The bearing capacity of asteroid (65803) Didymos estimated from boulder tracks

Abstract

The bearing capacity - the ability of a surface to support applied loads - is an important parameter for understanding and predicting the response of a surface. Previous work has inferred the bearing capacity and trafficability of specific regions of the Moon using orbital imagery and measurements of the boulder tracks visible on its surface. Here, we estimate the bearing capacity of the surface of an asteroid for the first time using DART/DRACO images of suspected boulder tracks on the surface of asteroid (65803) Didymos. Given the extremely low surface gravity environment, special attention is paid to the underlying assumptions of the geotechnical approach. The detailed analysis of the boulder tracks indicates that the boulders move from high to low gravitational potential, and provides constraints on whether the boulders may have ended their surface motion by entering a ballistic phase. From the 9 tracks identified with sufficient resolution to estimate their dimensions, we find an average boulder track width and length of 8.9 $\pm$ 1.5 m and 51.6 $\pm$ 13.3 m, respectively. From the track widths, the mean bearing capacity of Didymos is estimated to be 70 N/m², implying that every 1 m² of Didymos' surface at the track location can support only ~70 N of force before experiencing general shear failure. This value is at least 3 orders of magnitude less than the bearing capacity of dry sand on Earth, or lunar regolith.

Fig. 1. Identification of suspected boulder tracks on asteroid Didymos.

a The approximate equator (dashed magenta line), example boulder tracks (magenta arrows) and likely boulders (white arrows) on the surface of Didymos. b The 15 boulder tracks identified on the surface of Didymos are indicated by the magenta lines. The image used here is a cropped section of DRACO image 22206, after Laplacian filtering.

Fig. 2. Topography of Didymos at the boulder track locations.

a Map of the gravitational potential over the surface of the asteroid Didymos from ref. with the positions of the identified boulder tracks (Fig. 1) indicated. b The change in gravitational potential along each of the tracks is shown as a function of the normalized track length (i.e., along track distance/total track length) measured from higher to lower latitudes.

Fig. 3. The bearing capacity of the surface of Didymos estimated using a Monte Carlo simulation.

Uniform distributions are assumed for the key variables in the range of: ϕ ∈ [25;45]°, c ∈ [0;10] N/m², ρ ∈ [1000;3000] kg/m³, GM ∈ [33.9; 36.9] m³/s², R ∈ [383; 405] m, B ∈ [4.47; 13.33] m, D ∈ [0; 13.33] m. A total of 100,000 iterations are performed and the histogram of the results is shown in gray. The fitted lognormal distribution (shown in red) has a mean and mode of 70 and 17 N/m², respectively. The lognormal fit has parameters μ = 3.8 and σ = 1.0.

Fig. 4. The influence of uncertain parameters.

In these figures the bearing capacity assuming the mean track width (8.9 m) and the mean latitude (13°) is plotted as a function of normalized track depth. The parameters are varied individually while keeping the others equal to the baseline values (ϕ = 35°, c = 1 N/m², g_eff = 3.1 × 10⁻⁵ m/s², ρ = 2790 kg/m³). a Influence of varying the angle of internal friction from 25 to 45°. b Influence of varying the cohesion from 0 to 10 N/m². c Influence of varying the effective gravitational acceleration (g_eff) from 1 × 10⁻⁶ to 6.3 × 10⁻⁵ m/s², corresponding to a GM range of 35.4 ± 1.5 m³/s² and R = 394 ± 11 m. d Influence of varying the regolith density from 1000 to 3000 kg/m³.