Wave Velocities and Poisson Ratio in a Loose Sandy Martian Regolith Simulant Under Low Stresses: 2. Theoretical Analysis

Abstract

This paper presents a theoretical analysis of the data on wave velocity measurements at small stresses presented in a companion paper describing the experimental results on a Martian regolith loose sandy simulant (Fontainebleau sand) of the soil at the InSight landing site on Mars (Elysium Planitia). Experimental data of wave velocities and Poisson's ratio are interpreted in the light of a granular contact mechanics theory and completed accounting for rugosity effects that are suspected to have stronger effects in sands under low stresses. The asperities of a grain of Fontainebleau sand were investigated through Atomic Force Microscopy, but larger asperities had to be adopted so as to better fit the model prediction with experimental data. A good agreement between the experimental data and the model predictions is obtained for stress above 10 kPa. Below 5 kPa, an area in which asperities are suspected to have a stronger influence, the model is not fully satisfactory, showing that further experimental and theoretical investigation is necessary in a stress zone particularly relevant to surface soils in planets, with probably enhanced effects of asperities on the intergrain contact mechanics.

Velocity Measurements of Powdered Rock at Low Confining Pressures and Comparison to Lunar Shallow Seismic Velocity

“…This mismatch was not observed by Caicedo et al. (2023), who used the Bachrach model to describe Martian regolith simulant, perhaps due to the larger rounded grains used in their study. The uncemented sand model (Dvorkin & Nur, 1996, Equation ) shown in Figure 6 has been modified to use the effective moduli from the Bachrach model at critical porosity, which agrees with measured bulk moduli above 40% porosity but again overpredicting shear modulus, V P , and V S .…”

“…The modified CRM proposed by Bachrach et al (2000) (Equation A2; hereafter referred to as the Bachrach model) agrees with the bulk moduli measurements above 40% porosity but overpredicts shear modulus, V P , and V S , even with a high reduction in shear stiffness of the material compared to the Hertz-Mindlin model. This mismatch was not observed by Caicedo et al (2023), who used the Bachrach model to describe Martian regolith simulant, perhaps due to the larger rounded grains used in their study. The uncemented sand model (Dvorkin & Nur, 1996, Equation A4) shown in Figure 6 has been modified to use the effective moduli from the Bachrach model at critical porosity, which agrees with measured bulk moduli above 40% porosity but again overpredicting shear modulus, V P , and V S .…”

“…This modeling approach has recently been used by Caicedo et al. (2023) to describe the elastic behavior of Martian regolith simulant at low pressure. Zimmer et al.…”

“…The reduced contact area due to grain angularity is illustrated in Bachrach et al (2000, their Figure 2). This modeling approach has recently been used by Caicedo et al (2023) to describe the elastic behavior of Martian regolith simulant at low pressure. Zimmer et al (2007a) used an empirical fit to laboratory data that relies on a void-ratio relation and corrects for compaction.…”