Establishment of Lunar Soil Excavation Model and Experimental Simulation Study

Abstract

Understanding and clarifying the excavation mechanism of lunar soil, as well as the interaction between the sampling shovel and lunar soil, are crucial for improving surface sampling efficiency and ensuring equipment safety. Based on the Swick and Perumpral model, an excavation model for the sampling shovel during the surface sampling process was established. This study focuses on JLU-6 simulated lunar soil and conducts a total of 81 experiments to investigate the sampling depth, excavation torque, and sampling volume under different sampling conditions, such as excavation angles and soil compaction levels. In addition, discrete element simulations of the surface sampling excavation process were conducted. The results indicated that the mass of soil excavated by the sampling shovel increased with the sampling angle, while the sampling increment decreased as the angle increased. The sampling resistance also increased with the sampling angle, with most of the additional resistance being used to shear and break the soil layers, rather than being fully converted into an increase in the sampling volume. At the same time, the established excavation model was analyzed through both experiments and simulations. The analysis results show that the model can predict the excavation resistance based on the excavation angle and depth, providing a reference for in-orbit operations.

1. Introduction

With the continuous advancement of lunar surface missions, lunar soil sampling and return have become one of the key tasks in lunar exploration. Among these, the Chang’e-5 and Chang’e-6 missions have successfully completed their respective soil sampling and return operations [1,2,3,4]. However, due to the complex environment of lunar soil on the lunar surface and the difficulty of real-time monitoring, it is necessary to establish a corresponding surface sampling model. This model can be used to analyze the sampling process and predict its outcome, providing important theoretical support to ensure the successful completion of surface sampling tasks [5].

Currently, research on the excavation work of sampling shovels mainly relies on studies of ground soil excavation as a reference and basis. For the analysis of pushing resistance, the Rankine passive earth pressure theory based on the limit equilibrium method is predominantly used for calculations [6,7]. Foreign research on soil pushing resistance began relatively early. The earliest pushing resistance model was based on Terzaghi’s classical soil strength theory [8], using the principle of force equilibrium and applying a passive retaining wall model to establish a model based on a linear failure surface. In 1964, Osman [9] developed the Osman model using concepts such as curved failure surfaces. This model significantly improved accuracy compared to earlier machine–soil interaction models based on linear failure surfaces. In 1968, the Gill-VandenBerg [10,11] model built upon its predecessor by incorporating soil inertial forces and cohesion into the model while simplifying machine–soil friction forces. With the development of soil excavation ground tests during the Viking Mars mission, the Lockheed Martin model, tailored for bucket-wheel excavation devices, proposed a cohesion equation describing a non-quadratic relationship between resistance and excavation speed [12,13]. In the 1980s, the Swick–Perumpral model and the McKyes model provided different mathematical descriptions of soil excavation resistance for the cutting process between a simple two-dimensional bulldozer blade and soil [14,15]. In 2012, Zeng further developed the McKyes model by incorporating the effect of the velocity term on soil excavation resistance [16].

Due to inherent limitations in lunar soil theoretical models—including the insufficient representation of authentic regolith properties, inadequate characterization of vacuum/extreme temperature effects, and lack of microgravity behavior data—researchers predominantly rely on terrestrial soil simulations to conduct lunar excavation experiments for deep space mission planning. Several thermal models have been developed to address challenges in lunar surface sampling and resource extraction, including investigations into the thermophysical properties of regolith at cryogenic temperatures [17], numerical simulations of ice sublimation dynamics in cylindrical samples under varying thermal conditions [18], and high-resolution 3D topographic thermal analyses of polar regions to assess volatile stability and subsurface temperature gradients [19]. Bernold conducted experimental studies on the excavation resistance of different mechanisms using sand with a density distribution similar to that of lunar soil. He also analyzed and discussed excavation methods for lunar soil [20,21].

Boles et al. conducted experiments on the excavation resistance of sand under low gravity, focusing on the characteristics of the lunar surface’s low-gravity environment. They analyzed the impact of different gravity environments on excavation resistance [22]. With the development and large-scale use of simulated lunar soil, experimental research on lunar soil excavation resistance using simulated lunar soil has gradually increased. Michael et al. conducted excavation experiments on JSC-1A simulated lunar soil and measured the conventional excavation resistance of the simulated lunar soil [23]. Agui, based on conventional excavation, conducted excavation experiments on GRC-3 simulated lunar soil at different excavation depths and angles. He analyzed the excavation resistance of lunar soil under different excavation postures [24]. Alex et al. focused on JSC-1A simulated lunar soil and used methods such as vibratory and impact excavation to analyze and study the excavation resistance of lunar soil under different excavation techniques [25]. However, due to the challenges associated with vacuum and low-gravity environment testing, the accuracy of the results is difficult to validate against actual conditions on the lunar surface [26].

This paper focuses on JLU-6 simulated lunar soil as the research object and, in conjunction with the excavation tools used in the Chang’e series, establishes the corresponding excavation model. Through ground experiments and discrete element simulation tests, the excavation process on the lunar surface is analyzed. The established model is validated, and the excavation trends are analyzed and predicted. The results provide theoretical guidance for the operation of excavation mechanisms in orbit.

2. Model Construction

The lunar surface environment is harsh, and during the drilling and excavation of lunar soil, the unknown physical and mechanical parameters of the lunar surface soil pose risks, including damage to or destruction of sampling equipment, potentially leading to mission failure. Therefore, before excavation and sampling in an unknown exploratory environment, it is essential to first identify the relevant mechanical parameters of the lunar soil to analyze the excavation process through an excavation model. Conventional models often suffer from complex identification processes and insufficient computational capacity, which affect the real-time performance of the model and severely restrict its engineering application in actual excavation processes. In this section, based on the sampling process, a shovel excavation model suitable for lunar soil sampling is established to analyze the sampling process, thereby improving sampling efficiency and safety.

2.1. Analysis of Surface Sampling Process

For the loose lunar soil on the surface, a shovel excavation method can be used for sampling, with the specific actions of the excavation illustrated in Figure 1. Firstly, the sampling tool is adjusted to the appropriate height according to the proposed excavation depth, and then the sampling shovel rotates around the rotation center to rotate it to the position where the end of the sampling shovel is close to the lunar surface. At this time, the angle between the end of the sampling shovel and the horizontal plane is the α angle in Figure 2a. Then, the shovel rotates around a fixed axis, and its motion curve sweeps through the lunar soil, transferring the soil into the container. Afterward, the sampler is lifted, and the shovel and the upper cover close to form a sealed container. During the initial phase of excavation, the cutting plate is used to slice through the lunar soil to facilitate smooth insertion into the soil. Once the cutting plate is fully inserted into the lunar soil, the pushing plate makes contact with the soil, pushing the soil to be excavated, thereby completing the excavation process.

Through the analysis of the digging process, it is understood that when a digging component with a certain width moves through the soil at a set speed with a specific wedge angle and plowing depth, it not only generates interaction forces but also causes soil failure, as shown in Figure 2a. For the digging component, the force exerted by the soil on it is the soil resistance, which is the force that hinders its movement. The digging resistance of the sampler mainly includes lunar soil cohesion, additional resistance from accumulated lunar soil, friction between the lunar soil and the bottom and sides of the swing arm shovel bucket, inertial force, and additional loads. The force forms acting on the swing arm shovel during the lunar soil digging process are shown in Figure 2b. The penetration angle is α shown in Figure 2a. The digging angle β can be expressed as the shoveling process of angle (−α, α), and the total angle range is 2α.

2.2. Construction of the Digging Model

Based on the Swick and Perumpral model, a corresponding excavation model is established [27]. This model introduces a more complex machine–soil friction coefficient and inertial force caused by speed, in addition to considering the adhesion factors between the soil and the cutting blade. The total cutting resistance formula is shown in Equation (1) [28]. The parameters involved are shown in

Table 1. Model parameter reference table [29,30].

Model Symbol	Content	Parameter	Units	Values
Sampling scoop	Tool width	w	m	0.04
	Tool length	l	m	0.145
	Digging radius	L	m	0.205
Soil–soil	Cohesion	c	pa	200–1350
	Internal friction angle	Φ	deg	20–35
	Soil specific mass	γ	kg/m3	1–1.5 × 103
Soil–tools	External friction angle	δ	deg	32
	Shear plane failure angle	ρ	deg	=45 + Φ/2
Test	Tool depth	d	m	0–0.05
	Digging Angle	β	deg	20–40
Gravity	Earth gravity	ge	m/s2	9.8
	Lunar gravity	gl	m/s2	1.633

.

$$F_T=\left[\begin{array}{l}{\displaystyle \frac{-C_a\cos (\beta +\varphi +\rho )}{\sin \beta }}+{\displaystyle \frac{g\gamma d}{2}}(\mathrm{c}\mathrm{o}\mathrm{t}\beta +\mathrm{c}\mathrm{o}\mathrm{t}\rho )\mathrm{s}\mathrm{i}\mathrm{n}(\varphi +\rho )+\\ gq(\mathrm{c}\mathrm{o}\mathrm{t}\beta +\mathrm{c}\mathrm{o}\mathrm{t}\rho )\mathrm{s}\mathrm{i}\mathrm{n}(\varphi +\rho )+{\displaystyle \frac{c\cos \varphi }{\sin \rho }}+{\displaystyle \frac{\gamma v^2\sin \beta \cos \varphi }{\sin (\beta +\rho )}}\end{array}\right]\times {\displaystyle \frac{wd}{\sin (\beta +\varphi +\rho +\delta )}}$$

(1)

Based on the resistance F_T, the horizontal component H and the vertical component V during the digging process can be obtained. Their expressions are shown in Equations (2) and (3). The parameters involved are shown in Table 1.

$$H=T\sin (\beta +\delta )$$

(2)

$$V=T\cos (\beta +\delta )$$

(3)

The aforementioned basic model indicates that depth is the most significant factor affecting the digging force. In addition, the entry angle, cohesion, internal friction angle, and lunar soil density during the excavation process also have a considerable impact on the digging model. This model also considers the effect of shovel length on the torque. The simplified excavation torque model function is shown in Equation (4).

$$T=\left({\displaystyle \frac{3g\gamma d}{2}}\left(\cos \beta +\cot \rho \right)\sin \left(\varphi +\rho \right)+{\displaystyle \frac{c\cos \varphi }{2\sin \rho }}\right)\times {\displaystyle \frac{2wdL}{\sin \left(\varphi +\delta +\beta +\rho \right)}}$$

(4)

The model includes the digging angle β, internal friction angle Φ, shear plane failure angle ρ, and external friction angle δ, as shown in Table 1.

Here, based on the established model, the expressions for the impact of depth and compaction on the excavation torque T1, and the impact of cohesion on the excavation torque T2, are given as shown in Equations (5) and (6). T1 and T2 will provide a basis for analyzing the applicability of the model.

$$T_1={\displaystyle \frac{3g\gamma d}{2}}\left(\cos \beta +\cot \rho \right)\sin \left(\varphi +\rho \right)\times {\displaystyle \frac{2wdL}{\sin \left(\varphi +\delta +\beta +\rho \right)}}$$

(5)

$$T_2={\displaystyle \frac{c\cos \varphi }{2\sin \rho }}\times {\displaystyle \frac{2wdL}{\sin \left(\varphi +\delta +\beta +\rho \right)}}$$

(6)

3. Test Simulation Analysis and Verification

3.1. Ground Test Content

For the lunar surface soil sampling task, surface sampling tests are conducted to determine the optimal sampling scheme. The qualitative and quantitative relationships between sampling depth, digging torque, and sampling volume under different sampling conditions (such as digging angle and compaction) are explored. Figure 3 shows a schematic diagram of the digging test. The test bed is located in Jilin University. The digging actuator is equipped with a torque sensor to obtain torque data during the digging process. Sampling tests are conducted at a speed of 10°/s under different digging angles and compaction levels, and the digging traces, torque, and sampling volume are collected for analysis.

JLU-6 is designed as a simulant for the Chang’e-6 mission, which targets a landing region characterized by a mixture of lunar mare and highland geological features. The JLU-6 simulated lunar soil used in the experiment has a median particle size of 0.1 mm, with basalt accounting for 60% and anorthosite for 40%. The particle size distribution of JLU-6 is illustrated in Figure 4. Tests are conducted on the bulk density, cohesion, and internal friction angle of the simulated lunar soil to provide data support for parameter inversion and simulation analysis [31]. The calibration parameters are shown in

Table 2. Simulation of lunar soil bulk density test.

Max kg/m3	Min kg/m3	Trystate	Relative Compaction	Actual kg/m3
1550	1200	Loose	30%	1290
		Medium	50%	1350
		Dense	70%	1430

and

Table 3. Simulation of lunar soil direct shear test.

Trystate	Relative Compaction	Cohesion kpa	Internal Friction Angle °
Loose	30%	0.25	26.20
Medium	50%	0.50	27.4
Dense	70%	1.15	25.9

.

Table 4. Simulation of lunar soil penetration resistance test.

Depth/cm	Loose (kpa)	Medium (kpa)	Dense (kpa)
0	0	0	0
2.5	0	0	0
5	0	35	175
7.5	35	316	491
10	351	842	1053
12.5	1018	1123	1650

shows the test results of the penetration resistance of the simulated lunar soil in the soil trough of the test bench shown in Figure 3.

3.2. Establishment of Discrete Element Model

Lunar soil simulation based on the discrete element method is an effective way to study the properties of lunar soil and the interaction between machinery and soil. Its advantage lies in avoiding the complex and variable simulation of lunar soil particle shapes and compositions, instead using discrete elements centered on regular spherical particles. By establishing contact relationships between particles, it simulates the mechanical properties of lunar soil [32]. Additionally, using discrete element simulation technology(EDEM 2022) allows for low-cost simulation environments with 1/6 gravity acceleration, low pressure, and no water. By varying the bulk density of the lunar soil and the sampling angle of the shovel, a regression mathematical model is established between the input (sampling angle and bulk density) and the sampling output (sampling resistance and sampling efficiency).

The simulation will use the Hertz–Mindlin–JKR model, which simplifies lunar soil into a nonlinear elastoplastic model and considers cohesion between particles. The main parameters of this simulation model are shown in

Table 5. Simulation parameter settings [33].

Symbol	Content	Values
Particle	Density (kg/m3)	2500, 2900, 3400
	Diameter (mm)	1.5
	Shear modulus (GPa)	1.35 × 107
	Poisson ratio (−)	0.39
Sampling Scoop	Density (kg/m3)	5000
	Shear modulus (GPa)	1 × 108
	Poisson ratio (−)	0.5
Particle–Particle	Coefficient of Static Friction	0.75
	Coefficient of Rolling Friction	0.6
	Coefficient of Restitution	0.84
Particle–Scoop	Coefficient of Static Friction	0.5
	Coefficient of Rolling Friction	0.5
	Coefficient of Restitution	0.5
Test	Digging angle (°)	30, 50, 70
	Digging speed (°/s)	10
Model Parameter	Surface energy (J/m2)	0.1

. It is important to note that the bulk density of the lunar soil will be achieved by changing the compaction of the particle bed, with particle sizes following a normal distribution and an average diameter of 3 mm. To highlight the horizontal movement of particles during the digging process, a multi-layer particle bed in the horizontal direction (100 mm × 300 mm × 75 mm) is established. To eliminate the influence of boundary conditions, periodic boundary conditions are used in the length and width directions. The sampling shovel is simplified by removing the sample packaging structure, retaining only the swing arm shovel part.

The simulation considers digging resistance under three different digging angles (depths) and three lunar soil bulk density conditions. The impact of these two factors on digging resistance is analyzed using experimental design methods. A full factorial experimental method is used, and the experimental design scheme is shown in

Table 6. Test scheme design.

Angle (°)	Density (kg/m3)
30	1314
	1524
	1787
50	1314
	1524
	1787
70	1314
	1524
	1787

. To compare with the experiment, the simulation will consider the effects of real lunar gravity and Earth gravity.

3.3. Analysis of Test and Simulation Results

The experimental results will mainly include the reconstruction of the sampling profile, a comparative analysis of digging quality and efficiency, and the impact of sampling angle and lunar soil bulk density on sampling resistance, along with a regression analysis of the digging model. The digging process is shown in Figure 5a. As seen in Figure 5b, with the increase in digging angle (depth), the disturbance amplitude and range of the sampling shovel on the particles increase. Figure 5c–e show the profiles formed at digging angles of 30°, 50°, and 70°, respectively. A data analysis indicates that as the digging angle increases, the width and depth of the digging profile also increase.

Secondly, the force on the sampling shovel and the digging quality are analyzed, with ground test results shown in Figure 6. As the entry angle increases, the maximum digging depth also increases, and the maximum torque during digging shows a gradually increasing trend. The torque increase for a 30° entry angle is about 70% compared to a 25° entry angle, and for a 35° entry angle, the torque increase is between 50 and 80% compared to a 30° entry angle. The digging volume also significantly increases with the digging angle (digging depth). At the same digging angle, due to increased compaction, there is a slight increasing trend in the digging volume.

The simulation results are shown in Figure 7. Among them, the resistance of the sampling shovel rises rapidly in the initial excavation stage. When the excavation angle forms a certain angle with the normal direction of the granular bed, the excavation resistance reaches the maximum value. Subsequently, the excavation resistance gradually decreases. This is because in the initial excavation stage, the granular layer needs to be sheared and destroyed first. When the granular bed is sheared and destroyed, the shovel excavation resistance reaches the peak. The area formed by the shovel excavation resistance and the shovel excavation angle is the work performed to overcome the resistance during the sampling shovel excavation process. It can be seen from Figure 7a that when the shovel excavation angle is 70°, the energy consumed in the excavation process is much greater than that when the excavation angles are 30° and 50°. In other words, optimizing the sampling angle can reduce energy consumption while ensuring the excavation quality. Figure 7b shows the influence of the shovel excavation angle on the excavation quality. For different particle densities, as the shovel excavation angle increases, the total excavation mass increases, but the increment of the excavation mass decreases. Combined with Figure 7a, it can be observed that the shovel excavation efficiency decreases with the increase in the shovel excavation angle.

In summary, the sampling quality increases with the increase in the sampling angle, but the sampling increment decreases with the increase in the angle. The sampling resistance increases with the increase in the sampling angle, and most of the increased sampling resistance is used to shear and destroy the soil layer and is not completely converted into an increase in the sampling amount.

3.4. Model Applicability and Digging Trend Prediction

Through the experiments carried out above, we compared and analyzed the experimental data with the established shovel excavation model, verified the influence of the shovel excavation depth and density on the shovel excavation torque, analyzed the influence of the cohesion parameter in the shovel excavation model, and then discussed the feasibility analysis of the inversion of the cohesion parameter. Combined with the experimental data, we conducted a comparative verification analysis of the shovel excavation torque trend and judged the feasibility of the shovel excavation model in predicting the shovel excavation torque trend.

Through the experiments, the model values and experimental values of the torque change under different factors, as shown in Figure 8. Figure 8a shows the influence of the shovel excavation depth on the shovel excavation torque. It can be seen from the figure that the shovel excavation torque of the model and the experiment increases with the increase in the shovel excavation depth and shows a good correlation. The influence of the shovel excavation depth on the shovel excavation torque is significant, and the increase range of the shovel excavation torque within the set range of the shovel excavation depth exceeds 200%. The influence of the cohesion is relatively small. Due to the characteristics of the shovel excavation sampling process, the sampling depth has a corresponding relationship with the shovel excavation angle; that is, the shovel excavation depth can be obtained according to the shovel excavation angle. Figure 8b shows the influence of the density change on the shovel excavation torque. The results show that the model results and the experimental results show good consistency. And the density has a linear correlation with the total shovel excavation torque. The data in Figure 8c show that the cohesion has a linear correlation with the shovel excavation torque. And in the case of knowing other parameters, the size of the cohesion can be obtained by model inversion, as shown in Figure 8d.

Through the model established above, the torque trend in the shovel excavation process is predicted, and the obtained results are shown in Figure 9. Due to the symmetry of the shovel excavation action, the total shovel excavation angle of the model is determined to be 60° according to the entry angle of 30°. However, during the test process, affected by the soil accumulation and the self-weight of the soil in the shovel, the rotation angle of the test data is greater than 60°. But the model can still accurately reflect the trend of the shovel excavation torque, which can provide a judgment basis for the on-orbit test.

4. Conclusions

The sampling process and forces acting on lunar regolith were analyzed. Based on the Swick and Perumpral model, a shovel-excavation model suitable for the soft lunar regolith on the lunar surface was established. This model takes into account the effects of shovel-excavation depth, cohesion, and density on the shovel-excavation torque.

Through ground tests and discrete element simulations, the excavation process on the lunar regolith surface was simulated. The results of the tests and simulations show that the shovel-excavation depth has the most significant impact on the shovel-excavation resistance and torque, while the impact of density is relatively small. As the shovel-excavation depth increases, the total sampling amount increases, but the increment of the sampling amount decreases. The shovel-excavation efficiency decreases with the increase in the shovel-excavation angle.

The accuracy of the established shovel-excavation model was verified. The results indicate that the shovel-excavation depth has the most significant impact on the shovel-excavation torque, and the impact of cohesion is relatively small. The shovel-excavation torque increases with the increase in the shovel-excavation depth. There is a linear correlation between density, cohesion, and the shovel-excavation torque. The model inversion of density and cohesion is feasible, which can provide a basis for judgment in on-orbit tests.