华中科技大学 国家数字建造技术创新中心，土木与水利工程学院，湖北 武汉430074
引用格式：
周诚，李浩然，夏一峰，等. 离散元法在月面建造力学分析中的研究及应用［J］.中国粉体技术，2024，30（4）：26-42.
ZHOU C， LI H R， XIA Y F， et al. Research and application of DEM in the mechanical analysis of lunar construction［J］. China Powder Science and Technology，2024，30（4）：26−42.
DOI：10.13732/j.issn.1008-5548.2024.04.003
收稿日期：2024-03-27，修回日期：2024-05-16，上线日期：2024-06-25。
基金项目：国家重点研发计划项目，编号：2023YFB3711300；中国工程院战略研究与咨询项目，编号：2023-XZ-90、2023-JB-09-10。
第一作者简介：周诚（1982—），男，教授，博士，教育部青年长江学者，湖北省杰青，博士生导师，研究方向为月面建造。E-mail：charleschou@163. com。
摘要：【目的】 为了深入了解月面建造过程中月壤的力学特性，评估月基装备性能，优化月面建造作业，开展离散元法（discrete element method，DEM）在月壤接触力学领域的应用调查研究，旨在利用离散元法为未来月球基地建设提供理论指导和技术支持。【研究现状】基于地质勘探、资源采集及运输、建造作业等月面原位建造任务场景，分析月壤颗粒的建模与参数标定，介绍月基装备与月壤的接触作用研究现状，概述离散元法在钻-壤作用模拟、铲-壤作用模拟、轮-壤作用模拟及足-壤作用模拟中的应用，探讨基于离散元法的天然月基承载力分析。【展望】提出降低几何模型复杂度、优化粒间接触模型及参数是提高宏观尺度月壤离散元建模精度以应对大规模月面建造场景的有效方法。认为利用离散元法进行铲挖式月壤采集装置及足式月球车设计在未来可以为月面建造提供了可靠的技术支持。面向月面建造，离散元法将在水冰资源利用、建筑物月面承载力分析等方面提供科学依据。
关键词：月面建造；离散元法；月壤采集；月基装备；承载力
Significance In pursuit of a profound comprehension of the intricate mechanical characteristics exhibited by lunar regolith throughout lunar construction endeavors，and to meticulously scrutinize the efficacy of lunar surface equipment and refine the operational efficiency of lunar construction activities， this investigation delves into the application of the discrete element method （DEM） within the realm of lunar regolith contact mechanics. By harnessing the power of DEM， the primary objective is to provide not only theoretical insights but also practical and technical assistance for the meticulous planning and execution of future lunar base construction initiatives. Through the judicious application of DEM， it is envisaged that a robust framework can be established to guide and facilitate the successful realization of lunar base construction projects， thereby advancing humanity's exploration and utilization of extraterrestrial resources. It is crucial to acknowledge the immense challenges posed by lunar construction activities， where the understanding of lunar regolith behavior is paramount. By unraveling the complex interplay between lunar surface equipment and the dynamic lunar regolith， this investigation seeks to shed light on novel methodologies for optimizing construction operations on the lunar surface. The application of DEM offers a unique opportunity to simulate and analyze the intricate interactions between lunar regolith particles and construction equipment， providing valuable insights into the design and deployment of future lunar infrastructure.
Progress This research draws from a range of on-site lunar construction missions， including geological exploration， resource extraction and transport， and construction work， to analyze the application of the discrete element method （DEM） to the mechanics of lunar surface construction. Initially， the study critically examines the complex dynamics behind lunar weathering layer modelling and parameter calibration， elucidates methods for weathering layer modelling， and analyzes various particle contact models for different application scenarios， while summarizing effective methods for lunar weathering layer parameter calibration.In addition， this study delves into existing research to elucidate the complex interactions between lunar surface equipment and the lunar weathering layer. In the context of lunar soil collection， the study analyzes interactions such as drilling and shoveling，and investigates the effects of drilling and shoveling equipment structure and operating parameters on lunar soil collection performance from a DEM microscopic perspective. It also explores wheel rock and foot rock interactions to enhance lunar rover maneuverability and lander stability to ensure effective execution of lunar surface construction operations. Through careful exploration of these simulations， the study elucidates the underlying mechanics and dynamics that control these interactions， thereby enhancing the understanding and optimization of lunar construction methods. In addition， the study comprehensively analyzes the inherent carrying capacity of the lunar base， using the analytical power of the DEM to reveal the stability of the lunar habitat.This multifaceted exploration aims to provide valuable academic insights and practical guidance for the seamless advancement of lunar exploration efforts and the sustainable establishment of lunar infrastructure.
Conclusions and Prospects It is proposed that DEM can account for the microstructure and deformation of particulate materials such as water ice， including factors such as the shape， size， and arrangement of the particles. This enables DEM to more accurately simulate the deformation， damage and other behaviors of water ice under external forces. DEM cannot only simulate the mechanical behavior of granular materials， but also simulate the interaction between particles and fluids in multiphase fluid systems by combining with fluid dynamics methods. For particulate materials such as water ice， DEM can simulate interactions with liquid or gaseous media， such as the processes of particle deposition， suspension， and flow， etc. It can also be used to study the heat conduction behavior in the particulate system and the structural stability during the heating process， which is conducive to the optimization of the strategies and methods for water ice acquisition to support the lunar surface construction mission. In addition，when facing more complex unstructured terrain construction tasks， the terrain adaptability and obstacle-climbing ability of the foot-mounted lunar rover are more prominent. However， due to the complex mechanical control of the foot-mounted lunar rover， coupling simulation between DEM and dynamics is difficult， and the construction cost of unstructured terrain DEM models on the lunar surface is high. Therefore， improving the coupling performance of DEM and dynamics and enhancing the accuracy of macro-scale lunar soil DEM modeling are the challenges that foot-mounted lunar rover DEM simulations need to overcome in the future. Furthermore， current DEM study of the bearing capacity of lunar foundations， which focuses on simulating the mechanical behavior of lunar soil， can serve as a basis for assessing the support capacity of lunar soil for buildings. In the future， the feasibility of construction under different terrain conditions can also be considered， which will help to formulate more refined building plans， select the most suitable areas and locations for construction， and guide the design and construction process of buildings and ensure their stability and safety.
Keywords：lunar construction； discrete element method； lunar soil collection； lunar-based equipment； bearing capacity
［1］QIAN Y， XIAO L， WANG Q， et al. China's Chang'e-5 landing site：geology， stratigraphy， and provenance of materials［J］.Earth and Planetary Science Letters，2021，561：116855.
［2］MATHAVARAJ S， NEGI K， VAIBHAV G. ISRO's unprecedented journey to the moon［J］.Acta Astronautica，2020，177：286-298.
［3］WANG L， GUO D， LYU Z， et al.Introduction to NASA's artemis lunar exploration program［J］.Spacecraft Recovery & Remote Sensing，2020，41（5）：1-12.
［4］VASILIEV A， DALYAEV I， SLYUTA E. Design concept of lunar rover for the moon geological exploration［J］.Annals of DAAAM & Proceedings，2017，28.
［5］LIU Y， WANG C， PANG Y， et al. Water extraction from icy lunar regolith by drilling-based thermal method in a pilot-scale-unit［J］.Acta Astronautica，2023，202：386-399.
［6］LEACH N， CARLSON A， KHOSHNEVIS B， et al. Robotic construction by contour crafting： the case of lunar construction［J］.International Journal of Architectural Computing，2012，10（3）：423-438.
［7］GUO Y， CURTIS J S. Discrete element method simulations for complex granular flows［J］.Annual Review of Fluid Mechanics，2015，47：21-46.
［8］CARRIER III W， MITCHELL J K， MAHMOOD A. The nature of lunar soil［J］.Journal of the Soil Mechanics and Foundations Division，1973，99（10）：813-832.
［9］MATSUSHIMA T， KATAGIRI J， UESUGI K， et al. 3D shape characterization and image-based DEM simulation of the lunar soil simulant FJS-1［J］.Journal of Aerospace Engineering，2009，22（1）：15-23.
［10］KATAGIRI J， MATSUSHIMA T， YAMADA Y. Simple shear simulation of 3D irregularly-shaped particles by image-based DEM［J］.Granular Matter，2010，12：491-497.
［11］王思远，蒋明镜. 基于嫦娥五号月壤粒形特征的离散元模拟方法［J］.岩土工程学报，2024，46（4）：833-842.WANG S Y， JIANG M J. Lunar regolith simulations with discrete element method informed by Chang’E-5 mission’s lunar soil particle morphology［J］.Chinese Journal of Geotechnical Engineering，2024，46（4）：833-842.
［12］YANG W， WANG M， ZHOU Z， et al. Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model［J］.Geomechanics and Geophysics for Geo-Energy and Geo-Resources，2020，6：1-15.
［13］NAVARRO H A， DE SOUZA BRAUN M P. Determination of the normal spring stiffness coefficient in the linear spring-dashpot contact model of discrete element method［J］.Powder Technology，2013，246：707-722.
［14］ZHANG L， RU C Q. A refined JKR model for adhesion of a rigid sphere on a soft elastic substrate［J］.Journal of Applied Mechanics，2019，86（5）：051004.
［15］LIAKAS S， O’SULLIVAN C， SAROGLOU C. Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model［J］.Journal of Rock Mechanics and Geotechnical Engineering，2017，9（4）：575-584.
［16］CHENG K， WANG Y， YANG Q， et al. Determination of microscopic parameters of quartz sand through tri-axial test using the discrete element method［J］.Computers and Geotechnics，2017，92：22-40.
［17］ROESSLER T， KATTERFELD A. DEM parameter calibration of cohesive bulk materials using a simple angle of repose test［J］.Particuology，2019，45：105-115.
［18］EL-KASSEM B， SALLOUM N， BRINZ T， et al. A semi-automated DEM parameter calibration technique of powders based on different bulk responses extracted from Auger Dosing experiments［J］.KONA Powder and Particle Journal，2021，38：235-250.
［19］IRAZÁBAL J， SALAZAR F， VICENTE D J. A methodology for calibrating parameters in discrete element models based on machine learning surrogates［J］.Computational Particle Mechanics，2023，10（5）：1-17.
［20］WANG M， LU Z， WAN W， et al. A calibration framework for the microparameters of the DEM model using the improved PSO algorithm［J］.Advanced Powder Technology，2021，32（2）：358-369.
［21］SUDSAWAT S， CHONGCHITPAISAN P， ARUNYANART P. Calibrating polypropylene particle model parameters with upscaling and repose surface method［J］.EUREKA： Physics and Engineering，2023（6）：34-46.
［22］XIA R， LI B， WANG X， et al. Measurement and calibration of the discrete element parameters of wet bulk coal［J］.Measurement，2019，142：84-95.
［23］LIU T X， WEI C， MA L， et al. A study on force situation of the coring pipe caused by filling lunar regolith in the drilling process［J］.Applied Mechanics and Materials，2014，577：267-272.
［24］CHEN H， LI L， CUI Y， et al. A novel lunar soil coring approach based on particle unidirectional flow effect to reduce drag and increase efficiency ［J］.Advances in Space Research，2021，68（1）：117-33.
［25］LIU T， LIANG L， ZHAO Y， et al. Equivalent boundary model of lunar soil drilling simulation by DEM ［J］.Journal of Terramechanics，2020，91：85-95.
［26］HOU X Y， ZHAO D M， CUI J S， et al. Analysis and DEM simulation on the interaction characteristics between lunar soil and coring drill［J］.Applied Mechanics and Materials，2013，373：65-71.
［27］LIU T， ZHOU J， LIANG L， et al. Effect of drill bit structure on sample collecting of lunar soil drilling ［J］.Advances in Space Research，2021，68（1）：134-52.
［28］刘天喜，马亮，梁磊，等. 深层月壤采样钻具参数影响分析［J］.机械工程学报，2018，54（9）：27-36.LIU T X， MA L， LIANG L， et al. Analysis on influence of drill parameters in the sampling of deep lunar soil ［J］.Chinese Journal of Mechanical Engineering，2018，54（9）：27-36.
［29］CHEN T， ZHAO Z， SCHWARTZ S R， et al. Invariance of conveying capacity for drilling into lunar soil simulant ［J］.Advances in Space Research，2019，64（9）：1816-24.
［30］赵德明，姜生元，唐德威，等 . 月球次表层回转取样钻头构型设计［J］.吉林大学学报（工学版），2017，47（4）：1149-1158.ZHAO D M， JIANG S Y， TANG D W，et al. Structure design of lunar subsurface sampling drill［J］.Journal of Jilin University（Engineering and Technology Edition），2017，47（4）：1149-1158.
［31］ZHAO D， TANG D， HOU X，et al. Soil chip convey of lunar subsurface auger drill［J］.Advances in Space Research，2016，57（10）：2196-2203.
［32］HOU X Y， DENG Z Q， YUE H H， et al. Research on the impact of a drill bit on the original state of artificial lunar soil using DEM simulation［J］.Transactions of the Japan Society for Aeronautical and Space Sciences，2016，59（4）：236-42.
［33］谢宇明，卿启湘，汤钦卿. 月壤的钻取采样离散元动态行为研究［J］.工程设计学报，2013，20（6）：476-481.XIE Y M， QING Q X， TANG Q Q. Dynamically behavioral research of lunar soil drilling and sampling by DEM［J］.Chinese Journal of Engineering Design，2013，20（6）：476-481.
［34］崔建国，田野，刘君巍，等 . 月壤临界尺度颗粒运移特性对钻采阻力影响研究［J］.岩土工程学报，2021，43（9）：1715-1723.CUI J G， TIAN Y， LIU J W， et al. Influences of critical fragment migration characteristics of lunar soil on drilling resistance［J］.Chinese Journal of Geotechnical Engineering，2021，43（9）：1715-1723.
［35］庞勇，冯亚杰，孙启臣，等 . 月壤大颗粒对钻进力载影响的仿真及实验研究［J］.北京大学学报（自然科学版），2019，55（3）：397-404.PANG Y， FENG Y J， SUN Q C， et al. Simulation and experimental study on the effect of largegranular rocks in lunar soil on drilling load ［J］.Acta Scientiarum Naturalium Universitatis Pekinensis，2019，55（3）：397-404.
［36］刘天喜，魏承，马亮，等. 大颗粒岩块对月壤钻取过程的影响分析［J］.岩土工程学报，2014，36（11）：2118-2126.LIU T X， WEI C， MA L， et al. Effect of large granular rocks on drilling process of lunar soils ［J］.Chinese Journal of Geotechnical Engineering，2014，36（11）：2118-2126.
［37］CUI J， HOU X， WEN G， et al. DEM thermal simulation of bit and object in drilling of lunar soil simulant ［J］.Advances in Space Research，2018，62（5）：967-75.
［38］CUI J， HOU X， WEN G， et al. Thermal simulation of drilling into lunar rock simulant by discrete element method［J］.Acta Astronautica，2019，160：378-87.
［39］CUI J， CHEN B， LIU S， et al. Thermal simulations of drilling of cryogenic lunar soils containing water ice ［J］.Aerospace，2023，10（6）：510.
［40］CUI J， KUI L， ZHANG W， et al. Simulation of drilling temperature rise in frozen soil of lunar polar region based on discrete element theory［J］.Aerospace，2023，10（4）：368.
［41］ZHAO D， CHENG Z， ZHANG W， et al. Numerical modeling of thermal behavior during lunar soil drilling ［J］.Aerospace，2023，10（5）：472.
［42］BUI H H， KOBAYASHI T， FUKAGAWA R， et al. Numerical and experimental studies of gravity effect on the mechanism of lunar excavations［J］.Journal of Terramechanics，2009，46（3）：115-24.
［43］JIANG M， SHEN Z， UTILI S. DEM modeling of cantilever retaining excavations implications for lunar constructions［J］.Engineering Computations，2016，33（2）：366-94.
［44］蒋明镜，奚邦禄，申志福，等 . 不同重力下月壤水平推剪阻力离散元数值分析［J］.岩土工程学报，2015，37（7）：1300-1306.JIANG M J， XIU B L， SHIN Z F， et al. DEM analyses of horizontal pushing resistance under different gravity fields ［J］.Chinese Journal of Geotechnical Engineering，2015，37（7）：1300-1306.
［45］蒋明镜，奚邦禄，申志福，等 . 月壤水平开挖推剪阻力影响因素离散元数值分析［J］.岩土力学，2016，37（1）：229-236.JIANG M J， XIU B L， SHIN Z F， et al. Discrete element numerical analysis of factors affecting horizontal pushingresistance in lunar ground excavation ［J］.Rock and Soil Mechanics，2016，37（1）：229-236.
［46］XI B， JIANG M， CUI L. 3D DEM analysis of soil excavation test on lunar regolith simulant ［J］.Granular Matter，2021，23（1）：1-16.
［47］姚猛，郑燕红，赵志晖，等. 一种月表采样器合理铲挖深度的研究［J］.航天器工程，2017，26（3）：50-56.YAO M， ZHENG Y H， ZHAO Z H， et al. Research on reasonable excavation depth for lunar regolith sampler ［J］.Spacecraft Engineering，2017，26（3）：50-56.
［48］HOU X， DING T， YUE H， et al. A simulation study on a digging-typed lunar soil sampling device and its sampling characteristics based on discrete element method［C］//2015 IEEE International Conference on Robotics and Biomimetics （ROBIO）.New York：IEEE，2015：1554-1559.
［49］JIANG S， LIU R， LIN Y， et al. Design and test of a sampler for lunar surface regolith ［J］.Chinese Space Science and Technology，2019，39（1）：49-58.
［50］DACA A， TREMBLAY D， SKONIECZNY K. Expansion and experimental evaluation of scaling relations for the prediction of wheel performance in reduced gravity ［J］.Microgravity Science and Technology，2023，35（6）.
［51］JIANG M， LIU F， SHEN Z， et al. Distinct element simulation of lugged wheel performance under extraterrestrial environmental effects ［J］.Acta Astronautica，2014，99：37-51.
［52］李因武，李建桥，邹猛，等. 月壤力学性质对月球车牵引性能影响的模拟［J］.农业机械学报，2009（1）：1-4.LI Y W， LI J Q， ZOU M， et al. Simulation of traction ability of lunar rover withdifferent mechanics of lunar soil［J］.Transactions of the Chinese Society of Agricultural Machinery，2009（1）：1-4.
［53］SMITH W， PENG H. Modeling of wheel-soil interaction over rough terrain using the discrete element method ［J］.Journal of Terramechanics，2013，50（5/6）：277-87.
［54］JIANG M， DAI Y， CUI L， et al. Experimental and DEM analyses on wheel-soil interaction［J］.Journal of Terramechanics，2018，76：15-28.
［55］NAKASHIMA H， FUJII H， OIDA A， et al. Parametric analysis of lugged wheel performance for a lunar microrover by means of DEM ［J］.Journal of Terramechanics，2007，44（2）：153-62.
［56］ZHANG K， HOU X， XUE P， et al. Optimization on high adhesive ability of lunar rover wheel based on discrete element method［C］//ASME International Mechanical Engineering Congress and Exposition.New York：American Society of Mechanical Engineers，2016，50510.
［57］PANG H， ZHANG R， GE P， et al. 3D DEM analysis on tractive trafficability of a lunar rover wheel with bionic wheel lugs ［J］.Rendiconti Lincei-Scienze Fisiche E Naturali，2021，32（2）：377-87.
［58］LI W， GAO F， JIA Y. Tractive performance analysis on radially deployable wheel configuration of lunar rover vehicle by discrete element method ［J］.Chinese Journal of Mechanical Engineering，2008，21（5）：13-8.
［59］THOESEN A， MCBRYAN T， MICK D， et al. Comparative performance of granular scaling laws for lightweight grouser wheels in sand and lunar simulant ［J］.Powder Technology，2020，373：336-46.
［60］LI W， HUANG Y， CUI Y， et al. Trafficability analysis of lunar mare terrain by means of the discrete element method for wheeled rover locomotion ［J］.Journal of Terramechanics，2010，47（3）：161-72.
［61］NAKASHIMA H， FUJII H， OIDA A， et al. Discrete element method analysis of single wheel performance for a small lunar rover on sloped terrain ［J］.Journal of Terramechanics，2010，47（5）：307-21.
［62］ZHANG R， PANG H， DONG W， et al. Three-dimensional discrete element method simulation system of the interaction between irregular structure wheel and lunar soil simulant ［J］.Advances in Engineering Software，2020，148：102873.
［63］YIN C， SCHIAVONE P， QUAN Q， et al. Normal force on the asteroid regolith generated by the impact of lander footpad［J］.Acta Astronautica，2023，202：229-51.
［64］HOU X， XUE P， WANG Y， et al. Theoretical and discrete element simulation studies of aircraft landing impact ［J］.Journal of the Brazilian Society of Mechanical Sciences and Engineering，2018，40（3）：1-16.
［65］HOU X， XUE P， ZHANG K， et al. Simulation and research on landing impact between lander and lunar regolith based on DEM［C］//2016 IEEE International Conference on Mechatronics and Automation. New York： IEEE，2016：1489-1494.
［66］JI S， LIANG S. DEM-FEM-MBD coupling analysis of landing process of lunar lander considering landing mode and buffering mechanism ［J］.Advances in Space Research，2021，68（3）：1627-43.
［67］梁绍敏，王永滨，季顺迎 . 基于离散元方法的月球着陆器冲击月壤过程分析［J］.航天返回与遥感，2017，38（4）：55-63.LIANG S M，WANG Y B， JI S Y. Analysis of landing impact process of lunar landing lander based on discrete element method ［J］.Spacecraft Recovery & Remote Sensing，2017，38（4）：55-63.
［68］蒋明镜，郑敏，王闯. 月壤双轴试验的剪切带离散元数值分析［J］.岩土力学，2012，33（12）：3801-3809.JIANG M J， ZHENG M， WANG G. Distinct element analysis of shear band of lunar soil in biaxial tests ［J］.Rock and Soil Mechanics，2012，33（12）：3801-3809.
［69］JIANG M， ZHAO T， WANG X. DEM modelling of cone penetration tests in lunar soil ［J］.Granular Matter，2022，24（1）：1-16.
［70］LI Y， ZOU W， WU W， et al. Triaxial compression tests of QH-E lunar soil simulant under constant mean principal stress path using discrete element method simulations ［J］.Granular Matter，2018，20（4）：1-13.
［71］LI Y， WU W， CHU X， et al. Effects of stress paths on triaxial compression mechanical properties of QH-E lunar soil simulant studied by DEM simulation ［J］.Granular Matter，2020，22（2）：1-10.
［72］SHEN Y， HOU X， ZHANG K， et al. Study on the dynamic characteristics of a hammer-driven-type penetrators in the penetration process ［J］.Advances in Mechanical Engineering，2017，9（3）.
［73］LIN C X， TU F B， LING D S， et al. FEM-DEM coupled modeling of cone penetration tests in lunar soil ［J］.Journal of Central South University，2018，25（2）：392-405.
［74］奚邦禄，蒋明镜，莫品强，等 . 不同重力场下月基承载特性离散元数值分析［J］.中南大学学报（自然科学版），2023，54（8）：3226-3236.XI B L，JIANG M J，MO P Q， et al. DEM analyses on bearing behavior of lunar soil ground withdifferent gravity fields ［J］.Journal of Central South University（Science and Technology），2023，54（8）：3226-3236.
［75］XI B L， JIANG M J， MO P Q， et al. Bearing capacity of lunar soil ground under extraterrestrial environmental effects［J］.Computers and Geotechnics，2024，165：105923.
［76］XI B， JIANG M， MO P， et al. 3D DEM analysis of the bearing behavior of lunar soil simulant under different loading plates ［J］.Granular Matter，2023，25（4）.
