Sciences in Cold and Arid Regions ›› 2020, Vol. 12 ›› Issue (4): 234–241.doi: 10.3724/SP.J.1226.2020.00234

• • 上一篇    


  • 收稿日期:2020-03-05 接受日期:2020-06-09 出版日期:2020-08-31 发布日期:2020-09-04

Theoretical expressions for soil particle detachment rate due to saltation bombardment in wind erosion

XuYang Liu1,2(),WenXiao Ning1,2,ZhenTing Wang1   

  1. 1.Key Laboratory of Desert and Desertification, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China
    2.University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2020-03-05 Accepted:2020-06-09 Online:2020-08-31 Published:2020-09-04
  • Contact: XuYang Liu


Saltation bombardment is a dominate dust emission mechanism in wind erosion. For loose surfaces, splash entrainment has been well understood theoretically. However, the mass loss predictions of cohesive soils are generally empirical in most wind erosion models. In this study, the soil particle detachment of a bare, smooth, dry, and uncrusted soil surface caused by saltation bombardment is modeled by means of classical mechanics. It is shown that detachment rate can be analytically expressed in terms of the kinetic energy or mass flux of saltating grains and several common mechanical parameters of soils, including Poisson's ratio, Young's modulus, cohesion and friction angle. The novel expressions can describe dust emission rate from cohesive surfaces and are helpful to quantify the anti-erodibility of soil. It is proposed that the mechanical properties of soils should be appropriately included in physically-based wind erosion models.

Key words: wind erosion, saltation bombardment, cohesive soil, anti-erodibility



Coordinate componentx, y, zmPoisson's ratioν
Concentrated forcePNYoung's modulusEPa
Normal stressσx,?σy,?σzPaCohesioncPa
Shear stressτxy, τyz, τzxPaFriction angle?
Principal stressσ1,?σ2,?σ3PaEquatorial radiusam
Sand grain massmkgPolar radiusbm
Sand grain speedum/sImpact durationδt, Ts
Eroded volumeVm3Impact timesn
Mass flux densityqkg/(m2?s)Sand diameterdm
Surface heighthmDensityρs, ρbkg/m3
DisplacementwmRestitution coefficiente
Abrasion rateArg/sConstant coefficientsA
Abraded areaSm2



USCSDescriptionCohesion c (KPa)Young's modulus E (MPa)Friction angle ? (°)Anti-erodibility λ?(Pa)
SMSilty sands22163312.70
MLSilt loam75828290.72
CLSilty clay976.525589.59
OLOrganic silts52.5274.12
Al-Durrah M, Bradford JM, 1981. New methods of studying soil detachment due to waterdrop impact. Soil Science Society of America Journal, 45(5): 949-953. DOI: 10.2136/sssaj1981.03615995004500050026.x
doi: 10.2136/sssaj1981.03615995004500050026.x
Al-Durrah MM, Bradford JM, 1982. Parameters for describing soil detachment due to single waterdrop impact. Soil Science Society of America Journal, 46(4): 836-840. DOI: 10.2136/sssaj1982.03615995004600040034x.
doi: 10.2136/sssaj1982.03615995004600040034x
Alfaro S, Gomes L, 2001. Modeling mineral aerosol production by wind erosion: Emission intensities and aerosol size distributions in source areas. Journal of Geophysical Research, 106: 18075-18084. DOI: 10.1029/2000jd900339.
doi: 10.1029/2000jd900339
Anderson RS, 1986. Erosion profiles due to particles entrained by wind: Application of an aeolian sediment-transport model. Geological Society of America Bulletin, 97(10): 1270-1278. DOI: 10.1130/0016-7606(1986)97<1270:EPDTPE>2.0.CO;2.
doi: 10.1130/0016-7606(1986)97<1270:EPDTPE>2.0.CO;2
Anderson RS, Haff PK, 1991. Wind modification and bed response during saltation of sand in air. Aeolian grain transport 1, In: Barndorff-Nielsen OE, Willetts BB (eds.). Springer Vienna, Vienna, 21-51. DOI: 10.1007/978-3-7091-6706-9_2.
doi: 10.1007/978-3-7091-6706-9_2
Bagnold RA, 2005. The Physics of Blown Sand and Desert Dunes. Dover Publications, Mineola, N.Y..
Bolte K, Hartmann P, Fleige H, et al., 2011. Determination of critical soil water content and matric potential for wind erosion. Journal of Soils and Sediments, 11(2): 209-220. DOI: 10.1007/s11368-010-0281-8.
doi: 10.1007/s11368-010-0281-8
Borrelli P, Ballabio C, Panagos P, et al., 2014. Wind erosion susceptibility of European soils. Geoderma, 232-234, 471-478. DOI: 10.1016/j.geoderma.2014.06.008.
doi: 10.1016/j.geoderma.2014.06.008
Bridges NT, Laity JE, Greeley R, et al., 2004. Insights on rock abrasion and ventifact formation from laboratory and fielf analog atudies with applications to Mars. Planetary and Space Science, 52(1-3): 199-213. DOI: 10.1016/j.pss. 2003.08.026.
doi: 10.1016/j.pss. 2003.08.026
Bryan RB, 1968. The development, use and efficiency of indices of soil erodibility. Geoderma, 2(1): 5-26. DOI: 10.1016/0016-7061(68)90002-5.
doi: 10.1016/0016-7061(68)90002-5
Bryan RB, Govers G, Poesen J, 1989. The concept of soil erodibility and some problems of assessment and application. Catena, 16(4): 393-412. DOI: 10.1016/0341-8162(89)90023-4.
doi: 10.1016/0341-8162(89)90023-4
Chepil WS, Woodruff NP, 1963. The physics of wind erosion and its control. Advances in Agronomy, 15: 211-302. DOI: 10.1016/s0065-2113(08)60400-9.
doi: 10.1016/s0065-2113(08)60400-9
Comola F, Gaume J, Kok JF, et al., 2019. Cohesion-induced enhancement of aeolian saltation. Geophysical Research Letters, 46(10): 5566-5574. DOI: 10.1029/2019GL082195.
doi: 10.1029/2019GL082195
Comola F, Kok JF, Gaume J, et al., 2017. Fragmentation of wind-blown snow crystals: Blowing snow fragmentation. Geophysical Research Letters, 44(9): 4195-4203. DOI:10.1002/2.17GL073039.
doi: 10.1002/2.17GL073039
Comola F, Lehning M, 2017. Energy- and momentum-conserving model of splash entrainment in sand and snow saltation. Geophysical Research Letters, 44(3): 1601-1609. DOI: 10.1002/2016GL071822.
doi: 10.1002/2016GL071822
Cook HL, 1937. The nature and controlling variables of the water erosion process. Soil Science Society of America Journal, 1: 487-494. DOI: 10.2136/sssaj1937.03615995000100000085x.
doi: 10.2136/sssaj1937.03615995000100000085x
Dai Y, Zhang C, Cen S, et al., 2020. Abrasion of soil clods with different textures and moisture contents in sand flow environment. Aeolian Research, 46: 100614. DOI: 10.1016/j.aeolia.2020.100614.
doi: 10.1016/j.aeolia.2020.100614
De Oro LA, Colazo JC, Avecilla F, et al., 2019. Relative soil water content as a factor for wind erodibility in soils with different texture and aggregation. Aeolian Research, 37: 25-31. DOI: 10.1016/j.aeolia.2019.02.001.
doi: 10.1016/j.aeolia.2019.02.001
Fang Y, Chen H, Zou XY, et al., 2018. Shear strength of aeolian sand sediments. Transactions of the ASABE, 61(2): 583-590. DOI: 10.13031/trans.12537.
doi: 10.13031/trans.12537
Fredlund DG, Rahardjo H, 1993. Soil Mechanics for Unsaturated Soils. Wiley, New York.
Fryrear DW, Saleh A, Bilbro JD, 1998. A single event wind erosion model. Transactions of the ASAE, 41(5): 1369-1374.
Funk R, 2016. Assessment and measurement of wind erosion. Novel methods for monitoring and managing land and water resources in Siberia, In: Mueller L, Sheudshen AK, Eulenstein F (eds.). Springer International Publishing, pp. 425-449. DOI: 10.1007/978-3-319-24409-9_18.
doi: 10.1007/978-3-319-24409-9_18
Greeley R, Leach RN, Williams SH, et al., 1982. Rate of wind abrasion on Mars. Journal of Geophysical Research, 87(B12): 10009-10024. DOI: 10.1029/jb087ib12p10009.
doi: 10.1029/jb087ib12p10009
Hagen I, 1991. Wind erosion mechanics: Abrasion of aggregated soil. Transactions of the ASAE, 34(3): 0831-0837. DOI: 10.13031/2013.31737.
doi: 10.13031/2013.31737
Jarrah M, Mayel S, Tatarko J, et al., 2020. A review of wind erosion models: Data requirements, processes, and validity. CATENA, 187: 104388. DOI: 10.1016/j.catena. 2019. 104388.
doi: 10.1016/j.catena. 2019. 104388
Johnson KL, 1985. Contact Mechanics. Cambridge University Press, Cambridge.
Kok JF, 2011. A scaling theory for the size distribution of emitted dust aerosols suggests climate models underestimate the size of the global dust cycle. Proceedings of the National Academy of Sciences, 108(3): 1016-1021. DOI: 10. 1073/pnas.1014798108.
doi: 10. 1073/pnas.1014798108
Kok JF, Parteli EJR, Michaels TI, et al., 2012. The physics of wind-blown sand and dust. Reports on Progress in Physics, 75(10): 106901. DOI: 10.1088/0034-4885/75/10/106901.
doi: 10.1088/0034-4885/75/10/106901
Kurgansky M, 2018. To the theory of particle lifting by terrestrial and Martian dust devils. Icarus, 300: 97-102. DOI: 10.1016/j.icarus.2017.08.029.
doi: 10.1016/j.icarus.2017.08.029
Lal R, Shukla M, 2004. Principles of soil physics. Number v. 57 in Books in soils, plants, and the environment. M. Dekker, New York. DOI: 10.4324/9780203021231.
doi: 10.4324/9780203021231
Li G, Zhang J, Hermann HJ, et al., 2020. Study of aerodynamic grain entrainment in aeolian transport. Geophysical Research Letters, 47: e2019GL086574. DOI: 10.1029/2019GL086574.
doi: 10.1029/2019GL086574
Li JF, 2015. A study on shear strength and wind erosion-antierodibility of sieved soils. Ph.D. thesis, Beijing Normal University, Beijing.
Lurie AI, Belyaev A, 2005. Theory of elasticity. Foundations of Engineering Mechanics. Springer Berlin Heidelberg, Berlin, Heidelberg.
Mckenna Neuman C, 2003. Effects of temperature and humidity upon the entrainment of sedimentary particles by wind. Boundary-Layer Meteorology, 108(1): 61-89. DOI: 10. 1023/a:1023035201953.
doi: 10. 1023/a:1023035201953
Neakrase LDV, Balme MR, Esposito F, et al., 2016. Particle lifting processes in dust devils. Space Science Reviews, 203(1-4): 347-376. DOI: 10.1007/s11214-016-0296-6.
doi: 10.1007/s11214-016-0296-6
Nearing MA, Bradford JM, 1985. Single waterdrop splash detachment and mechanical properties of soils. Soil Science Society of America Journal, 49(3): 547-552. DOI: 10.2136/sssaj1985.03615995004900030003x.
doi: 10.2136/sssaj1985.03615995004900030003x
Ning WX, Huang XQ, Wang XS, et al., 2019. Abrasion rates of ventifacts. SN Applied Sciences, 1(8): 855. DOI: 10. 1007/s42452-019-0881-x.
doi: 10. 1007/s42452-019-0881-x
Pi H, Sharratt B, Feng G, et al., 2017. Evaluation of two empirical wind erosion models in arid and semi-arid regions of China and the USA. Environmental Modelling & Software, 91: 28-46. DOI: 10.1016/j.envsoft.2017.01.013.
doi: 10.1016/j.envsoft.2017.01.013
Popov VL, 2010. Contact mechanics and friction. Springer Berlin Heidelberg, Berlin, Heidelberg. DOI: 10.1007/978-3-642-10803-7.
doi: 10.1007/978-3-642-10803-7
Rice MA, McEwan IK, Mullins CE, 1999. A conceptual model of wind erosion of soil surfaces by saltating particles. Earth Surface Processes and Landforms, 24(5): 383-392. DOI: 10.1002/(sici)1096-9837(199905)24:5<383::aid-esp995>;2-k.
doi: 10.1002/(sici)1096-9837(199905)24:5<383::aid-esp995>;2-k
Rice MA, Mullins CE, McEwan IK, 1997. An analysis of soil crust strength in relation to potential abrasion by saltating particles. Earth Surface Processes and Land forms, 22(9): 869-883. DOI: 10.1002/(sici)1096-9837(199709)22:9<869::aid-esp785>;2-p.
doi: 10.1002/(sici)1096-9837(199709)22:9<869::aid-esp785>;2-p
Richards LA, 1953. Modulus of rupture as an index of crusting of soil. Soil Science Society of America Journal, 17(4): 321-323. DOI: 10.2136/sssaj1953.03615995001700040005x.
doi: 10.2136/sssaj1953.03615995001700040005x
Shao Y, 2008. Physics and modelling of wind erosion. Number 37 in Atmospheric and Oceanographic Sciences Library. Springer.
Shao Y, Klose M, 2016. A note on the stochastic nature of particle cohesive force and implications to threshold friction velocity for aerodynamic dust entrainment. Aeolian Research, 22: 123-125. DOI: 10.1016/j.aeolia.2016.08.004.
doi: 10.1016/j.aeolia.2016.08.004
Shao Y, Lu H, 2000. A simple expression for wind erosion threshold friction velocity. Journal of Geophysical Research: Atmospheres, 105(D17): 22437-22443. DOI: 10. 1029/2000jd900304.
doi: 10. 1029/2000jd900304
Shao Y, Raupach MR, Findlater PA, 1993. Effect of saltation bombardment on the entrainment of dust by wind. Journal of Geophysical Research, 98(D7): 12719-12726. DOI: 10.1029/93jd0039.
doi: 10.1029/93jd0039
Shield R, 1955. On Coulomb’s law of failure in soils. Journal of the Mechanics and Physics of Solids, 4(1): 10-16. DOI: 10.1016/0022-5096(55)90043-0.
doi: 10.1016/0022-5096(55)90043-0
Smalley IJ, 1970. Cohesion of soil particles and the intrinsic resistance of simple soil systems to wind erosion. Journal of Soil Science, 21(1): 154-161. DOI: 10.1111/j.1365-2389. 1970.tb01163.x.
doi: 10.1111/j.1365-2389. 1970.tb01163.x
Sunamura T, 2018. A fundamental equation for describing the rate of bedrock erosion by sediment-laden fluid flows in fluvial, coastal, and aeolian environments. Earth Surface Processes and Landforms, 43(15): 3022-3041. DOI: 10. 1002/esp.4467.
doi: 10. 1002/esp.4467
Terzaghi K, Peck RB, Mesri G, 1996. Soil Mechanics in Engineering Practice. Wiley, New York, 3rd ed edition.
Torri D, Sfalanga M, Sette MD, 1987. Splash detachment: Runoff depth and soil cohesion. Catena, 14(1): 149-155. DOI: 10.1016/S0341-8162(87)80013-9.
doi: 10.1016/S0341-8162(87)80013-9
van Pelt R, Zobeck T, Potter K, et al., 2004. Validation of the wind erosion stochastic simulator (WESS) and the revised wind erosion equation (RWEQ) for single events. Environmental Modelling & Software, 19(2): 191-198. DOI: 10. 1016/s1364-8152(03)00122-1.
doi: 10. 1016/s1364-8152(03)00122-1
Wagner LE, 2013. A history of Wind Erosion Prediction Models in the United States Department of Agriculture: The Wind Erosion Prediction System (WEPS). Aeolian Research, 10: 9-24. DOI: 10.1016/j.aeolia.2012.10.001.
doi: 10.1016/j.aeolia.2012.10.001
Wang ZT, 2006. Influence of moisture on the entrainment of sand by wind. Powder Technology, 164(2): 89-93. DOI: 10.1016/j.powtec.2006.03.001.
doi: 10.1016/j.powtec.2006.03.001
Wang ZT, 2016. A theoretical note on aerodynamic lifting in dust devils. Icarus, 265: 79-83. DOI: 10.1016/j.icarus. 2015.10.016.
doi: 10.1016/j.icarus. 2015.10.016
Wang ZT, 2020. Erosion model for brittle materials under low-speed impacts. Journal of Tribology-Transactions of the ASME, 142(7): 074501. DOI: 10.1115/1.4046019.
doi: 10.1115/1.4046019
Wang ZT, Wang HT, Niu QH, et al., 2011. Abrasion of yardangs. Physical Review E, 84(3): 031304. DOI: 10.1103/PhysRevE.84.031304.
doi: 10.1103/PhysRevE.84.031304
Wang ZT, Zhou YH, Zheng XJ, 2006. Tensile test of natural microbiotic crust. Catena, 67(2): 139-143. DOI: 10.1016/j.catena.2006.03.009.
doi: 10.1016/j.catena.2006.03.009
Webb NP, Herrick JE, van Zee JW, et al., 2015. Standard methods for wind erosion research and model development: Protocol for the national wind erosion research network. USDA-ARS Jornada Experimental Range.
Webb NP, McGowan HA, 2009. Approaches to modelling land erodibility by wind. Progress in Physical Geography, 33(5): 587-613. DOI: 10.1177/0309133309341604.
doi: 10.1177/0309133309341604
Webb NP, Strong CL, 2011. Soil erodibility dynamics and its representation for wind erosion and dust emission models. Aeolian Research, 3(2): 165-179. DOI: 10.1016/j.aeolia. 2011.03.002.
doi: 10.1016/j.aeolia. 2011.03.002
Wilson G, 1994. Modeling wind erosion: Detachment and maximum transport rate. Texas Tech University PhD thesis.
Woodruff NP, Siddoway FH, 1965. A wind erosion equation. Soil Science Society of America Journal, 29(5): 602-608. DOI: 10.2136/sssaj1965.03615995002900050035x.
doi: 10.2136/sssaj1965.03615995002900050035x
Zhang C, Wang X, Zou X, et al., 2018. Estimation of surface shear strength of undisturbed soils in the eastern part of northern China’s wind erosion area. Soil and Tillage Research, 178: 1-10. DOI: 10.1016/j.still.2017.12.014.
doi: 10.1016/j.still.2017.12.014
Zhang J, Teng Z, Huang N, et al., 2016. Surface renewal as a significant mechanism for dust emission. Atmospheric Chemistry and Physics, 16: 1-22. DOI: 10.5194/acp-16-15517-2016.
doi: 10.5194/acp-16-15517-2016
Zhang JQ, Zhang CL, Chang CP, et al., 2017. Comparison of wind erosion based on measurements and SWEEP simulation: A case study in Kangbao County, Hebei Province, China. Soil and Tillage Research, 165: 169-180. DOI: 10.1016/j.still.2016.08.006.
doi: 10.1016/j.still.2016.08.006
Zheng X, 2009. Mechanics of wind-blown sand movements. Environmental science and engineering. Environmental Science. Springer, Berlin. DOI: 10.1007/978-3-540-88254-1.
doi: 10.1007/978-3-540-88254-1
Zobeck TM, Sterk G, Funk R, et al., 2003. Measurement and data analysis methods for field-scale wind erosion studies and model validation. Earth Surface Processes and Landforms, 28(11): 1163-1188. DOI: 10.1002/esp.1033.
doi: 10.1002/esp.1033
Zou X, Zhang C, Cheng H, et al., 2015. Cogitation on developing a dynamic model of soil wind erosion. Science China Earth Sciences, 58(3): 462-473. DOI: 10.1007/s11430-014-5002-5.
doi: 10.1007/s11430-014-5002-5
No related articles found!
Full text



No Suggested Reading articles found!