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Impact cratering and spall failure of gabbro
Abstract
Both hypervelocity impact and dynamic spall experiments were carried out on a series of well-indurated samples of gabbro to examine the relation between spall strength and maximum spall ejecta thickness. The impact experiments carried out with 0.04- to 0.2-g, 5- to 6-km/sec projectiles produced decimeter- to centimeter-sized craters and demonstrated crater efficiencies of 6 × 10−9 g/erg, an order of magnitude greater than in metal and some two to three times that of previous experiments on less strong igneous rocks. Most of the crater volume (some 60 to 80%) is due to spall failure. Distribution of cumulative fragment number, as a function of mass of fragments with masses greater than 0.1 g yield values of b = d(log Nf)/d log(m) −0.5 −0.6, where N is the cumulative number of fragments and m is the mass of fragments. These values are in agreement or slightly higher than those obtained for less strong rocks and indicate that a large fraction of the ejecta resides in a few large fragments. The large fragments are plate-like with mean values of B/A and C/A 0.8 0.2, respectively (A = long, B = termediate, and C = short fragment axes). The small equant-dimensioned fragments (with mass < 0.1 g and B ∼ 0.1 mm) represent material which has been subjected to shear failure. The dynamic tensile strenght of San Marcos gabbro was determined at strain rates of 104 to 105 sec−1 to be 147 ± 9 MPa. This is 3 to 10 times greater than inferred from quasi-static (strain rate 100 sec−1) loading experiments. Utilizing these parameters in a continuum fracture model predicts a tensile strenght of , where ε is strain rate. It is suggested that the high spall strenght of basic igneous rocks gives rise to enhanced cratering efficiencies due to spall in the <102-m crater diamter strength-dominated regime. Although the impact spall mechanism can enhance cratering efficiencies it is unclear that resulting spall fragments achieve sufficient velocities such that fragments of basic rocks can escape from the surfaces of planets such as the Moon or Mars.
... In Figure 12, the relation between the kinetic energy of the projectile and the volume of the final crater in logarithmic coordinates is given. As shown, both the experimental results of this article and the experimental results by Lange et al. [16] are in the same fitting curve. It indicates that the volume of the final crater exponentially increased with the increase of the kinetic energy of the projectile, and the power function of the fitting curve has an exponent of 1.2 (mathematical correlation coefficient R 2 � 0.96). ...
... (2) For 0 < β < 1, equation (16) can be rewritten as follows: ...
... Generally, equation (16) can be regarded as the energy-scale expression, which is described by dimensionless Π V and Π Y . And equation (20) can be regarded as the momentum-scale expression, which is described by dimensionless π V and π Y . ...
To investigate the cratering effects of hypervelocity rod projectile impacting on rocks, a two-stage light gas gun was used to carry out 10 groups of small-scale experiments, whose velocity ranges from 1.5 km/s to 4.1 km/s. After each experiment, the morphology and size of the hypervelocity impacting crater were accurately obtained by using a device for image scanning. According to the morphology of the final crater, the impact crater can be divided into crushing area, spallation area, and radial crack area. Based on the experimental results of steel projectile vertical impacting on granite targets, the relationship between the depth and the diameter of the crater is analyzed, i.e., h/D≈0.1∼0.2; it shows that the depth of the crater is much smaller than the diameter of the crater, and the crater seems to be a shallow dish. The relation between the kinetic energy of the projectile and the size of the crater was discussed. With the increase of the projectile kinetic energy, it is uncertain whether the depth of the crater increases, but the volume of the crater will increase. Lastly, dimensionless analysis of the impact crater was carried out. Specifically, the limitations of point source solutions to hypervelocity rod projectile impact cratering have been proved, and there is no essential difference to calculate the final crater by using the energy scale or the momentum scale.
... Controlled experiments, such as those simulating meteorite impacts, are one possibility. Meteorite impact simulations can target natural stone, and use destructive methods such as thin sectioning to study subsurface damage [18][19][20]. However, these studies typically use spherical, single composition projectiles and have impact velocities exceeding 1.5 kms −1 , whereas small arms projectiles are typically ogive-nosed, composed of multiple materials, and have velocities in the range of 0.5-1.0 ...
... Zones of pervasive fracturing and crushing are evidenced as impact breccia beneath natural craters [43] and as heavily com-minuted grains in experimental samples [19,20]. Further similarities to hypervelocity experiments are the bowl-shaped crater, the shallow surrounding spall zone, and the penetrative radial fractures [18,19,44]. Greater fracture intensity values closer to the crater centre, and direct observation of surface and subsurface fractures support observations of a decreasing degree of grain size reduction with distance from the impact by Buhl et al. [44]. ...
The shift of armed conflicts to more urbanised environments has increased the risk to cultural heritage sites. Small arms impacts are ubiquitous in these circumstances, yet the effects and mechanisms of damage caused are not well known. A sandstone target was shot under controlled conditions to investigate surface and subsurface damage. A 3D model of the damaged block, created by structure from motion photogrammetry, shows that internal fracturing was at least as extensive as the visible surface fractures. Backscatter electron imaging of the damaged surface shows a shift from intragranular fracturing and grain size reduction at < 5 mm from the impact point to primarily circumgranular fracturing and grain ‘plucking’ at 20 mm from the impact point. Internal fracture intensity decreased with distance from the centre of the crater. Volumes around the impact point are therefore at greater risk of subsequent weathering deterioration, but significant damage extends to the periphery of the target, rendering whole blocks vulnerable. The surface crater, despite being one of the most conspicuous aspects of conflict damage, has many times less area than internal and surface fractures.
... where ( ) is the cumulative mass of fragments with a radius (volume 1/3 ) less than , is the total mass of fragments, can be related to the mean size or the maximum particle size. coal, soils and meteoric material that had been broken in various ways (Bennett, 1936;Dohnanyi, 1969;Donnison and Sugden, 1984;Fujiwara et al., 1977;Hartmann, 1969;Hawkins, 1960;Hellyer, 1970;Lange et al., 1984;Leemis, 2017;Mathis, 1979;McCrosky, 1968;Schoutens, 1979). Turcotte calculated from all those test results and reported his calculation as shown in Table 2.8, where the fractal dimensions for all these 21 cases range from 1.44 to 3.54. ...
... The concept of the fractal has been proposed as a mean of quantifying scale invariant processes (Bennett, 1936;Dohnanyi, 1969;Donnison and Sugden, 1984;Fujiwara et al., 1977;Hartmann, 1969;Hawkins, 1960;Hellyer, 1970;Lange et al., 1984;Mandelbrot, 1967;Mathis, 1979;McCrosky, 1968;Schoutens, 1979;Turcotte, 1986). According to Equation 2.47, the fractal dimension can be calculated by comparing the number of fragments against its characteristic size on a log-log space. ...
... where ( ) is the cumulative mass of fragments with a radius (volume 1/3 ) less than , is the total mass of fragments, can be related to the mean size or the maximum particle size. coal, soils and meteoric material that had been broken in various ways (Bennett, 1936;Dohnanyi, 1969;Donnison and Sugden, 1984;Fujiwara et al., 1977;Hartmann, 1969;Hawkins, 1960;Hellyer, 1970;Lange et al., 1984;Leemis, 2017;Mathis, 1979;McCrosky, 1968;Schoutens, 1979). Turcotte calculated from all those test results and reported his calculation as shown in Table 2.8, where the fractal dimensions for all these 21 cases range from 1.44 to 3.54. ...
... The concept of the fractal has been proposed as a mean of quantifying scale invariant processes (Bennett, 1936;Dohnanyi, 1969;Donnison and Sugden, 1984;Fujiwara et al., 1977;Hartmann, 1969;Hawkins, 1960;Hellyer, 1970;Lange et al., 1984;Mandelbrot, 1967;Mathis, 1979;McCrosky, 1968;Schoutens, 1979;Turcotte, 1986). According to Equation 2.47, the fractal dimension can be calculated by comparing the number of fragments against its characteristic size on a log-log space. ...
... These two target materials were chosen because roughly one-third of the Earth's known impact craters formed in sedimentary targets of which many contain carbonates as an important sedimentary rock and another third formed in mixed crystalline and sedimentary targets (Earth Impact Database 2017). A number of experiments into nonporous rocks like granite (H€ orz 1969;Burchell and Whitehorn 2003), basalt, and gabbro (Gault and Heitowit 1963;Moore et al. 1963;Lange et al. 1984) have been investigated, but only a few cratering experiments have been conducted in carbonates (Schneider and Wagner 1976;Lindgren et al. 2011;Kurosawa et al. 2012). The crater subsurfaces of these experiments have only been analyzed macroscopically, without correlating them with stress stages induced by the shock wave. ...
... Several authors who conducted impact experiments on different nonporous target materials such as granite, basalt, gabbro, and nephrite discriminated deformation zones in the target beneath the crater (Moore and Gault 1962;Moore et al. 1963;H€ orz 1969;Lange et al. 1984;Polanskey and Ahrens 1990). According to these authors, the uppermost part of the crater's subsurface is a very shallow zone of crushed rock, which is characterized by pulverization of grains and microfractures. ...
Two impact cratering experiments on nonporous rock targets were carried out to determine the influence of target composition on the structural mechanisms of subsurface deformation. Projectiles of 2.5 mm diameter were accelerated to ~5 km s−1 and impacted onto blocks of marble or quartzite. Subsurface deformation was mapped and analyzed on the microscale using thin sections of the bisected craters. Additionally, both experiments were modeled and the calculated strain zones underneath the craters were compared to experimental deformation features. Microanalysis shows that the formation of radial, tensile, and intragranular cracks is a common response of both nonporous materials to impact cratering. In the quartzite target, the subsurface damage is additionally characterized by highly localized deformation along shear bands with intense grain comminution, surrounded by damage zones. In contrast, the marble target shows closely spaced calcite twinning and cleavage activation. Crater diameter and depth as well as the damage lens underneath the crater are unexpectedly smaller in the marble target compared to the quartzite target, which is in contradiction to the marble's much weaker compressive and tensile strengths. However, numerical models result in craters that are similar in size as well as in strain accumulation at the end of transient crater formation, indicating that current models should still be viewed cautiously when compared to experimental details.
... Фрагментация «габбро» при высокоскоростном ударе В [17] исследовалась фрагментация горной породы «габбро», выбрасываемой из области кратера, образующегося при ударе высокоскоростной сферической частицы из стали или свинца (диаметр сферы 3,2 мм, скорость удара 5,2 и 4,6 км/с соответственно). Результаты для крупных фрагментов (массой более 0,1 г), для которых масса измерялась, и для более мелких фрагментов (массой менее 0,1 г), для анализа которых использовался ситовый метод, а их число оценивалось в предположении сферичности, приведены на рис. ...
... Эти данные анализировались авторами в рамках степенного распределения [2,17]. Однако использование распределения Гилварри для описания статистической составляющей фрагментации (формулы (9) и (15)) уместно и в этом случае. ...
630090 Новосибирск, silver@hydro.nsc.ru Получено распределение по размеру числа фрагментов, возникающих при разрушении стальной частицы при ударе по нормали по тонкому экрану со скоростью 2,5 ÷ 7,3 км/с. Для уменьшения числа крупных фрагментов экрана в запреградном облаке осколков использованы высокопори-стые пластинки из мелкодисперсного порошка меди. При увеличении давления соударения от 30 до 160 ГПа происходит изменение характера фрагментации стального ударника: от нерегуляр-ной фрагментации вблизи порога разрушения частицы до более однородного разрушения при максимальной скорости удара. Основной результат эксперимента — при уменьшении размера фрагментов плотность распределения числа фрагментов увеличивается и не стремится к нулю. Выполнен анализ данных в рамках экспоненциальных распределений Грэди и Гилварри. Ключевые слова: высокоскоростной удар, фрагментация, стальная сфера. ВВЕДЕНИЕ Несмотря на то, что проблеме фрагмента-ции твердого тела при динамическом разруше-нии посвящено множество работ (см., напри-мер, библиографию в [1, 2]), однозначного ре-шения она не имеет. Нет единого мнения даже по виду функциональной зависимости распре-деления числа фрагментов по размеру. Исполь-зуются как степенной закон, так и различные экспоненциальные соотношения, связывающие число частиц с линейным размером фрагмента x или его массой m. Разрушение высокоскоростных частиц из металла при ударе по тонкому экрану описыва-ется линейным экспоненциальным распределе-нием [1, 3, 4]. Эта модель основана на простых статистических предположениях и, на первый взгляд, подтверждена данными, полученными при рентгенографировании запреградного об-лака осколков. Но при использовании этого экс-периментального метода информация о мелких фрагментах, которые могут существенно вли-ять на распределение числа фрагментов по раз-мерам, теряется, так как они просто не вид-ны на пленке. Метод пластины-свидетеля ис-пользован в [5] для исследования запреградно-го осколочного поля при ударе стальной сфери-ческой частицы по экранам из дюралюминия; Работа выполнена при поддержке Российского фонда фундаментальных исследований (номер про-екта 00-01-00794) и гранта Президента РФ (номер НШ-2073.2003.1).
... For the Tillotson EOS parameters as well as the shear and bulk moduli we adopt the values given in Benz & Asphaug (1999) as summarized in Table 1. Following the reasoning in Maindl et al. (2013) the Weibull distribution parameters of basalt were set to measured values of Nakamura et al. (2007) and for ice we use those mentioned in Lange et al. (1984), see Table 2. ...
... (1) Nakamura et al. (2007); (2) Lange et al. (1984). Table 3. ...
Context. We investigate the effects of including material strength in
multi-material planetesimal collisions. Aims. The differences between
strengthless material models and including the full elasto-plastic model for
solid bodies with brittle failure and fragmentation when treating collisions of
asteroid-sized bodies as they occur frequently in early planetary systems are
demonstrated. Methods. We study impacts of bodies of Ceres-mass with a solid
rock target and an impactor with 30 wt% water content. The initial impact
velocities and impact parameters are varied between the escape velocity
v_\mbox{esc} to about 6 v_\mbox{esc} and from head-on collisions to close
fly-bys, respectively. We simulate the collisions using our own SPH code using
both strengthless material and the full elasto-plastic material model including
brittle failure. Results. The qualitative analysis results in significant
differences depending on whether material strength is included or not. This may
be an effect of the relatively low-energy impacts that cannot destroy the solid
material instantly. One of the most prominent differences is the higher degree
of fragmentation and shattered debris clouds in the solid case. As opposed to
giant impacts we also observe some water ice to get transferred from the
impactor to the target.
... are affected by gravity, yielding the so-called modified final crater (e.g. Melosh 1962; Lange et al. 1984). Such experimental craters into brittle rocks are generally 48 characterized by a central depression formed during the excavation stage, and an outer 49 spallation zone, which is the result of brittle tensile fracturing and spall fragment ejection. ...
... These general features have been described for experiments into gabbro (Lange et al. 1984; 51 Polanskey and Ahrens 1990), basalt (Moore et al. 1962; Gault et al. 1966), granite (Hörz 52 1969), sandstone (Baldwin et al. 2007; Kenkmann et al. 2011), water ice (Lange and Ahrens 53 1987; Grey et al. 2001; Grey and Burchell 2003), CO 2 ice (Burchell et al. 1998), and artificial 54 materials such as sintered aggregated glass (Love et al. 1993). ...
Hypervelocity (2.5–7.8 km/s) impact experiments into sandstone were carried out to investigate the influence of projectile velocity and mass, target pore space saturation, target-projectile density contrast, and target layer orientation on crater size and shape. Crater size increases with increasing projectile velocity and mass as well as with increasing target pore space saturation. Craters in water-saturated porous targets are generally shallower and larger in volume and in diameter than craters from equivalent impacts into dry porous sandstone. Morphometric analyses of the resultant craters, 5–40 cm in diameter, reveal features that are characteristic of all of our experimental craters regardless of impact conditions (I) a large central depression within a fragile, light-colored central part, and (II) an outer spallation zone with areas of incipient spallation. Two different mechanical processes, grain fragmentation and intergranular tensile fracturing, are recorded within these crater morphologies. Zone (I) approximates the shape of the transient crater formed by material compression, displacement, comminution, and excavation flow, whereas (II) is the result of intergranular tensile fracturing and spallation. The transient crater dimensions are reconstructed by fitting quadric parabolas to crater profiles from digital elevation models. The dimensions of this transient and of the final crater show the same trends: both increase in volume with increasing impact energy, and with increasing water saturation of the target pore space. The relative size of the transient crater (in percent of the final crater volume) decreases with increasing projectile mass and velocity, signifying a greater contribution of spallation on the final crater size when projectile mass and velocity are increased.
... Cone cracks are considered to propagate stably, requiring quasi-static conditions [43][44][45][46]. However, impact induced fracturing is generally thought to be a dynamic process, leading to multiple flaws propagating unstably instead of a single, stable fracture [25,47,48]. Furthermore, the cone crack experiments use target materials with no porosity, contrasting with the relatively porous (11-20%) targets presented here. ...
The immovable nature of built heritage means that it is particularly vulnerable during times of armed conflict. Although impacts from small arms and shrapnel leave relatively inconspicuous impact scars, they elevate the risk of future stone deterioration. This study investigates the subsurface damage caused by bullet impacts, which is not apparent from surface inspection, in order to better understand the geometry and mechanics of this form of conflict damage to heritage. Controlled firearm experiments were conducted to simulate conflict damage to sandstone and limestone buildings. The bullet impacts created conical fractures or zones of increased fracture intensity below the impact, radial fractures, and spallation, in addition to a crater. Dynamic fracture distinguishes the formation of these features from quasi static cone crack experiments, while the lack of a shockwave differentiates these bullet impacts from hypervelocity experiments. Damage was created by momentum transfer from the bullet, so that differences in target properties had large effects on the nature of the damage. The crater in the limestone target was almost an order of magnitude deeper than the sandstone crater, and large open fractures formed in the limestone below the crater floor, compared with zones of increased fracture intensity in the sandstone target. Microstructural analysis of subsurface damage showed that fracture intensity decreased with increasing distance from the impact centre, suggesting that regions proximal to the impact are at increased risk of future deterioration. Conical subsurface fractures dipping away from the impact beneath multiple impact craters could link up, creating a continuous fracture network. By providing pathways for moisture and other weathering agents, fractures enlarge the region at increased risk of deterioration. Their lack of surface expression makes understanding their formation a vital part of future surveying and post conflict assessments.
... For both the simple cone-shaped crater and the more complex two-part structures, radial fractures centred on the impact crater, and crushed target material on the crater floor, resemble damage resulting from hypervelocity experiments 28,30,31 . In this study, relatively undeformed projectile material (steel tip of NATO projectile) is embedded in the floor of the crater, unlike most hypervelocity experiments in which the projectile is melted and/ or ejected 32,33 . ...
Bullet impacts are a ubiquitous form of damage to the built environment resulting from armed conflicts. Bullet impacts into stone buildings result in surficial cratering, fracturing, and changes to material properties, such as permeability and surface hardness. Controlled experiments into two different sedimentary stones were conducted to characterise surface damage and to investigate the relationship between the impact energy (a function of engagement distance) and crater volumes. Simplified geometries of crater volume using only depth and diameter measurements showed that the volume of a simple cone provides the best approximation (within 5%) to crater volume measured from photogrammetry models. This result suggests a quick and efficient method of estimating crater volumes during field assessments of damage. Impact energy has little consistent effect on crater volume over the engagement distances studied (100–400 m), but different target materials result in an order of magnitude variation in measured crater volumes. Bullet impacts in the experiments are similar in appearance to damage caused by hypervelocity experiments, but crater excavation is driven by momentum transfer to the target rather than a hemispherical shock wave. Therefore in contrast to predictions of impact scaling relationships for hypervelocity experiments, target material plays the dominant role in controlling damage, not projectile energy.
... Table 3.1 shows a compilation of published results on the three-dimensional D-values for rocks deformed under high and low strain-rate settings. High strain-rate experiments to simulate shock-induced fragmentation indicate correlation between D-value and strain-rate; the D-value increases with increasing impact energy (Lange et al., 1984;Buhl et al., 2013). Studies on natural rock fragmentation provide a broad range of D-values between 1.88 and 3.98 (Table 3.1). ...
Although the mechanics of continental, seismogenic strike-slip faults have been primarily studied around active faults near Earth’s surface, large earthquakes on these faults commonly extend to depths between 10 and 20 km. At the base of seismogenic strike-slip faults, interaction and feedback between coseismic brittle fracturing and post- and interseismic viscous flow affect transient and long-term changes in stress cycling, fluid and heat transport, fault strength, and associated strain localization and deformation mechanisms. A primary goal of my dissertation is to explore the deeper structures of damage zones near the base of the seismogenic zone and to better understand the influence of the damaged rocks on rupture dynamics, by examining microstructures of exhumed fault rocks. My study area, the Sandhill Corner shear zone that is the longest strand of the Paleozoic Norumbega fault system in Maine, USA, represents large-displacement, seismogenic strike-slip faults at frictional-to-viscous transition depths (corresponding to temperatures of ~400–500 °C). The shear zone contains mutually overprinting pseudotachylyte and mylonite, and juxtaposes quartzofeldspathic mylonites and mica-rich schists. I analyzed fractured and fragmented garnet grains using particle size distributions, microfracture patterns, and electron backscatter diffraction fabrics. Microstructural studies of fragmented garnets reveal asymmetric distribution of dynamic pulverization with a width of ~70 m in the Sandhill Corner shear zone, and these results imply that the same damage processes observed around active seismogenic strike-slip faults operate at the base of the seismogenic zone. Garnet microstructures formed during earthquake cycles at the frictional-viscous transition can also provide evidence for dynamic pulverization even though the particle size distribution is modified by quasi-static fragmentation during post- and interseismic shearing. Elastic and seismic properties of the quartzofeldspathic rock and the mica-rich schist are quantified using the Thermo-Elastic and Seismic Analysis (TESA) numerical toolbox. The results illustrate how elastic contrast across bimaterial faults separating two different anisotropic materials affects preferred rupture propagation and asymmetric damage distribution. Strong anisotropy occurs in fault zones where preferentially aligned phyllosilicate minerals are a major component of the modal mineralogy. My findings suggest that the orientation and proportion of preferentially aligned phyllosilicates, or other highly anisotropic minerals, should be considered when investigating fault ruptures in anisotropic rocks.
... We also implemented a damage model using the Weibull distribution of strain level ò given by n(ò) = kò m (Weibull 1939). We used the Weibull parameters (m, k) = (16, 10 61 m −3 ) for basalt (Nakamura et al. 2007) and (9.1, 10 46 m −3 ) for ice (Lange et al. 1984), respectively. Figure 2 shows the geometry of an impact. ...
Although it is accepted that perfect-merging is not a realistic outcome of collisions, some researchers state that perfect-merging simulations can still be considered as quantitatively reliable representations of the final stage of terrestrial planet formation. Citing the work of Kokubo & Genda, they argue that the differences between the final planets in simulations with perfect-merging and those where collisions are resolved accurately are small, and it is justified to use perfect-merging results as an acceptable approximation to realistic simulations. In this paper, we show that this argument does not stand. We demonstrate that when the mass lost during collisions is taken into account, the final masses of the planets will be so different from those obtained from perfect-merging that the latter cannot be used as an approximation. We carried out a large number of smooth particle hydrodynamics simulations of embryo–embryo collisions and determined the amount of the mass and water lost in each impact. We applied the results to collisions in a typical perfect-merging simulation and showed that even when the mass loss in each collision is as small as 10%, perfect-merging can, on average, overestimate the masses of the final planets by ∼35% and their water content by more than 18%. Our analysis demonstrates that, while perfect-merging simulations are still a powerful tool in proving concepts, they cannot be used to make predictions, draw quantitative conclusions (especially about the past history of a planetary system), or serve as a valid approximation to the simulations in which collisions are resolved accurately.
... Macro-abrasion in our experiments likely occurred by dissipative plastic deformation (i.e., brittle wear; Bitter, 1963), expressed in surfaceparallel tensile failure and spalling of platelets ( Fig. 2A; Fig. S2; Lange et al., 1984;Polanskey and Ahrens, 1990). We expect the earlier onset of gravel-sized fragments for the small impactors was due to higher energy density (focused impact energy into a smaller contact area; Fig. 2C), resulting in larger fractures developing. ...
River incision into bedrock drives landscape evolution and couples surface changes to climate and tectonics in uplands. Mechanistic bedrock erosion modeling has focused on plucking—the hydraulic removal of large loosened rock fragments—and on abrasion—the slower fracturing-driven removal of rock due to impacts of transported sediment—which produces sand- or silt-sized fragments at the mineral grain scale (i.e., wear). An abrasion subregime (macro-abrasion) has been hypothesized to exist under high impact energies typical of cobble or boulder transport in mountain rivers, in which larger bedrock fragments can be generated. We conducted dry impact abrasion experiments across a wide range of impact energies and found that gravel-sized fragments were generated when the impact energy divided by squared impactor diameter exceeded 1 kJ/m2. However, the total abraded volume followed the same kinetic-energy scaling regardless of fragment size, holding over 13 orders of magnitude in impact energy and supporting a general abrasion law. Application to natural bedrock rivers shows that many of them likely can generate large fragments, especially in steep mountain streams and during large floods, transporting boulders in excess of 0.6 m diameter. In this regime, even single impacts can cause changes in riverbed topography that may drive morphodynamic feedbacks.
... Los esfuerzos tensionales también se presentan cerca de la superficie del objetivo como resultado de la interacción de las ondas de rarefacción y de choque, dando lugar a la espalación del material del objetivo (Melosh, 1984). La espalación es un proceso que prevalece de modo particular en los experimentos de craterización dominados por resistencia y que puede conllevar el agrandamiento de los volúmenes i diámetros de los cráteres así originados (Lange, 1984). ...
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Sanchez, M.A. ; Gil, A. y Simón, J.L. (2017): Las rocas de falla del cabalgamiento de Daroca (sector central de la Cordillera Ibérica): Interpretación reológica y cinemática. Geogaceta, 61: 75-78. (http://www.sociedadgeologica.es/archivos/geogacetas/geo61/geo61_19p75_78.pdf)
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Gutierrez, F, Carbonela, D., Sevil, J., Moreno, D., Linares, R, Comas, X., Zarroca, M., Roqué,C., McCalpin, J.P. (2020): Neotectonics and late Holocene paleoseismic evidence in the Plio-Quaternary Daroca Half-graben, Iberian Chain, NE Spain. Implications for fault sorce characterization. Journal of Structural Geology, 131: 1-17 (https://doi.org/10.1016/j.jsg.2019.103933)
... Fractal distribution of fragments i.e. scale-invariant size distribution was recorded in many physical processes including breaking of sea ice (Rothrock and Thorndike, 1984), rock fragmentation in nuclear explosions (Schoutens, 1979), projectiles (Lange et al., 1984), and asteroids (Donnison and Sugden, 1984). Most of the geological processes are also self-similar in nature i.e. follow fractal distribution. ...
Formation of the fragments of the wall-rock during dyking is one of the important manifestations of instantaneous magmatic events. This process is well documented at shallower depths of Earth’s crust but not at deeper levels. In this paper the in situ xenoliths of host rock nepheline syenite within a micro-shonkinite dyke emplaced at mid-crustal depths is described and the fractal theory applied to evaluate origin of the xenoliths. The nepheline syenite xenoliths are angular to oval shaped and sub-millimetre to ~50 cm long. The xenoliths are matrix supported with clasts and matrix being in equal proportions. Partly detached wall-rock fragments indicate incipient xenolith formation, which suggested that the model fragmentation processes is solely due to dyke emplacement. Fractal analytical techniques including clast size distribution, boundary roughness fractal dimension and clast circularity was carried out. The fractal data suggests that hydraulic (tensile) fracturing is the main process of host rock brecciation. However, the clast size and shape are further affected by postfragmentation processes including shear and thermal fracturing, and chemical erosion. The study demonstrates that dyking in an isotropic medium produces fractal size distributions of host rock xenoliths; however, post-fragmentation processes modify original fractal size distributions.
... The SPH code includes self-gravity, and in addition to hydrodynamic objects it is also capable of modeling full solid-body physics, with a von Mises plasticity model (Benz and Asphaug 1994) and a brittle failure/fragmentation model introduced to SPH by Benz and Asphaug (1995). This model is based on a Weibull distribution of flaws, with parameters from Nakamura et al. (2007) for basalt and from Lange et al. (1984) for water ice. The von Mises yield criterion does not consider the pressure dependence of shear strength and is therefore not the ideal choice for geologic materials, where shear strength is in general a complex function of pressure, and to a lesser degree also of temperature, strain, and even strain rate. ...
Collisions between large, similar-sized bodies are believed to shape the final characteristics and composition of terrestrial planets. Their inventories of volatiles such as water are either delivered or at least significantly modified by such events. Besides the transition from accretion to erosion with increasing impact velocity, similar-sized collisions can also result in hit-and-run outcomes for sufficiently oblique impact angles and large enough projectile-to-target mass ratios. We study volatile transfer and loss focusing on hit-and-run encounters by means of smooth particle hydrodynamics simulations, including all main parameters: impact velocity, impact angle, mass ratio and also the total colliding mass. We find a broad range of overall water losses, up to 75% in the most energetic hit-and-run events, and confirm the much more severe consequences for the smaller body also for stripping of volatile layers. Transfer of water between projectile and target inventories is found to be mostly rather inefficient, and final water contents are dominated by pre-collision inventories reduced by impact losses, for similar pre-collision water mass fractions. Comparison with our numerical results shows that current collision outcome models are not accurate enough to reliably predict these composition changes in hit-and-run events. To also account for non-mechanical losses, we estimate the amount of collisionally vaporized water over a broad range of masses and find that these contributions are particularly important in collisions of
∼
Mars-sized bodies, with sufficiently high impact energies, but still relatively low gravity. Our results clearly indicate that the cumulative effect of several (hit-and-run) collisions can efficiently strip protoplanets of their volatile layers, especially the smaller body, as it might be common, e.g., for Earth-mass planets in systems with Super-Earths. An accurate model for stripping of volatiles that can be included in future planet formation simulations has to account for the peculiarities of hit-and-run events and track compositional changes in both large post-collision fragments.
... When simulating collisions, we implement our damage model using Weibull parameters m and k. For basalt, we use m = 16 and k = 10 61 (m −3 ) (Nakamura et al. 2007) and for water-ice, we use m = 9.1 and k = 10 46 (m −3 ) (Lange et al. 1984). ...
It has been suggested that the comet-like activity of Main Belt Comets are due to the sublimation of sub-surface water-ice that has been exposed as a result of their surfaces being impacted by m-sized bodies. We have examined the viability of this scenario by simulating impacts between m-sized and km-sized objects using a smooth particle hydrodynamics approach. Simulations have been carried out for different values of the impact velocity and impact angle as well as different target material and water-mass fraction. Results indicate that for the range of impact velocities corresponding to those in the asteroid belt, the depth of an impact crater is slightly larger than 10 m suggesting that if the activation of MBCs is due to the sublimation of sub-surface water-ice, this ice has to exist no deeper than a few meters from the surface. Results also show that ice-exposure occurs in the bottom and on the interior surface of impact craters as well as the surface of the target where some of the ejected icy inclusions are re-accreted. While our results demonstrate that the impact scenario is indeed a viable mechanism to expose ice and trigger the activity of MBCs, they also indicate that the activity of the current MBCs is likely due to ice sublimation from multiple impact sites and/or the water contents of these objects (and other asteroids in the outer asteroid belt) is larger than the 5% that is traditionally considered in models of terrestrial planet formation providing more ice for sublimation. We present details of our simulations and discuss their results and implications.
... sect. 3.2) is implemented with Weibull parameters, which were measured for basalt by Nakamura et al. (2007), and for water ice we adopt values mentioned in Lange et al. (1984); see table 2. ...
Modern graphics processing units (GPUs) lead to a major increase in the performance of the computation of astrophysical simulations. Owing to the different nature of GPU architecture compared to traditional central processing units (CPUs) such as x86 architecture, existing numerical codes cannot be easily migrated to run on GPU. Here, we present a new implementation of the numerical method smooth particle hydrodynamics (SPH) using CUDA and the first astrophysical application of the new code: the collision between Ceres-sized objects. The new code allows for a tremendous increase in speed of astrophysical simulations with SPH and self-gravity at low costs for new hardware. We have implemented the SPH equations to model gas, liquids and elastic, and plastic solid bodies and added a fragmentation model for brittle materials. Self-gravity may be optionally included in the simulations and is treated by the use of a Barnes-Hut tree. We find an impressive performance gain using NVIDIA consumer devices compared to our existing OpenMP code. The new code is freely available to the community upon request.
... Mapping of deeply eroded impact structures on Earth (e.g., Sudbury, Ames at al., 2005; Riller, 2005; Upheavel Dome, Utah; Kenkmann, 2003) and Mars (Head and Mustard, 2006), and drilling of some others (Ries, Ernston and Pohl, 1974; Puchezh-Katunki, Pevzner et al., 1999) have confirmed intensive fracturing of target rocks. Explosive (Zenchenko and Tsvetkov, 1999) and high impact velocity experiments (Lange et al., 1984; Polanskey and Ahrens, 1990; Xia and Ahrens, 2001) have also revealed substantial target fracturing. With these experiments, three different regions of fragmentation near the crater were specified: 1) fractures immediately below the crater extend outward for at least 10 projectile diameters and are characterized by highdensity but small " shear " fractures; 2) a thin band of fractures initiated at the crater wall and arcing down into the target; and 3) " near surface " fractures that are radial in nature and both extend farther from the crater than the radial ones beneath the crater floor and are substantially wider. ...
Impact modeling and post-impact cooling studies predict a unique fracture and post-impact temperature distribution within the crater floor of large meteorite impact structures. The integration of numerical modeling results and their application to the observed geophysical and current topographic data provides new insights into the early evolution of the deeply eroded Sudbury Structure. The modeling shows a maximum depth of melting of 30-40 km (depending on impact angle and impact velocity). However, melt from upper target layers (< 10 km) is mainly ejected during the excavation stage of crater formation, and the remaining melt is strongly biased to melt derived from lower crustal material. Two-dimensional thermal evolution modeling with various granophyre/norite thickness ratios shows that irrespective of the granophyre/norite thickness ratio, the hottest part of the Sudbury Igneous Complex (SIC) was near the crater center at the melt-pool bottom and within the crater floor, which supports precipitation of sulfides toward the crater floor. The 2D cooling models give compelling evidence for longevity of melt at the bottom of the SIC and partial remelting of the crater floor. The numerical model results are compared with observed topographic, seismic and magnetic data and provide important constraints on their interpretation. A unique slow cooling history is manifested in the broad magnetic signature of the SIC and the adjacent crater floor, and its pronounced remanent magnetization. The vast damage zone and the complex fracture pattern predicted for the crater floor is well preserved in the new high-resolution topographic data for the Sudbury Structure. These regional topographic data allow the distinction between inside-basin fabric (radial topographic lineaments) and crater-floor topographic fabric (radial and contact parallel lineaments), which corroborates the numerical modeling results of radial and concentric faults propagating up to tens of kilometers from the crater center.
... We use Weibull flaw distribution parameters of basalt based on directly measured data by Nakamura et al. [39] and for ice we adopt the values mentioned in Lange et al. [40]: m basalt = 16, k basalt = 10 61 m −3 , m ice = 9.1, k ice = 10 46 m −3 . ...
As part of a national scientific network 'Pathways to Habitability' the
formation of planets and the delivery of water onto these planets is a key
question as water is essential for the development of life. In the first part
of the paper we summarize the state of the art of planet formation - which is
still under debate in the astronomical community - before we show our results
on this topic. The outcome of our numerical simulations depends a lot on the
choice of the initial distribution of planetesimals and planetary embryos after
gas disappeared in the protoplanetary disk. We also take into account that some
of these planetesimals of sizes in the order of the mass of the Moon already
contained water; the quantity depends on the distance from the Sun - close-by
bodies are dry, but starting from a distance of about 2 AU they can contain
substantial amounts of water. We assume that the gas giants and terrestrial
planets are already formed when we check the collisions of the small bodies
containing water (in the order of a few percent) with the terrestrial planets.
We thus are able to give an estimate of the respective contribution to the
actual water content (of some Earth-oceans) in the mantle, in the crust and on
the surface of Earth. In the second part we discuss in more detail how the
formation of larger bodies after a collision may happen as the outcome depends
on parameters like collision velocity, impact angle, and the materials
involved. We present results obtained by SPH (Smooth Particle Hydrodynamics)
simulations. We briefly describe this method and show different scenarios with
respect to the formed bodies, possible fragmentation and the water content
before and after the collision. In an appendix we discuss detection methods for
extrasolar planets (close to 2000 such objects have been discovered so far).
... Tensile stresses also occur near the target surface as the result of interaction of the shock and rarefaction wave, leading to the spallation of target material (Melosh 1984). Spallation is a particularly dominant process in strength-dominated cratering experiments and can greatly enhance crater volumes and diameters (e.g., Lange et al. 1984). It is therefore important for the evaluation of cratering experiments to be able to discern between spallation processes on the one hand, and fragmentation and excavation processes of the transient crater on the other hand. ...
Impact cratering experiments were performed on quartzite, tuff, and dry and water-saturated sandstones in the framework of the MEMIN research unit. 2.5–12 mm diameter projectiles were accelerated to ∼5 km/s. Evaluation of the resulting craters shows that crater volumes and crater efficiencies of large-scale experiments are greater than predicted by strength scaling laws. A method to approximate the transient crater volume shows that this effect is largely due to an increase in spallation. Strength scaling laws are used to determine the reduction of tensile strength in large-scale experiments and show a decrease by a factor of 1.8–3.6. This strength reduction can be correlated with a decrease in strain rate for larger projectiles, and with the Weibull theory of strength reduction for larger rock sample sizes. Further variations in spallation are observed between different target materials; a decrease in spall is suggested to be controlled by increased porosity.
... Impacts of pressure higher than 1 MPa have significant energy to widen the existing cracks. In such cases crack propagating mechanisms have been identified as spall and compression induced tensile microcracks that nucleate at preexisting flaws (Lange et al., 1984). Repeated shock loading can produce the effect of cyclic loading and reduce the overall compressive strength of material which makes comminution much easier. ...
Milling is an energy intensive process and it is considered as one of the most energy inefficient processes. Electrical and mechanical shock loading can be used to develop a pre-treatment methodology to enhance energy efficiency of comminution and liberation of minerals. Coal and Banded Hematite Jasper (BHJ) Iron ores samples were taken for the study to know the effect of shock loading. These samples were exposed to 5 electric shocks of 300 kV using an electric shock loading device. A diaphragmless shock tube was used to produce 3 and 6 compressed air shocks of Mach number 2.12 to treat the coal and Iron ore samples. Microscopic, comminution and liberation studies were carried out to compare the effectiveness of these approaches. It was found that electric shock loading can comminute the coal samples more effectively and increases the yield of carbon by 40% at 1.6 gm/cc density over the untreated coal samples. Mechanical shock loading showed improved milling performance for both the materials and 12.90% and 8.1% reduction in the D80 of the particles was observed during grinding for treated samples of coal and iron, respectively. Liberation of minerals in BHJ Iron ore was found unaffected due to low intensity of the mechanical shock waves and non conductivity of minerals. Compressed air based shock loading is easier to operate than electrical shock loading and it needs to be explored further to improve the energy efficacy of comminution.
... Specifically, the higher values fall into the wide range of values given for rock fragmentation (AN and SAMMIS 1994;BLENKINSOP 1991;CHESTER et al. 2005;STORTI et al. 2003). Impact experiments show an increase of D-values with increasing impact energy (LANGE et al. 1984), and cratering and shock-recovery experiments suggest a correlation with strain rate (BUHL et al. 2013). Studies on natural impacts provide D-values within 1.2-1.8 ...
Shock-induced fragmentation structures of basement rocks and their limestone cover in and around the Ries
impact crater (Germany) were recorded on outcrop, hand sample, and thin-section scale, and quantified mainly by fractal geometry methods. Quantification was performed by automated procedures and in areas of squarecentimetres to square-decametres with a maximum resolution of micrometre scale. In 2D and on all scales, the fragmentation structures form complex, statistically self-similar patterns (fractals) with specific
characteristics: (i) The pattern fractality is scale-dependent. (ii) Three different power-law relationships exist,
which reflect the effect of three fragmentation processes. (iii) The fracture patterns are anisotropic and
inhomogeneous over larger areas. (iv) Complexity and anisotropy of the fracture patterns vary systematically.
Such systematic variation appears typical for impact-related fragmentation.
... The particle size distribution (PSD) of ejecta fragments provides information on the formation of secondary impact craters, the size distribution of space debris, the energy partitioning during an impact and the amount of fine ejecta from large terrestrial impacts that may influence Earth's post-impact climate. Particle size distributions of ejected material were analyzed for impact cratering experiments into various geologic materials like sandstone , granite (Hörz, 1969), water-ice (Cintala et al., 1985;Arakawa, 1999;Miljković et al., 2011), silicate-ice mixture (Koschny and Grün, 2001), basalt Fujiwara et al., 1977;Takagi et al., 1984;Asada, 1985;Nakamura and Fujiwara, 1991;Durda and Flynn, 1999), gabbro (Lange et al., 1984;Cintala and Hörz, 1984), dunite (Takasawa et al., 2011) andgypsum (Miljković et al., 2011). For particle size distributions in the literature several different representations were used, such as: the fragment mass/cumulative number (e.g., Durda and Flynn, 1999), the particle size/ cumulative mass fraction (e.g., Cintala and Hörz, 1984), the particle size/cumulative number (e.g., Asada, 1985), and several more. ...
The particle size distribution (PSD) of impact crater ejecta is an important parameter that is useful for understanding the formation of natural craters, the distribution of space debris, the influence of impact events on climate and energy partitioning in impact events. 11 impact experiments into dry and water-saturated sandstone were performed and analyzed. The experiments span a range of impact velocities from 2.5 to 5.3 km s−1 using projectile sizes from 2.5 to 12 mm. Kinetic impact energies between 874 and 80,338 J were achieved. Ejecta of these experiments was collected and the PSD was measured and quantified with power law fits. The resulting power law exponents lie between 2.54 and 2.74. Our results do not show an influence of impact energy or impact velocity on the PSD of impact ejecta. A significant increase in the PSD values was found from dry to water-saturated sandstone targets. We suggest that water saturation of the target has multiple effects on ejecta fragmentation. A comparison of our experimental data with data from the literature shows no correlation between the target material lithology and the ejecta PSD. Interestingly, literature data for disruption experiments revealed a strong influence imparted energy density on the D-values. PSD values were used to calculate the energy spent for target fragmentation and show that the fraction of impact energy used for comminution is in the lower single-digit percentage.
... Experiments performed on solid geo-materials were commonly using dense or low-porous 16 rocks like basalt and gabbro Heitowit 1963, Moore et al. 1963;Lange et al. 1984;17 Polanskey and Ahrens 1990), granite (Hörz 1969;Burchell and Whitehorn 2003), or lime18 stone (Ahrens and Rubin 1993), or utilizing glass (Field 1971), or ice (Lange and Ahrens 19 1987). Only sparse literature is concerned with impact cratering in solid and porous materials 20 like sandstone (Maurer and Rinehart 1960;Shoemaker et al. 1963;Baldwin et al. 2007, 21 Kenkmann et al. 2011), sintered glass beads ( Love et al. 1993;Michikami et al. 2007), gyp ...
Hypervelocity impact experiments on dry and water-saturated targets of
fine-grained quartz sandstone, performed within the MEMIN project, have
been investigated to determine the effects of porosity and pore space
saturation on deformation mechanisms in the crater's subsurface. A dry
sandstone cube and a 90% water-saturated sandstone cube (Seeberger
Sandstein, 20 cm side length, about 23% porosity) were impacted at the
Fraunhofer EMI acceleration facilities by 2.5 mm diameter steel spheres
at 4.8 and 5.3 km s-1, respectively. Microstructural
postimpact analyses of the bisected craters revealed differences in the
subsurface deformation for the dry and the wet target experiments.
Enhanced grain comminution and compaction in the dry experiment and a
wider extent of localized deformation in the saturated experiment
suggest a direct influence of pore water on deformation mechanisms. We
suggest that the pore water reduces the shock impedance mismatch between
grains and pore space, and thus reduces the peak stresses at grain-grain
contacts. This effect inhibits profound grain comminution and effective
compaction, but allows for reduced shock wave attenuation and a more
effective transport of energy into the target. The reduced shock wave
attenuation is supposed to be responsible for the enhanced crater growth
and the development of "near surface" fractures in the wet target.
... Compared to granular material, experimental data from hypervelocity impacts into consolidated rocks are sparse. Amongst others gabbro (e.g., Lange et al. 1984;Polanskey and Ahrens 1990), granite (e.g., Hörz 1969;Burchell and Whitehorn 2003) and basalt (Gault et al. 1963;Gault 1973) as well as a basalt grout (Housen 1992) were used as target materials. Impact experiments on porous sintered targets were conducted by Michikami et al. (2007). ...
This study deals with the investigation of highly dynamic processes
associated with hypervelocity impacts on porous sandstone. For the
impact experiments, two light-gas accelerators with different calibers
were used, capable of accelerating steel projectiles with diameters
ranging from 2.5 to 12 mm to several kilometers per second. The
projectiles impacted on dry and water-saturated Seeberger Sandstone
targets. The study includes investigations of the influence of pore
water on the shape of the ejecta cloud as well as transient crater
growth. The results show a significant influence of pore water on ejecta
behavior. Steeper ejecta cone angles are observed if the impacts are
conducted on wet sandstones. The transient crater grows at a faster rate
and reaches a larger diameter if the target is water saturated. In our
experiments, target porosity leads to smaller crater sizes compared with
nonporous targets. Water within the pore space reduces porosity and
counteracts this process. Power law fits were applied to the crater
growth curves. The results show an increase in the scaling exponent μ
with increasing pore space saturation.
... Coefficient fits for the normalized v max are reasonable to have the data overlie, or collapse, on one curve for non-dimensional x-values Table 2 Material properties. Values taken from Lange et al. (1984), Ai and Ahrens (2006), and Spray (2010) ...
Ejecta velocity measurements were made during impacts into solid planetary materials. Ejecta velocity fields overlie each other when normalized by vmax, v50%mass, and v50%KE; these correspond to the maximum velocity and median values of mass and kinetic energy among ejecta velocities. Semi-empirical models were developed to provide predictive capabilities of 10th, 50th, and 90th percentiles of the distributions of mass, momentum and kinetic energy with respect to ejecta velocity. Lastly, a functional equation describing the probability density distribution of mass, momentum and kinetic energy among ejecta velocities was derived. Data and predictive models are valuable in the development and validation of numerical models, where comparison between experiments and simulations rely on well characterized measurements.
The immovable nature of built heritage means that it is particularly vulnerable during times of armed conflict. Although impacts from small arms and shrapnel leave relatively inconspicuous impact scars, they may elevate the risk of future stone deterioration. This study investigates the subsurface damage caused by bullet impacts, which is not apparent from surface inspection, in order to better understand the geometry and mechanics of this form of conflict damage to heritage. Controlled firearm experiments were conducted to simulate conflict damage to sandstone and limestone buildings. The bullet impacts created conical fractures or zones of increased fracture intensity below the impact, radial fractures and spallation, in addition to a crater. Dynamic fracture distinguishes the formation of these features from quasi static cone crack experiments, while the lack of a shockwave differentiates these bullet impacts from hypervelocity experiments. Damage was created by momentum transfer from the bullet, so that differences in target properties had large effects on the nature of the damage. The crater in the limestone target was almost an order of magnitude deeper than the sandstone crater, and large open fractures formed in the limestone below the crater floor, compared with zones of increased fracture intensity in the sandstone target. Microstructural analysis of subsurface damage showed that fracture intensity decreased with increasing distance from the impact centre, suggesting that regions proximal to the impact are at increased risk of future deterioration. Conical subsurface fractures dipping away from the impact beneath multiple impact craters could link up, creating a continuous fracture network. By providing pathways for moisture and other weathering agents, fractures enlarge the region at increased risk of deterioration. Their lack of surface expression makes understanding their formation a vital part of future surveying and post conflict assessments.
The shift of armed conflicts to more urbanised environments has increased risk to cultural her-itage sites. Small arms impacts are ubiquitous in these circumstances, yet the effects and mecha-nisms of damage caused are not well known. A sandstone target was shot under controlled con-ditions to investigate surface and subsurface damage. A 3D model of the damaged block, created by structure from motion photogrammetry, shows that internal fracturing was at least as exten-sive as the visible surface fractures. Back scatter electron imaging of the damaged surface shows a shift from intragranular fracturing and grain size reduction at <5 mm from the impact point, to primarily circumgranular fracturing and grain ‘plucking’ at 20 mm from the impact point. In-ternal fracture intensity decreased with distance from the centre of the crater. Volumes around the impact point are therefore at greater risk of subsequent weathering deterioration, but signif-icant damage extends to the periphery of the target, rendering whole blocks vulnerable. The surface crater, despite being one of the most conspicuous aspects of conflict damage, has many times less area than internal and surface fractures.
We conducted four sets of impact experiments using sedimentary rock targets and three different kinds of projectiles at a variety of impact angles in order to examine how the density of a projectile affects the dimensions of a crater as the angle of impact decreases, the threshold angle for the formation of elliptical craters, and the threshold angle for the formation of pits. The crater profiles, crater volume, equivalent diameter, length, width, depth, and ellipticity of each set were carefully measured to be used in comparison with small craters that formed on the weak rocky surfaces of planetary bodies. The results indicate that the crater volume, equivalent diameter, width, and depth decrease with the impact angle, while the length of the crater within a set does not decrease monotonically with impact angle. This trend in crater length is consistent with the results of previous studies. Although craters formed at higher impact angles have a central pit, the pit becomes unclear and eventually disappears as the impact angle decreases. A larger threshold angle is required for the formation of pits at slower impact velocity than at higher impact velocity. Our results suggest that the presence of a central pit is indicative of impacts at higher angles and/or higher velocity. The ratio of the volume of craters resulting from oblique impacts to that of craters formed by normal impacts was proportional to the power of the sine of the impact angle. The power index was found to range between 1.46 and 2.20, with an average of 1.57. Comparison of the averaged power index to the power index of the π-group crater scaling rules, it is experimentally suggested that the hypothesis indicating that the vertical velocity component controls crater formation is plausible on a brittle target. The threshold angles for the formation of elliptical craters for three different kind of projectiles were almost consistent with those obtained in previous studies. Our results strongly suggested that the threshold angle for the formation of elliptical craters for high-density impactor, such as iron meteorites, are higher than for rocky impactors. We then obtained a relationship between the threshold angle for the formation of pits and the cratering efficiency. It is revealed that the threshold angle for the formation of pits is greater than the threshold angle for the formation of elliptical craters, when the cratering efficiency is in the range 7–30. A well-developed pit-spall structure in the crater may be used to indicate both, the impact angle and the vertical component of the impact velocity.
We present the second release of the now open source smoothed particle hydrodynamics code miluphcuda. The code is designed to run on Nvidia CUDA capable devices. It handles one to three dimensional problems and includes modules to solve the equations for viscid and inviscid hydrodynamical flows, the equations of continuum mechanics using SPH, and self-gravity with a Barnes-Hut tree. The covered material models include different porosity and plasticity models. Several equations of states, especially for impact physics, are implemented. The basic ideas of the numerical scheme are presented, the usage of the code is explained and its versatility is shown by means of different applications. The code is hereby publicly available.
Establishing a lunar base requires the design and construction of infrastructure that can withstand the Moon’s hazardous environment. This study explores the effects of micrometeoroid impacts on a biopolymer-bound soil composite (BSC), a novel construction material that leverages in situ resource utilization to significantly reduce costs associated with resource transportation from Earth. Using a small fraction of biopolymer to bind regolith, BSC can be used to build radiation and micrometeoroid shielding for habitats, stable landing and launching pads, and pavements that help to contain dust. To determine the relationship between hypervelocity impacts and BSC material damage, 19 hypervelocity impact experiments were conducted on BSC targets. Analytical power-law relationships were derived to predict transient crater dimensions, such as volume and diameter, from projectile features, such as diameter, density, and velocity. The scaling exponents determined for BSC transient crater volume and diameter are comparable to those of quartzite, sandstone, and basalt and indicate that crater formation in BSC is largely driven by the kinetic energy of the projectile, as expected for cohesive low-porosity materials.
This paper aims to investigate the fractal characteristics of concrete fragments produced by impact fragmentation. The dynamic compressive tests for concretes with different static strengths were conducted by split Hopkinson pressure bar apparatus under various strain rates. The results indicate that the fragments size distribution of concrete after impact fragmentation can be statistically regarded as a fractal. The corresponding fractal dimension, as calculated by mass-size relationship, is an ideal indicator to describe the fragmentation degree. Under impact loading, the fractal dimension of impact fragmentation increases with strain rate. For a given loading rate, concrete with a higher static strength is less fragmented and has a smaller fractal dimension. In a word, the more serious the fragmentation is, the larger the fractal dimension obtained. The variation of fractal dimension essentially depends on the development of cracks inside and the compactness of concrete. Moreover, the dynamic compressive strength and impact toughness of concrete demonstrate an increasing trend with fractal dimension of impact fragmentation. Under a given fractal dimension, concrete with a higher static strength exhibits larger dynamic compressive strength and impact toughness. A modified renormalization group model can be used to describe the fractal behavior of impact fragmentation of concrete by taking the strain rate effect into account. To get closer to the real fragmentation process, this model can be further modified by assuming that the subelements produced each time have different sizes. In addition, based on mercury intrusion porosimetry tests, it is found that the pore structure of concrete also possesses obvious fractal characteristics. Concrete with lower porosity and finer pore structure exhibits a larger pore fractal dimension.
Hypervelocity impact experiments on porous tuff targets were carried out to determine the effect of porosity on deformation mechanisms in the crater's subsurface. Blocks of Weibern Tuff with about 43% porosity were impacted by 2.5 mm and 12.0 mm diameter steel spheres with velocities between 4.8 km s−1 and 5.6 km s−1. The postimpact subsurface damage was quantified with computer tomography as well as with meso- and microscale analyses of the bisected crater subsurface. The intensity and style of deformation in mineral clasts and the tuff matrix were mapped and their decay with subsurface depth was determined. Subsurface deformation styles include pore space compaction, clast rotation, as well as microfracture formation. Evaluation of the deformation indicates near-surface energy coupling at a calculated depth of burial of ~2 projectile diameters (dp), which is in conflict with the crater shape, which displays a deep, central penetration tube. Subsurface damage extends to ~2 dp beneath the crater floor in the experiments with 2.5 mm projectiles and increases to ~3 dp for 12 mm projectiles. Based on overprinting relationships and the geometrical orientation of deformation features, a sequence of subsurface deformation events was derived (1) matrix compaction, (2) intragranular crack formation in clasts, (3) deformation band formation in the compacted matrix, (4) tensile fracturing.
This chapter discusses physical processes affecting interplanetary dust grains, including processes determining dust formation, growth, disruption, and alteration. Computer simulations and laboratory studies of coagulation and aggregation show that mutual collisions between solid grains determine the growth of solid aggregates in the early solar system when the impact energies are too low to destroy the colliding grains. On the other hand, fragmentation occurs at the high impact energies that currently prevail, generating dust from meteoroids, asteroid, and satellite surfaces as well as from sublimating comets. Such impact processes are discussed based on a compilation of laboratory measurements (e.g., size, shape, velocity and spin distributions of fragments). Gradual alteration of the dust grains occurs in the present solar system due to solar radiation and energetic particle impact. Sublimation, sputtering and charging can alter the nature of interplanetary dust grains. Dust grain temperatures, erosion rates due to solar-wind-induced sputtering, and surface charges are studied. The evidence for alteration of physical/chemical/mineralogical properties of interplanetary dust grains is still rather poor. Therefore, we discuss the expected changes, referring to those physical processes that can be simulated in laboratory experiments, and to their analogues obtained through theoretical modeling.
The scale invariance of geological phenomena is one of the first concepts taught to a student of geology. It is pointed out that an object with a scale, i.e., a coin, a rock hammer, a person, must be included whenever a photograph of a geological feature is taken. Without the scale, it is often impossible to determine whether the photograph covers 10 cm or 10 km. A specific example is folded, layered sedimentary rocks that occur over this range of scales. Another example is an aerial photograph of a rocky coastline. Without an object with a characteristic dimension, such as a tree or house, the elevation of the photograph cannot be determined. In this context, Mandelbrot (1967) introduced the concept of fractals. Because of scale invariance, the length of a coastline increases as the length of the measuring rod decreases according to a power law; the power determines the fractal dimension of the coastline.
This paper derives mathematically how crater depth and crater damage depend on impact velocity, mass of projectiles, and strength and porosity properties of rocky targets. In this impact model, stage I is based on an one-dimensional impact assumption and Rankine-Hugoniot jump conditions. Stage II is based on cavity expansion process in target materials considering Mohr-Coulomb criterion and porosity. The derived formulae could be seen as specific forms of Holsapple-Housen model in strength regime, and the model quantitatively predicts 1) the crater depth in tuff, dry sandstone, quartzit, gabbro and ice targets, and 2) the damage depth in dry sandstone and gabbro targets. The porosity effects on crater depth and damage depth are also discussed and compared with existing results from numerical calculations, and it shows that a higher porosity yields a deeper crater depth but a shallower damage depth.
Distributions of length and mass are important to mineral producers whose products contain trace asbestos and to biological scientists who experiment with asbestos. Analysis of 56 distributions of the length of asbestos fibers shows that length frequency follows a power law, from which the population's fractal dimension can be determined. From empirical observations of width, thickness, and density in combination with length, the frequency ofincremental mass can be calculated. Formany asbestos samples, the proportion of total mass of an asbestos population increases as the mass and length of individual fiben and bundles of fibers increase. Measurement srategies should be designed to include the longest fibers (SEM or OM) for weight-based abundances. Where a population's mass is concentrated in the shonest fibers, the TEM is the most appropriate instnrment for gathering dimensional dak. In either case, the application of the fractal model enables the entire mass of the population to be estimated from a random sample, provided the mass of the largest and smallest pa$icles in the population are known or can be estimated. Where asbestos is a contaminant, its abundance can be estimated if the total mass of the sample examined is known. Une connaissance de la distribution de la longueur et de la masse des particules s'avbre importante pour les producteurs de minerai dont les produits contiennent des traces d'amiante, ainsi que pour les biologistes qui effectuent des expdriences avec de I'amiante. Une analyse de cinquante-six distributions de la longueur de fibres d'amiante d6montre que la frdquence des longueurs rdpond h une fonction i puissance, de laquelle il est possible de d6terminer la dimension fractale de la population. A partir d'observations empiriques portant sur la largeur, 1'6paisseur et la densit6, combin6es aux mesures de longueur, il est possible de calculer la fr6quence de la masse incr6mentielle. Dans le cas de plusieurs 6chantillons d'amiante, la proportion de la masse totale d'une population augmente d mesure qu'augmentent la masse et la longueur des fibres individuelles et des essaims de fibres. ks protocoles de mesurage devraient inclure les fibres les plus longues (telles que mesurdes au microscope dlectronique d balayage et au microscope optique) pour une caract6risation pond6rale d'une population. Dans le cas oi la masse d'une population est concentr6e dans les fibres les plus courtes, c'est par microscopie dlectronique par transmission qu'il faudrait caractdriser les dimensions de la population. Dans l'un ou I'autre des cas, I'application d'un modble fractal permet d'estimer les propri6tds d'une masse entibre e partird'un 6chantillon quelconque, pourvu qu'on puisse connaltre ou estimer la masse de la particule la plus grande et celle de la plus petite d'une population. Dans les situation oi I'amiante agit comme contaminant, son abondance peut 6tre estimde si on connait la masse totale de l'dchantillon. Mots-cl6 s: amiante. concentmtion d'amiante. fractal.
Quartzite cobbles in Lower Triassic Buntsandstein conglomerates from northeastern Spain display unusual millimeter- to centimeter-sized circular craters, commonly having central mounds and surrounded by radial fractures. The conglomerates are also marked by intense fracturing down to microscopic scale. These features have traditionally been attributed to tectonic compression and pressure dissolution at cobble contacts. Sections through the cratered cobbles reveal pervasive internal fracturing, segments detached along concave spall fractures, and zones marked by quartz grains with planar deformation features. Comparison with results of impact experiments on artificial conglomerates suggests that these features were produced by internal accelerations, grain collisions, and spallation related to shock-wave propagation through inhomogeneous deposits. The proximity of the outcrops to the Azuara and proposed Rubielos de la Cérida impact structures suggests that shock deformation of conglomerates can provide an easily recognizable regional impact signature.
Particle size distribution (PSD) is an often used parameter to describe and quantify fragmentation of deformed rock. Our analyses of shock deformed sandstone show that dynamic fragmentation influences the PSD, expressed as fractal dimension (D-value). Image analysis was used to derive fractal dimensions from a hypervelocity impact cratering experiment (2.5 mm steel sphere, 4.8 km/s) and a planar shock recovery experiment (2.5 GPa). The D-values in the cratering experiment decrease from 1.74 at the crater floor to 0.84 at a distance of 7.2 mm to the crater floor. The D-values found in this experiment are closely related to the microstructural features found at distinct distances from the crater floor. The obtained values are in good agreement with the D-values reported for fault zones, impact sites and deformation experiments. The D-value measured in the shock recovery experiment is 2.42. Such high D-values were usually attributed to abrasive processes related to high strain. Since the strain in our experiment is only ∼23% we suggest that at highly dynamic deformation very high d-values can be reached at small strain. To quantify this, numerical impact modelling has been used to estimate strain rates for the impact experiment. This is related to the activation of more inherent flaws and fracture bifurcation at very high strain rates ∼>102 s−1.
Articles entered into the data base at the Lunar and Planetary Institute
Library, May - October, 1984. Concerning: The Moon. Space utilization
(including lunar base). Planets: Jupiter, Mars, Mercury, Neptune, Pluto,
Saturn, Uranus, Venus. Other objects: asteroids, comets, meteorites,
cosmic dust, other particles, etc.
Impact cratering experiments using basalt target were performed.
Diameters, depths, and volumes of 16 craters were measured. Preliminary
analyses of these values showed scaling laws consistent with previous
studies.
Detailed morphometric crater analyses of hypervelocity impact
experiments were carried out to investigate the influence of impact
velocity and target pore space saturation on crater size and morphology.
Extension of impact cratering calculations to late times, for example, for a 12 km/s of a 5 km radius silicate impactor onto a silicate target is observed to give a rebounding (oscillating) crater that comes to rest with a broad central peak of ~ 5 km radius some 20 min. after impact. Oscillating craters also form vertical faults (in target rocks) as a result of initial shear zone banding. Present damage, D, models take into account generation of cracks that accommodate the finite strain of the rock. Here D = (1-m/m_0) where m is either an elastic modulus or strength of the target rocks and m0 is initial value. Refraction seismic data for terrestrial craters demonstrate that damage zones extend to a depth H below the surface. H varies from ~ 1 km for small, strength-controlled craters such as Meteor Crater and extends to 14 km for the 300 km diameter Vredefort Crater. Experiments with 0.15 m targets yield measured values of ~ 3.5 cm for the characteristic attenuation distance to the stress levels of tensional failure for impacts conducted with a 1 km/s, 700 mg aluminum projectile into gabbro. These results are generally concordant with the observed depth that tensile cracks are driven by an impact and the shock pressure has decayed at this distance to a value about the measured spall strength.
Porosity has been directly measured for eight lunar meteorite breccias
and calculated for two more on the basis of literature density
measurements. Lunar meteorite regolith breccias display systematically
low porosity in comparison to otherwise analogous Apollo regolith
breccias. Among seven meteoritic regolith breccias, porosity ranges from
1 to 11% and averages 7.5+/-(1-σ)3.2%, whereas for 44 analogous
Apollo samples (porosities mostly calculated from literature density
data) the average is 25+/-(1-σ)7%. The origin of this disparity is
enigmatic, but the trend probably reflects mainly a bias in favor of
strong, compact breccias among fragments that manage to survive the
violent process of launch to lunar escape velocity (2.38 km/s). In
addition, compaction during launch may play an important role. The
population of lunar meteorites is clearly not a random, unmodified
sample of lithic materials near the surface of the parent body.
The velocity and attenuation of ultrasonic stress waves in gabbroic rock samples (San Marcos, California) subjected to shock loading in the 2 GPa range were studied. From P wave velocity measurements we determined the damage parameter Dp and crack density ε of the samples and related these to the attenuation coefficient (quality factor) under dynamic strains of 2×10-7 and at a frequency of 2 MHz using the ultrasonic pulse-echo method. A fit to the data yields the P wave spatial attenuation coefficient at a frequency of 2 MHz, alphap(Dp)=1.1+28.2Dp (decibels per centimeter). From the relation between the attenuation coefficient and quality factor, the quality factor Q is given by Q-1=0.011(1+25.6Dp)(1-Dp)1/2. Using O'Connell-Budiansky theory relating crack density to velocity, the parameter in Walsh's theory was determined based on experimental data. An approximate method is also proposed to estimate the average half-length of cracks based on the attenuation measurements.
Holsapple and Schmidt (1980) previously addressed the problem of the scaling of explosive cratering. Their analysis included results which show under which conditions the scaling can be bounded between quarter-root and cube-root rules. The present investigation is an extension of the earlier analysis and approaches the case of impact cratering. More restrictive bounds are found for impact cratering than for the explosive case. These stronger results come from considering the role of the impactor momentum as an independent variable for impact cratering. Attention is given to impact cratering variables, general scaling rules, the bounds on scaling rules, a generalization to more variables, and previous scaling rules and results.
The dynamic tensile strength of icy media is measured at strain rates on the order of 10,000/sec to aid in the understanding of impact and cratering phenomena. Compressed samples consisting of ice and ice-silicate mixtures with 5 and 30 wt % sand were impacted at temperatures between 230 and 250 K by projectile plexiglas plates imparting the required strain rates in less than 0.75 microsec. Taking the tensile stress corresponding to the transition from intact to spalled or fragmented samples as the dynamic tensile strength, strengths of 17, 20 and 22 MPa were obtained for the pure ice, 5 wt % sand, and 30 wt % sand specimens, respectively. The values lie considerably above those observed in static testing. A continuum fracturing model is used to obtain relations between tensile strength and stress rate as well as to derive stress and damage histories during tensile loading and the size distribution of icy fragments as a function of strain rate.
It is argued that SNC (shergottite, nakhlite, chassignite) meteorites are ejecta from Mars. The mineralogy and chemistry of these objects is discussed, including rare earth element content, potassium/uranium ratios, oxidation state, oxygen isotopes, ages and isotopic evolution, magnetism, shock and texture. The possibility of SNC's deriving from Mercury, Venus, earth, moon, or a eucrite parent body is argued against. Mercury is too volatile-poor and anhydrous, Venus's atmosphere too thick and hot and its gravitational field too large, earth's oxygen isotope content too different from that of SNC's, the moon too different isotopically and chemically, and the ages of eucrites too different. Models suggest that SNC's could have escaped from Mars's gravitational field, and their composition supports Martian origin. Statistically, they could have reached the earth within their measured shock ages. Objections to the hypothesis are also discussed.
Low velocity impact experiments (0.14 to l km/s) carried out in polycrystalline water ice targets at 257 and 81 K resulted in interactions which can be assigned to four fragmentation classes, cratering, erosion, disruption, and total fragmentation. Specific kinetic energies for the transitions between these classes range from l x 10^5 to 7 x 10^5 ergs/g for 81 K ice and from 3 x 10^5 to ~ 2 x 10^6 ergs/g for 257 K ice. These values are about one to two orders of magnitude below those for silicate rocks. The mass vs. cumulative number distribution of fragments in our experiments can be described by a simple power law, similar to that observed in fragmented rocks in both the laboratory
and in nature. The logarithmic slopes of cumulative number vs. fragment weight vary between - 0.9 and - 1.8 decreasing with increasing projectile energy and are approximately independent of target temperature. The shapes of fragments resulting from erosion and disruption of ice targets are
significantly less spherical for 257 K targets than for 81 K targets. Fragment sphericity increases with increasing projectile energy at 257 K, but no similar trend is observed for 81 K ice. Our results support the hypothesis that the specific projectile energy is a measure for target
comminution for a relatively wide range of projectile energies and target masses. We apply our results to the collisional interaction of icy planetary bodies and find that the complete destruction of a target body with radii between 50 m and 100 km· range from 10^(17) to 10^(27) ergs. Energies corresponding to basaltic bodies of the same size range from 10^(18) to 10^(28) ergs. Our experiments suggest that regolith components on icy planets resemble those on rocky planetary bodies in size and shape. We
predict that the initial shapes of icy particles in the Saturnian ring system were roughly spherical. The initial mass distribution of ring particles should follow a power law with a slope of ~ - 1.5.
Fracture and fragmentation studies on 80 ml/kg Anvil Points oil shale with plate impact, Hopkinson bar, capacitor discharge, and HE techniques have shown that the dynamic fracture stress, fracture energy, and fragment size depend on the rate of tensile loading. A model coupling fracture, fragmentation, and stress wave propagation and based on the activation and growth of an initial Weibull distribution of fracture-producing flaws has been found effective in describing the observed rate-dependent fracture phenomena from static to high strain-rate impulse loading. The fracture model has been incorporated into one- and two-dimensional stress-wave computer codes and is being used to evaluate blasting geometries and stress-pulse tailoring for in situ rubblization of oil shale.
Dynamic fracture strengths of a representative suite of crustal rocks have been determined. The rocks investigated included silicates and carbonates of varying grain size and porosity, oil shale with several kerogen contents and orientations, and fused silica. With the exception of fused silica, fracture strengths ranged from a few tens of MPa to slightly over 100 MPa. Rate dependence of fracture stress and fracture energy appears to be important in determining the dynamic strength of rock.
This paper presents evidence for and against the association of
particular meteoritic classes with various candidate objects, as well as
regarding the original solar system location of the parent bodies.
Chemical, isotopic and petrographic evidence, dynamical theories, and
spectrophotometric data are used to address the problem of the
identification of the sources of both chondrites and differentiated
meteorites. It is concluded that bodies which at least at present fit
the observational definition of an asteroid represent the only plausible
sources for the great majority of the meteorites analyzed.
It is pointed out that the formation of craters and ejecta in geologic
materials by impact or explosive detonation can occur by a wide variety
of mechanisms. Shockey et al. (1973, 1974) have developed a
computational model (NAG/FRAG) that simulates the activation, growth,
and coalescence of preexisting flaws in rock and other solids to form
fragments. More recently, the model was written in a form suitable for
testing against data from cratering or axially symmetric penetration
experiments. The results of such tests are presented. Good agreement was
obtained between computed and observed cratering behavior in Arkansas
novaculite and basalt. It was one of the objectives of the reported work
to generate by experiment simple, unambiguous crater size data and
ejecta size distributions in a well-characterized hard rock and compare
these data with the predictions of the NAG/FRAG computational model. The
second objective was the computational simulation of a large scale
cratering event to draw conclusions about the feasibility of using
NAG/FRAG to predict cratering behavior in rock.
An approach is described for predicting fragment size distributions for rock under dynamic loading conditions. The approach is (1) to determine the nature and order of the physical processes occurring in the rock during loading that lead to fragment formation, (2) to treat each process computationally and (3) to insert the resulting fragmentation model into a wave propagation code which calculates the stress history in the rock caused by the dynamic load.The approach was applied to Arkansas novaculite under one-dimensional-strain impact loads. Plate slap experiments were carried out to support model development and determine values of those rock properties required for the model. A calculation was made to simulate the conditions of one of the dynamic impact experiments and compute the resulting fragment size distribution. The agreement between calculated and measured fragment size distribution illustrates that fragmentation behavior can be predicted from a few measurable rock properties.
A relatively simple indentation technique for the rapid measurement of fracture surface energy, , of small samples is described. The reliability of this technique is assessed by testing soda-lime glass for which there are good independent fracture mechanics determinations of fracture surface energy. The indentation technique gives a value for of 4.33 J m–2 which compares favourably with the accepted value of 3.8 J m–2. Fracture surface energies of the {010} and {001} cleavage planes of single crystal olivine (modal composition Fo88Fa12) are then determined and compared with theoretical estimates of the thermodynamic surface energy, , calculated from atomistic parameters ( is equal to in the absence of dissipative processes during crack extension). The experimental values for {010} and {001} are respectively 0.98 J m–2 and 1.26 J m–2. The calculated values of {010} and {001} are respectively in the range from 0.37 J m–2 to 8.63 J m–2 and 12.06 J m–2. The particular advantages of the indentation technique for the study of the fracture surface energies of geological materials are outlined.
A crater 30 cm in diameter and 4.4 cm in depth was produced upon impact of an aluminium sphere with a homogeneous granite
target. The volume excavated was 748 cm3, the mass ejected 1933 g. The crater geometry is compared with previous laboratory experiments.
Mineralogical investigations revealed that shock induced, microscopic fracturing is lowest in the direction of uniaxial compression,
followed by a 45° profile. Due to reflections of stress waves at the free surface, the horizontal profile displayed the highest
fracture index.
Kinking of biotite was very common in samples close to the crater walls (≈ 50 kb). However it faded out at a distance which
corresponds to approximately 10 kb. This seems to be the lower pressure limit for the formation of kink bands under shock
conditions.
The basaltic achondrite, shergottite, nakhlite, and chassignite meteorites appear to define a petrological and geochemical sequence. Assuming that they developed from basaltic liquids produced by low pressure partial melting of plagioclase peridotites, their petrological and chemical distinctions can be understood in terms of the compositional differences between their source periodites. The source regions of basaltic achondrite magmas were alkali-poor, metal-bearing peridotites in which pigeonite and/or orthopyroxene was the only pyroxene. By simultaneously increasing the ratio of high-Ca pyroxene to low-Ca pyroxene, the alkali content of the feldspar, the oxidation state, and the overall volatile content of the basaltic achondrite source peridotite, peridotites capable of yielding the parent liquids of the shergottites can be produced. Further increases can produce peridotites capable of yielding the parent liquids of the nakhlites and chassignites.
Addition of a volatile-rich component to the volatile-poor type of peridotite required for the source regions of the eucrites appears to be capable of producing the required series of peridotites. Alternatively, progressive volatile-loss from a volatile-rich material, possibly of roughly cosmic composition, could have produced this sequence of peridotites. A simple two-component model of planetary compositions is, to a first approximation, consistent with the petrology and chemistry of these igneous meteorite groups.
Collected data are presented on mass distributions of fragmented rocks. These can be used to interpret extraterrestrial rock samples. Lunar surface material disturbed by Surveyors is broken in a way characteristic of low-energy, mechnical breakage, as expected. Debris around decameter-scale lunar craters with strewn rock fields also exhibits this property, suggesting that many such craters are secondary impacts. Centimeter-scale debris on the lunar maria shows evidence of extensive regrinding, probably due to repeated primary and secondary impacts, but such debris near Tycho appears not to have been so extensively ground; evidently this results from Tycho's young age. Telescopic asteroids have evidently been fragmented by attenuated shock waves in sporadic collisions, while meteorites are apparently the debris from repeated and/or hypervelocity collisions.
As a simulation of collisional processes among solid bodies of various sizes in the solar system, polycarbonate projectiles of mass 0.37 g were impacted against cubic basaltic rocks of about 2 to 10 cm and larger with a velocity of 2.6 km/sec. The corresponding energy imparted per unit mass of target ranges from about 106 to 109 ergs/g. The phenomena are classified into four categories with increasing target size: (1) complete destruction, (2) remaining core, (3) transition region, and (4) crater formation. Empirical formulas for the cumulative mass of the fragments and the mass of the maximum fragment are given. The similarity of these formulas is briefly discussed. The experimental results are applied to the examination of the hypothesis that a single Martian satellite was once ruptured by impact, leaving the present two satellites. It is suggested that the radius of the parent satellite was larger than about 30 km.
The dynamic tensile strength of four rocks are determined. A flat plate impact experiment is employed to generate approximately one-microsecond-duration tensile stress pulses in rock samples by superposing rarefaction waves to induce fracture. It is noted that the effect of chemical weathering and other factors has not been explicitly studied. The given tensile strengths are based on a series of experiments on each rock where determination of incipient spallation is made by terminal microscopic examination. The data are generally consistent with previous determinations, at least one of which was for a significantly chemically altered but physically coherent rock.
A model for the ejection of material from an impact crater which links ejection velocity, fragment size, and shock pressure through a simplified stress-wave propagation and reflection scheme is presented. It is shown that a small amount of material (0.01 to 0.05 projectile mass) may be ejected at high velocity without suffering petrologically detectable shock pressures. The largest fragments ejected at any velocity are spalls that originate from the target planet's surface. The spall size is proportional to the radius of the primary impactor and the target tensile strength and inversely proportional to ejection velocity. The shock level in the spalls is low, typically half of the dynamic crushing strength of the rock. The model also predicts the aspect ratio of the spalled fragments, the angle of ejection, and the sizes and shock level of other fragments originating deeper in the target. Comparison with observational and experimental data shows generally good agreement.
Current equation-of-state formulations, used for finite-difference cratering flow calculations, are cast into a framework permitting comparison of peak pressures attained upon impact of a sphere, with a half-space, along the impact symmetry axis, to one-dimensional impedance match solutions. On the basis of this formulation and application of thermochemical data, the regimes of melting and vaporization are examined. For the purpose of identifying material which will, upon isentropic release from the impact-induced shock state, result in a solid just brought to its melting point, i.e., incipiently melted (IM), completely melted (CM), just brought to its boiling point, i.e., incipiently vaporized (IV), and completely vaporized (CV) state, the pressures at which the critical isentropes intersect the Hugoniots of iron and gabbroic anorthosite (GA) are examined in detail. The latter rock type is assumed to be representative of the lunar highlands. The Hugoniot pressures, for which IM, CM, IV, and CV will occur upon isentropic expansion, are calculated to range from 2.2 to
16.8 Mbar, respectively for iron. For the high-pressure phase (hpp) assemblage of GA, modelled as a mixture of plagioclase in the hollandite structure and pyroxene in the perovskite structure, IM, CM, IV, and CV are calculated to occur upon isentropic expansion from Hugoniot states ranging from 0.43 to 5.9 Mbar, respectively. The spatial attenuation of shock pressure along the impact axis is
found to be clearly represented by two regimes, if the peak pressure, P, and radius normalized to that of the projectile, r, are fitted to expressions of the form P ∝ r^α. At distances from 2.2 to 5.6 projectile radii into a GA target, the constant, a, is on the order of -0.2. This low-attenuation rate, near-field regime, extends further into the target at the slower impact velocities and arises because of
the slightly divergent flow associated with the penetration of a spherical projectile. For the near-field impact regime, an impact at 5 km/sec of an iron object with a GA surface will induce CM for GA but
the iron will remain solid. At 15 km/sec, partial vaporization (PV) occurs for both GA and iron, whereas at 45 km/sec, CV occurs in both materials. Similar calculations are summarized for a GA meteoroid striking a GA surface at velocities ranging from 5 to 45 km/sec. At greater radii, in thefar-field regime, the exponent, a, varies systematically from -1.45 to -2.15 for impacts of GA onto GA as the impact velocity is increased from 5 to 45 km/sec. For an iron projectile impacting at speeds of 5-45 km/sec, the exponent, a, varies from -1.67 to -2.95. By comparison, the equivalent value of a, reported for both contained and surface explosions in various rocks is ~ -2. It is suggested that, given field data on shock attenuation (based on identification of various shock metamorphic features versus distance), overall crater size, and some chemical data as to the type of meteoroid which produced a crater, quantitative bounds on the impact velocity of the meteorite may be obtained.
Spray lz~jet'ted .fi'om the Lunar Surface by Meteoroid Impact
- E M Shoemaker
- J Moore
GAUI.T, D. E., E. M. SHOEMAKER, AND H, J. MOORE (19631. Spray lz~jet'ted.fi'om the Lunar Surface by Meteoroid Impact. NASA Tech. Note D-1767.
Batholith and Associated Rocks qf Corona, Elsinore, and San Luis Rey Quad-rangles. Southern Calffbrnia Geol. Soc. of America, Memoir 29 Impact ejection, spallation and the origin of meteorites, l('arns Petrology of the San Marcos gabbro
- E S Larsen
- Jr
LARSEN, E. S., JR. (1948). Batholith and Associated Rocks qf Corona, Elsinore, and San Luis Rey Quad-rangles. Southern Calffbrnia Geol. Soc. of America, Memoir 29. MELOSH, H. J. (19841. Impact ejection, spallation and the origin of meteorites, l('arns, in press. MILLER, F. S. (19371. Petrology of the San Marcos gabbro, Southern California. Bull. Geol. Soc. Amer. 48, 1397-1426.
Spray Ejected from the Lunar Surface by Meteroid Impact
- Gault
Petrology of the San Marcos gabbro, Southern California
- Miller