# Freeze-Thaw Effect on Riverbank Stability

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Slope Stability Analysis and Modeling

#### 2.1. Bank Stability Mechanics

#### Forces on the Potential Sliding Mass

^{2}; ${F}_{cp}$ is the lateral hydrostatic pressure, kN/m

^{2}; ${F}_{x}$ and ${F}_{z}$ are the horizontal and vertical components of ${F}_{cp}$, respectively; $\omega $ is the angle between ${F}_{cp}$ and the horizontal direction, °; $\alpha $ is the angle between ${F}_{cp}$ and the potential sliding surface, °; ${U}_{w}$ is the pore water pressure, kN/m

^{2}; ${P}_{d}$ is the infiltration water pressure, kN/m

^{2}; $e$ is the angle between the infiltration water pressure and the normal direction of the sliding surface, °; ${h}_{w}$ is the groundwater level, m; $\xi $ is the river water level, m; $\beta $ is the inclination of the potential sliding surface, °; $i$ is the slope inclination, °; $b$ is the top width of the potential sliding mass, m; $H$ is the potential sliding depth, m; ${H}_{1}$ is the depth of the bank slope, m; ${H}_{2}$ is the depth of the bank tensile fracture, m; ${H}_{3}$ is the depth of the residual tensile fracture, m.

^{3}; ${\gamma}_{sat}$ is the specific weight of saturated soil, kN/m

^{3}. and

^{2}; ${\gamma}_{w}$ is the specific weight water and is set to 10 kN/m

^{3}consider the turbidity of the river water; h is the depth from the water surface, m. The hydrostatic pressure can be decomposed into horizontal hydrostatic pressure ${F}_{x}$ and vertical hydrostatic pressure ${F}_{z}$, then the total hydrostatic pressure is:

#### 2.2. Modeling Bank Slope Instability

## 3. Model Application and Analysis

#### 3.1. Study Site

#### 3.2. Bank Stability Analysis

#### 3.3. Factors Affecting Bank Stability

#### 3.3.1. Freeze-Thaw Effect

#### 3.3.2. Effect of Infiltration Water Pressure

#### 3.3.3. Effect of Bank Slope

## 4. Conclusions

- (1)
- When the river water level is constant, the safety factor of bank stability decreases with the rising groundwater level. When the groundwater level is constant, the safety coefficient of bank stability declines with the decreasing river water level, with a trend of thawing period < dry period < low water period < flooding period < wet period.
- (2)
- The freeze-thaw action significantly changes the mechanical properties of the bank material, leading to a 24.35–29.13% reduction in the safety factor of bank stability, indicating the important effect of the freeze-thaw in reducing the bank stability.
- (3)
- When the groundwater level is lower than the river water level, the infiltration water pressure mainly shows an inhibitory effect on the bank stability. The safety factor of bank stability will increase. By contrast, when the groundwater level is higher, the infiltration water pressure plays a destabilizing role.
- (4)
- When the river water level is below 4 m, there is a possibility of bank collapse under different bank slope angles, and the safety factor decreases with larger bank slope angles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Hooke, J.M. An analysis of the processes of river bank erosion. J. Hydrol.
**1979**, 42, 39–62. [Google Scholar] [CrossRef] - Chen, D.; Duan, J.G. Modeling width adjustment in meandering channels. J. Hydrol.
**2006**, 321, 59–76. [Google Scholar] [CrossRef] - Henshaw, A.J.; Thorne, C.R.; Clifford, N.J. Identifying causes and controls of river bank erosion in a British upland catchment. Catena
**2012**, 100, 107–119. [Google Scholar] [CrossRef] - Xia, J.Q.; Zong, Q.L.; Deng, S.S.; Xu, Q.X.; Lu, J.Y. Seasonal variations in composite riverbank stability in the Lower Jingjiang Reach, China. J. Hydrol.
**2014**, 519, 3664–3673. [Google Scholar] [CrossRef] - Xia, J.Q.; Zong, Q.L. Mechanism of Bank Failure in Jingjiang Section of Yangtze River and Its Numerical Simulation; Science Press: Beijing, China, 2015; pp. 155–167. (In Chinese) [Google Scholar]
- Lu, Y.; Lu, Y.J.; Zhang, X.N. Influence of river water level landing on slope stability. Adv. Water Science.
**2008**, 19, 389–393. (In Chinese) [Google Scholar] - Guo, Y.; Shen, W. Monitoring and Experiment on the Effect of Freeze-Thaw on Soil Cutting Slope Stability. Procedia Environ. Sci.
**2011**, 10, 1115–1121. [Google Scholar] [CrossRef] - Xie, H.; Yu, K.Z. Analysis of factors affecting bank stability in construction of Yangtze River dry embankment protection project. People’s Yangtze River.
**2006**, 37, 93–94+101. (In Chinese) [Google Scholar] - Hoomehr, S.; Akinola, A.; Wynn-Thompson, T.; Garnand, W.; Eick, M.J. Water Temperature, pH, and Road Salt Impacts on the Fluvial Erosion of Cohesive Streambanks. Water
**2018**, 10, 302. [Google Scholar] [CrossRef] - Xu, W.; He, S.L. Analysis of influencing factors of riverbank collapse. Regul. Huai River.
**2019**, 4, 22–24. (In Chinese) [Google Scholar] - Osman, A.M.; Thorne, C.R.; Member, A. Riverbank stability analysis. I: Theory. J. Hydraul. Eng.
**1988**, 114, 134–150. [Google Scholar] [CrossRef] - Zhang, X.N.; Jiang, C.F.; Ying, Q.; Chen, C.Y. Review of research on bank collapse in natural rivers. Adv. Sci. Technol. Water Resour.
**2008**, 28, 80–83. (In Chinese) [Google Scholar] - Zhang, X.N.; Jiang, C.F.; Chen, C.Y.; Ying, Q. Analysis of influencing factors of river bank failure. J. River Sea Univ. (Nat. Sci. Ed.)
**2009**, 37, 36–40. (In Chinese) [Google Scholar] - Zhang, F.Z.; Chen, X.P. Study on the effect of river scour on seepage and deformation of embankment. Geotechnics
**2011**, 32, 441–447. (In Chinese) [Google Scholar] - Simon, A.; Curini, A.; Darby, S.E.; Langendoen, E.J. Bank and near-bank processes in an incised channel. Geomorphology
**2000**, 35, 193–217. [Google Scholar] [CrossRef] - Couper, P. Effects of silt–clay content on the susceptibility of river banks to subaerial erosion. Geomorphology
**2003**, 56, 95–108. [Google Scholar] [CrossRef] - Chiang, S.W.; Tsai, T.L.; Yang, J.H. Conjunction effect of stream water level and groundwater flow for riverbank stability analysis. Environ. Earth Sci.
**2011**, 62, 707–715. [Google Scholar] [CrossRef] - Karmaker, T.; Dutta, S. Erodibility of fine soil from the composite river bank of Brahmaputra in India. Hydrol. Processes.
**2011**, 25, 104–111. [Google Scholar] [CrossRef] - Kimiaghalam, N.; Goharrokhi, M.; Clark, S.P.; Ahmari, H. A comprehensive fluvial geomorphology study of riverbank erosion on the Red River in Winnipeg, Manitoba, Canada. J. Hydrol.
**2015**, 529, 1488–1498. [Google Scholar] [CrossRef] - Thoron, C.R.; Tovey, N.K. Stability of composite riverbanks. Earth Surf. Processes Landf.
**1981**, 6, 469–484. [Google Scholar] [CrossRef] - Wang, Y.G.; Kuang, S.F. Study of critical collapse height of river banks. J. Water Resour.
**2007**, 10, 1158–1165. (In Chinese) [Google Scholar] - Wang, J.; Zong, Q.L.; Yue, H.Y.; Liu, Z.X. Effects of alternating wet and dry on the mechanical properties of shoreland soils in a typical section of the Jingjiang River section of the Yangtze River. J. Agric. Eng.
**2019**, 35, 144–152. (In Chinese) [Google Scholar] - Wang, X.D.; Li, S.Y.; Sun, Y.F.; Zhang, C.B.; Liu, G.W. Influence of freeze–thaw cycling on the soil mechanical properties of open-pit mine dump under different moisture contents. Environ. Earth Sci.
**2021**, 80, 279. [Google Scholar] [CrossRef] - Simon, A.; Collison, A.J.C. Pore-water pressure effects on the detachment of cohesive streambeds: Seepage forces and matric suction. Earth Surf. Processes Landf.
**2001**, 26, 1421–1442. [Google Scholar] [CrossRef] - Tang, L.Y.; Li, G.; Li, Z.; Jin, L.; Yang, G.S. Shear properties and pore structure characteristics of soil–rock mixture under freeze–thaw cycles. Bull. Eng. Geol. Environ.
**2021**, 80, 3233–3249. [Google Scholar] [CrossRef] - Darby, S.E.; Thorne, C.R. Development and testing of riverbank-stability analysis. J. Hydraul. Eng.
**1996**, 122, 443–454. [Google Scholar] [CrossRef] - Samadi, A.; Davoudi, M.H.; Amiri-Tokaldany, E. Experimental study of cantilever failure in the upper part of cohesive riverbanks. Res. J. Environ. Sci.
**2011**, 5, 444–460. [Google Scholar] [CrossRef] - Wang, Y.G.; Kuang, S.F. Research on bank collapse types and collapse modes. Sediment Res.
**2014**, 1, 13–20. [Google Scholar] - Rinaldi, M.; Casagli, N. Stability of streambanks formed in partially saturated soils and effect of negative pore water pressures: The Sieve River (Italy). Geomorphology
**1999**, 26, 253–277. [Google Scholar] [CrossRef] - Deng, S.; Xia, J.Q.; Zhou, M.R.; Li, J.; Zhu, Y.H. Coupled modeling of bank retreat processes in the Upper Jingjiang Reach, China. Earth Surf. Processes Landf.
**2018**, 43, 2863–2875. [Google Scholar] [CrossRef] - Zhang, Z.H.; Wang, W.D.; Zhang, Y.B. Improvement of transfer coefficient method under the consideration of hydrodynamic pressure. Eng. Fail. Anal.
**2021**, 124, 1167–1170. [Google Scholar] [CrossRef] - Amiri-tokaldany, E.; Darby, S.E.; Tosswell, P. Bank stability analysis for predicting reach-scale land loss and sediment yield. J. Am. Water Resour. Assoc.
**2003**, 39, 897–909. [Google Scholar] [CrossRef] - Amiri-tokaldany, E.; Darby, S.E.; Tosswell, P. Coupling bank stability and bed deformation models to predict equilibrium bed topography in river bends. J. Hydraul. Eng.
**2007**, 113, 1167–1170. [Google Scholar] [CrossRef] - Lai, Y.G.; Thomas, R.E.; Ozeren, Y.; Simon, A.; Greimann, B.P.; Wu, K. Modeling of multilayer cohesive bank erosion with a coupled bank stability and mobile-bed model. Geomorphology
**2015**, 243, 116–129. [Google Scholar] [CrossRef] - Li, C.; Quan, D.; Zhang, Y.; Shi, X.H.; Guo, Z.Y. Characteristics of water-sand movement process and evolution trend of the Yellow River (Inner Mongolia section). J. Soil Water Conserv.
**2020**, 34, 41–46+53. (In Chinese) [Google Scholar] - Li, Y.; Su, H.F.; Wang, L. Advances in shore slope stability research. Constr. Technol.
**2017**, 46, 1225–1229. (In Chinese) [Google Scholar] - Simon, A. Mass Wasting Algorithms in an Alluvial Channel Model. In Proceedings of the 5th Federal Inter-Agency Sedimentation Conference, Las Vegas, NV, USA, 22–29 August 1991. [Google Scholar]
- Zhang, X.N.; Jiang, C.F.; Chen, C.Y.; Ying, Q. Types and characteristics of river bank failure. Prog. Water Resour. Hydropower Sci. Technol.
**2008**, 28, 66–70. (In Chinese) [Google Scholar] - Xia, J.Q.; Zong, Q.L.; Xu, Q.X.; Deng, C.Y. Characteristics of binary structure riverbank soils and bank failure mechanism in the lower Jingjiang River. Adv. Water Sci.
**2013**, 24, 810–820. (In Chinese) [Google Scholar] - Ran, R.; Liu, Y.F. Analysis of the influence of reservoir bank slope morphology on its stability using BSTEM model. Groundwater
**2011**, 33, 162–165. (In Chinese) [Google Scholar] - Yang, Z.; Li, C.; Ji, H.L.; Sun, C.; Shi, Z.F. Study on the characteristics of temperature and humidity changes in the embankment soil of the Yellow River during the freeze-thaw period and the influencing factors. Arid. Zone Resour. Environ.
**2021**, 35, 76–83. (In Chinese) [Google Scholar]

**Figure 3.**Schematic diagram of forces on the sliding surface of the riverbank (after Darby and Thorne with modification.).

**Figure 8.**Effect of freezing and thawing on soil cohesion and angle of internal friction. (

**a**) Soil cohesion, (

**b**) Angle of internal friction.

Natural Specific Weight, (kN/m^{3}) | Saturated Specific Weight, (kN/m^{3}) | $\mathbf{Median}\mathbf{Particle}\mathbf{Size},$${D}_{50}/\left(\mathsf{\mu}m\right)$ | Dry Density, (g/cm^{3}) | Experimental Values | Valid Values | ||
---|---|---|---|---|---|---|---|

$\mathit{C}$$,\left(kPa\right)$ | $\mathit{\phi}$ | ${\mathit{C}}^{\prime}$$,\left(kPa\right)$ | ${\mathit{\phi}}^{\prime}$ | ||||

18.1 | 19.3 | 33.55 | 1.58 | 35.5 | 30 | 24.85 | 27 |

**Table 2.**Bank slope stability under different combinations of groundwater level and river water level.

$\mathbf{Groundwater}\mathbf{Level}{\mathit{h}}_{\mathit{w}}/\mathbf{m}$ | 0 | −0.5 | −1 | −1.5 | −2.0 | −2.5 | −3.0 | |
---|---|---|---|---|---|---|---|---|

$\mathbf{River}\mathbf{Water}\mathbf{Level}\mathit{\xi}/\mathbf{m}$ | ||||||||

−1 | + | + | + | + | + | + | + | |

−2 | + | + | + | + | + | + | + | |

−3 | - | + | + | + | + | + | + | |

−4 | - | - | + | + | + | + | + | |

−5 | - | - | - | + | + | + | + | |

−6 | - | - | - | - | + | + | + | |

−7 | - | - | - | - | + | + | + | |

−8 | - | - | - | - | - | + | + |

Parameters | Thawing Period | Dry Period | Wet Period | Flooding Period | Low Flow Period |
---|---|---|---|---|---|

$\mathbf{Cohesion}{\mathit{C}}^{\mathbf{\prime}}$$/kPa$ | 16.8 | 16.8 | 24.85 | 24.85 | 24.85 |

$\mathbf{Friction}\mathbf{angle}{\mathbf{\phi}}^{\mathbf{\prime}}$/° | 25.2 | 25.2 | 27 | 27 | 27 |

$\mathbf{Ground}\mathbf{water}\mathbf{level}{\mathit{h}}_{\mathit{w}}$/m | 0 | −3 | −3 | −0.5 | −0.5 |

$\mathbf{River}\mathbf{water}\mathbf{level}\mathit{\xi}$/m | −5 | −5 | −1.5 | −1.5 | −4 |

Safety factor | 0.75 | 1.26 | 4.16 | 2.14 | 1.29 |

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**MDPI and ACS Style**

Li, C.; Yang, Z.; Shen, H.T.; Mou, X.
Freeze-Thaw Effect on Riverbank Stability. *Water* **2022**, *14*, 2479.
https://doi.org/10.3390/w14162479

**AMA Style**

Li C, Yang Z, Shen HT, Mou X.
Freeze-Thaw Effect on Riverbank Stability. *Water*. 2022; 14(16):2479.
https://doi.org/10.3390/w14162479

**Chicago/Turabian Style**

Li, Chao, Zhen Yang, Hung Tao Shen, and Xianyou Mou.
2022. "Freeze-Thaw Effect on Riverbank Stability" *Water* 14, no. 16: 2479.
https://doi.org/10.3390/w14162479