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

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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

Figure 1

The normal impact between a saltating sand grain and a half-space comprised of the soil. u and P are the vertical speed of the saltating grain and the collision force acting upon the soil. Given an arbitrary point N under the coordinate of (x, y, z), the stress and displacement can be computed. The eroded volume is denoted by a semi-elliptical shape with the equatorial and polar radii of a and b, respectively"

Table 1

Meanings and symbols of the main variables and parameters. The international system of units is applied"

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

Figure 2

The abrasion rate of brown calcic soil is in direct proportion to the cube of mass flux. The wind tunnel experiment was performed by Dai et al. (2020)"

Table 2

Comparison of anti-erodibilities between several erodible soils. The unified soil classification system (USCS) is adopted. The mechanical parameters are sourced from the geotechnical information available at A constant Poisson's ratio of ν= 0.3 is assumed"

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
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