The MEMIN research unit: Scaling impact cratering experiments in porous sandstones

Michael H. Poelchau1*, Thomas Kenkmann1, Klaus Thoma2, Tobias Hoerth2, Anja Dufresne1, Frank Schäfer2

1Institut für Geowissenschaften, Albertstraße 23b, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany

2Fraunhofer-Institut für Kurzzeitdynamik Ernst-Mach Institut, EMI, Eckerstraße 4; 79104 Freiburg, Germany

*michael.poelchau@geologie.uni-freiburg.de

Abstract

The MEMIN research unit (Multidisciplinary Experimental and Modeling Impact research Network) is focused on analyzing experimental impact craters and experimental cratering processes in geological materials. MEMIN is interested in understanding how porosity and pore space saturation influence the cratering process. Here we present results of a series of impact experiments into porous wet and dry sandstone targets. Steel, iron meteorite and aluminum projectiles ranging in size from 2.5 to 12 mm were accelerated to velocities of 2.5-7.8 km/s, yielding craters with diameters between 3.9 and 40 cm. Results show that the target’s porosity reduces crater volumes and cratering efficiency relative to non-porous rocks. Saturation of pore space with water to 50% and 90% increasingly counteracts the effects of porosity, leading to larger but flatter craters. Spallation becomes more dominant in larger-scale experiments and leads to an increase in cratering efficiency with increasing projectile size for constant impact velocities. The volume of spalled material is estimated using parabolic fits to the crater morphology, yielding approximations of the transient crater volume. For impacts at the same velocity these transient craters show a constant cratering efficiency that is not affected by projectile size.

INTRODUCTION

There are numerous planetary settings in which impact cratering occurs into a target material that has some degree of porosity, e.g. in regoliths on dry, airless bodies, in cometary material, or in materials formed by water and air-driven sedimentary processes. The pore space in these materials can be filled by ice or liquid water, as is common for impacts on Mars or impacts formed in sediments on Earth (e.g., Carr et al. 1977; Kenkmann and Schönian 2006; Smith et al. 2009). Impact experiments into wet and dry porous materials are therefore necessary for gaining a better understanding of cratering processes on these types of planetary surfaces. The analysis of strength-dominated experiments can give important insights into the mechanisms of target subsurface damaging, and how porosity and pore fluids affect rock fracturing and deformation. Also, with the

continuously increasing resolution of remote sensing imagery on the Moon and Mars, small, strength-dominated craters can be observed in greater detail, and require a better understanding of how the target interacts with the crater formation process. This in turn has potential implications e.g. for crater size-frequency distributions (e.g., Wünnemann et al. 2011; Hiesinger et al. 2012).

The general effects of porosity on cratering have been reported in several experimental studies (e.g. Love et al. 1993; Housen and Holsapple 2003; Michikami et al. 2007; Schultz et al. 2007). There is an obvious shock impedance mismatch between mineral grains and the neighboring empty or gas-filled pore spaces. Closing of pore space during shock compression leads to localized high-pressure and temperature spots (Kieffer et al. 1976), and the resulting post-shock temperatures in quartz sand or sandstone are much higher than in single quartz crystals shocked at the same pressures (Stöffler and Langenhorst 1994). This consumes additional energy that is removed from the shock wave, causing a decrease in shock pressures and reducing the resulting excavation flow field more rapidly as the shock wave progresses (e.g., Zel’dovich and Raizer 1967). Saturating pore space with fluids counteracts the effects of porosity. Plane wave shock experiments show that less damaging occurs and more of the original porosity remains intact when pores are supported with water (Hiltl et al. 2000), and that shock wave velocities and peak spall velocities are higher e.g. for water-saturated tuffs than for their dry counterparts (Butkovitch 1971; Erskine et al. 1994).

Crater volumes and cratering efficiency (the ratio of excavated mass to projectile mass) are thus generally reduced by porosity. This effect can be inferred when gravity-regime experiments performed in loose, porous sand are scaled relative to non-porous materials (e.g., Schmidt and Housen 1987) or in numerical models that include a porosity model (e.g. Wünnemann et al. 2006; Wünnemann et al. 2011), although other physical parameters like cohesion can also reduce cratering efficiency and need to be considered separately (Wünnemann et al. 2011).

Until this study, there were few data available for strength-dominated cratering experiments into porous rocks. Shoemaker et al. (1963) reported on one impact experiment into dry Coconino sandstone, and Baldwin et al. (2007) performed four shots, one each into a dry and a water-saturated Coconino sandstone and a dry and water-saturated “uncharacterized” sandstone. Schäfer et al. (2006) and Kenkmann et al. (2011) reported on two shots into a dry and a water-saturated sandstone (Seeberger Sandstein), performed as a prefeasibility study for the MEMIN program. Results from these papers show a general trend that craters in targets with water saturated pore space have larger volumes than those in dry targets.

With recent occurrence of impact events like Carancas (Kenkmann et al. 2009; Tancredi et al. 2009) or the discovery of small craters like Kamil (Folco et al. 2011) that were formed in porous or water-bearing sediments, potentially strength-dominated impacts remain of importance for the terrestrial and planetary cratering record. Therefore, experimental work on impact cratering remains necessary to understand the details of these complex processes.

In this paper, the results of 18 impact experiments into dry and wet sandstones are presented with a focus on quantifying and scaling the effects of porosity and pore space saturation on crater size in the strength regime. These results are part of a larger study in the framework of the MEMIN (Multidisciplinary Experimental and Modeling Impact research Network) research unit.

EXPERIMENTAL METHODS

Target material:

Blocks of the target sandstone were quarried by the TRACO Company in Thuringia, Germany, in a quarry on the Großer Seeberg near Gotha. The sandstone is referred to as Seeberger Sandstein. The sandstone is a well-sorted fluviatile deposit of the Upper Norian-Rhaetian stage of the Upper Triassic (209 – 200 Ma; Stück et al. 2011) and is commonly used as a dimension stone. A specific stratigraphic layer (“layer 3”) was chosen as target material due to its high quartz content and small grain sizes. The average grain size is 100±25 µm, based on laser diffraction analysis of lightly ground target material, using a Malvern™ Mastersizer at the University of Freiburg. Sieve analysis delivers comparable results. XRF analysis performed at the Museum of Natural History, Berlin, shows a quartz content of ~89 vol.%, along with ~10 vol.% phyllosilicates (mostly clay minerals and subordinate micas), and small amounts of accessory minerals (Ebert et al. 2012). Reddish-brown rings of limonite are often visible.

The bulk density (2.05±0.04 g/cm³) was determined by weighing dried samples and measuring their volume. Average porosity of 23.1±0.5% was calculated for four dry 20-cm edge length cubes using a grain density of 2.65 g/cm³. Vacuum pycnometer measurements performed at the University of Freiburg on three 75x49 mm cylinders gave similar porosity values of 23.0±0.4% (Table 1).

Uniaxial compressive strength (UCS) and tensile strength were measured on uncased cylindrical sandstone samples (74x150 mm) in a uniaxial loading frame at the University of Freiburg. Samples were loaded a rate of ~0.5 kN/s. The UCS is 67.3±2.7 MPa perpendicular to the layering of the sandstone for oven-dried samples. 55.8±1.5 MPa was measured for samples saturated with tap water to ~55% over two weeks, and samples saturated to ~90% over two weeks in a vacuum chamber had a UCS of 58.4±0.8 MPa. Tensile strength was determined in Brazil tests and gave values of 4.7±0.8 MPa for tensile stress oriented parallel to the layering of oven-dried samples. Tensile strength measured perpendicular to the layering gave 4.1±0.7 MPa for dry samples, 3.4±0.5 MPa for ~55% saturated samples and 4.3±0.4 MPa for ~90% saturated samples (Table 1).

For the two pilot study shots (Kenkmann et al. 2011), the coarser-grained “layer 5” of Seeberger Sandstein was used with a density of 2.27 g/cm³, a porosity of 17.9%, a dry UCS of 62.4 MPa and a wet UCS of 47.0 MPa. Further specifications of the material properties of layer 5 are given in Kenkmann et al. (2011).

Projectiles:

Three types of metal projectiles were selected for the experiments (Table 2), based on the content of specific trace elements that were used to observe target-projectile mixing and fractionation processes (Ebert et al. 2012). Several projectiles were made of Campo del Cielo meteorite, a IAB main group iron meteorite containing 6.6 wt% Ni and 0.4 wt% Co (Ebert et al. 2012), with a density that varied slightly between 7.83-7.91 g/cm³ for individual projectiles. D290-1 steel (density 8.1 g/cm³) was chosen as an additional material due to the high content in trace elements (W: 6.3wt%, Co: 5.1wt%, Mo: 4.8wt%, Cr: 4.2wt%, V: 1.9wt%, Ni: 0.3wt%, Mn: 0.2wt%). Two shots were carried out with high Ni-Cr aluminum alloy projectiles (55X G28J1) with a density of 2.7 g/cm³. The projectiles used in the pilot study were AlSl 4130 steel with a density of 7.8 g/cm³ (Kenkmann et al. 2011).

Light gas accelerators:

Impact experiments were performed at the facilities of the Fraunhofer Ernst-Mach-Institute (EMI) in Freiburg and Efringen-Kirchen, Germany. Two horizontal two-stage light gas guns were used (Fig. 1). The “space gun” (SLGG) has a 40 mm caliber, 1.8 m long pump tube combined with an 8.5 mm caliber, 1.5 m long launch tube, and is capable of accelerating several mg of mass up to 8-9 km/s. The “extra large” light gas gun (XLLGG) consists of a 154 mm caliber, 22 m long pump tube in combination with a 39 mm caliber, 12 m long launch tube, and can accelerate several hundred grams up to 5-6 km/s. For more details on the working principle and specifications of the XLLGG, see Lexow et al. (2012).

Experimental setup:

Sandstone targets used in the SLGG were 20 cm edge length cubes, and 50 cm cubes and 80x80x50 cm blocks in the XLLGG. A few weeks prior to the experiments, several sandstone blocks were submerged in basins filled with tap water and saturated to ~50% under atmospheric pressure. Two 20 cm cubes were further saturated to ~90% (Table 2) by placing the submerged cubes in a vacuum chamber at ~30 mbar pressure. The degree of pore space saturation was determined by weighing the blocks before and after watering (Buhl et al. 2012) and has an estimated error of ±3%.

All blocks were positioned in the target chamber with their layering perpendicular to the impact trajectory, except experiment A8-5128, where layering was parallel to the impact trajectory. Each block was equipped with an array of ultrasound sensors (Fig. 1) which were glued or drilled to all free block surfaces. The sensor arrays recorded the initial pressure wave of the impact and subsequent post impact vibrations. The majority of blocks (excluding experiments A3-5124 to A8-5128) were marked with a “bullseye” on the target surface (Sommer et al. 2012), consisting of three concentric rings of paint spiked with chemical tracers that had specific elemental ratios.

Specific witness plates, termed here as “ejecta catchers”, were developed in the course of the first experiments for a localized retrieval of ejected particles with high spatial resolution. Best results were achieved with blocks of phenolic foam and with Plexiglas plates covered with a ~3 mm thick layer of degassed Vaseline. The ejecta catchers were placed opposite to the target surface at 24-28 cm distance in the SLGG experiments and 50-53 cm distance in the XLLGG experiments (Fig. 1). The SLGG target chamber was small enough to allow all ejecta to be retrieved that was not caught in the ejecta catchers. For the XLLGG experiments, a plywood box with Plexiglas panels was mounted around the target surface to retain the ejecta (Sommer et al. 2012).

Impact conditions:

An overview of experimental conditions is given in Table 2. Shots at the SLGG were performed with 2.5 mm diameter D290-1 steel spheres at roughly 5 km/s, while two aluminum spheres with 5 mm and 2.5 mm diameter were use to achieve higher velocities at 7.0 and 7.8 km/s, respectively. SLGG target chamber pressure was reduced to between 1 and 100 mbar. Shots at the XLLGG were performed with 1 cm iron meteorite spheres accelerated to velocities between 2.5 and 4.6 km/s, and with 1.2 cm D290-1 steel and iron meteorite spheres at 4.6 km/s. The XLLGG target chamber was evacuated to ~50 mbar pressure and then flooded with N2 gas to ~300 mbar. The two shots of the pilot study (P1-2808 and P2-2809; Table 2) were also performed at the XLLGG under similar conditions. Details for these two experiments can be found in Kenkmann et al. (2011).

Projectile velocities were measured as the projectile passed two laser barriers in the blast tank of the light gas guns (Fig. 1) and were corrected for the deceleration that occurred at the distance between the laser barriers and the impact point. Measurements have an estimated error of ±1% (Lexow et al. 2012). These barriers were also used as triggers for the high speed camera that was used to observe and quantify the ejection process (Hoerth et al. 2012), filming at up to 5*105 frames per second.

The evaluation of these experiments is subject to detailed analyses presented in several papers in this issue. The analysis of results of high-speed videos is given in Hoerth et al. (2012), and the distribution of fragments in the ejecta catchers is discussed in Sommer et al. (2012). Target subsurface damaging is evaluated in Moser et al. (2012) and Buhl et al. (2012), while chemical fractionation processes at the projectile-target interface are analyzed in Ebert et al. (2012) and Kenkmann et al. (2012). See also Güldemeister et al. (2012) for mesoscale numerical models of the sandstone’s behavior under shock loading, and Kowitz et al. (2012) for results of shock recovery experiments performed on the target material.

Measurement of crater dimensions:

Crater depth, diameter and volume (Table 3) were measured non-intrusively using a 3D laser scanner (Dufresne et al. 2012). A few crater volumes were also cross-checked by filling the craters with 0.8-mm diameter glass beads and then measuring the volume of the beads used. The two methods showed less than 3% discrepancy. Weighing the targets before and after the experiment proved to be more inaccurate, possibly due to changing moisture levels in the sandstones in the lower pressure environment of the target chamber. The 3D scanner has a depth precision of 0.1 mm, therefore the volumes of the craters in the SLGG experiments have an error of 2-4% depending on their size, and the craters from the XLLGG experiments have an error of 0.5-1%.

RESULTS AND DISCUSSION

Crater shape and morphology:

A detailed analysis of crater morphology, spallation and the implications for constraining the transient crater in MEMIN experiments can be found in Dufresne et al. (2012). An overview is given here. All craters show an area of white, crushed rock in the central depression of the crater (Fig. 2). In most cases, a small pit has formed as a small circular area about 2-3 times larger than the projectile directly below the point of impact. A peak, i.e. a small conical protrusion was formed in one of the impacts (experiment A15-5185). Similar peaks have also been reported in impact experiments by Lange & Ahrens (1987).

The crater morphology is severely affected by spallation processes (Fig. 2). Large, cm-sized spall plates (Fig. 2d) were ejected from the outer areas of the crater, thus greatly enlarging crater volume and diameter. This process is irregular and leads to erratic, non-circular crater shapes. Often incipient spall plates are retained in the crater, possibly due to target inhomogeneities, and give the impression that only a minor increase in impact energy would have dislodged the plate, thus increasing the mean crater diameter and crater volume. These plates can be either wedge shaped pieces still stuck within the crater, or visible only as single, concentric fractures located outside of the

crater on the target surface (Fig. 2c). This leads to a large error margin for crater diameters, as shown in Figure 3.

Crater depth (d), diameter (D) and depth-diameter ratios (d/D) are given in Table 3 and are plotted in Figure 4. Dry sandstones impacted with steel or iron meteorite projectiles show d/D ratios of 0.18-0.19 for 2.5 mm projectiles and 0.19-0.24 for 10-12 mm projectiles, while aluminum projectiles yield lower ratios of 0.14 and 0.16. Sandstone targets saturated to 50% and 90% also have lower d/D ratios of 0.13-0.19.

Discussion of crater shape and morphology:

Due to the variation for individual crater diameters, interpretation of d/D gives only general trends. Nonetheless, our data imply that experimental parameters affect d/D.

1) Increasing the projectile density to target density ratio (ρp/ρt) leads to higher d/D ratios and deeper crater morphologies, as seen when the two shots with aluminum projectiles are compared to shots with steel or iron meteorite projectiles (Fig. 4). Application of a standard t-test shows that the increase in d/D is statistically significant for the MEMIN sandstones. Data from Smrekar et al. (1986) show the same effect; shots into diorite with steel projectiles led to higher average d/D ratios than shots with aluminum projectiles (Fig. 4). Burchell and Johnson (2005) varied ρp/ρt over an order of magnitude for impacts into water ice, but only saw a vague increase in d/D due to a large degree of scattering. A correlation of d/D with ρp/ρt is also well known from impacts into metal targets (e.g. Goodman and Liles, 1963), where trends are much more tightly constrained due to the lack of spallation.

2) Increased pore space saturation can potentially decrease d/D. Shots at the SLGG showed an average decrease in d/D from dry (0.19) to saturated blocks (0.19-0.14), while shots at the XLLGG showed a decrease from 0.19 to 0.18 and 0.13 for experiments E1-3382 to E3-3384 and from 0.23 to 0.16 for the pilot shots, both with dry and ~50% saturated targets (Table 3). A statistical treatment of the datasets for dry and wet targets using a standard t-test shows that the dry d/D is significantly different from wet d/D. Baldwin et al. (2007) produced similar results for dry and ~100% saturated sandstones, where d/D decreased from 0.15 to 0.11 for Coconino sandstone, but remained at 0.22 for an unclassified sandstone. The general trend for d/D to decrease with pore space saturation is presumably caused by a “reduction” of the effects of porosity. The impedance mismatch between quartz grains and pores is lowered by the presence of water, reducing pore space collapse and compaction in the center of the crater. Love et al. (1993) and Michikami et al. (2007) have shown in impacts into sintered glass bead targets of varying porosity that penetration depth and the resulting d/D strongly increases with increasing porosity. Somewhat surprisingly, porosity effects are not clearly visible when the MEMIN shots into dry sandstones are compared to impacts in nonporous brittle materials (Fig. 4). Our data are lower than d/D for steel projectile impacts into diorite (Smrekar et al. 1986, Fig. 4) and only slightly higher than the mean d/D ratios for aluminum projectile impacts into granite (Burchell and Whitehorn 2003). Possibly, variations in the crystalline rocks’ tensile strength could affect d/D, or, as discussed below, differences in impact velocity play a larger role.

3) An increase in impact velocity is also expected to reduce d/D (e.g., Holsapple 1980; reported there as the equivalent depth of burst). This effect was not observed in the MEMIN d/D data. A rough decrease in d/D with increasing velocity can be seen for example in ice (Shrine et al. 2002) and granite experiments (Burchell and Johnson 2005), where impact velocities ranged from 1-7 km/s and

1-6 km/s, respectively, and the same type of projectile was used. Similar results are reported for particulate targets (e.g. Barnouin-Jha et al. 2007) and metal targets (Goodman and Liles 1963; for ρp/ρt >1). Perhaps this trend would become apparent in the MEMIN data if a larger range of velocities were to be used.

Spallation will certainly also have an effect on crater diameters and thus on d/D, and is expected to be controlled by projectile and target properties, for example projectile size or tensile strength of the target (e.g. Melosh 1984). This will be subject to a more detailed analysis in the future.

Crater volumes:

MEMIN crater volumes are plotted against the kinetic energy of the projectile in Fig. 5. SLGG shots plot on the left side of the diagram at ~1kJ energy, while XLLGG shots are on the right at ~10kJ to ~80kJ. A decrease in crater volume appears to correlate with decreasing projectile density, although more data are needed to confirm this trend. More importantly, the effect of pore space saturation can be observed here, showing a general increase in crater volume for successively higher saturation levels. For example, crater volumes are ~4 times larger in 90% saturated sandstones than in dry sandstones for roughly the same impact energies (Table 3).

The increase in crater volume with increased pore space saturation is presumably due to a combination of at least two factors. First, uniaxial compressive strength (UCS) is reduced from 67 MPa to ~57 MPa for both 50% and 90% water saturation (Table 1). This is most likely the result of swelling clay minerals that absorb water in the sandstone, reducing the rock’s cohesion. Moreover, a phenomenon in quartz termed stress corrosion can contribute to strength reduction (Atkinson 1984). This phenomenon is described as the reaction of strained Si-O bonds at crack tips with water and subsequent increase in crack formation velocities during strain. Second, filling pore space with water reduces open pore space and thus reduces the shock impedance mismatch between quartz crystals and voids. The variations in strength can be compensated using strength scaling methods. This approach is used to separate strength effects from porosity effects and is described in the following segments below.

PI-GROUP SCALING

Scaling laws are useful for comparing different cratering datasets in order to determine the effects physical parameters have on crater size. Here we use scaling laws to assess the effects of three parameters: 1) The effect of porosity on crater volumes and cratering efficiency relative to non-porous rocks. 2) The capacity of pore space saturation to counteract porosity effects. 3) The influence of projectile diameter on spallation in the strength regime.

Scaling exponents:

Much discussion can be found in the literature on how projectile mass and velocity can each affect crater size separately. Examples shown for cratering experiments in sand (Fig. 1 in Oberbeck 1977) or water (Fig. 8 in Holsapple and Schmidt 1982) reveal that for the same impact energy, more massive projectiles form larger craters than higher-velocity projectiles, or in other words, observing impact energy alone does not usually give unambiguous crater volumes. Projectile mass and velocity both have to be considered to obtain a single volume (assuming other parameters like gravity, strength or

target and projectile density are kept constant). For the strength regime, Holsapple (1993) gives a generalized equation for the crater volume in non-porous materials:

V ∝ m/ρt * (ρt vi²/Y)3µ/2 * (ρt/ρp)1-3ν (1)

where V is the crater volume, m, ρp and vi are the projectile mass, density and velocity, ρt is the target density, Y is a measure of target strength, and µ and ν are scaling exponents. µ is thus important for determining at what rate V increases with vi and m. The limits for µ are defined as 1/3 < µ < 2/3, meaning that V increases at a rate that lies between momentum scaling (V ∝ mvi) and energy scaling (V ∝ mvi

2; Holsapple 1993).

When considering fixed materials for the target and projectile, the density and strength terms can be omitted from equation (1), giving a simplified form:

V ∝ m (vi2)3µ/2 (2)

Equation (2) can be rewritten as

V ∝ m1-3µ/2 (mvi2)3µ/2 (3)

or

V ∝ m1-3µ/2 E3µ/2 (4)

where E is kinetic energy. Using the mass and energy data for dry MEMIN sandstone targets, and excluding MEMIN experiments with aluminum projectiles, a multiple linear regression using equation (4) gives

V ∝ m0.25±0.14 E0.86±0.15 (5)

which corresponds to µ = 0.57±0.10 as the exponent of the energy term. Errors are standard deviation.

For a more generalized approach, dimensionless π-group scaling of crater sizes (e.g. Holsapple 1993) is a useful solution for determining how projectile mass, velocity and density, target density, and target strength or gravity affect the crater diameter or volume. The cratering efficiency πV, defined here as

πV = V ρt /m (6)

can be plotted against the gravity term π2, where

π2 = (ρtga) / (ρtvi²) = ga / vi² (7)

which is the ratio of the lithostatic pressure in the target at the depth of the projectile radius a and the gravitational acceleration g to the inertial stress of the target material at impact velocity. Dimensionless terms are also given in the strength-regime. Here, instead of the gravity term, the strength term

π3 = Y / (ρtvi²) (8)

is used where Y is any measure of the target’s strength in units of stress and ρtvi² again is the inertial stress or “initial dynamic pressure” (Holsapple 1993). Cratering efficiency can be plotted against the strength term when equation (1) is modified, giving

V ρt /m ∝ (ρt vi²/Y)3µ/2 * (ρt/ρp)1-3ν (9)

or

πV ∝ π3-3µ/2 * π4

1-3ν (10)

where the density term π4 = ρt/ρp and π41-3ν is used to correct the effects of varying target to

projectile density ratios.

A linear regression of all MEMIN data for dry sandstone targets using equation (9) yields values for both scaling exponents, with µ = 0.38±0.16 and ν = 0.41±0.11. While the value for µ is still within the limits defined above, it is much lower than the value determined with equation (4). This is most likely an unwanted effect of variation in πV due to projectile size (Fig. 6), and is discussed further below. A linear regression of MEMIN experiments on dry targets using only 10-12 mm projectiles gives a steeper slope with a value of µ = 0.55±0.10. This value is in good agreement with values for µ determined through scaling crater diameter growth of individual MEMIN experiments in dry sandstone (Hoerth et al. 2012). Their values for µ lie between 0.49 and 0.56.

A regression of impact experiments into basalt targets with aluminum, steel and polyethylene projectiles (Moore et al. 1963; data retrieved from Holsapple and Housen 2004) gives µ = 0.62±0.05 and ν = 0.35±0.05. Lower scaling exponents are expected for porous materials from the literature (e.g., Holsapple 1993; Holsapple and Housen 2007) although values reported there are generally lower, with µ = 0.55 for “hard rock” and µ = 0.41 for porous sand. On the other hand, Wünnemann et al. (2011) found no change in µ for numerical models that varied porosity from 0 to 35%.

Strength scaling:

In Fig. 6, MEMIN πV values are plotted against π3 values. Dry craters formed at lower impact velocities (2.5-3.5 km/s, Table 2) have higher π3 values and lie further to the right. Water saturation of the sandstone targets leads to a higher target density and reduced strength (Table 1), which reduces π3 values and shifts data points to the left, compared to impacts on dry targets at the same velocity. The density term that corrects unequal target and projectile densities shifts data points of impacts with higher projectile densities to the left. The data have a negative slope, meaning that impacts with smaller π3 values (e.g., higher impact velocity or weaker target strength) have a higher cratering efficiency.

In theory, two impacts at the same velocity using the same materials (i.e., with the same π3 values) should have the same cratering efficiency in the strength regime, regardless of projectile size and mass. For the MEMIN data, experiments with larger (10-12 mm) projectiles generally have a higher cratering efficiency than experiments with small (2.5 mm) projectiles (Fig. 6). This appears to be the effect of a longer pressure pulse generated by the larger projectiles. Ahrens and Rubin (1993) and Meyers (1994) show that the duration of tensile pressure pulses affect the amount of fractures

formed in rock samples. This means that longer pulses should increase the volume of spalled material, leading to larger craters. This effect and its implications are discussed in more detail below.

In Fig. 6, impact experiments into basalt targets with aluminum, steel and polyethylene projectiles (Moore and Gault 1962; Moore et al. 1963; Holsapple and Housen 2004) are plotted for comparison as a typical non-porous rock. The trend of the least-squares fit of the basalt data shows that MEMIN sandstones have a reduced cratering efficiency compared to the average of basalts with the same π3-values. The reduction of cratering efficiency is interpreted to be an effect of the sandstone’s porosity. Saturation of the sandstone’s pore space counteracts this effect. The two experiments with 90% saturated targets lie slightly above the basalt trend, suggesting that a nearly complete saturation of pore space with water cancels out the effects of porosity on cratering efficiency.

Quantifying porosity effects:

When comparing materials with different porosity, a problem arises that, at least for most geological materials, increased porosity reduces the compressive strength of the material (e.g., Palchik 2006). Therefore, while the reduced strength increases crater volumes, the increased porosity reduces the volume, resulting in similar sized craters in different materials. To address this problem, MEMIN crater values were compared to the strength scaled cratering efficiency of a theoretical, non-porous “sandstone” with the same strength. This was done by taking the trend of the basalt craters in Fig. 6 and calculating which cratering efficiency the MEMIN data would have with their individual π3 values. For this calculation it is assumed that non-porous brittle materials have the same slope as basalt (µ=0.62). The equation was used in the form shown in Fig 6. where

V ρt /m = K [(Y/ρt vi²) (ρp/ρt)(1-3ν)(2/3µ)]-3µ/2 (11)

For the basalt data, the constant K=0.8895 was used. The theoretical crater volumes are then derived from the cratering efficiency values and used to show how much the actual craters in sandstone have been “reduced” by porosity. These values are referred to as normalized crater volumes (VN; i.e., the ratio of measured volume to calculated volume) and are plotted against the pore space φ in Fig. 7a. For saturated sandstone targets, φ refers to the remaining, empty pore space. For example, 50% water saturated sandstone targets with 23% porosity have φ=11.5%.

Craters in dry MEMIN sandstone targets formed with 2.5 mm projectiles have only 20-40% of the expected “non-porous” volume, while craters formed with 10-12 mm projectiles lie at higher values of 45-70%, presumably due to the increased amount of spallation caused by larger projectile diameters. 50% water saturated targets show a crater volume reduction to 50-80%, while 90% saturated targets show a slight increase to 120% of the calculated volume. This once again reflects the capacity of pore space saturation to counteract porosity. The craters formed in basalt shown in Fig. 7a display a large amount of scattering. Therefore, caution should be used to avoid over-interpreting the MEMIN data.

In Fig. 7b, data from impact experiments into sintered glass bead targets (Love et al. 1993; Michikami et al. 2007) are additionally plotted. The glass bead targets were manufactured with varying compressive strengths and porosities, and thus give an opportunity to compare data over a wider parameter range. Both datasets used low-porosity (5-10%) targets for a few cratering experiments. These values were used to adjust the constant K in equation (11). For the Love et al. (1993) dataset, a

value of K=2.0 was used; for the Michikami et al. (2007) dataset K=3.5. These values were estimated for Fig. 7b using an arbitrary fit. The results suggest that craters formed in targets with 30-60% porosity have crater volumes that are 1-10% of the size expected for non-porous targets with the same strength. A trend fitted to all data in Fig. 7b gives VN = 1.10 e-0.077φ and implies that when porosity is observed as an isolated parameter, it exponentially reduces crater volumes. It should be noted that this relationship is based on cratering experiments with a limited range of velocities (~1-8 km/s) and projectile sizes (~1-12 mm). The difference in scaling exponents between sandstones and basalts may alter the trend determined here if a larger range of velocities or π3 values are observed. Also, even in this limited range, the projectile size appears to influence crater volume. The effects of projectile size on spallation and crater volume are discussed in the following segment.

Spallation and the transient crater:

The reflection and interaction of the shock wave with the target surface creates tensile stresses that lead to the ejection of spall plates, which become successively larger further away from the point of impact (Melosh 1984; Grady and Kipp 1987). The volume and erratic behavior of these spall plates play a much more dominant role in these experiments than on a planetary scale (e.g. Melosh 1984). Therefore, separating spall processes from the excavation flow that forms the transient crater is of general interest.

To discern transient craters from final craters with spalled material, Kenkmann et al. (2011) and Dufresne et al. (2012) applied a method of fitting parabolas to the scanned profiles of the MEMIN craters, using the morphology of the central depression and ejecta angles as constraints for the parabolas. Volumes are calculated from the rotational shape of the parabolas, and for each crater, the average of fits of up to 18 profile orientations is given (Table 4). This delivers a good first-order approximation of the presumed transient crater, with an error of under 20% for individual volumes (Fig. 8).

As seen in Figs. 6 and 7, there is a correlation between cratering efficiency and projectile size, where experiments with 10-12 mm projectiles have a higher cratering efficiency than experiments with 2.5 mm projectiles that where performed under otherwise equal conditions in dry sandstone targets. Ahrens and Rubin (1993) performed planar shock wave experiments on Bedford limestone and observed that the onset of microcracking and spallation both occurred at lower tensile stresses when the shock pulse duration was increased from 0.5 to 1.3 µs. Similar results of several other experimental campaigns are also described e.g. in Meyers (1994) that confirm the effects of tensile pulse duration on fracture formation. MEMIN experiments with 12 mm projectiles should generate shock pulses with roughly 5 times the duration of 2.5 mm projectiles, which should in turn generate larger volumes of spalled material.

The cratering efficiencies of the dry MEMIN sandstones and their estimated transient craters are plotted against the gravity-scaled size π2 in Fig. 9. In theory, cratering efficiency is independent of projectile size in the strength regime under the assumption that the material strength is scale-independent. In this case, cratering efficiency only changes with impact velocity, leading to a horizontal line in the π2 diagram. The transient craters of MEMIN experiments performed at ~5 km/s show this behavior, while the final craters of the experiments increase in cratering efficiency for larger projectile sizes, indicating an increase in spallation.

Gault (1973) observed that at energies above 0.1-1 GJ for explosion tests in brittle rocks, large spall plates are held back by gravity and are no longer ejected from the crater. For impact experiments with steel projectiles at 5 km/s, these energies would be achieved using 12-28 cm diameter projectiles (Fig. 9). We have marked this transition in Fig. 9 and expect that above this transition cratering efficiency should gradually be reduced to that of the transient craters. It should be stressed that this is only a qualitative suggestion of how cratering efficiency may decrease when large-scale spallation is halted by gravity.

The two solid curves in Fig. 9 show a transition from the strength regime to the gravity regime for increasing projectile sizes at impact velocities of 5 and 10 km/s. These curves were calculated using the formula given in Holsapple (1993), where

πV = K1 [π2 + (K2 π3)(2 + µ)/2]-3µ/(2 + µ) (12)

Values for “hard rock” are suggested by Holsapple (1993), where K1 = 0.095 and µ = 0.55. K2 = 67 was used to fit the 5 km/s curve to the transient craters. These values are arbitrarily chosen. While Fig. 9 most likely does not precisely reflect the sandstone’s transition from the strength regime to the gravity regime, it does give a basic idea of how the experiments could be extrapolated to planetary scales. In this scenario, the Earth’s gravity would begin to affect the cratering efficiency for steel projectiles larger than ~10 m (for both 5 and 10 km/s impacts). Compare also Fig. 7 in Schmidt (1980), where explosive craters in granite and sandstone show a similar size-dependent strength behavior but have a transition into the gravity regime at larger π2 values.

Finally, to put the MEMIN experiments into a planetary perspective, our data have been plotted in a volume-energy diagram expanded to crater volumes and energies relevant for terrestrial cratering (Fig. 10). Explosion craters are added that are compiled in Holsapple and Housen (2004). The explosion craters chosen were formed in rock described as “sandstone, siltstone”, and only those were selected that had a scaled burial depth (i.e. the ratio of burial depth of an explosive charge to the radius of the explosive charge) between 0 and 2 to roughly approximate impact point sources (Holsapple 1980). These explosion experiments are listed in Holsapple and Housen (2004) as part of the Air Force Weapons Lab, Mixed Company and Middel Course series. Barringer crater and the newly discovered Egyptian Kamil crater (Folco et al. 2011) were added as two larger impacts into sandstone targets (Coconino sandstone and Gilf Kebir Fm.). Kamil crater may still be strongly influenced by strength as a crater with 45 m diameter. The impact energy and volume are estimated at ~50 GJ and ~3800 m³, based on Folco et al. (2011) and Folco (pers. comm.). At its size, Barringer crater is well within the gravity regime, where strength scaling should have little influence. Barringer crater’s assumed energy and volume range are 0.5-40 MtTNT (Kring 2007) and 0.075-0.1 km³ (Roddy et al. 1977).

CONCLUSIONS

MEMIN’s experimental campaigns have resulted in a new data set of impact craters formed in dry and water-saturated sandstones. The application of pi-group scaling methods shows the effects of several physical parameters:

1) Porosity, when observed as an isolated material property independent of strength, reduces crater volumes in the strength regime. Based on the range of data observed here, an increase in porosity exponentially decreases crater volume (for constant strengths).

2) Pore space saturation effectively counteracts the effects of the sandstone’s porosity on crater volume reduction. When strength effects are taken into account, sandstone targets saturated with water to 90% show approximately the same scaled volumes as non-porous rocks.

3) The size of the projectile influences crater volumes and cratering efficiency of brittle materials in the strength regime. Larger projectiles produce longer shock pulses that increase the amount of spalled crater material. Thus, when impacts at the same velocity are compared, cratering efficiency increases with increasing projectile diameter. When only the transient craters of these experiments are observed, the cratering efficiency remains approximately constant. These spallation effects are expected to influence the volumes of small impacts up to a few meters in diameter, above which gravity should begin to retain larger spall plates.

Acknowledgements

We are first and foremost grateful for the DFG for funding the MEMIN research unit. The quality of this paper was greatly improved by helpful and very detailed reviews of Olivier Barnouin, Alex Deutsch and an anonymous “scaling expert”. Many thanks go to the committed and professional light gas gun technicians at the EMI, and special thanks go to Dieter Müller for the construction of the ejecta container. We appreciate the assistance of ALU student assistants Anthony Ueno, Lukas Knoll, Timm Reisinger, Leonie Hirmke and Michael Rudolph and EMI student assistants Tobias Kunz, Martin Lange, Dominic Heunoske and Hannes Krietsch during and after the campaigns. Thanks also go to Herbert Ickler for rock preparation, Florian Müller for handling the Vaseline, and Ghislain Trullenque for UCS measurements. Jay Piatek and Jana Berlin were kind enough to supply us with initial Campo del Cielo samples. Finally, we appreciate all the input and discussions with all of the MEMIN researchers and numerous other colleagues that have helped to deepen our understanding of the processes and results we have observed in these experiments. The research unit is DFG FOR 887, and these are projects KE 732/17-1 and KE 732/16-1.

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Fig. 1: Simplified schematic overview of a two-stage light gas gun (top) and the experimental setup (bottom), viewed from above. Not to scale.

Fig. 2: Experimental impact craters in sandstone targets. a) A 10.5 cm diameter crater (experiment A15-5185) formed in a 20 cm edge-length target. b) A 6.4 cm diameter crater produced in experiment A3-5124. c) An 18.5 cm crater formed in a cube-shaped, 50 cm edge-length target (experiment D5-3300). A concentric fracture to the right of the crater (arrows) marks an incipient spall plate. d) The experimental setup (E3-3383) at the XLLGG, showing the ejecta catchers on the left and a 34 cm crater on the right. The target surface and catchers are encased in a plywood box with Plexiglas side panels. Ultrasound sensors are attached to the target, and large spall plates are on the floor of the catcher assembly.

Fig. 3: The average crater diameter D, calculated from 18 individual profile measurements for each crater, plotted against the minimum and maximum diameter value in %.

Fig. 4: A comparison of MEMIN depth-diameter (d/D) values with values from the literature, plotted against the ratio of projectile to target density (ρp/ρt). Data from Smrekar et al. (1986) and Burchell & Whitehorn (2003) are plotted as mean values with 1σ error bars. Increased projectile density leads to higher d/D ratios (dashed lines), while increasing pore space saturation reduces d/D ratios. Differences between d/D ratios in varying studies can partly be attributed to impact velocity effects, and most likely also reflect different spallation behavior of the impacted materials. MEMIN experiments using aluminum projectiles are plotted on the left at lower ρp/ρt values, steel and iron meteorite projectiles are on the right. Large circles depict experiments with 10-12 mm projectiles, small circles show experiments performed with 2.5 mm projectiles.

Fig. 5: Crater volumes of MEMIN impacts experiments into dry and water saturated sandstone plotted against the kinetic energy of the projectile. Increasing projectile mass, projectile velocity or target saturation leads to larger crater volumes, while impacts with aluminum projectiles form smaller craters than with higher-density steel or iron meteorite projectiles. SLGG shots using smaller projectiles are on the left-hand side of the diagram. Error bars are smaller than the plotted symbol size.

Fig. 6: Strength scaling of MEMIN craters in sandstones compared with craters in non-porous basalts from Moore et al. (1963). The cratering efficiency πV of MEMIN sandstones is reduced relative to the average trend of basalts (dashed line). This is interpreted as an effect of porosity. πV is increased for water saturated targets, and 90% water-saturated targets slightly exceed the basalt trend. The solid line is a fit to MEMIN dry XLLGG data. Large circles depict experiments with 10-12 mm projectiles, small circles show experiments performed with 2.5 mm projectiles.

Fig. 7: The reduction of crater volume in porous materials relative to the volume calculated for non-porous materials of the same strength in equation (11) is plotted against the material’s pore space. a) Dry MEMIN sandstones have down to 20% of the size expected for non-porous rocks with identical strength, while pore space saturation counteracts volume reduction by reducing porosity. Experiments with 10-12 mm projectiles (large circles) yielded larger crater volumes than experiments with 2.5 mm projectiles (small circles), most likely due to the influence of projectile size on spallation. The dashed line shows the average crater volume expected for non-porous targets. b) Sintered glass beads with 30 to 60% porosity show an even stronger crater volume reduction down to between 1 and 10% of the size expected for non-porous rocks with the same strength. A regression of the data suggests that porosity has an exponential influence on crater volume. Note the logarithmic y-axis in b).

Fig. 8: A comparison of measured final crater volumes of MEMIN experiments in dry sandstone targets and transient crater volumes from Dufresne et al. (2012) representing crater volumes without spall material. Craters formed by 10-12 mm projectiles on the right of the plot show a larger difference between final and transient crater volumes than craters formed by 2.5 mm projectiles on the left, indicating an increase in spallation volume with projectile size. The inset shows a digital profile of experiment D4-3299 with a parabola fitted to approximate the transient crater.

Fig. 9: Cratering efficiency of impacts into MEMIN sandstones in the strength regime and gravity regime. MEMIN craters formed at ~5 km/s (filled circles) show an increase in cratering efficiency with increasing size due to enhanced spallation, while their estimated transient craters (open circles) remain constant in the strength regime. The gravity-controlled cutoff for the ejection of large spall plates (dashed line) is based on observations of spall behavior in explosion craters by Gault (1973). We assume that beyond this point cratering efficiency should be gradually reduced to “transient crater sizes” (possibly following the dotted blue line). Solid lines are calculated from equation (7) using “hard rock” material constants suggested in Holsapple (1993), and show a possible transition from the strength regime to the gravity regime for impacts on Earth at 5 and 10 km/s. Crosses show the size of iron projectiles at 5 km/s.

Fig. 10: Comparison of MEMIN crater volumes with explosion craters, Kamil Crater, Egypt, and Barringer crater, Arizona. Shallow depth of burial explosion craters were formed in sandstone and siltstone targets; Kamil and Barringer were formed in sandstones. Crater diameters are displayed next to selected data points.

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Table 1: Sandstone target material properties

dry Seeberger Sandstein1 50% sat.2 Seeberger 90% sat.2 Seeberger

Density [g/cm³] 2.05 ± 0.04 2.17 ± 0.04 2.26 ± 0.04

Unsaturated pore space [%] 23.1 ± 0.5 11.5 ± 0.3 2.3 ± 0.1

Uniaxial compressive strength (UCS) [MPa] 67.3 ± 2.7 55.8 ± 1.5 58.4 ± 0.8

Tensile strength3 [MPa] 4.1 ± 0.7 3.4 ± 0.5 4.3 ± 0.4

1sandstone quarried from "layer 3" (TRACO company)

2"sat." refers to saturation level of sandstone with tap water

3tensile strength from Brazil tests measured perpendicular to layering

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Table 2: Experimental impact parameters

Experiment Facility Target dimensions [cm]

Water saturation

Chamber pressure [mbar]

Projectile Material L [mm] m [g] vi [km/s] E [J] P [GPa]

P1-2808 XLLGG 100x100x50 - ~500 AlSl 4130 Steel 10 4.10 5.3 58413 70

P2-2809 XLLGG 100x100x50 44% ~500 AlSl 4130 Steel 10 4.10 5.3 56913 -

D2-3296 XLLGG 50x50x50 - ~300 D290-1 Steel 10 4.10 4.4 39688 52

D3-3298 XLLGG 50x50x50 - 305 Iron Meteorite 10 4.12 4.6 42627 55

D4-3299 XLLGG 50x50x50 - 340 Iron Meteorite 10 4.14 3.5 25113 37

D5-3300 XLLGG 50x50x50 - 390 Iron Meteorite 10 4.12 2.5 12813 22

E1-3382 XLLGG 80x80x50 - 280 D290-1 Steel 12 7.31 4.6 76032 55

E2-3383 XLLGG 80x80x50 50% 310 D290-1 Steel 12 7.32 4.6 76805 -

E3-3384 XLLGG 80x80x50 50% 292 Iron Meteorite 12 7.09 4.6 74655 -

A3-5124 SLGG 20x20x20 - 5 D290-1 Steel 2.5 0.0670 5.0 838 63

A5-5125 SLGG 20x20x20 - 100 D290-1 Steel 2.5 0.0672 5.1 874 65

A6-5126 SLGG 20x20x20 - 100 D290-1 Steel 2.5 0.0671 4.8 773 59

A8-5128 SLGG 20x20x20 - 100 D290-1 Steel 2.5 0.0672 5.1 874 65

A11-5181 SLGG 20x20x20 90% 100 D290-1 Steel 2.5 0.0670 5.3 941 -

A12-5183 SLGG 20x20x20 90% 60 D290-1 Steel 2.5 0.0676 5.3 932 -

A13-5182 SLGG 20x20x20 50% 100 D290-1 Steel 2.5 0.0667 5.3 919 -

A15-5185 SLGG 20x20x20 - 1 55X G28J1 Alu 5.0 0.1792 7.0 4353 70

A16-5186 SLGG 20x20x20 - 1 55X G28J1 Alu 2.5 0.0224 7.8 673 83

L: projectile diameter m: projectile mass; vi: projectile velocity; E: kinetic energy; P: peak impact

pressure estimates calculated for planar impact approximation using parameters for Coconino

sandstone, steel and Al coefficients; XLLGG: extra large light gas gun; SLGG space light gas gun; iron

meteorite is from Campo del Cielo samples; experiments P1-2808 and P2-2809 are from Kenkmann

et al. (2011)

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Table 3: Experimental crater dimensions

Experiment Facility Water saturation vi [km/s] E [J] d [cm] D [cm] d/D ρp/ρt V [cm³] Vρt / m

P1-2808 XLLGG - 5.3 58413 5.60 24.3 0.23 3.44 715.4 396.09

P2-2809 XLLGG 44% 5.3 56913 4.50 28.7 0.16 3.32 1098.7 629.74

D2-3296 XLLGG - 4.4 39688 5.15 24.2 0.21 3.92 629.2 306.92

D3-3298 XLLGG - 4.6 42835 5.50 24.1 0.23 3.93 612.1 297.11

D4-3299 XLLGG - 3.5 25358 4.40 18.4 0.24 3.95 309.3 149.43

D5-3300 XLLGG - 2.5 12875 3.73 18.5 0.20 3.93 242.9 117.92

E1-3382 XLLGG - 4.6 76032 6.80 36.6 0.19 4.23 1574.3 411.19

E2-3383 XLLGG 50% 4.6 76805 5.96 33.8 0.18 3.97 1297.6 361.47

E3-3384 XLLGG 50% 4.6 74655 5.10 40.0 0.13 3.84 1828.9 526.46

A3-5124 SLGG - 5.0 838 1.15 6.4 0.18 4.06 8.3 248.75

A5-5125 SLGG - 5.1 873 1.17 6.2 0.19 4.06 8.8 262.38

A6-5126 SLGG - 4.8 773 1.10 5.8 0.19 4.06 7.6 227.45

A8-5128 SLGG - 5.1 874 0.95 5.1 0.19 4.06 6.3 188.90

A11-5181 SLGG 90% 5.3 941 1.43 10.2 0.14 3.78 31.1 997.99

A12-5183 SLGG 90% 5.3 932 1.80 9.4 0.19 3.78 34.2 1088.10

A13-5182 SLGG 50% 5.3 919 1.40 7.5 0.19 3.98 13.4 409.84

A15-5185 SLGG - 7.0 4353 1.43 10.5 0.14 1.37 42.9 479.17

A16-5186 SLGG - 7.8 673 0.64 3.9 0.16 1.37 2.6 236.34

vi: projectile velocity; E: kinetic energy; d: crater depth; D: crater diameter; ρp: projectile density; ρt:

target density; V: crater volume; m: projectile mass; XLLGG: extra large light gas gun; SLGG space

light gas gun; experiments P1-2808 and P2-2809 are from Kenkmann et al. 2011

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Table 4: Transient crater volumes from Dufresne et al. (submitted)

Experiment Facility V [cm³] Vtc [cm³] Vtc error [cm³]

P1-2808 XLLGG 715 229 11.8

D2-3296 XLLGG 629 269 11.2

D3-3298 XLLGG 612 209 31.9

D4-3299 XLLGG 309 130 13.6

D5-3300 XLLGG 242 128 12.4

E1-3382 XLLGG 1574 248 48.9

A3-5124 SLGG 8.3 4.4 0.19

A5-5125 SLGG 8.8 4.8 0.36

A6-5126 SLGG 7.6 3.4 0.41

A8-5128 SLGG 6.3 4.7 0.19

V: volume of the final crater

Vtc: volume of the transient crater (without spall)

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Powder chamber

Pump tube Launch tube Blast tank Target chamber

Piston Sabot

Hydrogen gas

Sabot

LaserLaser

Projectile

Flash Camera

Sandstonetarget

Ultrasound sensorsEjectacatcher

Ejectacatcher

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a) b)

c)

d)

1 cm

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‐10

0

10

20

30

Δ D [%

]

Dry sandstone Dry sandstone, Al projectile 50% sat. sandstone 90% sat. sandstone

‐30

‐20

0 5 10 15 20 25 30 35 40 45

Mean crater diameter [cm]

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0,2

0,3

epth‐Diameter ra

tio

MEMIN dry sandstone

MEMIN 50% sat. sandstone

MEMIN 90% sat. sandstone

Granite (Burchell and Whitehorn 2003)

Diorite (Smrekar et al. 1986)Fe projectiles

0,11 2 3 4

d/D: D

e

ρp/ρt: Projectile density‐target density ratio

Al projectiles

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100

1000

10000

rater v

olum

e [cm³]

Dry sandstoneDry sandstone, Al proj.50% sat. sandstone90% sat. sandstone

2.5 mm projectiles

10‐12 mm projectiles

1

10

100 1000 10000 100000

V: Cr

E: Impact energy [J]

saturatio

n 5 mm projectile

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1000

10000

= V * ρ t/ m

Dry sandstoneDry sandstone, Al proj.50% sat. sandstone90% sat. sandstoneBasalt (Moore et al. 1963)

πV = 0.89±1.14(π3 * π40.13)‐0.95±0.07

10

100

1E‐04 1E‐03 1E‐02 1E‐01

π V

(Y / ρt vi²) * (ρp / ρt)(1‐3ν)(2/3µ)

πV = 1.21±2.68(π3 * π40.11)‐0.82±0.15

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1.6

1.8

2v o

lum

eMEMIN dry sandstoneMEMIN 50% sat. sandstoneMEMIN 90% sat. sandstoneBasalt (Moore et al. 1963)

a)

0,6

0.8

1

1.2

1.4

orm

alize

d cr

ater

vol

um

( )

0

0.2

0.4

0.6

0 5 10 15 20 25

V N: N

orm

al

φ: (unsaturated) pore space [%]

1

10

me

MEMIN dry sandstoneMEMIN 50% sat. sandstoneMEMIN 90% sat. sandstoneBasalt (Moore et al. 1963)

l ( l )

b)

0 5 10 15 20 25

φ: (unsaturated) pore space [%]

0.1

1

a lize

d cr

ater

vol

ume

MEMIN 90% sat. sandstoneBasalt (Moore et al. 1963)Sintered glass (Love et al. 1993)Sintered glass (Michikami et al. 2007)

0,001

0.01

V N: N

orm

alize

d

VN = 1.10±0.10 e-0.077±0.004φ

0.0010 10 20 30 40 50 60 70

V

φ: Pore space [%]

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1

10

100

1000

10000

100 1000 10000 100000

V: C

rate

r vol

ume

[cm

³]

E: Impact energy [J]

final craters with spall transient craters

-50

-25

0

-100 -50 0 50 100 mm

transientcrater

spallspall

For Peer Review Only

πV = 27168π20.226

1

10

100

1000

10000

1E‐12 1E‐10 1E‐08 1E‐06 1E‐04 1E‐02

π V: V

 * ρ

t/m

π : g*a / v ²

5 km/s

10 km/s

Strength regime

large‐scale spallstopped by gravity

0.1 mm 1 cm 1 m

100 m

10 km

11E‐12 1E‐10 1E‐08 1E‐06 1E‐04 1E‐02

π2: g*a / vi²

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1E+15MEMIN dry craters

MEMIN transient crater1.2 km

1E+12

m³]

y

MEMIN transient crater

Shallow depth of burial explosions

Barringer crater

Kamil crater

1.2 km

45

1E+09

r volum

e [cm³]

Kamil crater

15 m

45 m

1E+06

V: Crater v

olu

2 m

1E+03

V: C

30 cm

2 m

1E+001E+00 1E+03 1E+06 1E+09 1E+12 1E+15 1E+18

E: Energy [J]

6 cm

1E+00 1E+03 1E+06 1E+09 1E+12 1E+15 1E+18

E: Energy [J]

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