Compaction of Granular Packings - Determination of the Turnover Pressure as a Function of Grain Size

Compaction of granular packings – Determination of the turnover pressure as a function of grain size. J. N. Cybulski1, B. Gundlach1 and C. Güttler1, 1Institut für Planetologie, Universität Münster, Wilhelm-KlemmStr. 10, 48149 Münster, Germany Introduction: Understanding the compressional behaviour of the Moon´s regolith is fundamental to comprehending the surfaces development over time. In the context of our work, the turnover pressure is a measure for the transition from loose, weak bounded surface material to denser deeper material due to hydrostatic pressure [1], which can be measured experimentally. This study aims to derive the turnover pressure as a function of the regolith grain size, allowing to define the stratigraphic profile of the regolith in terms of the volume filling factor [1]. The understanding of this relation is crucial to sufficiently constrain mechanical and physical properties like the thermal conductivity [2]. Previous work: The turnover pressure was introduced in the prescription of [3] as 𝜙(𝑝)=𝜙2−𝜙2−𝜙1 exp[log(𝑝)−log⁡(𝑝m) ∆]+1 with 𝜙1 being the volume filling factor before compression, 𝜙2 being the volume filling factor at maximum compression, ∆ is a measure of the exponential width and 𝑝m defines the centre point between 𝜙1 and 𝜙2. The steepness of the transition is the greatest at 𝑝m. The relation between the turnover pressure 𝑝m and the grain size r is often described as a power law 𝑝𝑚(𝑟)∝𝑟𝛼 where the value for the power 𝛼 is debated as 𝛼 =4/3 [1] or 𝛼 =2⁡[4]. Both relations were derived by describing the development of the volume filling factor with mechanical properties of the sampled grains [1, 4]. Figure 1 visualises the clear differences in regard of the two proposed dependencies. It should be noted, that the experimental work of [1] used r > 5 μm only and the model of [4] grains with r < 5 μm mostly. Therefore, the relation might potentially not be described by one slope but a gradual transition depending on r (J. Blum, pers. comm.). Figure 1 also shows a clear lack of available data and a significant uncertainty in measured values of 𝑝m. Figure 1: Slopes of proposed dependency with slopes 𝛼 =4/3 [1] and 𝛼 =2 [4]. The relations are fitted to the measurement of [3, circle] in blue and to the measurement of [1, square] with r = 500 μm in red. (modified after Figure 2 of [5]) Experiment: To obtain more and accurate measurements, a similar approach to the omnidirectional compression experiment of [3] will be used. A dust sample with a diameter of 20 mm and a height of max. 10 mm to avoid the Jannsen effect [6, 7] will be omnidirectionally compressed by a piston within a borehole inside a cylinder. The dust samples will vary in shape and in grain size distribution. The design will allow a precise measurement of the compression displacement via distance sensors. Initially, the sample will be compressed by weights and the exerted pressure determined with an underlying scale. In a subsequent step the piston will be connected to a force sensor which will be connected to a motor to more precisely measure the exerted force and therefore pressure. Finally, the experiment will be conducted in a vacuum chamber, eliminating measurement deviations due to atmospheric influences like moisture within the sample and air pressure. The resulting data will help to determine a detailed relation between 𝑝m and r and constrain the mechanical and physical properties of the regolith. References: [1] Schräpler R. et al. (2015) Icarus, 257, 33-46. [2] Bürger J. et al. (2024) JGR: Planets, 129(3), e2023JE008152. [3] Güttler C. et al. (2009) The Astrophysical Journal, 701(1), 130-141. [4] Tatsuuma M. et al. (2023) The Astrophysical Journal, 953(1), 6. [5] Bürger J. et al. (unpublished, pers. comm.), corrigendum on [2]. [6] Janssen, H. A. (1895) Zeitschr. d.Vereines deutscher Ingenieure, 39, 1045. [7] Sperl M. (2006) Granular Matter, 8(2), 59-65.