The Theoretical Approach to the Modelling of Gully Erosion in Cohesive Soil
Abstract
:1. Introduction
2. Materials and Methods
2.1. Gully Erosion by Water
2.2. Instant and Local Rate of Soil Particle Detachment
2.3. Probability Density Function for the Rate of Detachment
2.4. The Main Resistance and Driving Forces
2.5. Probability Density Function for the Factors of Soil Erosion
2.6. The Algorithm of Erosion Rate Calculation
- The probability density p(kCC) in the part of the cohesion PDF where resistance forces are less than driving forces decreases due to the erosion EiC of soil with particular cohesion CiCThe initial PDF transforms into intermediate PDF (p*)
- Simultaneously, the intermediate PDF of cohesion is transformed due to the exposition of fresh initial soil in the “windows” of the eroded surface layer to PDF of armored soil (pa)
2.7. The Materials for Comparison of Calculations with Measurements
3. Results
3.1. General Numerical Experiments
3.2. The Comparison of Calculated Erosion Rates with the Measured
4. Discussion
5. Conclusions
Funding
Conflicts of Interest
References
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N Plot–Soil–Run | Q, l/s | U, m/s | W, m | d, m | U* | σU | E, m/s | Re | Fr |
---|---|---|---|---|---|---|---|---|---|
1–b2–3 | 3.13 | 1.19 | 0.46 | 0.0057 | 0.12 | 0.26 | 2.29 × 10−7 | 6020 | 5.0 |
1–b2–4 | 4.01 | 1.30 | 0.46 | 0.0067 | 0.13 | 0.28 | 2.33 × 10−7 | 7670 | 5.1 |
1–b2–5 | 5.12 | 1.40 | 0.47 | 0.0077 | 0.14 | 0.30 | 2.29 × 10−7 | 9510 | 5.1 |
1–b2–6 | 6.86 | 1.53 | 0.49 | 0.0092 | 0.15 | 0.33 | 5.49 × 10−7 | 12,340 | 5.1 |
1–b2–7 | 11.13 | 1.79 | 0.51 | 0.0121 | 0.17 | 0.38 | 1.66 × 10−6 | 19,070 | 5.2 |
2–b4–3 | 1.48 | 1.20 | 0.28 | 0.0043 | 0.14 | 0.31 | 3.13 × 10−8 | 4590 | 5.8 |
2–b4–4 | 2.22 | 1.56 | 0.29 | 0.0049 | 0.15 | 0.33 | 4.8 × 10−8 | 6750 | 7.1 |
2–b4–5 | 3.04 | 1.66 | 0.29 | 0.0062 | 0.17 | 0.38 | 8.54 × 10−8 | 9100 | 6.7 |
2–b4–6 | 4.01 | 1.91 | 0.30 | 0.0070 | 0.18 | 0.40 | 1.4 × 10−7 | 11,810 | 7.3 |
2–b4–7 | 5.92 | 2.15 | 0.31 | 0.0089 | 0.21 | 0.46 | 3.49 × 10−7 | 16,830 | 7.3 |
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Sidorchuk, A. The Theoretical Approach to the Modelling of Gully Erosion in Cohesive Soil. Earth 2022, 3, 228-244. https://doi.org/10.3390/earth3010015
Sidorchuk A. The Theoretical Approach to the Modelling of Gully Erosion in Cohesive Soil. Earth. 2022; 3(1):228-244. https://doi.org/10.3390/earth3010015
Chicago/Turabian StyleSidorchuk, Aleksey. 2022. "The Theoretical Approach to the Modelling of Gully Erosion in Cohesive Soil" Earth 3, no. 1: 228-244. https://doi.org/10.3390/earth3010015