, rocks that have either been created or modified by an impact (e.g., [START_REF] Osinski | Impact ejecta emplacement on terrestrial planets[END_REF][START_REF] Stöffler | Shock metamorphism of planetary silicate rocks and sediments: Proposal for an updated classification system[END_REF].

On Earth, where we can readily access and assess such deposits (even if they are comparatively rare), proximal impactites have been classified into three groups: shocked target rocks, impact breccias, and impact melt rocks (e.g., [START_REF] Stöffler | Impactites. Metamorphic rocks: A classification and glossary of terms[END_REF][START_REF] Osinski | Impact cratering: Processes and products[END_REF][START_REF] Stöffler | Shock metamorphism of planetary silicate rocks and sediments: Proposal for an updated classification system[END_REF]. Impact breccias are characterised by their clast contents, the most distinctive of which are impact meltbearing breccias ("suevites"). Impactites as observed on Earth are also often variably altered (typically argillic alteration and zeolitisation) by the hydrothermal system that forms following the impact (e.g., Osinski et al., 2013;[START_REF] Kirsimäe | Impact-induced hydrothermal activity. Impact Cratering: Processes and Products[END_REF] or by supergene alteration [START_REF] Muttik | Stable isotope composition of smectite in suevites at the Ries crater, Germany: Implications for hydrous alteration of impactites[END_REF][START_REF] Muttik | Boron isotope composition of secondary smectite in suevites at the Ries crater, Germany: boron fractionation in weathering and hydrothermal processes[END_REF].

The petrophysical properties of impactites, such as porosity, permeability, Young's modulus, and strength, are valuable input parameters for a wide range of modelling. For example, the porosity and permeability of impactites are required in models designed to understand fluid flow within the hydrothermal systems associated with impact craters (e.g., [START_REF] Rathbun | Hydrothermal systems associated with Martian impact craters[END_REF]Abramov andKring, 2004, 2005;[START_REF] Sanford | A simulation of the hydrothermal response to the Chesapeake Bay bolide impact[END_REF][START_REF] Versh | Development of potential ecological niches in impactinduced hydrothermal systems: The small-to-medium size impacts[END_REF][START_REF] Abramov | Numerical modeling of impact-induced hydrothermal activity at the Chicxulub crater[END_REF][START_REF] Barnhart | Martian post-impact hydrothermal systems incorporating freezing[END_REF].

Further, for heavily impacted crusts such as that of Mars and Mercury, the porosity and permeability of impactites may provide useful constraints for estimates of crustal porosity and permeability. Porosity and permeability estimates of the Martian crust, for example, are required for the modelling of outflow channel formation (e.g., [START_REF] Gulick | Magmatic intrusions and a hydrothermal origin for fluvial valleys on Mars[END_REF][START_REF] Manga | Martian floods at Cerberus Fossae can be produced by groundwater discharge[END_REF]Hanna and Phillips, 2005;[START_REF] Andrews-Hanna | Hydrological modeling of outflow channels and chaos regions on Mars[END_REF][START_REF] Musiol | Outflow activity near Hadriaca Patera, Mars: Fluid-tectonic interaction investigated with High Resolution Stereo Camera stereo data and finite element modeling[END_REF], crustal hydrothermal convection (e.g., [START_REF] Travis | On the role of widespread subsurface convection in bringing liquid water close to Mars' surface[END_REF], hydrothermal crustal cooling (e.g., [START_REF] Parmentier | Early evolution of Mars with mantle compositional stratification or hydrothermal crustal cooling[END_REF], methane release into the atmosphere (e.g., [START_REF] Lyons | Formation of methane on Mars by fluid-rock interaction in the crust[END_REF][START_REF] Etiope | Low temperature production and exhalation of methane from serpentinized rocks on Earth: a potential analog for methane production on Mars[END_REF], and groundwater flow (e.g., [START_REF] Grimm | On the secular evolution of groundwater on Mars[END_REF][START_REF] Harrison | Regionally compartmented groundwater flow on Mars[END_REF]. Additionally, knowledge of the mechanical behaviour and strength of impactites is important for our understanding of impact crater collapse (e.g., [START_REF] Melosh | Impact crater collapse[END_REF][START_REF] Wünnemann | Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target[END_REF], the modelling of impact crater geometry (e.g., Collins, 2004;[START_REF] Potter | Estimating transient crater size using the crustal annular bulge: Insights from numerical modeling of lunar basin-scale impacts[END_REF], and values of uniaxial compressive strength of crustal rocks are needed for characterising the strength and stability of rock masses using tools such as rock mass rating (RMR) or the geological strength index (GSI) (e.g., [START_REF] Schultz | Brittle strength of basaltic rock masses with applications to Venus[END_REF][START_REF] Schultz | Stability of rock slopes in Valles Marineris, Mars[END_REF][START_REF] Neuffer | Mechanisms of slope failure in Valles Marineris, Mars[END_REF]Nahm and Schultz, 2007;[START_REF] Okubo | Constraints on mechanisms for the growth of gully alcoves in Gasa crater, Mars, from two-dimensional stability assessments of rock slopes[END_REF][START_REF] Brunetti | Analysis of a new geomorphological inventory of landslides in Valles Marineris, Mars[END_REF][START_REF] Klimczak | Limits on the brittle strength of planetary lithospheres undergoing global contraction[END_REF][START_REF] Klimczak | A rock-mechanical assessment of Mercury's global tectonic fabric[END_REF]. Further, strength values for impactites could help inform studies that provide rock strength estimates from rover drilling and abrasion data (e.g., [START_REF] Thomson | Estimating rock compressive strength from Rock Abrasion Tool (RAT) grinds[END_REF][START_REF] Peters | Uniaxial compressive strengths of rocks drilled at Gale Crater, Mars[END_REF], as well as improving physical weathering rate estimates (e.g., [START_REF] Viles | Simulating weathering of basalt on Mars and Earth by thermal cycling[END_REF][START_REF] Eppes | Cracks in Martian boulders exhibit preferred orientations that point to solar-induced thermal stress[END_REF].

Despite the need for robust input parameters for a variety of modelling studies, there are, to our knowledge, only two studies that provide laboratory-measured values for the permeability of impact melt-bearing breccia [START_REF] Parnell | Permeability data for impact breccias imply focussed hydrothermal fluid flow[END_REF]Heap et al., 2020a), and but one that provides values of uniaxial compressive strength (Heap et al., 2020a). Other studies have, however, provided other physical property values for impactites. For example, values of density, porosity, thermal conductivity, elastic wave velocities, and magnetic susceptibility are available for impactites from the Chicxulub impact crater (Mexico) (e.g., Mayr et al., 2008a;[START_REF] Elbra | Physical properties of the Yaxcopoil-1 deep drill core, Chicxulub impact structure, Mexico[END_REF][START_REF] Christeson | Extraordinary rocks from the peak ring of the Chicxulub impact crater: Pwave velocity, density, and porosity measurements from IODP/ICDP Expedition 364[END_REF]. [START_REF] Parnell | Permeability data for impact breccias imply focussed hydrothermal fluid flow[END_REF] found that the permeability of impact breccias from the Haughton (Canada), Ries (Germany), and Rochechouart (France) impact craters to be between ~1 × 10 -16 and ~1 × 10 -15 m 2 . Heap et al. (2020a) measured the porosity, permeability, and uniaxial compressive strength of samples of impact melt-bearing breccia collected from two locations at the Ries impact crater. They found average connected porosities of 0.24 and 0.25, and average uniaxial compressive strengths of 34.2 and 29.2 MPa, for samples taken from the quarries at Seelbronn and Altenbürg, respectively. The average permeability of these impact melt-bearing breccias was found to be ~2 × 10 -15 m 2 (Heap et al., 2020a). However, notwithstanding these few studies, petrophysical measurements are currently unavailable for altered impactites and thus a full assessment of the mechanical behaviour, failure modes (brittle or ductile), and deformation micromechanisms of impactites is absent. The paucity of studies that report petrophysical and mechanical properties of impactites reflects, in part, the poor preservation potential of impact craters and their impactites on Earth [START_REF] Grieve | The record of past impacts on Earth[END_REF]. As a result, the Ries impact crater (Figure 1), one of only several impact craters on Earth with well-preserved and easily accessible impact melt-bearing breccias [START_REF] Osinski | Impact ejecta emplacement on terrestrial planets[END_REF], serves as an ideal location to sample and study impactites.

The Ries crater (Figure 1) is a double-layer rampart crater with an inner-and outer-ring diameter of about 12 and 24 km, respectively (e.g., [START_REF] Wünnemann | Is Ries crater typical for its size? An analysis based upon old and new geophysical data and numerical modeling[END_REF] Figure 1), that shares similarities with Martian craters (e.g., [START_REF] Sturm | The Ries impact, a double-layer rampart crater on Earth[END_REF]. The crater formed following an impact into a layer of sedimentary rocks 600-700 m thick overlying a crystalline basement (e.g., [START_REF] Pohl | The Ries impact crater[END_REF][START_REF] Stöffler | Ries crater and suevite revisited-Observations and modeling Part I: Observations[END_REF] about 15 million years ago (e.g., [START_REF] Rocholl | Comment on "A high-precision 40Ar/39Ar age for the Nördlinger Ries impact crater, Germany, and implications for the accurate dating of terrestrial impact events[END_REF]. Types of impactite identified at Ries crater include [START_REF] Von Engelhardt | Distribution, petrography and shock metamorphism of the ejecta of the Ries crater in Germany-A review[END_REF]): shocked target rocks; breccia derived mainly from the sedimentary cover (the "Bunte breccia", e.g., [START_REF] Hörz | Bunte Breccia of the Ries: Continuous deposits of large impact craters[END_REF]); polymict crystalline breccia; impact melt-bearing breccias ("suevite", e.g., von Engelhardt et al., 1995("suevite", e.g., von Engelhardt et al., , 1997)); and impact melt rocks (e.g., [START_REF] Osinski | The nature of the groundmass of surficial suevite from the Ries impact structure, Germany, and constraints on its origin[END_REF][START_REF] Pohl | The Ries impact crater[END_REF]. We focus here on providing rock physical and mechanical properties (porosity, permeability, Young's modulus, compressive strength, and failure mode) for samples of suevite, a type of impact melt-bearing breccia found at the Ries impact crater. There are three types of suevite at Ries crater: (1) "crater suevite", which is up to 300 m thick and covered by Miocene lake sediments; (2) "outer suevite", which is only ≤ 25 m thick and outcrops up to 22 km from the centre of the structure; and (3) dyke suevite, found in the parautochthonous crater basement and in ejected crystalline megablocks (e.g., [START_REF] Stöffler | Ries crater and suevite revisited-Observations and modeling Part I: Observations[END_REF]. These poorly sorted impact melt-bearing breccias formed as a result of the welding of glass/melt and lithic fragments deposited by fluidised granular density currents (e.g., Siegert et al., 2017;see also von Engelhardt, 1997;[START_REF] Newsom | The formation of the Ries crater, West Germany: Evidence of atmospheric interactions during a larger cratering event[END_REF][START_REF] Stöffler | Ries crater and suevite revisited-Observations and modeling Part I: Observations[END_REF] generated following the impact. Suevites at Ries contain centimetre-sized fragments of sedimentary and crystalline rocks (e.g., [START_REF] Graup | Terrestrial chondrules, glass spherules and accretionary lapilli from the suevite, Ries Crater, Germany[END_REF][START_REF] Von Engelhardt | Distribution, petrography and shock metamorphism of the ejecta of the Ries crater in Germany-A review[END_REF][START_REF] Von Engelhardt | Suevite breccia of the Ries impact crater, Germany: Petrography, chemistry and shock metamorphism of crystalline rock clasts[END_REF] and angular fragments and aerodynamically shaped bombs of impact melt glass [START_REF] Stähle | Impact glasses from the suevite of the Nördlinger Ries[END_REF][START_REF] Osinski | Impact glasses in fallout suevites from the Ries impact structure, Germany: An analytical SEM study[END_REF]. These clasts are hosted within a matrix of impact melt glass, rock and mineral fragments, crystallites, and clay minerals (and sometimes zeolites) that formed as a result of post-deposition hydrothermal alteration and weathering [START_REF] Newsom | Fluidization and hydrothermal alteration of the suevite deposit at the Ries crater, West Germany, and implications for Mars[END_REF][START_REF] Von Engelhardt | Distribution, petrography and shock metamorphism of the ejecta of the Ries crater in Germany-A review[END_REF][START_REF] Von Engelhardt | Suevite breccia of the Ries impact crater, Germany: Petrography, chemistry and shock metamorphism of crystalline rock clasts[END_REF][START_REF] Osinski | The nature of the groundmass of surficial suevite from the Ries impact structure, Germany, and constraints on its origin[END_REF][START_REF] Osinski | Hydrothermal activity associated with the Ries impact event, Germany[END_REF][START_REF] Muttik | Post-impact alteration of surficial suevites in Ries crater, Germany: Hydrothermal modification or weathering processes?[END_REF][START_REF] Muttik | Boron isotope composition of secondary smectite in suevites at the Ries crater, Germany: boron fractionation in weathering and hydrothermal processes[END_REF][START_REF] Sapers | Evidence for a spatially extensive hydrothermal system at the Ries impact structure, Germany[END_REF]. High-pressure minerals, such as coesite [START_REF] Stöffler | Zones of impact metamorphism in the crystalline rocks of the Nördlinger Ries crater[END_REF][START_REF] Stähle | Shock-induced growth and metastability of stishovite and coesite in lithic clasts from suevite of the Ries impact crater (Germany)[END_REF] and diamond [START_REF] Schmitt | Distribution and origin of diamonds in the Ries cater, Germany[END_REF][START_REF] Stöffler | Ries crater and suevite revisited-Observations and modeling Part I: Observations[END_REF], have also been identified. Coesite, a high-pressure silica phase, is the mineral that confirmed the impact origin of these deposits in the 1960s [START_REF] Shoemaker | New evidence for the impact origin of the Ries Basin, Bavaria, Germany[END_REF].

Here, we present a laboratory study designed to first report the petrophysical properties (porosity, permeability, Young's modulus, and uniaxial compressive strength) of variably altered suevites (impact melt-bearing breccia) from Reis crater (building on data recently published by Heap et al., 2020a). We then present the results of a suite of triaxial deformation experiments designed to better understand and contrast the mechanical behaviour of relatively unaltered and altered suevites. We complement these mechanical data with microstructural work to determine the operative deformation micromechanisms. We then provide permeability and micromechanical modelling to better understand the fluid flow and mechanical properties of these samples. Since upscaled values are of most importance for large-scale models, we use techniques often employed in geotechnical engineering to provide values of strength, Young's modulus, and permeability relevant for longer lengthscales. Finally, we outline the implications of these data for planetary bodies that record protracted periods of impact bombardment.

Experimental materials and methods

Blocks of suevite (impact melt-bearing breccia) were collected from three different quarries located within or adjacent to the Ries impact crater in Nördlingen:

the Seelbronn quarry (one block: SUE), the Altenbürg quarry (one block: ALT), and the Aumühle quarry (three blocks: AU1, AU2, and AU3) (Figure 1). These blocks were selected due to their visible differences in alteration (colour). The blocks from all three quarries are poorly sorted clastic rocks that contain millimetre-and centimetre-sized clasts of glass (aerodynamically shaped bombs and angular fragments), crystalline rocks (Variscan granites and pre-Variscan gneisses and amphibolites), and sedimentary rocks within a fine-grained matrix (as described in von [START_REF] Von Engelhardt | Distribution, petrography and shock metamorphism of the ejecta of the Ries crater in Germany-A review[END_REF][START_REF] Von Engelhardt | Suevite breccia of the Ries impact crater, Germany: Petrography, chemistry and shock metamorphism of crystalline rock clasts[END_REF][START_REF] Stöffler | Ries crater and suevite revisited-Observations and modeling Part I: Observations[END_REF]; photographs of representative 25 mm-diameter core samples are shown in Figure 2.

The mineral content of the five blocks was quantified using X-ray powder diffraction (XRPD). Powdered aliquots of each block, containing an internal standard of 20 wt.% ZnO, were ground for 8 min with 10 ml of isopropyl alcohol in a McCrone micronising mill using zirconium dioxide cylinder elements. The XRPD analyses were performed on powder mounts using a Bruker D8 advance eco X-ray diffractometer (CuKα, automatic divergence slit, 15 mm irradiated sample length, anti-air scatter screen, 2.5° primary and secondary soller slits, step-scan from 2 to 75° 2Q with 0.01° increments per second, counting time one second per increment, 40 kV, 25 mA). The phases in the whole rock powders were quantified using the Rietveld program BGMN [START_REF] Bergmann | BGMN-a new fundamental parameters based Rietveld program for laboratory X-ray sources, its use in quantitative analysis and structure investigations[END_REF] and Profex 4.0.2 graphical user interface [START_REF] Döbelin | Profex: a graphical user interface for the Rietveld refinement program BGMN[END_REF]. To identify the clay minerals, <2 µm fractions were also separated by gravitational settling. Oriented mounts containing the <2 µm fraction were X-rayed in an air-dried and ethylene-glycolated state.

Thin sections were prepared from offcuts taken from blocks from each of the three quarries (SUE, ALT, and AU1) and their microstructure was examined using a Tescan Vega 2 XMU system backscattered scanning electron microscope (SEM).

To assess the pore-throat size distribution of our blocks, we performed mercury injection porosimetry on offcuts (between 3 and 5 g) of blocks SUE, ALT, and AU1 using a Micromeritics Autopore IV 9500. The mercury equilibration time and filling pressure were 10 s and ~3860 Pa, respectively, and the evacuation time and evacuation pressure were 5 min and 50 µmHg, respectively. The pressure range was ~690 Pa to ~414 MPa.

Cylindrical samples were cored from each block in the same orientation with diameters of 20 or 25 mm (Figure 2). These samples were then precision-ground to a nominal length of 40 or 60 mm, respectively. The samples were cored so as to avoid centimetre-sized clasts. The prepared cylindrical samples were then washed with water to remove any water-soluble grinding fluid and vacuum dried at 40 °C in an oven for at least 48 hours.

The connected porosity of each cylindrical sample was then determined using the skeletal (connected) volume of the sample measured by a helium pycnometer (Micromeritics AccuPyc II 1340), and the bulk volume of the sample calculated using the sample dimensions.

Permeabilities of the 25 mm-diameter cylindrical samples were measured with a nitrogen gas permeameter [START_REF] Farquharson | Evidence for the development of permeability anisotropy in lava domes and volcanic conduits[END_REF][START_REF] Heap | Exploring the scale-dependent permeability of fractured andesite[END_REF] under a confining pressure of 1 MPa. Permeability was measured using the steady-state method. Steady-state volumetric flow rates were determined (using a gas flowmeter) for several differential pressures (acquired with a pressure transducer). These data were used to calculate permeability using Darcy's law and to check whether the Forchheimer [START_REF] Forchheimer | Wasserbewegung durch boden[END_REF] or Klinkenburg (Klinkenburg, 1941) corrections were required. These corrections were applied when necessary on a case-by-case basis.

The 25 mm-diameter samples were deformed uniaxially using a uniaxial load frame. Dry samples were deformed at an axial strain rate of 10 -5 s -1 until macroscopic failure (that is, the formation of a macroscopic fracture). A lubricating wax was placed on the end-faces of the samples to avoid problems with friction between the sample and the pistons. During deformation, axial displacement and axial load were measured with a linear variable differential transducer (LVDT) and a load cell, respectively. The deformation of the loading column itself (including endcaps and piston) was removed from the axial displacement signal. Axial displacement and axial load were converted to axial strain and axial stress using the sample dimensions. The static Young's modulus was calculated using the slope of the strain-stress curve within the linear elastic region (e.g., [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF].

Triaxial deformation experiments were performed on 20 mm-diameter samples (a detailed schematic of the device is provided in [START_REF] Farquharson | Inelastic compaction and permeability evolution in volcanic rock[END_REF]). Dry samples were deformed at a constant strain rate of 10 -5 s -1 until macroscopic failure (for the brittle experiments) or until an axial strain of 6% was reached (for the ductile experiments). A strain of 6% was chosen as a cut-off because this value is large enough for observing the ductile behaviour and for recovering a sample for analysis, but not too large to require unreasonable experimental times. (The choice of this cut-off strain amount does not impact on our interpretation or conclusions.)

Experiments were performed at a range of constant confining pressures, from 2.5 to 80 MPa. Within a given experiment, the confining pressure was held constant using a confining pressure intensifier. Axial displacement and axial load were measured during deformation using an LVDT and a load cell, respectively. Axial displacement (following removal of the deformation of the loading column) and axial load were converted to axial strain and axial stress, respectively, using the sample dimensions.

Additional triaxial experiments were performed in which the differential stress was held at a constant 2 MPa and the confining pressure was increased in steps of 3-15 MPa.

The confining pressure was only increased once the axial strain had stabilised, i.e., when the sample had equilibrated to the new confining pressure (with typical durations on the order of 30 minutes to an hour). The confining pressure was increased in this stepwise manner until the onset of inelastic behaviour, signalled by a large increase in axial strain. We assume a simple effective pressure law where the effective pressure (Peff) is the confining pressure minus the pore fluid pressure (zero for the experiments performed herein). We consider compressive stresses and strains as positive.

Results

Mineral content and microstructure

The mineral content for all the blocks collected is provided in Table 1. Blocks SUE and ALT are primarily composed of amorphous phases, plagioclase, smectite, calcite, and quartz, with minor quantities of coesite, K-feldspar, biotite, and Fe oxides, such as hematite or goethite (Table 1). The main difference between blocks SUE and ALT is that SUE contains more plagioclase and ALT contains more calcite (Table 1).

The blocks from the Aumühle quarry (AU1, AU2, and AU3), which are all similar in composition, contain much fewer amorphous phases and much more smectite than the blocks from Seelbronn (SUE) and Altenbürg (ALT) (Table 1).

Representative backscattered SEM images of the SUE, ALT, and AU1 blocks are shown in Figure 3. All three blocks contain poorly sorted angular fragments (quartz, calcite, K-feldspar, plagioclase) within a fine-grained matrix (Figure 3). The SEM images clearly show that the block from the Aumühle quarry (AU1; Figure 3c) is much more porous (black pixels) than those from the Seelbronn (SUE; Figure 3a) and Altenbürg (ALT; Figure 3b) quarries. We also note that blocks SUE and ALT are pervasively microcracked (Figures 3a and 3b,respectively).

The pore-throat size distributions for the SUE, ALT, and AU1 blocks are provided as Figure 4. These data show that AU contains a greater volume of large pore throats than SUE and ALT. For example, ~50% of the volume of pore throats within AU are greater than 0.1 µm, whereas pore throats greater than 0.1 µm only comprise 30 and 35% of the volume of pore throats in ALT and SUE, respectively (Figure 4). The ALT sample contains a large volume of small pore throats: ~60% of the volume of pore throats within ALT is less than 0.01 µm, whereas pore throats less than 0.01 µm only comprise 40 and 15% of the volume of pore throats in SUE and AU, respectively.

Porosity and permeability

The average connected porosities of the blocks from the quarries at Seelbronn (SUE), Altenbürg (ALT), and Aumühle (AU) are 0.238, 0.237, and 0.390, respectively (Table 2). Their average permeabilities are 1.95 × 10 -15 , 2.02 × 10 -15 , and 8.20 × 10 -15 m 2 , respectively (Table 2). Our data show that permeability increases as a function of increasing porosity. The samples from Aumühle (AU) are more porous and more permeable than those from Seelbronn (SUE) and Altenbürg (ALT) (Figure 5; Table 2)

Uniaxial compressive strength and static Young's modulus

Representative axial stress-strain curves for samples from each of the three quarries are provided in Figure 6a. First, axial stress is a non-linearly increasing function of axial strain, typically attributed to the closure of pre-existing microcracks (section "OA" labelled on the SUE curve in Figure 6a). This stage is followed by a quasi-linear elastic stage, from which the static Young's modulus was determined (section "AB"; Figure 6a). Following the elastic deformation stage, the axial stress is a non-linearly decreasing function of axial strain, typically interpreted as due to the nucleation and growth of microcracks (section "BC"; Figure 6a). The peak stress (the uniaxial compressive strength of the sample) is followed by strain softening and a stress drop associated with the macroscopic failure of the sample (Figure 6a). The average uniaxial compressive strengths of the blocks from the quarries at Seelbronn (SUE), Altenbürg (ALT), and Aumühle (AU) are 34.2, 29.2, and 12.9 MPa, respectively (Table 2). Our data show that uniaxial compressive strength decreases as a function of increasing porosity. The samples from Aumühle (AU) are weaker than those from Seelbronn (SUE) and Altenbürg (ALT) (Figure 6; Table 2). Static Young's modulus as a function of connected porosity is shown in Figure 7. The average Young's moduli are 6.5, 5.7, and 3.0 GPa for the blocks from the quarries at Seelbronn (SUE), Altenbürg (ALT), and Aumühle (AU), respectively (Table 2). We find that Young's modulus decreases as a function of increasing porosity. The samples from Aumühle (AU) have a lower Young's modulus than those from Seelbronn (SUE) and Altenbürg (ALT) (Figure 7; Table 2) 3 3). The suevites from Seelbronn and Aumühle were selected for triaxial testing because they represent the endmembers in terms of alteration, porosity, and strength (Table 2). For sample SUE, the experiments performed at Peff of 0, 5, 10, and 15 MPa clearly show the post-peak stress drop associated with brittle behaviour (i.e., the formation of a shear fracture; see [START_REF] Wong | The brittle-ductile transition in porous rock: A review[END_REF] for a review on brittle and ductile behaviour of porous rocks).

The differential stress at failure also increases as the effective pressure increases from 0 to 15 MPa (Figure 8a; Table 3). Although the stress-strain curve for the sample deformed at 20 MPa appears to be different to those for samples deformed at pressures ≤15 MPa, there is a subtle stress drop (following an axial strain of ~5%; Figure 8a).

The sample deformed at 20 MPa can therefore be considered brittle (the postdeformation sample contained a shear fracture), but its style of failure is very close to the transition between brittle and ductile behaviour.

The stress-strain curves for the samples deformed at 30, 50, and 80 MPa are typical of ductile behaviour: there is no peak stress or stress drop associated with the formation of a shear fracture (Figure 8a; [START_REF] Wong | The brittle-ductile transition in porous rock: A review[END_REF]. Further, the experiments performed at 50 and 80 MPa show strain-hardening behaviour (where differential stress increases as a function of axial strain: Figure 8a). For sample AU1, the experiments performed at Peff of 0, 2.5, and 5 MPa deformed in a brittle manner, whereas the experiments performed at Peff of 10, 15, and 20 MPa were ductile (Figure 8b). The tests performed at Peff of 15 and 20 MPa show strain-hardening behaviour (Figure 8b). The block from the quarry at Aumühle (AU1) therefore transitioned from brittle to ductile behaviour at a lower effective pressure (i.e., depth) than the block from Seelbronn (SUE).

Post-deformation microstructures

To better understand the operative micromechanical processes during brittle and ductile behaviour, thin sections were prepared of the samples of SUE deformed at Peff of 10 and 80 MPa. Backscattered SEM images of the sample deformed at 10 MPa (i.e., in the brittle regime) show a large shear fracture and associated off-fault microcracking (orientated sub-parallel to the maximum principal stress) (Figures 9a and9b). The sample deformed at 80 MPa (i.e., in the ductile regime) did not contain a shear fracture.

Instead, deformation was accommodated by the cataclastic collapse of pores (Figures 9c and9d). Microcracks are seen to radiate from the collapsed pores (Figure 9c and9d).

Discussion

The permeability of impact melt-bearing breccia

Although data in the literature are rare, the permeability of the suevites measured herein (Table 2) compare well with published measurements. For example, [START_REF] Parnell | Permeability data for impact breccias imply focussed hydrothermal fluid flow[END_REF] determined the permeability of two samples from the Ries crater to be 1.58 × 10 -15 and 2.67 × 10 -15 m 2 . These authors also reported the permeability of samples from the impact craters at Rochechouart and Haughton as ~1 × 10 -15 m 2 and between ~1 × 10 -16 and ~1 × 10 -15 m 2 , respectively. The permeability of impact meltbearing breccia from the Chicxulub impact crater was estimated as between ~1 × 10 -18 and ~1 × 10 -15 m 2 [START_REF] Mayr | Estimation of hydraulic permeability considering the micro morphology of rocks of the borehole YAXCOPOIL-1 (Impact crater Chicxulub, Mexico)[END_REF]. These measurements highlight a remarkable similarity worldwide in permeability of impact melt-bearing breccia from different impact craters formed within different lithologies. In strong contrast, the permeability of lavas of the same composition, erupted from the same volcano, can vary by as much as five or six orders of magnitude (e.g., [START_REF] Farquharson | Permeability and porosity relationships of edifice-forming andesites: a combined field and laboratory study[END_REF].

We compare our suite of data with a model for the permeability of partially welded granular media [START_REF] Wadsworth | Universal scaling of fluid permeability during volcanic welding and sediment diagenesis[END_REF] that has been validated against geological porous materials including welded volcanic rocks and sandstones of various diagenetic maturity. This model starts from the assumption that the system was first a granular deposit of particles with mean radius 〈𝑟〉. Because suevite-forming systems begin as droplets and particles deposited in density currents, this is a valid starting assumption, and consistent with similar cases such as the permeability of variably welded deposits of pyroclastic density currents. From that initial granular state, the model assumes that the particles weld together, reducing the internal pore surface areas.

Typically, the [START_REF] Wadsworth | Universal scaling of fluid permeability during volcanic welding and sediment diagenesis[END_REF] model would require a solution to relate the particle size distribution centred around 〈𝑟〉 to a distribution of sizes of characteristic pores centred around 〈𝑎〉. However, here we have directly measured 〈𝑎〉 (Figure 4), negating the need for this interim step.

We take the 〈𝑎〉 from the SUE measurement of pore-throat sizes (Figure 4) as intermediate among the three measurements, and find that 〈𝑎〉 = 1.09 µm (we therefore assume that the pore-throat size is a good approximation of the pore size). We then assume that the pore surface area, 𝑠, is related by [START_REF] Torquato | Random heterogeneous materials: Microstructure and macroscopic properties[END_REF]:

𝑠 = - 3(1 -𝜙) ln(1 -𝜙) 〈𝑎〉 (1).
This relation assumes that 𝑠 is given by the surface area of a suite of overlapping spherical pores [START_REF] Wadsworth | Universal scaling of fluid permeability during volcanic welding and sediment diagenesis[END_REF]. The permeability, 𝑘, is given by [START_REF] Wadsworth | Universal scaling of fluid permeability during volcanic welding and sediment diagenesis[END_REF][START_REF] Martys | Universal scaling of fluid permeability for sphere packings[END_REF]:

𝑘 = 2[1 -(𝜙 -𝜙 8 )] 𝑠 : (𝜙 -𝜙 8 ) ; (2),
where 𝜙 8 is the percolation threshold below which all the pores have pinched off, and the permeability is zero, and 𝑛 is a percolation exponent. On theoretical grounds, 𝑛 = 4.4 was derived for porous overlapping sphere systems [START_REF] Halperin | Differences between lattice and continuum percolation transport exponents[END_REF], leaving only 𝜙 8 unconstrained in this model.

We fit Equation (2) to our complete dataset, allowing 𝜙 8 to vary freely using a root-mean-square error between model and data as a minimisation target. We find that the best results are found using 𝜙 8 = 0.075 and that to within 5% accuracy, 0.06 ≲ 𝜙 8 ≲ 0.1 is valid. This range of values is consistent with the range of 𝜙 8 found for sintering or welding angular particles [START_REF] Wadsworth | Universal scaling of fluid permeability during volcanic welding and sediment diagenesis[END_REF][START_REF] Heap | The permeability evolution of tuffisites and implications for outgassing through dense rhyolitic magma[END_REF].

Therefore, what we present is a theoretically grounded model for the permeability of welded granular media that is applicable to suevites across the range of porosities measured herein (Figure 10).

4.2

The uniaxial compressive strength and Young's modulus of impact melt-bearing breccia To our knowledge, the values of uniaxial compressive strength for suevites reported here (Table 2) and in Heap et al. (2020a) are the only such values yet reported for this rock type. Nonetheless, we find that the samples we assay here have properties similar to other rock types found on Earth. For example, poorly sorted clastic volcanic rocks from Mt. Meager volcano, Canada-welded block-and-ash flow deposits-have a similar strength to the samples we report here. The uniaxial compressive strength of welded block-and-ash flow from Mt. Meager volcano is ~20 MPa when the porosity is between 0.2 and 0.25 (i.e., the porosity range of the samples measured herein: Table 2) (Heap et al., 2015a); this strength value lies between those we find for the Altenbürg (ALT) and Aumühle (AU) samples (Figure 6b).

Our data show that uniaxial compressive strength decreases as a function of increasing porosity (Figure 6b), in agreement with studies on sedimentary (e.g., [START_REF] Chang | Empirical relations between rock strength and physical properties in sedimentary rocks[END_REF][START_REF] Baud | Effects of porosity and crack density on the compressive strength of rocks[END_REF] and volcanic rocks (e.g., [START_REF] Al-Harthi | The porosity and engineering properties of vesicular basalt in Saudi Arabia[END_REF]Heap et al., 2014a;[START_REF] Schaefer | Geomechanical rock properties of a basaltic volcano[END_REF][START_REF] Harnett | Evolution of Mechanical Properties of Lava Dome Rocks Across the 1995-2010 Eruption of Soufrière Hills Volcano, Montserrat[END_REF]. Although the relatively high porosity of the samples from Aumühle quarry could explain their relative weakness, we also note that studies have shown that alteration can result in a strength reduction (e.g., del [START_REF] Del Potro | The decrease in the shear strength of volcanic materials with argillic hydrothermal alteration, insights from the summit region of Teide stratovolcano, Tenerife[END_REF][START_REF] Pola | Influence of alteration on physical properties of volcanic rocks[END_REF][START_REF] Wyering | Mechanical and physical properties of hydrothermally altered rocks, Taupo Volcanic Zone, New Zealand[END_REF][START_REF] Frolova | Effects of hydrothermal alterations on physical and mechanical properties of rocks in the Kuril-Kamchatka island arc[END_REF]. The blocks from the Aumühle quarry are more altered than those from Seelbronn or Altenbürg: more of the amorphous phases have been altered to smectite (Table 1).

Therefore, the relative weakness of samples from Aumühle (Figure 6b) can be explained by a combination of their higher porosity and greater degree of alteration.

The pore-emanating crack model of [START_REF] Sammis | The failure of brittle porous solids under compressive stress states[END_REF] is often used to better understand the mechanical behaviour of porous materials, including rocks (e.g., [START_REF] Baud | Effects of porosity and crack density on the compressive strength of rocks[END_REF]. This model describes a two-dimensional elastic medium populated The two unknowns in the equation are 𝐾 DE and 𝑟. Therefore, at this stage, it is prudent to first estimate the value or values of the term 𝐾 DE /√𝜋𝑟 that best describe the experimental data. Our experimental data cannot be well described using a single value of 𝐾 DE /√𝜋𝑟 (Figure 11). The data can be bracketed between two theoretical curves where 𝐾 DE /√𝜋𝑟 equals 3.5 and 20 MPa (Figure 11). In the absence of measurements of 𝐾 DE for impact melt-bearing breccia, we can use the value of 𝐾 DE identified to describe the welded block-and-ash flow deposits from Mt. Meager volcano: 𝐾 DE = 0.15 MPa.m - 1/2 (Heap et al., 2015a). This value of 𝐾 DE yields values of 𝑟 between ~18 and ~585 µm.

Therefore, if 𝐾 DE = 0.15 MPa.m -1/2 is an appropriate value, our modelling suggests that strength of the suevites is controlled by the largest pores (see our microstructural analysis and our mercury injection data; Figures 3 and4). Of note, the pore-emanating crack model of [START_REF] Sammis | The failure of brittle porous solids under compressive stress states[END_REF] describes a medium that contains pores of a uniform radius, which we know to be a simplification of our experimental materials (see Figures 3 and4). We further emphasise that the 𝐾 DE of the block from Aumühle may be lower than that for the other blocks due to the greater alteration intensity (Table 1). Finally, the blocks from Seelbronn and Altenbürg also contain microcracks, which are not considered in the [START_REF] Sammis | The failure of brittle porous solids under compressive stress states[END_REF] model. Nevertheless, micromechanical models such as that proposed by [START_REF] Sammis | The failure of brittle porous solids under compressive stress states[END_REF] can help glean information as to the first-order controls on the mechanical behaviour and strength of brittle materials.

To our knowledge, the values of Young's modulus for suevites reported here (Table 2) are the only such values reported. Our data show that Young's modulus decreases as a function of increasing porosity (Figure 7), in agreement with previous studies (e.g., [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF]. Chemical alteration is also known to influence the Young's modulus of rocks and can result in increases to Young's modulus when the alteration is pore-filling (e.g., [START_REF] Frolova | Effects of hydrothermal alterations on physical and mechanical properties of rocks in the Kuril-Kamchatka island arc[END_REF][START_REF] Mordensky | Physical and mechanical property relationships of a shallow intrusion and volcanic host rock, Pinnacle Ridge, Mt. Ruapehu, New Zealand[END_REF][START_REF] Durán | Mineral alteration and fracture influence on the elastic properties of volcaniclastic rocks[END_REF] and decreases to Young's modulus in the case of dissolution (e.g., [START_REF] Frolova | Effects of hydrothermal alterations on physical and mechanical properties of rocks in the Kuril-Kamchatka island arc[END_REF]. The low Young's modulus of samples from Aumühle (Figure 7) can therefore be explained by a combination of their higher porosity and greater degree of alteration.

Failure envelopes for impact melt-bearing breccia

The mechanical behaviour of porous materials is best compared on a graph of differential stress, 𝑄, as a function of the effective mean stress, 𝑃 [START_REF] Wong | The brittle-ductile transition in porous rock: A review[END_REF]. 𝑃 is given by 𝑃 = (𝜎 J + 2𝜎 Q )/3) -𝑃𝑝, where 𝑃𝑝 is the pore fluid pressure (0 MPa in our experiments), 𝜎 J is the maximum principal compressive stress (the axial stress in our experiments), and 𝜎 Q is the minimum principal compressive stress (the confining pressure in our experiments). The failure envelope of a material can be delineated by plotting the differential stress at failure as a function of the effective mean stress at failure. Deformation experiments must therefore be performed at a range of effective pressures to map the failure envelope.

Failure in the brittle regime is defined as the differential stress at the peak stress (as indicated in Figure 6a), and failure in the ductile regime is defined as the differential stress at the onset of inelastic compaction, termed C* [START_REF] Wong | The brittle-ductile transition in porous rock: A review[END_REF]. 𝑃 * is the term given for the onset of inelastic compaction under hydrostatic conditions (i.e., when 𝑄 = 0) (e.g., [START_REF] Zhang | Micromechanics of pressure-induced grain crushing in porous rocks[END_REF][START_REF] Wong | The brittle-ductile transition in porous rock: A review[END_REF]. C* was determined using the evolution of the volume of the sample during deformation, monitored by the confining pressure intensifier. C* can be observed as an inflection point in the data of differential stress as a function of the change in confining fluid volume (i.e., sample volume).

In our experiments in which we held the differential stress at 2 MPa and increased the confining pressure, C* was 2 MPa and 𝑃 was calculated using the confining pressure required for inelastic compaction (monitored using the axial strain signal). A sample can be considered pre-failure if the state of stress plots inside the failure envelope, and failed if the state of stress plots outside the failure envelope. The sample will have failed in a brittle or ductile manner if the stress state falls outside the failure envelope to the left or right, respectively. The failure envelopes for the suevites from Seelbronn (SUE) and Aumühle (AU1) are shown in Figure 12 (with data available in Table 3). The failure envelope for SUE is much larger than that for AU1. In other words, SUE is pre-failure for much more of the stress space represented. The transition from brittle to ductile behaviour, represented by the "top" of the failure envelope, is at an effective pressure of ~30 and ~10 MPa for SUE and AU1, respectively (Table 3).

As discussed above, the relative weakness of the blocks from Aumühle is likely due to a combination of higher porosity (Tables 2 and3) and greater alteration intensity (Table 1) than for the samples from Seelbronn or Altenbürg. The position of 𝑃 * for SUE and AU1 is estimated to be 90 ± 5 and 22 ± 5 MPa, respectively (Figure 12).

Deformation micromechanisms

Our microstructural work indicates that the operative deformation micromechanisms of these suevite samples are microcracking and cataclastic pore collapse in the brittle and ductile fields, respectively (Figure 9a and9b). Failure in the brittle regime is the result of the initiation and propagation of microcracks, preferentially aligned to the direction of maximum principal compressive stress (Figure 9a and 9b), which coalesce to form a macroscopic, through-going shear fracture (see also [START_REF] Lockner | Quasi-static fault growth and shear fracture energy in granite[END_REF]Aben et al., 2019). Porosity reduction in the ductile regime is driven by the cataclastic collapse of pores (Figure 9c and9d). This deformation micromechanism has been previously observed in porous limestones (e.g., [START_REF] Zhu | Micromechanics of cataclastic pore collapse in limestone[END_REF][START_REF] Vajdova | Micromechanics of inelastic compaction in two allochemical limestones[END_REF] and porous volcanic rocks (e.g., [START_REF] Loaiza | Mechanical behavior and localized failure modes in a porous basalt from the Azores[END_REF][START_REF] Adelinet | Deformation modes in an Icelandic basalt: from brittle failure to localized deformation bands[END_REF][START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF][START_REF] Heap | Fracture and compaction of andesite in a volcanic edifice[END_REF]Heap et al., , 2015c;;[START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Mount Etna basalt[END_REF].

Of particular interest, because of their ability to reduce permeability and create permeability anisotropy, is whether such compaction is localised into bands.

Compaction bands have been well documented in studies on porous sandstone, and form as a result of grain crushing (e.g., [START_REF] Baud | Compaction localization in porous sandstones: spatial evolution of damage and acoustic emission activity[END_REF][START_REF] Baud | Shear-enhanced compaction and strain localization: Inelastic deformation and constitutive modeling of four porous sandstones[END_REF][START_REF] Fortin | Acoustic emission and velocities associated with the formation of compaction bands in sandstone[END_REF][START_REF] Stanchits | Initiation and propagation of compaction bands in dry and wet Bentheim sandstone[END_REF][START_REF] Baud | Mechanical compaction and strain localization in Bleurswiller sandstone[END_REF]. Compaction bands have also been observed in porous limestones (e.g., [START_REF] Cilona | The effects of rock heterogeneity on compaction localization in porous carbonates[END_REF][START_REF] Baud | Inelastic Compaction in High-Porosity Limestone Monitored Using Acoustic Emissions[END_REF][START_REF] Huang | Synchrotron X-ray imaging in 4D: Multiscale failure and compaction localization in triaxially compressed porous limestone[END_REF] and porous volcanic rocks (e.g., [START_REF] Loaiza | Mechanical behavior and localized failure modes in a porous basalt from the Azores[END_REF][START_REF] Adelinet | Deformation modes in an Icelandic basalt: from brittle failure to localized deformation bands[END_REF][START_REF] Heap | Fracture and compaction of andesite in a volcanic edifice[END_REF]Heap et al., , 2017a)). We observed no evidence of compaction bands in our samples: pore collapse (Figure 9c and9d) was distributed throughout the sample. In addition, we did not observe small stress drops in the ductile stress-strain curves (Figure 8), which have also been associated with the formation of compaction bands in laboratory experiments.

Therefore, similar to porous tuff from Alban Hills, Italy [START_REF] Zhu | Micromechanics of cataclastic pore collapse in limestone[END_REF] and Whakaari volcano, New Zealand (Heap et al., 2015c), i.e., granular volcanic rocks with a similar genesis and texture to the suevites studied herein, inelastic compaction in suevite does not appear to localise into bands. The absence of compaction bands in these materials may be related to their wide grain size distribution (e.g., Figure 3), a factor known to suppress compaction localisation in sandstones [START_REF] Cheung | Effect of grain size distribution on the development of compaction localization in porous sandstone[END_REF].

Micromechanics of hydrostatic compaction

To investigate the micromechanics of hydrostatic compaction, we follow the approach outlined by [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF]. By considering the stresses required to yield a single macropore embedded within an effective medium, and by adopting the Mohr-Coulomb failure criterion, the onset of inelastic hydrostatic compaction, 𝑃 * , is related to uniaxial compressive strength by [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF]:

𝑃 * = 2𝜎 G /3 (4).
Figure 13a shows 𝑃 * as a function of uniaxial compressive strength for the SUE and AU1 suevites and a collection of tuffs (volcanic rocks that share textural similarities to the studied suevites). All of these data plot above the theoretical line delineated by Equation ( 4). As discussed in [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF], this distribution of samples is likely because the effective medium is less porous than the matrix of these rocks, i.e., the matrix contains numerous micropores, as exposed by our microstructural observations (Figure 3) and our mercury injection experiments (Figure 4). We can study the influence of micropores on the onset of inelastic hydrostatic compaction by combining Equations ( 3) and ( 4) [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF]:

𝑆 * = 𝐾 DE (𝜙 * /𝜙) H.IJI √𝜋𝑎 * (5),
where 𝑎 * is the average radius of a micropore, 𝜙 * is the porosity of the effective medium, and 𝑆 * captures the cooperative influence of the fracture toughness, micropore radius, and the partitioning of macro-and microporosity [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF]. This model describes a dual porosity medium of a macropore surrounded by many micropores. We find that SUE and AU1 are best described by values of 𝑆 * of 70 and 14 MPa, respectively (Figure 13b). We note that these values of 𝑆 * are similar to those predicted for tuffs (Figure 13b; [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF].

The average micropore radius can then be estimated using 𝑎 * > (𝐾 DE /𝑆 * ) : /𝜋 [START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF]. Assuming 𝐾 DE = 0.15 MPa.m -1/2 (Heap et al., 2015a), the average micropore radius for SUE and AU1 are 1.5 and 36.5 µm, respectively. These pore radii predictions are in agreement with the pore throat radii determined by our mercury injection experiments (Figure 4). The modelling described above therefore highlights an important role for micropores in controlling the onset of inelastic hydrostatic compaction in the studied materials.

Upscaling laboratory measurements for use in large-scale modelling

The laboratory experiments described herein were performed on samples with diameters of 20 or 25 mm. These measurements, therefore, do not consider the influence of macroscopic fractures, which are well known to influence permeability (e.g., [START_REF] Brace | Permeability of crystalline rocks: New in situ measurements[END_REF][START_REF] Clauser | Permeability of crystalline rocks[END_REF][START_REF] Neuman | Generalized scaling of permeabilities: Validation and effect of support scale[END_REF][START_REF] Heap | Exploring the scale-dependent permeability of fractured andesite[END_REF][START_REF] Farquharson | Upscaling permeability in anisotropic volcanic systems[END_REF], strength (e.g., [START_REF] Hoek | Hoek-Brown failure criterion-2002 edition[END_REF], and Young's modulus (e.g., [START_REF] Hoek | Empirical estimation of rock mass modulus[END_REF]. Since the crusts of heavily impacted planetary bodies are likely highly fractured (e.g., [START_REF] Wieczorek | The crust of the Moon as seen by GRAIL[END_REF][START_REF] Heap | Low surface gravitational acceleration of Mars results in a thick and weak lithosphere: Implications for topography, volcanism, and hydrology[END_REF][START_REF] Lognonné | Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data[END_REF], these laboratory values must be upscaled before they can be used in large-scale models.

The strength of a fractured rock-mass can be estimated with the generalised Hoek-Brown failure criterion [START_REF] Hoek | Hoek-Brown failure criterion-2002 edition[END_REF]:

𝜎 J V = 𝜎 Q V + 𝐶 X Y𝑚 [ 𝜎 Q V 𝐶 X + 𝑠\ ] (6),
where 𝜎 J V and 𝜎 Q V are the effective maximum and minimum principal stresses, respectively, 𝐶 X is the laboratory-measured uniaxial compressive strength, and mb, s, and a are unitless fitting parameters [START_REF] Hoek | Hoek-Brown failure criterion-2002 edition[END_REF]:

𝑚 [ = 𝑚 ^ 𝑒𝑥𝑝 a 𝐺𝑆𝐼 -100 28 -14𝐷 f (7), 𝑠 = 𝑒𝑥𝑝 a 𝐺𝑆𝐼 -100 9 -3𝐷 f (8), 𝑎 = 1 2 + 1 6 g𝑒𝑥𝑝 a- 𝐺𝑆𝐼 15 f + 𝑒𝑥𝑝 a- 20 3 fh (9).
GSI is the Geological Strength Index, a unitless value between 0 and 100 that describes the rock-mass characteristics [START_REF] Marinos | The geological strength index: applications and limitations[END_REF]. High values of GSI represent intact or massive rock masses, whereas low GSI values represent blocky and fractured rock masses with weathered fracture surfaces and clay-filled fractures [START_REF] Marinos | The geological strength index: applications and limitations[END_REF]. D is a unitless disturbance factor related to anthropogenic blasting damage in large excavations (we therefore use D = 0 in our study; the full equation is provided here for completeness). Finally, unitless constant 𝑚 ^ describes the shape of the failure envelope on a graph of 𝜎 J V as a function of 𝜎 Q V , and is therefore related to the microstructural and mineralogical attributes of the rock [START_REF] Eberhardt | The hoek-brown failure criterion[END_REF].

To provide strengths for suevite rock masses, we require estimates for 𝐶 X , 𝑚 ^, and GSI. Values of 𝐶 X can be taken directly from our experimental data, and we take values of 44.7 and 14.5 MPa for the SUE and AU1 suevites, respectively (excluding outliers). Values of 𝑚 ^ can be estimated using our triaxial experimental data. We estimate 𝑚 ^, using the data fitting function (modified cuckoo fit algorithm, basic error summation, and absolute error type) in RocData (Rocscience, 2017), to be 12 and 4.7

for the SUE and AU1 suevites, respectively (Figure 14). In the absence of GSI estimates, we use the suggested average for volcanic rock masses of 55 suggested by [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF]. However, because of the variability in GSI values for natural outcrops (estimates of GSI for volcanic rock outcrops, for example, typically range between disintegrated (GSI = 20-40) and blocky (GSI = 65-85); see [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF] and references therein), we provide rock mass strength estimates for GSI = 45-65 (i.e., GSI = 55 ± 10). We can now model the compressive strength of SUE and AU1 as a function of depth (using 𝑃 = 𝜌𝑔ℎ, where 𝑃 is the lithostatic pressure, ℎ is the depth, 𝑔 is the acceleration due to gravity, and 𝜌 is the bulk rock density (taken as 2000 kg/m 3 , guided by our laboratory density measurements)) (Figure 15). In the following analyses we provide strength estimates for rock masses on Mars (i.e., 𝑔 = 3.711 m/s 2 ).

We compare our strength estimations for SUE and AU1 with that for basalt (Figure 15), which is lithologically representative of much of the surface materials of the inner Solar System worlds (e.g., [START_REF] Byrne | A comparison of inner Solar System volcanism[END_REF]. To do so, we performed six uniaxial compressive strength experiments on dry samples of Volvic basalt (Chaîne des Puys, France). The connected porosity and uniaxial compressive strength of these samples were determined as described in the methods section. To estimate the strength of a basaltic rock-mass, we used a value of 𝐶 X of 92.6 MPa (Table 4), an 𝑚 ^ of 22 (see [START_REF] Schultz | Limits on strength and deformation properties of jointed basaltic rock masses[END_REF], and a GSI of 55 ± 10 [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF]. We increased the bulk rock density from 2000 to 2300 kg/m 3 , as guided by our laboratory density measurements for Volvic basalt. We find that the upscaled compressive strength of suevite is much lower than that of basalt (Figure 15). For example, the rock-mass strength of SUE, AU1, and Volvic basalt are, respectively, ~11, ~25, and ~45 MPa at a depth of 0.5 km (Figure 15). Furthermore, the basalt will remain brittle over the range of depth (up to 5 km)

shown in Figure 15; the suevites from Seelbronn (SUE) and Aumühle (AU1) will be ductile at depths of about 1 and 4 km, respectively (Figure 15). We note that, based on the depth of impact craters (e.g., [START_REF] Boyce | Ancient oceans in the northern lowlands of Mars: Evidence from impact crater depth/diameter relationships[END_REF][START_REF] Stepinski | Machine cataloging of impact craters on Mars[END_REF], impact meltbearing breccias are unlikely to exist below a couple of kilometres in the lithosphere.

We further note that we use data for Volvic basalt for illustrative purposes: the porosity of basalt on Mars will certainly vary and its strength is very much porosity-dependent (e.g., [START_REF] Al-Harthi | The porosity and engineering properties of vesicular basalt in Saudi Arabia[END_REF].

The Young's modulus of a fractured rock-mass, 𝐸 mn , can be estimated using the Hoek-Diederichs equation [START_REF] Hoek | Empirical estimation of rock mass modulus[END_REF]:

𝐸 mn = 𝐸 ^o0.02 + Y1 - 𝐷 2 p1 + 𝑒𝑥𝑝 (60 + 15𝐷 -𝐺𝑆𝐼) 11 q rJ \ s (10).
Here, 𝐸 ^ is the "intact" Young's modulus measured from the elastic portion of the stress-strain curve of a rock deforming in compression (i.e., the data of Figure 7; Table 2). We take D = 0 (see above) and assume an average GSI of 55 [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF].

We also determined the intact (Table 4) and rock-mass Young's modulus for Volvic basalt. The data are presented in Figure 16 and show that the Young's modulus of a rock-mass is much lower than intact Young's modulus. For example, the range of Young's modulus for SUE suevite was reduced from 3.5-8.1 to 1.4-3.3 GPa (Figure 16). These data also show that the intact and rock-mass Young's modulus of suevite is much lower than that for basalt (Figure 16). Of course, the Young's modulus of Volvic basalt represents that value of a basalt with a porosity of 0.2 (Table 4), but the porosity, and therefore Young's modulus, of basalt on Mars likely varies considerably. As for our rock mass strength estimations, we can also provide rock mass Young's modulus estimations for GSI = 55 ± 10. The average rock mass Young's moduli in this GSI range are 1.5-4.1, 1.3-3.6, 0.7-1.9, and 3.6-10.2 GPa for SUE, ALT, AU, and Volvic basalt, respectively.

The permeability of a rock-mass can be estimated if the macrofracture density and width, the permeability of the host-rock, and the permeability of the fractures is known (e.g., [START_REF] Heap | Exploring the scale-dependent permeability of fractured andesite[END_REF]. Once rock-mass permeabilities are known, these values can be used to estimate permeability on larger scales (e.g., [START_REF] Farquharson | Upscaling permeability in anisotropic volcanic systems[END_REF]. The permeability of a rock-mass, 𝑘 t , can be estimated using the following two-dimensional model that considers flow in parallel layers:

𝑘 t = (𝑤 ^ • 𝑘 H ) + (𝑤 w • 𝑘 w ) 𝑊 (11),
where 𝑤 ^ and 𝑘 H and 𝑤 w and 𝑘 w and are the width and permeability of the intact hostrock and fractures, respectively, and 𝑊 is the width of the rock-mass. If we take 𝑘 H to be 5.0 ´ 10 -15 m 2 (Table 2), and assume a constant fracture width of 0.25 mm and a 𝑘 w of 1.0 ´ 10 -9 m 2 (see [START_REF] Heap | Exploring the scale-dependent permeability of fractured andesite[END_REF], we can plot rock-mass permeability as a function of fracture density (Figure 17). To compare these data with those for basalt, we measured the permeability of one sample of Volvic basalt using the approach described in the methods section (Table 4). For the basalt calculations, we used 𝑘 H = 2.4 ´ 10 -14 m 2 (Table 4), and again assumed a constant fracture width of 0.25 mm and a 𝑘 w of 1.0 ´ 10 -9 m 2 (Figure 17). We assume a constant fracture width of 0.25 mm because this fracture width corresponds to the laboratory-measured value of 𝑘 w (see [START_REF] Heap | Exploring the scale-dependent permeability of fractured andesite[END_REF]. The permeability of large-aperture fractures is likely higher than the values of 𝑘 w provided herein, the permeability of which could be estimated using 𝑘 w = ℎ : /12 (Zimmerman and Bodvarsson, 1996), where ℎ is the fracture width.

We find that, at very low fracture densities (between 0 and 2 fractures per metre), the basaltic rock-mass is more permeable than the suevite rock-mass (Figure 17). Above two fractures per metre, the equivalent permeabilities of the basalt and suevite rock masses are very similar (Figure 17). Figure 17 also shows that only a few macroscopic fractures per metre can increase the permeability of the rock-mass by two orders of magnitude. Above a macroscopic fracture density of about 10 fractures per metre, the equivalent permeability of the rock-mass does not increase significantly as a function of increasing fracture density (Figure 17). We emphasise that the permeability of basalt on the sample scale can be very low (e.g., 10 -19 m 2 ; Nara et al., 2011) and will depend on both porosity and void-space connectivity. Therefore, the equivalent permeability of low porosity basalt on Mars may be considerably lower than the estimates for Volvic basalt provided herein, especially at low macrofracture densities.

Although there are a number of assumptions built into our upscaling calculations (for strength, Young's modulus, and permeability), these calculations are designed to emphasise that care should be taken when deciding on physical property values for large-scale models.

Implications for impacted planetary bodies

Our findings show that suevites can have high porosities and low strength values (e.g., Figure 15), which is not surprising given the destructive nature of large impact events and the damage to rock masses that ensues (e.g., [START_REF] Morgan | The formation of peak rings in large impact craters[END_REF]. For example, the compressive strength of suevite can be 2-4 times lower than that for basalt, a rock representative of much of the surface materials of the inner Solar System worlds (e.g., [START_REF] Byrne | A comparison of inner Solar System volcanism[END_REF], at a depth of 0.5 km (for Mars; Figure 15). Our experiments also show that suevite will be ductile at shallow depths (Figure 8), which will likely affect, for example, the propagation of large fractures and dykes.

Most of inner Solar System worlds show evidence for protracted histories of impact bombardment. The "intercrater plains" on Mercury, which occupy ~75% of the planet surface [START_REF] Whitten | Intercrater plains on Mercury: Insights into unit definition, characterization, and origin from MESSENGER datasets[END_REF][START_REF] Byrne | The tectonic character of Mercury. Mercury: The View After MESSENGER[END_REF], are heavily cratered and record more than 4 Gyr of impacts [START_REF] Marchi | Global resurfacing of Mercury 4.0-4.1 billion years ago by heavy bombardment and volcanism[END_REF]. The southern uplands on Mars are similarly cratered and comparably old [START_REF] Tanaka | Geologic Map of Mars[END_REF], as is much of the Moon's surface, especially the lunar highlands (e.g., [START_REF] Fassett | Lunar impact basins: Stratigraphy, sequence and ages from superposed impact crater populations measured from Lunar Orbiter Laser Altimeter (LOLA) data[END_REF]. Our study suggests that the rock masses that comprise these older, bombarded crusts are therefore substantially weaker and more porous and permeable than the younger plains material on these worlds, e.g., Mercury's smooth plains, the northern lowland plains on Mars, and the lunar maria (cf. [START_REF] Byrne | A comparison of inner Solar System volcanism[END_REF]. Indeed, the difference in tectonic style of crustal shortening between the intercrater and smooth plains on Mercury has been attributed to the destruction, via impact bombardment, of any internal fabric in the former terrain type that the latter may still possess [START_REF] Byrne | Mercury: global tectonics on a contracting planet[END_REF]. And although further weakening of crustal rocks by alteration likely did not have affect the airless bodies, e.g., Mercury or the Moon, such systems were probably present on Mars [START_REF] Rathbun | Hydrothermal systems associated with Martian impact craters[END_REF]Osinski et al., 2013). (We exclude Venus from this discussion because the second planet has anomalously few impact craters (Phillips et al., 1991), and it not clear what effect(s) its high mean surface temperature (~470 °C) might have had on those rocks that were impacted.)

In any case, our results here add to the few available data for the strength of planetary materials damaged by impact bombardment. It is therefore prudent to use such values in calculations of, for instance, the strength of the upper lithosphere of planetary bodies, when employing values for intact rock can lead to substantially different outcomes than for-more realistically-weak rock (e.g., [START_REF] Klimczak | Limits on the brittle strength of planetary lithospheres undergoing global contraction[END_REF][START_REF] Klimczak | A rock-mechanical assessment of Mercury's global tectonic fabric[END_REF]. Indeed, results from the NASA Gravity Recovery and Interior Laboratory (GRAIL) mission showed the Moon to have an average crustal porosity of 12% to a depth of at least several kilometres [START_REF] Wieczorek | The crust of the Moon as seen by GRAIL[END_REF], varying regionally to as much as 22%-comparable to those values we find for the Seelbronn (SUE) and Altenbürg (ALT) samples.

Conclusions

We provide here petrophysical property data (porosity, permeability, Young's modulus, and uniaxial compressive strength) for suevite (a type of melt-bearing impact breccia) from the Ries crater in Germany. We further performed triaxial experiments to determine the pressure (i.e., depth) required for the brittle-ductile transition. Until now, petrophysical and mechanical data for melt-bearing impact breccia were rare or absent. It is our hope that these data, and our upscaling approaches, can improve fluid flow modelling, slope and crater stability assessments, crustal strength estimates, and physical weathering rate estimates for and the interpretation of large-scale structural features on planetary bodies on which protracted records of impact bombardment are preserved. "AU" includes samples from blocks AU1, AU2, and AU3 (see Table 2). (b) Uniaxial compressive strength as a function of connected porosity for these samples.

"AU" includes samples from blocks AU1, AU2, and AU3 (see Table 2). "AU" includes samples from blocks AU1, AU2, and AU3 (see Table 2). The dashed line is the modelled curve (Equation ( 2)). (data given in Table 3). is estimated to be 90 ± 5 and 22 ± 5 MPa (symbol size is larger than the error bar).

Modelled curves are provided using Equation (5). On both panels we also provide data for tuff, a volcanic rock with a similar texture to the studied suevites (data from [START_REF] Heard | High-pressure mechanical properties of Mt[END_REF][START_REF] Aversa | The mechanical behaviour of a pyroclastic rock: yield strength and "destructuration" effects[END_REF][START_REF] Lockner | Energy dissipation in Calico Hills tuff due to pore collapse[END_REF][START_REF] Zhu | Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff[END_REF][START_REF] Heap | The permeability and elastic moduli of tuff from Campi Flegrei, Italy: implications for ground deformation modelling[END_REF][START_REF] Marmoni | Gravitational slope-deformation of a resurgent caldera: New insights from the mechanical behaviour of Mt. Nuovo tuffs (Ischia Island, Italy)[END_REF][START_REF] Heap | Fire resistance of the Mt. Epomeo Green Tuff, a widely-used building stone on Ischia Island (Italy)[END_REF]. 2.0 ± 0.5 1.9 ± 0.5 1.8 ± 0.5 1.8 ± 0.5 1.9 ± 0.5 Hematite/Goethite 0.2 ± 0.1 0.2 ± 0.1 0.4 ± 0.2 0.4 ± 0.2 0.2 ± 0.2 Amorphous phases 28 ± 5 33 ± 5 32 ± 8 32 ± 8 30 ± 8

Table 2. The physical and mechanical properties (porosity, permeability, Young's modulus, and uniaxial compressive strength) of dry impact melt-bearing breccia ("suevite") collected from the Ries impact crater, Germany. Asterisk denotes data from Heap et al. (2020a).

Sample

  Figures 8a (forSUE) and Figure 8b (for AU1) (a mechanical summary of the triaxial

  by circular pores of uniform radius 𝑟. Tensile cracks emanate (in the direction of the maximum principal compressive stress) when the applied stress reaches the critical stress intensity factor, 𝐾 DE (sometimes called the fracture toughness). These cracks then propagate and coalesce to induce the macroscopic failure of the elastic medium. An analytical approximation of the pore-emanating crack model of[START_REF] Sammis | The failure of brittle porous solids under compressive stress states[END_REF] was derived by[START_REF] Zhu | Micromechanics of cataclastic pore collapse in limestone[END_REF] in the case of uniaxial compression, to model the uniaxial compressive strength, 𝜎 G , as a function of porosity, 𝜙:

FiguresFigure 1 .

 1 Figures

  Figure 1. (a) Map of Germany showing the location of Nördlingen (in red). (b) Map

Figure 2 .

 2 Figure 2. Photographs of representative 25 mm-diameter cylindrical core samples

Figure 3 .

 3 Figure 3. Backscattered electron microscope images of impact melt-bearing breccias

Figure 4 .Figure 5 .

 45 Figure 4. Cumulative void space as a function of the equivalent pore throat radius for

Figure 6 .

 6 Figure 6. (a) Representative uniaxial stress-strain curves for impact melt-bearing

Figure 7 .

 7 Figure 7. Static Young's modulus as a function of connected porosity for impact melt-

Figure 8 .

 8 Figure 8. (a) Stress-strain curves for the impact melt-bearing breccias ("suevites")

Figure 9 .

 9 Figure 9. Backscattered electron microscope images of deformed samples of impact

Figure 10 .

 10 Figure 10. Permeability as a function of connected porosity for impact melt-bearing

Figure 11 .

 11 Figure 11. Uniaxial compressive strength as a function of connected porosity for

Figure 12 .

 12 Figure 12. Differential stress, 𝑄, (peak stress in the brittle regime and C* in the ductile

Figure 13 .

 13 Figure 13. (a) The onset of inelastic hydrostatic compaction, 𝑃 * , as a function of the

Figure 14 .

 14 Figure 14. Data from triaxial experiments performed on samples of impact melt-

Figure 15 .

 15 Figure 15. Crustal strength profiles (for Mars) for impact melt-bearing breccias

Figure 16 .

 16 Figure 16. "Intact" (coloured symbols) and rock-mass (white symbols) Young's

Figure 17 .

 17 Figure 17. Equivalent permeability as a function of macrofracture density for impact

Table 1 .

 1 Quantitative bulk mineralogical composition, determined using X-ray powder diffraction (XRPD), for the five impact melt-bearing breccias ("suevite") blocks used in this study. The error associated with the estimation of the content of amorphous phases is a conservative estimate. "n.d.": not detected.

		Altenbürg	Seelbronn	Aumühle	Aumühle	Aumühle
	Mineral	(ALT) (values in	(SUE) (values in	1 (AU1) (values in	2 (AU2) (values in	3 (AU3) (values in
		wt.%)	wt.%)	wt.%)	wt.%)	wt.%)
	Quartz	9 ± 1	10 ± 1	11 ± 1	11 ± 1	11 ± 1
	Coesite	1.7 ± 0.3	1.4 ± 0.3	0.7 ± 0.2	0.8 ± 0.2	0.9 ± 0.2
	K-feldspar	3.1 ± 0.5	1.7 ± 0.5	4.5 ± 0.8	3.5 ± 0.5	4.3 ± 0.4
	Plagioclase	18 ± 2	27 ± 3	17 ± 2	16 ± 2	15 ± 2
	Calcite	13 ± 1	2.1 ± 0.2	2.6 ± 1.2	1.1 ± 1.2	0.6 ± 0.3
	Smectite	25 ± 3	23 ± 3	31 ± 4	34 ± 4	37 ± 4
	Amphibole	1.7 ± 0.3	n.d.	n.d.	n.d.	n.d.
	Biotite

Table 3 .

 3 Mechanical data from the triaxial deformation experiments on dry impact melt-bearing breccia ("suevite") performed for this study. The asterisk denotes samples that were held at a differential stress of 2 MPa and the confining pressure was increased until C* was reached (see methods section for more details).

		Connected	Permeability	Young's	Uniaxial
		porosity	(m 2 )	modulus	compressive
				(GPa)	strength
					(MPa)
	SUE1*	0.241	6.33 ´ 10 -15	3.5	18.4
	SUE2*	0.197	6.22 ´ 10 -16	8.1	48.6
	SUE3*	0.238	5.68 ´ 10 -15	-	-
	SUE4*	0.221	7.40 ´ 10 -16	4.7	21.7
	SUE5*	0.190	9.53 ´ 10 -16	7.9	42.2
	SUE6*	0.184	1.08 ´ 10 -15	-	-
	SUE7*	0.197	1.42 ´ 10 -15	-	-
	SUE8*	0.204	6.32 ´ 10 -16	6.4	32.8
	SUE9*	0.240	1.47 ´ 10 -15	-	-
	SUE10*	0.198	5.84 ´ 10 -16	7.7	43.3
	SUE12*	0.195	-	6.2	32.8
	SUE20*	0.228	-	7.6	34.1
	ALT1*	0.242	1.02 ´ 10 -15	6.1	31.7
	ALT2*	0.261	2.54 ´ 10 -15	-	31.6
	ALT3*	0.261	2.44 ´ 10 -15	-	-
	ALT4*	0.233	3.13 ´ 10 -15	5.7	25.3
	ALT5*	0.243	1.76 ´ 10 -15	-	-
	ALT6*	0.262	3.16 ´ 10 -15	5.0	17.7
	ALT7*	0.238	1.19 ´ 10 -15	-	-
	ALT8*	0.261	1.84 ´ 10 -15	4.3	22.5
	ALT9*	0.261	2.13 ´ 10 -15	-	-
	ALT10*	0.231	9.54 ´ 10 -16	7.1	33.0
	ALT12*	0.245	-	6.1	34.8
	ALT13*	0.223	-	6.3	33.6
	ALT14*	0.242	-	6.1	34.6
	ALT15*	0.248	-	4.8	26.9
	AU1_1	0.387	4.78 ´ 10 -15	3.4	14.7
	AU1_2	0.392	5.66 ´ 10 -15	3.6	15.0
	AU1_3	0.388	5.38 ´ 10 -15	3.7	15.0
	AU1_4	0.384	1.57 ´ 10 -14	3.9	15.7
	AU1_5	0.386	6.59 ´ 10 -15	2.9	14.0
	AU1_6	0.380	4.29 ´ 10 -15	4.1	15.0
	AU1_7	0.396	4.53 ´ 10 -15	3.3	14.3

Table 4 .

 4 The physical and mechanical properties (porosity, permeability, Young's modulus, and uniaxial compressive strength) of dry Volvic basalt (Chaîne des Puys, France). Asterisk denotes data from[START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF].

	Sample	Connected	Permeability	Young's	Uniaxial
		porosity
			(m 2 )	modulus	compressive
				(GPa)	strength
					(MPa)
	VB2	0.20	2.35 ´ 10 -14	17.1*	94.6
	VB6	0.21	-	15.4*	96.5
	VB8	0.20	-	16.8*	84.2
	VB9	0.21	-	15.2*	91.1
	VB10	0.21	-	16.1*	94.8
	VB12	0.21	-	16.1*	94.7

Acknowledgements

The first author acknowledges a Prix d'Espoirs grant, awarded by the University of Strasbourg. Olivier Lengliné is warmly thanked for driving the author to and from Nördlingen (Germany). Alexandra Kushnir is thanked for field assistance, Patrick Baud for discussions, Bertrand Renaudié for his help with the preparation of samples, and Marlène Villeneuve for determining the values of 𝑚 ^ using RocData. We thank Lea Mertens and Matthias Wittner for providing the suevite block from the Seelbronn quarry (Wittner -Steinbearbeitung und Denkmalpflege, Nördlingen, Germany). PKB acknowledges support from North Carolina State University. We thank Chris Okubo and one anonymous reviewer for comments that helped improve this manuscript.

Data availability

The data collected for this study can be found in Tables 1234.


MD Erwan Donal
email: erwan.donal@chu-rennes.fr

Guillaume L'official

Wojciech Kosmala²

Heart Failure with preserved Ejection Fraction: Defining phenotypes

Heart failure with preserved ejection (HFpEF) has been increasingly recognized as an epidemic and various phenotypes have now been suggested [START_REF] Pieske | How to diagnose heart failure with preserved ejection fraction: the HFA-PEFF diagnostic algorithm: a consensus recommendation from the Heart Failure Association (HFA) of the European Society of Cardiology (ESC)[END_REF]. The clinical presentation as well as medical history may vary in this condition. Some patients experience multifold hospitalizations, and others complain of breathlessness and have a similar decrease in quality of life, but have never been hospitalized. Some patients have severe, recurrent congestion, and others are essentially symptomatic only when exercising.

The modern concept of HFpEF was proposed by Luchi et al., who in 1982 described a group of patients with typical heart failure symptoms associated with preserved (≥ 50%) left ventricular ejection fraction (LVEF) [START_REF] Luchi | Left ventricular function in hospitalized geriatric patients[END_REF]. The heterogeneity of this syndrome was one of the reasons that several randomized studies using simple criteria did not provide evidence for effective therapies, and over the years, being wiser with the experience from these trials, we are seeking treatment strategies that could be phenotype specific for a segment of the HFpEF population [START_REF] Solomon | Angiotensin-Neprilysin Inhibition in Heart Failure with Preserved Ejection Fraction[END_REF][START_REF] Pitt | Spironolactone for heart failure with preserved ejection fraction[END_REF][START_REF] Pieske | Vericiguat in patients with worsening chronic heart failure and preserved ejection fraction: results of the SOluble guanylate Cyclase stimulatoR in heArT failurE patientS with PRESERVED EF (SOCRATES-PRESERVED) study[END_REF]. The array of tested remedies is quite vast and still increasing, including both pharmacological agents and implantable devices [START_REF] Silverman | Treatment of Heart Failure With Preserved Ejection Fraction (HFpEF): the Phenotype-Guided Approach[END_REF].

Recently, HFpEF has been re-defined by the European Society of Cardiology (ESC) as preserved left ventricular EF (LVEF ≥ 50%), with evidence of diastolic dysfunction and structural heart disease, in the context of elevated biomarkers, and classic signs and symptoms of heart failure [START_REF] Pieske | How to diagnose heart failure with preserved ejection fraction: the HFA-PEFF diagnostic algorithm: a consensus recommendation from the Heart Failure Association (HFA) of the European Society of Cardiology (ESC)[END_REF]. The importance of echocardiography and dynamic testing is reflected in the score that is the essence of the proposed diagnostic algorithm [START_REF] Shah | Echocardiographic Features of Patients With Heart Failure and Preserved Left Ventricular Ejection Fraction[END_REF]. By using a comprehensive, alternative-based evaluation process, this new approach improves the accuracy of HFpEF identification, and probably is more effective in identifying the "never-hospitalized" patients who are complaining mainly of exertional dyspnea. On the other hand, it does not permit a priori stratification of patients according to the occurrence and severity of symptoms. Other scores and pathophysiologically-based diagnostic approaches have been proposed, but their relevance in the context of patient selection for interventions providing symptomatic and prognostic improvement has not been validated [START_REF] Shah | Cardiac structure and function and prognosis in heart failure with preserved ejection fraction: findings from the echocardiographic study of the Treatment of Preserved Cardiac Function Heart Failure with an Aldosterone Antagonist (TOPCAT) Trial[END_REF][START_REF] Senni | New strategies for heart failure with preserved ejection fraction: the importance of targeted therapies for heart failure phenotypes[END_REF][START_REF] Selvaraj | Application of Diagnostic Algorithms for Heart Failure With Preserved Ejection Fraction to the Community[END_REF].

The manuscript by Reddy et al in the current issue of the Journal deserves special attention and careful analysis [START_REF] Reddy | Characterization of the progression from ambulatory to hospitalized heart failure with preserved ejection fraction[END_REF]. It is based on 7 NIH sponsored multicenter trials in HFpEF and focuses on the distinction between patients with and without HF hospitalization. The hospitalization phenotype is characterized by a larger burden of non-cardiac pathologies including more advanced renal dysfunction, COPD and anemia, more impaired functional capacity and worse outcomes. Interestingly, the quality of life and resting echocardiographic profile are similar in both subsets stratified on the basis of hospitalization history. Nevertheless, these observations might suggest that the 2 categories may require different management approaches, with multiorgan protection and prevention of recurrent congestion in the "hospitalized" group vs. a focus on improving exercise capacity in the "never-hospitalized" subset.

The authors emphasize that it is not clear whether these 2 groups of patients represent the same disease process at different stages or different clinical phenotypes (figure 1). A potential transition from the less-diseased to the more-diseased HFpEF category was previously postulated but is not proven [START_REF] Kosmala | Contributions of Nondiastolic Factors to Exercise Intolerance in Heart Failure With Preserved Ejection Fraction[END_REF]. As a consequence, if the contribution from the non-cardiac organs to the disease process is not a distinctive feature of the "hospitalized" phenotype, approaches that prevent the progression of extra-cardiac pathologies should be considered in patients with HFpEF who have never experienced a HF hospitalization. As a consequence in might be important to search for the common denominator contributing to the progression of multi-organ abnormalities e.g. systemic inflammation [START_REF] Donal | Value of exercise echocardiography in heart failure with preserved ejection fraction: a substudy from the KaRen study[END_REF].

The current paper is a retrospective, multi-trial analysis, in which the extent of echocardiography use was limited by the protocols of the original studies. It is likely that the inclusion of additional echocardiographic parameters, especially LV and LA strain, and RV/pulmonary indices, might have improved the characterization of clinically-derived phenotypes and provided more information relevant for decision-making. Furthermore, an important source of prognostic data in patients without HF hospitalization would have been exercise echocardiography, with quantification of LV diastolic and systolic responses to exertion.

Accordingly, extended imaging might add to the "macroscopic" phenotyping proposed by Reddy et al [START_REF] Reddy | Characterization of the progression from ambulatory to hospitalized heart failure with preserved ejection fraction[END_REF][START_REF] Donal | Importance of combined left atrial size and estimated pulmonary pressure for clinical outcome in patients presenting with heart failure with preserved ejection fraction[END_REF]. Despite this limitation, the results set the stage for further studies. What were the results of PARAGON -HF in non-hospitalized patients(15)? Given the vasodilating properties of sacubitril/valsartan, this treatment could be more beneficial in patients who need more afterload reduction than a decrease in fluid retention. The relative and absolute benefits of sacubitril/valsartan compared with valsartan alone in HFpEF appear to be amplified when initiated in the high-risk window after hospitalization. On the other hand, patients hospitalized or recently hospitalized might require a more aggressive diuresis by agents that are safe for the kidney and liver like the gliflozins [START_REF] Mcmurray | The Dapagliflozin And Prevention of Adverse-outcomes in Heart Failure (DAPA-HF) trial: baseline characteristics[END_REF]. Accordingly, the work by Reddy et al. may facilitate the interpretation of trial findings and provide guidance on specific treatment approaches [START_REF] Reddy | Characterization of the progression from ambulatory to hospitalized heart failure with preserved ejection fraction[END_REF].

Another issue that needs to be addressed is the clinical impact of atrial fibrillation, as well as the approaches to the management of this arrhythmia in both HF hospitalization-based phenotypes.

The presence of atrial fibrillation may be an important component of the phenotypic profiling in HFpEF and should be taken into account when planning therapeutic strategies [START_REF] Kosmala | Heart Failure With Preserved Ejection Fraction and Atrial Fibrillation: How to Fight Allied Enemies[END_REF].

To summarize, the current contribution underscores once again the need for phenotype-specific therapy in patients categorized as having HFpEF. The presence of HF hospitalization in the patient history is a powerful determinant of the clinical presentation and outcome. The putative pathophysiological differences between patients with HFpEF with and without HF hospitalizations need to be more profoundly explored in future studies. The potential therapeutic implications of this approach to HFpEF heterogeneity based on the history of HF hospitalization might be worth considering to improve patient management. We believe that the wider use of echocardiography in the phenotyping process may aid in establishing efficient treatments in this highly prevalent condition.

Figure 1 :

 1 Figure 1: two phenotypes with distinct pathophysiology or two stage of the same disease?