The Collapse Mechanism of Slope Rill Sidewall under Composite Erosion of Freeze-Thaw Cycles and Water
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Methods
3. Results and Discussion
3.1. Analysis of the Causes of Rill Sidewalls Collapse by Water Erosion under Freeze-Thaw Cycles
3.2. Analysis of the Collapse Causes of Rill Sidewalls by Water Erosion under One-Time Freeze-Thaw Cycles Effects of Different Minimum Temperatures
3.3. Analysis of the Collapse Mechanism of Rill Sidewall under Freeze-Thaw and Water Flow Action
- (1)
- Influence of different water contents and freeze-thaw cycles on the friction angle in the soil:
- φ—the soil’s internal friction angle (°);
- ω—the water content of sample soil (m3/m3).
- φ—the soil’s internal friction angle (°);
- n—number of freeze-thaw cycles.
- φ—the soil’s internal friction angle (°);
- n—number of freeze-thaw cycles;
- ω—the water content of sample soil (m3/m3);
- a1, b1, c1, p1—coefficients of the equation;
- elucidates the influence of the two-factor interaction on the internal friction angle within the soil of the rill sidewall, as depicted in Figure 9, with an R2 value exceeding 0.99.
- (2)
- Fitting a rill sidewall moisture field expression:
- ω—the water content of sample soil (m3/m3);
- t—expansive erosion test duration (min);
- t0—onset time of change in soil moisture content (min);
- t1—end time of change in soil moisture content (min);
- t2—expansive erosion test end time (min);
- ω1—final water content of the soil layer (m3/m3);
- k—the change rate of soil moisture content;
- m—coefficient of the equation; m is approximately equal to the initial water content of the soil.
- k—the change rate of soil moisture content;
- n—number of freeze-thaw cycles;
- a2, b2, c2—coefficients of the equation.
- k—the change rate of soil moisture content;
- z—distance of the rill sidewall soil layer from the bottom (cm);
- c3, p2—coefficients of the equation.
- k—the change rate of soil moisture content;
- n—number of freeze-thaw cycles;
- z—distance of the rill sidewall soil layer from the bottom (cm);
- a2, b2, c2, c3, p2—coefficients of the equation;
- can aptly depict the influence of two-factor interaction on the change rate of soil water content within the rill sidewall, as illustrated in Figure 11, with an R2 value exceeding 0.9.
- ω—the water content of sample soil (m3/m3);
- n—number of freeze-thaw cycles;
- z—distance of the rill sidewall soil layer from the bottom (cm);
- t—expansive erosion test duration (min);
- t0—onset time of change in soil moisture content (min);
- t1—end time of change in soil moisture content (min);
- t2—expansive erosion test end time (min);
- ω1—final water content of the soil layer (m3/m3);
- a2, b2, c2, c3, p2, m—coefficients of the equation; m is approximately equal to the initial water content of the soil.
- (3)
- Mechanism analysis of the collapse causation of rill sidewall after freeze-thaw cycles in the water erosion test:
- G—the gravity of rill sidewall soils (N);
- H—rill sidewall heights (cm);
- z0—depth of the rill water flow (cm);
- 2D—length of destabilized zone (cm), calculated from the location of cracking;
- ρd—soil dry density (g/cm3);
- ω—the water content of sample soil (m3/m3);
- α—slope inclination (°);
- g—gravity acceleration (N/kg).
- M—the bending moment within the destabilization zone (N·cm);
- G—the gravity of rill sidewall soils (N);
- D—perpendicular distance from the fulcrum the line of force (cm).
- while the bending moment resisting crack formation in this zone is designated as:
- M′—the bending moment resisting crack formation in this zone (N·cm);
- Ea—the soil pressure (N);
- D′—the height of the soil pressure action location (cm).
- Ea—the soil pressure (N);
- H—rill sidewall heights (cm);
- z0—depth of the rill water flow (cm);
- k0—the static earth pressure coefficient;
- ρd—soil dry density (g/cm3);
- ω—the water content of sample soil (m3/m3);
- g—gravity acceleration (N/kg);
- z—distance of the rill sidewall soil layer from the bottom (cm);
- T—the interfacial shear within the instability zone (N);
- H—rill sidewall heights (cm);
- z0—depth of the rill water flow (cm);
- hl—the depth of the crack at the top of the rill sidewall (cm);
- τ—the shear stress (N/cm2);
- z—distance of the rill sidewall soil layer from the bottom (cm);
- τ—the shear stress (N/cm2);
- ρd—soil dry density (g/cm3);
- ω—the water content of sample soil (m3/m3);
- g—gravity acceleration (N/kg).
- H—rill sidewall heights (cm);
- z—distance of the rill sidewall soil layer from the bottom (cm);
- φ—the soil’s internal friction angle (°).
- T—the interfacial shear within the instability zone (N);
- H—rill sidewall heights (cm);
- z0—depth of the rill water flow (cm);
- hl—the depth of the crack at the top of the rill sidewall (cm);
- ρd—soil dry density (g/cm3);
- ω—the water content of sample soil (m3/m3);
- g—gravity acceleration (N/kg).
- z—distance of the rill sidewall soil layer from the bottom (cm);
- φ—the soil’s internal friction angle (°).
4. Conclusions
- (1)
- Freeze-thaw cycles exert a notable influence on the soil structure of rill sidewalls, promoting capillary phenomena within the soils. A single cycle of freezing and thawing exerted the most pronounced impact on the structure of the rill sidewall soil, with the moisture field within the rill sidewall soil undergoing more significant changes under negative soil temperatures;
- (2)
- Freeze-thaw cycles contribute to enhancing the internal friction angle of the soil, while the internal friction angle tends to decrease with increasing soil water content. Accurately fitted expressions were derived to represent the interaction effect between the number of freeze-thaw cycles and soil water content on the internal friction angle of the soil during expanded erosion by rill water flow;
- (3)
- The impact of the number of freeze-thaw cycles on the rate of soil water content change at various locations along the rill sidewall can be precisely described using a logarithmic function. Furthermore, an equation was developed to effectively capture the interaction between the number of freeze-thaw cycles and the distance of the soil layer from the bottom of the rill sidewall in influencing the rate of water content change at each location of the rill sidewall;
- (4)
- By deriving expressions for the bending moment and resistance to cracking within the instability zone of the rill sidewall following freeze-thaw cycles during the expansion and erosion caused by rill water flow, the exact location of the crack at the top of the rill sidewall can be determined based on the equality between them. Furthermore, an expression for the changing gravitational forces and shear forces at the interface within the instability zone of the rill sidewall can be derived, based on their equivalence, enabling the calculation of the critical state of instability and collapse of the rill sidewall.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Huang, W.; Shao, S.; Liu, Y.; Xu, X.; Zhang, W.; Liu, Y. The Collapse Mechanism of Slope Rill Sidewall under Composite Erosion of Freeze-Thaw Cycles and Water. Sustainability 2024, 16, 4144. https://doi.org/10.3390/su16104144
Huang W, Shao S, Liu Y, Xu X, Zhang W, Liu Y. The Collapse Mechanism of Slope Rill Sidewall under Composite Erosion of Freeze-Thaw Cycles and Water. Sustainability. 2024; 16(10):4144. https://doi.org/10.3390/su16104144
Chicago/Turabian StyleHuang, Wenbin, Shuai Shao, Yuhang Liu, Xiangtian Xu, Weidong Zhang, and Yong Liu. 2024. "The Collapse Mechanism of Slope Rill Sidewall under Composite Erosion of Freeze-Thaw Cycles and Water" Sustainability 16, no. 10: 4144. https://doi.org/10.3390/su16104144