Study on Mechanical Properties of QH-E Lunar Soil Simulant under Conventional Triaxial and Cyclic Triaxial Tests

Study of the mechanical properties of lunar soil simulant is the key to conducting lunar soil sampling and lunar base construction. In this paper, conventional and cyclic triaxial tests are performed by using discrete element method (DEM) to study the mechanical properties of QH-E lunar soil simulant. The results indicate that the confining pressure has an important impact on the shear strength and dynamic modulus of QH-E lunar soil simulant. In the conventional triaxial test, with the increasing of the confining pressure, both the peak deviatoric stress and residual stress increase, and the relevant results have been supported by experiments. In cyclic triaxial test, the area of cyclic hysteresis loop decreases with the increasing of the number of cycles, the axial strain and dynamic modulus first increase and then tend to be stable with the increasing of the number of cycles. Moreover, the axial strain increases with increasing confining pressure, while dynamic modulus decreases at a specific cyclic stress ratio (CSR) condition.


Introduction
Due to the special low gravity environment and formation process of lunar soil, there are significant differences in basic physical and mechanical properties between lunar soil and Earth's soil [1].It is necessary to have a clear understanding of the mechanical properties of lunar soil simulant at low stress levels.Previous research work on the mechanical properties of lunar soil simulant mainly focused on the static properties (such as: shear strength, volumetric deformation characteristics, and shear bands, etc.) [2][3][4][5][6][7][8], few studies have been conducted on the dynamic properties of lunar soil simulant under cyclic triaxial test.Though there are some studies on the dynamic properties of geotechnical engineering under cyclic loading [9][10][11], these studies mainly focused on earth soils (sand, clay, frozen soil) by carrying out a series of cyclic triaxial experiments or numerical simulations.According to the project of the International Lunar Research Station (ILRS), Lunar transportation and operation facility will be constructed by 2035 for exploration and use of the Moon [12].Thus, it is important to explore the dynamic mechanical properties and its influencing factors of lunar soil.Zhang et al. [13] conducted GDS resonant column tests to investigate the dynamic properties of lunar soil simulant (CAS-1), and discussed the effects of the confining pressure and porosity on the dynamic shear modulus and damping ratio.Prabu et al. [14] investigated the dynamic properties of the new LSS-ISAC-1 lunar highland simulant, and the variation patterns of shear modulus and damping ratio were obtained by cyclic triaxial experiments.Although there is limited studies on the dynamic behavior of lunar soil simulant under cyclic triaxial experiments, it has been aroused great interest in the dynamic behavior of lunar soil simulant.At present, the research on the dynamic mechanical properties of lunar soil simulant is still in its initial stage, and more in-depth exploration is needed by conjunction with numerical simulations.The lunar soil is mainly composed of dispersed particles and can be regarded as a granular material [1].The discrete element method (DEM) is becoming an emerging research direction in the field of lunar soil to study the basic physical, mechanical, and geotechnical engineering properties of lunar soil and numerical simulation of the interaction between lunar probes and lunar soil.Particle flow code (PFC) as an effective discrete element numerical simulation method, has been widely applied to investigate the mechanical behaviors of lunar soil under triaxial compression tests [15][16][17][18].In our previous studies [16][17][18], PFC3D simulations were performed to investigate the static mechanical behaviors (strength and deformation characteristics) of QH-E lunar soil simulant under triaxial compression tests.In this paper, the static and dynamic characteristics of QH-E lunar soil simulant under conventional triaxial and cyclic triaxial tests are further investigated by using PFC3D simulations.The influences of number of cycles and confining pressure on the mechanical properties of QH-E lunar soil simulant are discussed.Based on these, the mechanical properties and related influencing factors of QH-E lunar soil simulant are further analyzed, which will be helpful to gain theoretical basis for lunar soil sampling and the construction of the lunar space station.

Simulation model and process
In this DEM numerical simulations, PFC3D was used to investigate the mechanical properties of lunar soil simulant under conventional triaxial and cyclic triaxial tests.The shear strength and dynamic modulus of lunar soil simulant under different low confining pressures were analyzed.The parallel bond model was used, which can add cohesion and transmit torque between particles, and effectively simulate the mutual cohesion and interlock caused by angular particle shapes of lunar soil.Figure 1 shows a cylindrical sample of conventional triaxial and cyclic triaxial tests, which containing 40,673 unbreakable sphere particles with an initial porosity of 0.38.A random particle size distribution for lunar soil ranging from 1mm to 1.5 mm in diameter in Figure 2, is used to improve the computational efficiency [16][17][18].Table .1 shows the parameters of PFC3D numerical simulation of QH-E lunar soil simulant.In this study, cyclic stress ratio (CSR) is defined as the ratio of dynamic deviatoric stress d  to the confining pressure P. The number of cycles N =30 is applied in the simulation.The sine loading waveform is applied on the samples during the triaxial tests.The low confining pressure is chosen as 6.25kPa, 12.5kPa, and 25kPa respectively, to simulate the low gravity environment of lunar surface.

Stress-strain curves under conventional and cyclic triaxial tests
In triaxial compression experiments, confining pressure is crucial for the shear strength and volumetric deformation characteristics of the specimen.To analyze the shear strength of the specimen, the deviatoric stress-strain curves at various low confining pressures are given.Figure 2(a) shows the deviatoric stress-strain curves of QH-E lunar soil simulant under low confining pressures (6.25, 12.5, 25 kPa) obtained from experimental tests and PFC3D simulations under conventional triaxial tests.It can be seen from Figure 2(a) that the deviatoric stress-strain curves obtained from the experimental tests are basically consistent with those from PFC3D simulations.Moreover, it can be seen from the curves that under the given three low confining pressures, a significant strain softening phenomenon is observed in the QH-E lunar soil simulant.The deviatoric stress-strain curve including two stages: a hardening stage before peak deviatoric stress and a softening stage after peak stress.The softening stage can be further decomposed into a rapid softening stage and a residual strain stage.With the increases of the confining pressure, both the peak deviatoric stress and residual stress increase, which indicates that the confining pressure has an important effect on the shear strength of QH-E lunar soil simulant.Figure 2(b) shows the cyclic curve of deviatoric stress verses axial strain at the confining pressure P =25kPa, the cyclic stress ratio CSR=0.6 and the number of cycles N=30.It can be seen from Figure 2(b) that the hysteresis loop shows obvious differences in the first cycle and subsequent cycles, and the area in the first hysteresis loop is the largest.With the increase of the number of cycles, the decreases in the area of hysteresis loop, and the stress-strain curves of the two adjacent cycles basically coincide at the number of cycles N=30.The reason why is that the lunar soil simulant is relatively loose in the initial stage of triaxial compression, and then it gradually changes from sparse to dense as increasing in the number of cycles.

Variations of axial strain and dynamic modulus under cyclic triaxial tests
The variations of the axial strain and dynamics modulus of QH-E lunar soil simulant under cyclic triaxial tests are shown in Figure 3.At CSR=0.8, it is found that in the initial several cycles, the axial strain and dynamic modulus increase obviously at first, and then increases slowly with increasing of the number of cycles and gradually tends to a stable.This is because as increasing in the number of cycles, the sample gradually becomes dense, the deformation becomes smaller at the same loading conditions.From Figure 3(a), the higher the confining pressure is, the greater the axial strain is, and the amplitude of axial strain increased is also bigger.When the confining pressure P=25 kPa, CSR=0.8 and cycle number N=30, the axial strain has the highest value of 0.12.when the confining pressures P=12.5, and 6.25 kPa, the values of the axial strain are about 0.058 and 0.028, respectively.The variations of dynamic modulus at three different confining pressures of 6.25, 12.5 and 25 kPa are shown in Figure 3(b).The lower the confining pressure is, the higher the dynamic modulus is.It is found the dynamic modulus has the highest value of about 3.2 GPa at P=25 kPa, CSR=0.8 and N=30.when the confining pressures P=12.5, and 25 kPa, the values of the dynamic modulus are about 2.6 and 2.2 GPa, respectively.This indicates that the confining pressure has also a significant impact on the dynamic modulus and the dynamic modulus increases with decreases in confining pressure at a given CSR condition.

Conclusion
In this paper, the mechanical behaviors of QH-E lunar soil simulant under conventional and cyclic triaxial tests are investigated by using DEM, the influences of confining pressure on the dynamic modulus, axial strain and peak deviatoric stress are analyzed.The results found that the QH-E lunar soil simulant exhibits significant strain softening phenomenon in the conventional triaxial test, both the peak deviatoric stress and residual stress increase as the confining pressure increases.In cyclic triaxial test, the hysteresis loop shows obvious differences in the first cycle and subsequent cycles, the area of hysteresis loop decreases with increasing in the number of cycles.The axial strain and dynamic modulus first increase and then gradually trend to be stable with increasing in the number of cycles, which present similar variation characteristics to other sandy soils.Moreover, the axial strain increases but dynamic modulus decreases with increasing confining pressure at a specific cyclic stress ratio condition.

Figure 2 .
Figure 2. The deviatoric stress-axial strain curves under (a) conventional triaxial test and (b) cyclic triaxial test.

Figure 3 .
Figure 3. Variations of (a) axial strain and (b) dynamic modulus with increasing in the number of cycles.