PS10
DEM 解析における月模擬砂 FJS-1 の力学挙動再現を目的とした粒子モデル作成と校正
Creation and Calibration of a Particle Models for
Reproducing the Mechanical Behavior of Lunar Soil
Simulant FJS-1 in DEM Analysis
松尾昂輝 1, 梶原健生 2, 渡辺公貴 2, 川口正隆 2, 田中和人 212

同志社大学大学院，Graduate School of life and Medical Science Doshisha
同志社大学，Doshisha University

1. Introdction
The soft ground composed of fine particles called regolith on the lunar surface poses obstacles such asslippage and getting stuck for rovers during traversal1). Therefore, understanding the mechanical propertiesof lunar soil and predicting and evaluating the traversal performance of rovers are crucial for establishing
future mobility technologies. The Discrete Element Method (DEM) numerical simulation is expected to be
useful due to its ability to visualize the interaction between sand and wheels exhibiting nonlinear movements
and consider in-situ factors such as low-gravity environments. In DEM analysis for evaluating the traversal
performance of rovers, spherical elements are generally used for soil particles from the perspective of contact
detection and computational speed. However, it has been revealed that the particle size distribution andparticle shape of irregular powder materials like regolith significantly influence the mechanical properties ofthe powder2). In this study, to reproduce the mechanical behavior of the lunar simulant sand FJS-1 in DEM
analysis, we constructed a particle model based on three-dimensional observations using X-ray CT andcalibrated DEM parameters through angle of repose experiments.
2.

DEM methodology and calibration approach

2.1. X-ray CT measurement and particle modelling.
In soil mechanics, it is known that parameters such as particle shape, size distribution, and porosity havesignificant effects on the mechanical properties of the soil2). This experiment aimed to model and simulate theirregular particle shapes of the lunar simulant sand FJS-13). We measured the 3D shapes of the particles byusing a high-resolution 3D X-ray microscope (Rigaku Corporation, nano3DX). The 3D particle images
obtained from the observations are shown in Figure 1. For each particle shown in Figure 1, a bounding box asshown in Figure 2 was constructed, and the dimensions of each side were defined as a, b, and c. When setting
the conditions a ≤ b ≤ c, the bounding box in Figure 2 can be divided into four cases. Based on these four cases,
1 of 5the particle shapes were classified into the four shapes shown in Figure 3, and particle models were created.
In creating the particle models, the arrangement of spherical elements in each model was made to satisfy theconditions (i) ~ (iv) below.
i.

The four particle models are respectively composed of spherical elements with the same diameter.

ii.

The spherical elements in each model should be arranged to match the average packing density ofthe particles within the bounding box.

iii.

The particles are arranged to be inscribed within a bounding rectangular box.

iv.

The number of sphere elements that make up the particle model should be set to a minimum.

Figure 1. The 3D image of FJS-1 Particles.

Figure 3. Particle models of lunar soil simulant.

Figure 2. Bounding box circumscribed to particles.

Figure 4. AoR measurement experiment.

2.2. Measurement of AoR
The angle of repose (AoR) is a fundamental indicator used to evaluate the mechanical properties of granularmaterials and has been widely utilized for calibrating DEM parameters. An overview of the AoR measurement
experiment is shown in Figure 4. At the start of the experiment, the lunar simulant soil discharged into the tray
below funnel and accumulates in a conical shape. The funnel bottom was kept within 5 mm of the lunar soil
simulant tip during the experiment to reduce the impact of particle falling speed on the AoR. Additionally, avibrating motor with speed control was used to impart a 100 Hz micro-vibration to the funnel and slide,
preventing the adhesion of the simulant sand to these apparatus surfaces. Furthermore, a mesh with a size of
1.0 mm × 1.0 mm was set on the top of the funnel to exclude particles with an equivalent diameter of 1.0 mm
or greater that were not DEM analysis. Under these conditions, the AoR was measured five times. After theexperiment, images of the deposited simulant soil were captured with a camera positioned horizontallyrelative to the funnel. The images were binarized as shown in Figure 5, and edge detection was performed to2 of 5

delineate the surface profile without losing its roughness. The two-dimensional coordinates of the divided
lines were calculated, and the AoR was determined.
𝜙𝑟 = tan−1 𝑎(1)From equation (1), the angle of repose obtained in this experiment was 40.9 ± 1.17°.

(a) Binary image of the deposited FJS-1.
Figure 5.

(b) Edge-detected image.

Method of calculating AoR.

2.3. Calibration of the DEM parameters of lunar soil simulant
The fluid analysis software Ansys Rocky 2023 R.1.1 was used to simulate the angle of repose measurement.
Among the many parameters to be input to the simulation, it has been reported that the static and rolling
friction coefficients have a high contribution to the angle of repose 5). Therefore, in this research, simulation
was calibrated by matching the experimental values of the angle of repose with the analytical response, using
as variables the static friction coefficient 𝜇1 and the rolling friction coefficient 𝜇2 of the particles, which areconsidered difficult to measure directly. The employed apparatus for measuring the AoR in the simulation isshown in Fig. 6. The particle model used was the described in section 2.1. The particle size and shape
distributions of the model are shown in Figure 7. Other parameters used in the simulation are listed in Table
1 below. Considering that FJS-1 particles have adhesive properties, a model combining the contact theory ofHertz-Mindlin with the adhesion theory of JKR was used as the contact model in this simulation6).

Figure 6. The employed apparatus forFigure 7. Particle size distribution in simulation.

measuring the AoR in simulation.
3 of 5Table 1. Material parameters in DEM simulation.

Parameter

Value

Bulk density of lunar soil simulant [kg/m 3]

1360

Young’s modulus of lunar soil simulant [MPa]42.5

Poisson’s ratio of lunar soil simulant

0.25

Inner restitution coefficient of lunar soil simulant

0.5

Inner static friction coefficient of lunar soil simulant

0.2 - 0.4

Inner rolling friction coefficient of lunar soil simulant

0.01 - 0.15

Surface energy for lunar soil simulant [J/m2 ]
3.

0.01

Results

3.1. Effect of static and rolling friction coefficients on AoR
As shown in Table 1, the static friction coefficient 𝜇1 was varied from 0.2 to 0.5 in 0.1 increments and therolling friction coefficient 𝜇2 was varied from 0.01 to 0.15 in 0.07 increments for a total of 9 simulations. The
results are shown in Figure 8. A comparison of simulated and experimental AoR is shown in Figure 9.

Figure 8. interaction effect of μ1 and μ2 on AoR

Figure 9. Comparison of simulated and experimental AoR.

In Figure 8, the larger the static friction coefficient 𝜇1 is, the higher the value of the AoR is for the larger
rolling friction coefficient 𝜇2 . Figure9 shows that at (𝜇1 , 𝜇2 ) = (0.4, 0.01), the AoR is 41.1°, which is the closest
value to the experimental result. Based on this result, multiple regression analysis was conducted with AoR
as the dependent variable and 𝜇1 and 𝜇2 as independent variables. The regression equation can be
expressed as Equation (2) below.
𝐴𝑜𝑅 = 103𝜇1 + 25.4762𝜇2 + 0.2619(2)

From Equation (2), it can be observed that the contribution of 𝜇1 to the angle of repose is higher comparedto 𝜇2 .

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3.2. Effect of the gravity acceleration on AoR
To investigate the effect of gravity on AoR, three DEM simulations under varying gravity conditions of 1/6
G and 1 G were performed. The parameters used in these simulations were the same as the optimal solutionsof the regression model except the gravity acceleration. Results are shown in Figure 10.

(a) 1 G.

(b) 1/6G.

Figure 10. Comparison AoR for varying gravity conditions
As you can see in Figure 10, the results demonstrated that the AoR is higher at lower gravity.
4.

Conclusion
This study aimed to reproduce the mechanical behavior of the lunar soil simulant FJS-1, which has irregularparticle shape, and revealed that it can be calibrated by creating a particle model other than spherical elements
and varying two coefficients, which are the static friction coefficient and the rolling friction coefficient. The
accurate setting of DEM input parameters for the lunar soil simulant by calibration is expected to clarify theinteraction between the lunar simulant sand and rover wheels in DEM analyses for future lunar exploration,and to be applied to the prediction of rover running performance.
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