The effect of a thin weak layer covering a basalt block on the impact cratering process

doi:10.1016/j.icarus.2012.01.018

Icarus

Volume 218, Issue 2, April 2012, Pages 751-759

https://doi.org/10.1016/j.icarus.2012.01.018 Get rights and content

Abstract

To clarify the effect of a surface regolith layer on the formation of craters in bedrock, we conducted impact-cratering experiments on two-layered targets composed of a basalt block covered with a mortar layer. A nylon projectile was impacted on the targets at velocities of 2 and 4 km s⁻¹, and we investigated the crater size formed on the basalt. The crater size decreased with increased mortar thickness and decreased projectile mass and impact velocity. The normalized crater volume, π_V, of all the data was successfully scaled by the following exponential equation with a reduction length λ₀: $π_{V} = b_{0} π_{Y}^{- b_{1}} \exp (- λ / λ_{0})$ , where λ is the normalized thickness T/L_p, T and L_p are the mortar thickness and the projectile length, respectively, b₀ and b₁ are fitted parameters obtained for a homogeneous basalt target, 10^−2.7±0.7 and −1.4 ± 0.3, respectively, and λ₀ is obtained to be 0.38 ± 0.03. This empirical equation showing the effect of the mortar layer was physically explained by an improved non-dimensional scaling parameter, $π_{Y}^{*}$ , defined by $π_{Y}^{*} = Y / (ρ_{t} u_{p}^{2})$ , where u_p was the particle velocity of the mortar layer at the boundary between the mortar and the basalt. We performed the impact experiments to obtain the attenuation rate of the particle velocity in the mortar layer and derived the empirical equation of $\frac{u_{p}}{v_{i}} = 0.50 \exp (- \frac{λ}{1.03})$ , where v_i is the impact velocity of the projectile. We propose a simple model for the crater formation on the basalt block that the surface mortar layer with the impact velocity of u_p collides on the surface of the basalt block, and we confirmed that this model could reproduce our empirical equation showing the effect of the surface layer on the crater volume of basalt.

Highlights

► Impact cratering experiments on a basalt block covered with a mortar layer were conducted at the velocity of 2 and 4 km s⁻¹. ► The mortar layer thicker than a 1.5 projectile length can protect the basalt from the cratering completely. ► The crater scaling law in the strength regime was improved for bedrock covered with a weak layer. ► The effect of the weak layer was expressed by the exponential equation of the thickness normalized by the projectile length.

Introduction

There have been many experimental studies on impact cratering on sand, ice, and rocks, which are important geological materials constituting planets, satellites, and asteroids (Melosh, 1989). In the previous studies, the cratering experiments were carried out for a homogeneous target without any internal structures such as inclusions or layers; however, the surfaces of asteroids and satellites without atmosphere are usually covered with a regolith layer made of impact fragments and the bedrock resides below it. This regolith layer could affect the crater formation process on the bedrock, although the density and the mechanical strength of the regolith are smaller and weaker than those of the bedrock. The regolith thickness could be the most important parameter affecting the size of craters formed on the bedrock. We can ignore the existence of a regolith layer if it is much thinner than the size of a colliding projectile, but a crater might be formed on the regolith layer if it is thicker than the colliding projectile’s size. Therefore, we want to study the affect of a regolith layer on the crater size in the bedrock quantitatively, and we want to determine how thick the regolith layer would have to be to stop the formation of a crater in the bedrock.

The effects of a regolith layer on crater formation have been studied very little in laboratory experiments. There was a series of famous experimental studies conducted by Oberbeck and Ouaide (1967), who investigated the crater morphology of small craters (<1 km in the diameter) on the moon. They performed cratering experiments on a layered target simulating the lunar surface covered with a regolith layer and found that the crater type changed at a critical value, R_c, described by the ratio of the crater diameter to the upper layer thickness. This result suggested the possibility of estimating the regolith thickness from the crater diameter necessary for the change of the crater type (Oberbeck and Quaide, 1968, Quaide and Oberbeck, 1968). Oberbeck and Quaide were pioneers in the study of impact cratering on heterogeneous targets (e.g., layered targets), and our research was fully motivated by their successive results.

Since the studies made in the 1960s, there have been many cratering experiments on homogeneous targets, and the experimental results have been used to construct various crater scaling laws (Kawakami et al., 1983, Mizutani et al., 1983, Holsapple, 1993, Holsapple, 1994). In particular, the crater scaling laws proposed by Holsapple and coworkers for homogeneous targets have been widely accepted and used by researchers in their studies related to crater geology and planetary impact events. Recent planetary explorations such as those of Kaguya and the LRO (Lunar Reconnaissance Orbiter) have enabled us to observe craters less than 1 km in diameter, and such tiny craters could be formed in the strength regime, wherein the crater size is controlled by the target strength. A crater scaling law in the strength regime is necessary for the study of these tiny craters, and the Pi-scaling law in the strength regime proposed by Holsapple (1994) can be applied in such cases. However, on the lunar surface, tiny craters with unusual shapes such as a concentric crater and a flat-bottomed crater have been observed, and their formation was surely affected by the surface thin regolith layer and controlled by the surface strength. The crater formation in the strength regime should be studied to improve the crater scaling law while considering the surface thin regolith layer. The improvement of the crater scaling law would be useful not only for studying the lunar surface but also for studying the asteroids covered with regolith, such as Eros.

We have attempted to improve the crater scaling law in the strength regime proposed by Holsapple, 1993, Holsapple, 1994 to include the effect of a layered structure, and we were especially interested in the effect of a thin weak layer such as a regolith layer on the scaling law. Thus, the impact cratering experiments in the laboratory were conducted by using a basalt block covered with a thin mortar layer simulating a typical planetary surface in which a basaltic crust was covered with a self-compacted regolith layer.

Section snippets

Sample preparation

Layered targets were prepared by covering a basalt block with a thin mortar layer. The side lengths of the basalt blocks were 5, 10, and ∼20 cm, and these sizes were chosen depending on the projectile kinetic energy with the goal of avoiding disruption of the basalt block. The size and mass of the basalt block for each shot are shown in Table 1. The surface of the basalt block was flattened using a diamond saw so we could set a mortar layer on it. The basalt came from the Kinosaki area, in

Particle velocity measurements

Fig. 3 shows a summary of the particle velocity measurements (Table 2), and the relationship between the particle velocity and the mortar thickness was used to derive the empirical relationship. The particle velocity, u_p, is normalized by the projectile impact velocity, v_i, in each shot, and the mortar thickness, T, is normalized by the projectile length, L_p, of 5.0 mm for all the shots. All data can be fitted by one exponential equation very well as follows: $\frac{u_{p}}{v_{i}} = 0.50 \exp (- \frac{T / L_{p}}{1.03}) .$

However, Eq.(1)

New scaling parameter, $π_{Y}^{*}$ , for a layered target

Using Eq. (7), we obtained the semi-empirical scaling law of the crater volume for a basalt block protected by a thin mortar layer as follows: $π_{V} = b_{0} π_{Y}^{- b_{1}} \exp (- λ / λ_{0}) .$ This semi-empirical equation can be explained based on the elementary physical process expected for a two-layered target. In Section 3.1, we described our measurement of the particle velocity of mortar at various distances from the impact point and derived the empirical equation shown as Eq. (1). The actual force excavating the basalt

Acknowledgments

We appreciate Dr. K. R. Housen for his helpful review on our manuscript. We thank Mr. S. Nakatsubo of the Contribution Division of the Institute of Low Temperature Science, Hokkaido University, for his technical help. This work was supported in part by Grants-in Aid for Scientific Research (17340127 and 20340118) from the Japan Ministry of Education, Culture, Sports, Science and Technology, and a grant for a Joint Research Program from the Institute of Low Temperature Science, Hokkaido

References (15)

K.A. Holsapple
Catastrophic disruptions and cratering of Solar System bodies: A review and new results
Planet. Space Sci.
(1994)
T. Kadono
Hypervelocity impact into low density material and cometary outburst
Planet. Space Sci.
(1999)
M. Kato et al.
Ice-on-ice impact experiments
Icarus
(1995)
H. Mizutani et al.
New scaling laws on impact fragmentation
Icarus
(1990)
V.R. Oberbeck et al.
Genetic implications of lunar regolith thickness variations
Icarus
(1968)
M. Setoh et al.
High- and low-velocity impact experiments on porous sintered glass bead targets of different compressive strengths: Outcome sensitivity and scaling
Icarus
(2010)
T. Ahrens
Equation of state

There are more references available in the full text version of this article.

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The effect of a thin weak layer covering a basalt block on the impact cratering process

Abstract

Highlights

Introduction

Section snippets

Sample preparation

Particle velocity measurements

New scaling parameter, πY∗, for a layered target

Acknowledgments

Planet. Space Sci.

Planet. Space Sci.

Icarus

Icarus

Icarus

Icarus

Equation of state

New scaling parameter, $π_{Y}^{*}$ , for a layered target