Cold Compaction and Macro‐Porosity Removal in Rubble‐Pile Asteroids: 1. Theory

Abstract

Many asteroids are likely to be have been shattered by collisions into fragments and reaccumulated as gravitationally‐bound rubble piles. These bodies may contain large porosities, although this picture may be complicated by compaction inside the asteroid body. Estimates of asteroid mass and volume imply a negative correlation between size and porosity for stony asteroids. Asteroids that are suspected to be metallic appear to contain larger porosities than stony asteroids of similar sizes. To understand these observations, we develop models for cold compaction of fragments of different materials. The initial boulder size distributions are assumed to be narrow. We focus on macro‐porosity between the boulders and do not consider micro‐porosity inside the boulders. In our model of silicate/chondritic boulders, compaction is assumed to occur through cataclastic fracturing, which creates small pieces that fill the pores between residual large boulders, leading to fractal‐like distributions. This fracturing occurs when compression leads to stresses exceeding the tensile strength of the boulders. Combining this model with data on meteorite strength, we suggest that the compaction of chondritic boulders can be significant at pressures of several megapascals. In our model of metal boulders, we consider cold welding and boulder deformation (through ductile yielding or brittle‐like fracturing, depending on the stress and intrinsic crack size). Given the properties of iron meteorites, we infer that compaction in metallic rubble piles, caused by ductile or brittle deformation, is small, and that cold welding may lead to large (≳50%) porosities if the boulders are of ∼1 m sizes.

Cold Compaction and Macro‐Porosity Removal in Rubble‐Pile Asteroids: 2. Applications

“…The reduction of boulder micro‐porosity below ∼35%–40% under cold environments would involve the crushing of the boulder's constituent mineral grains. As single‐crystal mineral grains are stronger than rock boulders (in which fracturing develops by separating the constituent mineral grains without breaking them; see discussion in Zhang et al., 2022), micro‐porosity reduction typically occurs at higher pressures than macro‐porosity reduction. According to experiments on dust particles (as chondrite matrix analogs), this process (micro‐porosity removal below the solid fraction of ∼60%) initiates at several 10 MPa and continues until ∼1 GPa to be complete (e.g., Beitz et al., 2013).…”

“…In this paper, we apply cold compaction models developed in a companion paper (Zhang et al., 2022) to interpret observations of asteroid densities. We consider non‐rotating, spherically symmetric bodies under hydrostatic equilibrium to perform one‐dimensional calculations of the internal structures of asteroids.…”

“…where P is the assemblage pressure, s i is the boulder size, and 𝐴𝐴 A is the pull-off force of a pair of adhered boulders (Lammali et al, 2021;Than et al, 2017). In Zhang et al (2022), we collected results of experiments on compression of cohesive powders (Güttler et al, 2009;Omura & Nakamura, 2017;Than et al, 2020;Yasui & Arakawa, 2009) and suggested that the compaction of such assemblages can be described by the following relation,…”

“…In this series of papers, we assume that the static strength of chondritic boulders varies with size following Equation 2, because (a) the theory of Bažant (1984), together with the strength measurements performed on meteorite samples and concrete structures, suggests that the strength depends significantly on size only when the samples are much greater than the material inhomogeneity length scale, and (b) studies on flaw size distributions in terrestrial rocks and meteorite samples (e.g., Bryson et al, 2018; suggest a Weibull modulus of m ≈ 6 (also see Zhang et al, 2022). In the limit that the object size is much larger than the material inhomogeneity length scale (such that s is large compared to λℓ), Equation A3 coincides with Equation 2 of the main text, if we take 𝐴𝐴  = (𝐸𝐸∕𝜎𝜎0) 𝑚𝑚 (𝜆𝜆𝓁𝓁) −3 Π −1 and m = 6.…”

“…In a companion paper (Zhang et al., 2022), we developed theoretical models for cold compaction of chondritic and metallic rubble piles. In this paper, we apply these models to discuss the aforementioned observations regarding asteroid densities.…”