# Experimental Assessment of Dust Emissions on Compacted Soils Degraded by Traffic

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{10}(particle diameters less than or equal to 10 µm) emissions generated by vehicle traffic on unpaved roadways [10]. However, this model is purely empirical and shows significant discrepancies with in-situ measurements on rural unpaved roads [11] as well as on earthworks haul roads [12]. Studies have shown the effect of vehicle characteristics [11,13] and soil properties [14] on dust emission. These approaches, based on in-situ measurements, were mainly empirical. Therefore, the appearance of the particle by soil degradation and the associated lift are two mechanisms that are not yet sufficiently well-modeled.

## 2. Convective Turbulent Dust Emission Model

#### 2.1. Description of the Klose and Shao’s Model

_{d}(kg·m

^{−2}·s

^{−1}) of particles having a diameter d can be expressed as Equation (1):

_{d}is the particle number concentration per unit of volume (m

^{−3}), T

_{p}is the particle response time (s), f is the lifting force expressed in newtons (N), f

_{i}is the interparticle cohesive force (N) and δ

_{vc}is the thickness of the viscous sublayer area where the particles are sheared. δ

_{vc}is given by Equation (2):

^{−6}m

^{2}·s

^{−1}at 25 °C) and u

^{*}the friction velocity (m·s

^{−1}).

_{p}is given by Equation (3):

^{−3}) and $\rho $ the air density (1.184 kg·m

^{−3}at 25 °C).

^{−1}) in the longitudinal, vertical and spanwise directions respectively. These fluctuations depend on time, so the Reynolds shear stresses are not constant. Thus, $\tau $ is a stochastic quantity that obeys a probability distribution p(τ) depending on the Probability Distribution Functions (PDF) of u′, v′ and w′.

_{i}) mainly depends on the Van der Walls interactions, electrostatic forces as well as capillary and chemical binding forces [21]. These interactions are affected by many parameters including, but not limited to, the particle size, the particle shape, the mineral composition and the surface roughness. Therefore, cohesive forces are difficult to estimate. It is more convenient to treat these forces as stochastic variables following a probability distribution p(f

_{i}). Finally, according to [19], the total convective dust emission flux can be given by Equation (6):

^{2}) up to 0.71 were obtained when comparing model predictions with observations both at a site-based scale [22,23] and a regional scale [24].

#### 2.2. Determination of the Model Input Parameters

#### 2.2.1. Particle Size Distribution (PSD) and Quantity of Particles Subjected to Lift

#### 2.2.2. Cohesive Forces

_{i}) and ${\sigma}_{{f}_{i}}$ its geometric standard deviation (N).

_{i}for particles having diameters of 1 μm, 2 μm, 3.5 μm, 7.5 μm and 20 μm. The geometric standard deviation for the log-normal distribution ${\sigma}_{{f}_{i}}$ is inversely proportional to the particle diameter. The distribution functions p(f

_{i}) cover a wide range for fine particles, demonstrating the need to consider the stochastic behavior of cohesive forces when examining dust emission.

#### 2.2.3. Lifting Forces

_{u′}. Thus, the Reynolds shear stresses distribution function p(τ) is a product distribution [36] (p. 160), given by Equation (11):

## 3. Experimental Facilities and Measurement Techniques

#### 3.1. Compaction and Degradation of the Soil Samples

#### 3.1.1. Compaction

^{3}rectangular samples. The compacting process consisted of pouring the required quantity of soil to be compacted into the container placed inside the base. A displacement table gradually lifted the container while a smooth wheel moved over the surface until the soil was compacted to a height of 28.5 mm in the container.

#### 3.1.2. Soil Degradation by Traffic Simulation

#### 3.2. Soil-Atmosphere Interaction: Wind Tunnel Experiments

^{2}and was 1 m long. The airflow was generated by a 3 kW engine. The mean turbulence intensity in the test section outside the boundary layer was low (<1%). Before wind tunnel experiments, the soil samples were sprayed with a lacquer (Struers

^{TM}) to prevent the boundary layer from being disrupted by dust emissions. Roughness measurements with a rotating LASER profilometer before and after lacquer application showed that this did not alter the surface roughness.

_{∞}= 8 m·s

^{−1}et U

_{∞}= 16 m·s

^{−1}). They were defined to fit with typical truck speeds on construction sites (between 30 and 60 km·h

^{−1}). The coordinate system was such that x corresponded to the horizontal axis (positive downstream), y and z being the vertical (positive upward) and spanwise (positive from the left to the right looking from the entrance of the test section) directions, respectively. The origin O was taken at the center of the leading edge of the sample, on the channel centreline. The vertical profiles of the velocity were measured at the centreline (z = 0) of the test section at four given positions depicted by points 1 to 4 in Figure 4. The first point was used as a reference on the PVC floor of the wind tunnel (x = −0.03 m) while the three other points were located on the soil sample (x = 0.05, 0.15 and 0.27 m). In Figure 4, the flow is from the left to the right.

_{*}was determined using the method developed by Djenedi et al. [44]. It can be applied regardless of the surface roughness and the Reynolds number of the flow. By a trial-and-error method, the value of u* was found by matching each vertical velocity profile with the normalized velocity defect form given by Equation (13):

_{i}(I = 1,2,…,6) and q

_{j}(j = 1, 2, …, 5) are:

_{1}= 110.50, p

_{2}= −230.50, p

_{3}= 114.50, p

_{4}= 7.24, p

_{5}= −6.38 × 10

^{−3}, p

_{6}= −4.60 × 10

^{−5};

_{1}= −10.07, q

_{2}= 15.56, q

_{3}= 4.47 × 10

^{−1}, q

_{4}= −8.20 × 10

^{−4}and q

_{5}= −1.79 × 10

^{−6}.

_{*}is the displacement thickness (m) and θ is the momentum thickness (m), given by Equations (16) and (17), respectively:

## 4. Results and Discussion

#### 4.1. Soil Degradation by Traffic

#### 4.1.1. Detachment of Particles from the Soil Surface

^{2}for each tire in the present study). Figure 5 shows the evolution of D as a function of the number of wheel passes for each of the samples.

_{i}(I = 1, 2, …, 5) are coefficients determined from the experiments and detailed in Table 3.

#### 4.1.2. PSD of Particles Segregated from the Soils during Traffic Degradation

_{min}and d

_{max}represent the minimum and maximum soil particle diameter (µm) respectively.

_{initial soil}is known, it is possible to predict the granulometry of the particles detached after N wheel passes, that is p(d)

_{N passes}(Equation (20)):

_{model}) and the area under the experimental curve (p(d)

_{exp}), according to Equation (21):

#### 4.2. Boundary-Layer Characterization

^{*}and δ

_{vs}calculated from Equations (15), (13) and (2), respectively). Considering H, all profiles corresponded to either a fully turbulent flow or a transitional regime.

_{vs}= 300 µm for U

_{∞}= 8 m/s and δ

_{vs}= 135 µm for U

_{∞}= 16 m/s. It is worthwhile to note that a variation of 50% of this parameter in the model led to a variation of the dust flow of less than 2%.

#### 4.3. Application of the CTDE Model

#### 4.3.1. Estimation of Dust Emissions from Studied Soils

_{∞}= 8 m/s. Figure 8a shows the streamwise turbulence intensity above the sample. Figure 8b shows the PDF of the velocity fluctuations corresponding to the point depicted by a green cross (x = 0.27 m; y = 0.0001 m) in Figure 8a. The velocity fluctuations appeared to follow a normal distribution defined by Equation (22):

_{10}were assessed for 100, 1000 and 10,000 wheel passes. The corresponding results are presented in Figure 10 for U

_{∞}= 8 m·s

^{−1}and U

_{∞}= 16 m·s

^{−1}.

_{10}. For the three soils, the turbulence generated for the largest velocity (U

_{∞}= 16 m/s) led to a dust flux about 30 times greater than for the smallest velocity (U

_{∞}= 8 m/s). This value is found to be high when compared with the results from Etyemezian et al. [47] who carried out in-situ measurements of dust concentrations related to vehicle traffic on unpaved roads. Their work showed that dust emissions were approximately correlated with vehicle speed to the power 3 and therefore a doubling of the speed results in an eightfold increase in emissions. This shows that turbulence is not the main contributor to dust emissions when a vehicle is in motion. The shear between the tires and the ground must have a major influence, which is not considered in the tests presented herein.

#### 4.3.2. Comparison with Field Data

_{10}emitted per kilometer travelled by the vehicle (kg·vkt

^{−1}, kilogram per vehicle kilometer travelled), a unit used in many other studies [11,13,14,47]. The results of these measurements were related to US Army truck circulation and are presented in Table 5. Emission factors per unit area (EF in kg·m

^{−2}) are presented for vehicle speeds of 30 km·h

^{−1}(≈ 8 m·s

^{−1}) and 60 km·h

^{−1}(≈ 16 m·s

^{−1}) in order to make a comparison with the present experimental results.

^{−2}·s

^{−1}. These fluxes are in the same orders of magnitude as those estimated for S50K50 and S75K25 soils at 1000 and 10,000 wheel passes (see Figure 10). Nevertheless, the measurements of Gillies et al. [11] were carried out on a soil with a silt content (particle diameter < 75 µm) less than 7%, whereas S50K50 and S75K25 soils had silt contents of 44% and 73%, respectively. Thus, it is reasonable to think that vehicle traffic on these soils would have led to higher dust emissions than those estimated in Figure 10. Indeed, on this figure, dust emissions were generated by turbulence corresponding to an airflow having a speed of about 30 km·h

^{−1}and 60 km·h

^{−1}. When a truck moves at these speeds, turbulence is generated in the wake of the vehicle, which was not being considered during the wind tunnel experiments.

## 5. Conclusions and Perspectives

^{−1}and 16 m·s

^{−1}were considered above the traffic degraded soils. The study was focused on the characterization of the turbulence intensities and Reynolds shear stresses generated in the near ground turbulent flow.

^{−1}led to dust emissions 30 times higher than those estimated at 8 m·s

^{−1}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Model for the Determination of the PSD of Particles Detached from a Soil by Traffic

**Figure A1.**Deviation from the initial soil particle size distribution at 20,000 wheel passes on the sample (

**a**) S0K100, (

**b**) S50K50 and (

**c**) S75K25. For the latter sample, the deviations at 10,000 passes (

**d**) and 2000 passes (

**e**) are also presented. The dashed curves represent the model of Equation (31).

- A function was constructed allowing the description of the sinusoidal variation. This function looked like:$$difference=A\times d\times \mathrm{sin}\left(d\right)$$
- The scales in Figure A1 were semi-logarithmic, so the function took the following form:$$difference=A\times \mathrm{ln}\left(d\right)\times \mathrm{sin}\left[\mathrm{ln}\left(d\right)\right]$$
- The curves in Figure A1 were defined between d
_{min}et d_{max}and can be approximated as having a period equal to d_{max}-d_{min}, which gave the following function:$$difference=A\times \mathrm{ln}\left(\frac{d}{{d}_{min}}\right)\times sin\left[\frac{2\pi}{\mathrm{ln}\left(\frac{{d}_{max}}{{d}_{min}}\right)}\times \mathrm{ln}\left(\frac{d}{{d}_{min}}\right)\right]$$ - On the definition domain, the curves were first negative and then positive. This was the inverse of the behaviour of the function given by Equation (25). A final modification was therefore necessary:$$difference=A\times \mathrm{ln}\left(\frac{d}{{d}_{min}}\right)\times sin\left[\frac{2\pi}{\mathrm{ln}\left(\frac{{d}_{max}}{{d}_{min}}\right)}\times \mathrm{ln}\left(\frac{d}{{d}_{min}}\right)+\pi \right]$$
- It was therefore a question of determining the amplitude function A which was written as:$$A={f}_{soil}\left(typeofsoil\right)\times {g}_{N}\left(N\right)$$
_{soil}a function depending on the type of soil and ${g}_{N}$ a function depending on the number of wheel passes N. - The ${g}_{N}$ function was determined from the curves in Figure A1c–e. Assuming that f
_{soil}= 1, the value of ${g}_{N}$ corresponded to the amplitude A of Equation (26). Then, ${g}_{N}$ was determined by trial-and-error in order to minimize the average weighted deviation between experimental and theoretical curves. The weighted deviation was defined by:$$weighteddeviation=\left|experimentalvalue\times \left(experimentalvalue-theoreticalvalue\right)\right|$$A weighted deviation criterion was chosen in order to minimize the difference between experimental and theoretical curves for the amplitude peaks, which were the most important parts of the curve to model. According to that, it appeared that the best approximation for the function ${g}_{N}$ was a second-degree function:$${g}_{N}\left(N\right)=9.72\times {10}^{-10}{N}^{2}-4.92\times {10}^{-5}N+1.09$$ - The f
_{soil}function was determined using the curves in Figure A1a–c. These three curves corresponded to the case where ${\mathrm{g}}_{\mathrm{N}}$(N = 20,000) = 0.49. The amplitude of the difference between 20,000 passes and initial soil was low for S0K100 (clay), medium for S75K25 and high for S50K50. Thus, it was considered that this amplitude depended on the product of the percentage of clay by the percentage of sand in the soil ($\%clay\times \%sand$). According to this definition and based on the particle size distributions of the three soils, S0K100 had 20% clay and 7% sand ($\%clay\times \%sand=140$), S50K50 had 13% clay and 36,6% sand ($\%clay\times \%sand=475.8$) and S75K25 had 6,7% clay and 64% sand ($\%clay\times \%sand=428.8$). The amplitude function of Equation (26) to approximate the curves in Figure A1a–c was therefore:$$A\left(N=\mathrm{20,000}\right)={f}_{N}\left(\%clay\times \%sand\right)\times {g}_{N}\left(N=\mathrm{20,000}\right)={f}_{N}\left(\%clay\times \%sand\right)\times 0.49$$

_{soil}function was assessed by trial-and-error to minimize the weighted deviation (Equation (28)). The best approximation for f

_{soil}was:

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**Figure 1.**Log-normal distributions of cohesive forces f

_{i}for particles of 1 μm, 2 μm, 3.5 μm, 7.5 μm and 20 μm diameter, according to Equation (7).

**Figure 3.**(

**a**) Side view of the VECTRA traffic simulator; (

**b**) Front view of the schematic layout; (

**c**) and (

**d**) tires used in this study.

**Figure 4.**Wind tunnel facility and zoom on the soil sample. Green crosses represent the velocity gradient measuring points with their Cartesian coordinates (x,y,z). Distances are in m.

**Figure 6.**Particle size distributions of loose particles and initial soils for sample (

**a**) S0K100, (

**b**) S50K50 and (

**c**) S75K25.

**Figure 7.**Particle size distributions measured (solid lines) and modeled (Equation (20), dashed lines) for sample (

**a**) S0K100, (

**b**) S50K50 and (

**c**) S75K25.

**Figure 8.**Example, for sample IV at a velocity of 8 m/s, of the process of determining p(τ). (

**a**) Velocity fluctuations above the soil surface; (

**b**) PDF of u′, at the measuring point designated by the cross, with determination of the parameters μ and σ from Equation (21); (

**c**) PDF of τ determined using Equation (11).

**Figure 9.**PDF of τ for the position x = 0.27 m and for (

**a**) U

_{∞}= 8 m/s and (

**b**) U

_{∞}= 16 m/s. The dotted lines represent the average curves that have been chosen to be implemented in the dust emission model.

**Figure 10.**Estimated PM

_{10}emissions of the three soils for 100, 1000 and 10,000 wheel passes and for both flow velocities U∞ = 8 m/s and U∞ = 16 m/s.

Sample | Soil | Dry Density after Compaction (kg·m^{−3}) | Water Content during Compaction (%) | Water Content during Traffic Degradation (%) | Number of Wheel Passes (N) | Tire Type ^{a} |
---|---|---|---|---|---|---|

Sample I | S0K100 | 1470.00 | 28.20 | 21.12 | 20,000 | M |

Sample II | S50K50 | 1801.00 | 16.00 | 12.98 | 20,000 | M |

Sample III | S75K25 | 1873.00 | 12.40 | 9.45 | 20,000 | M |

Sample IV | S75K25 | 1873.00 | 12.40 | 8.95 | 10,000 | M |

Sample V | S75K25 | 1873.00 | 12.40 | 9.30 | 20,000 | C |

^{a}M: tire MITAS FL-08; C: tire CONTINENTAL IC 10 (Figure 3).

Height from the Surface (y in mm) | Vertical Spacing between Two Measuring Points (mm) | Number of Measuring Points |
---|---|---|

$0\le y\le 2$ | 0.10 | 21 |

$2.2\le y\le 3$ | 0.20 | 5 |

$3.5\le y\le 5$ | 0.50 | 4 |

$6\le y\le 10$ | 1.00 | 5 |

$12\le y\le 20$ | 2.00 | 5 |

$30\le y\le 50$ | 10.00 | 3 |

Soil | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | Corresponding Equation |
---|---|---|---|---|---|---|

S0K100 | $-5.69\times {10}^{-2}$ | $3.23\times {10}^{3}$ | $-1.24\times {10}^{-5}$ | $4.86\times {10}^{-1}$ | $4.20\times {10}^{2}$ | (18-a) |

S50K50 | $1.38\times {10}^{1}$ | $-8.51\times {10}^{2}$ | $4.41\times {10}^{-1}$ | $2.14\times {10}^{2}$ | $-1.50\times {10}^{4}$ | (18-b) |

S75K25 | $1.11\times {10}^{-1}$ | $8.40\times {10}^{3}$ | $1.26\times {10}^{-4}$ | $2.09\times {10}^{1}$ | $1.58\times {10}^{4}$ | (18-c) |

Position | U_{∞} = 8 m/s | U_{∞} = 16 m/s | |||||
---|---|---|---|---|---|---|---|

H | u_{*} (m/s) | δ_{vs} (µm) | H | u_{*} (m/s) | δ_{vs} (µm) | ||

Sample I | x = −0.03 m | 1.72 | 0.26 | 300 | 1.23 | 0.51 | 153 |

x = 0.05 m | 1.45 | 0.29 | 269 | 1.23 | 0.44 | 177 | |

x = 0.15 m | 1.37 | 0.28 | 278 | 1.30 | 0.58 | 134 | |

x = 0.27 m | 1.26 | 0.24 | 325 | 1.26 | 0.53 | 147 | |

Sample III | x = −0.03 m | 1.78 | 0.32 | 244 | 1.39 | 0.54 | 144 |

x = 0.05 m | 1.22 | 0.30 | 260 | 1.52 | 0.62 | 126 | |

x = 0.15 m | 1.50 | 0.34 | 229 | 1.33 | 0.66 | 118 | |

x = 0.27 m | 1.38 | 0.31 | 252 | 1.35 | 0.62 | 126 | |

Sample IV | x = −0.03 m | 1.70 | 0.32 | 244 | 1.32 | 0.55 | 142 |

x = 0.05 m | 2.18 | 0.72 | 108 | 2.03 | 1.37 | 57 | |

x = 0.15 m | 1.71 | 0.27 | 289 | 1.23 | 0.73 | 107 | |

x = 0.27 m | 1.24 | 0.21 | 371 | 1.22 | 0.51 | 153 | |

Sample V | x = -0.03 m | 1.62 | 0.32 | 244 | 1.73 | 0.65 | 120 |

x = 0.05 m | 1.42 | 0.17 | 459 | 1.16 | 0.42 | 186 | |

x = 0.15 m | 1.39 | 0.24 | 325 | 1.23 | 0.62 | 126 | |

x = 0.27 m | 1.19 | 0.17 | 459 | 1.16 | 0.45 | 173 |

**Table 5.**Vehicle characteristics and dust emission factors for the study of Gillies et al. [11].

Vehicle Type | Weight (kg) | Tire Width (m) | EF (kg·vkt^{−1}) | EF (kg·m^{−2}) ^{b} | |
---|---|---|---|---|---|

U_{t} = 30 km·h^{−1} | U_{t} = 60 km·h^{−1} | ||||

GMC C5500 | 5 227 | 0.245 | 0.0019 × U_{t} ^{a} | 0.0012 | 0.0023 |

M977 HEMTT | 17 727 | 0.400 | 0.0048 × U_{t} | 0.0018 | 0.0036 |

M923A2 (5-ton) | 14 318 | 0.355 | 0.0047 × U_{t} | 0.0020 | 0.0040 |

M1078 LMTV | 8 060 | 0.395 | 0.0018 × U_{t} | 0.0007 | 0.0014 |

^{a}U

_{t}: truck speed (km·h

^{−1});

^{b}The emission factor expressed in mass per unit area is calculated by considering the wheels/road contact area along the truck journey (contact area = 2 × tire width × distance travelled).

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**MDPI and ACS Style**

Le Vern, M.; Sediki, O.; Razakamanantsoa, A.; Murzyn, F.; Larrarte, F.
Experimental Assessment of Dust Emissions on Compacted Soils Degraded by Traffic. *Atmosphere* **2020**, *11*, 369.
https://doi.org/10.3390/atmos11040369

**AMA Style**

Le Vern M, Sediki O, Razakamanantsoa A, Murzyn F, Larrarte F.
Experimental Assessment of Dust Emissions on Compacted Soils Degraded by Traffic. *Atmosphere*. 2020; 11(4):369.
https://doi.org/10.3390/atmos11040369

**Chicago/Turabian Style**

Le Vern, Mickael, Ouardia Sediki, Andry Razakamanantsoa, Frédéric Murzyn, and Frédérique Larrarte.
2020. "Experimental Assessment of Dust Emissions on Compacted Soils Degraded by Traffic" *Atmosphere* 11, no. 4: 369.
https://doi.org/10.3390/atmos11040369