# The Influences of Riparian Vegetation on Bank Failures of a Small Meadow-Type Meandering River

^{1}

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## Abstract

**:**

^{2}≥ 0.76. The block width predicted from the proposed equilibrium equation deviated from in situ measurements by approximately 22.1%, a discrepancy highly subject to the overestimation of root reinforcement using Wu’s model. By reducing the coefficient of Wu’s model from 1.2 to 0.85, the proposed equilibrium equation was reliable to predict the width of bank collapse. However, its applicability to other study areas needs to be verified in further studies.

## 1. Introduction

## 2. Study Area

^{2}in size. The river channel lies at an elevation of 3400–4200 m.a.s.l. with a mean channel gradient of 0.19%. This area has a plateau, periglacial humid climate with a mean annual temperature of −4 °C. It has two distinct seasons, a warm and rainy season from May to October and a cold, dry, and windy season from November to April. Mean annual precipitation is 329–560 mm, only a fraction of the mean annual evaporation of 1278 mm [27]. The vegetation of the area is predominantly alpine meadow and alpine grassland meadows [28]. These meadows comprise perennial Cyperaceae plants, Gramineae plants, forbs, and a small variety of shrubs. Soil type is alpine meadow soil, while swamp meadow soil is also common. Soil layer is thin with a coarse texture, and the soil organic matter is predominantly distributed in the surface layer.

## 3. Methods

#### 3.1. Field Sample Collection

#### 3.2. Laboratory Analysis

## 4. Theoretical Foundations

_{1}and d

_{2}are the vertical thickness of the soil-root composite and the transitional sandy block, respectively; b

_{c}refers to the width of the collapsed block; G

_{1}and G

_{2}are the self-weight of the soil-root composite and sand layer, respectively. They are calculated as:

_{1}and F

_{2}in Equation (1) are the critical shear strength of the soil-root composite and the maximum cohesion of the transitional sandy layer, respectively. ${F}_{2}={c}_{2}{d}_{2}$ (c

_{2}is the cohesion of the sandy layer that can be determined through shear strength tests of the field samples).

_{0}is the shear strength of the soil without roots; $\Delta {S}_{1}$ represents the reinforced shear strength caused by the roots traversing through the collapsed surface. If most of the roots have reached their critical tensile strength, the entire undermined block will collapse, which follows the assumption that the root surface of the collapsed site bears enough friction and binding force and that it has enough anchoring length to protect the root from being pulled out. According to the root reinforcement model proposed by Wu et al. [31], ΔS

_{1}can be approximated as

_{N}is the average tensile strength of roots in unit soil, which is also called the root area ratio, A

_{r}/A

_{s}is the ratio of the sum of the cross-sectional area of the roots on the collapsed surface to the collapsed area.

_{1}, G

_{2}, F

_{1}and F

_{2}are plugged into Equation (1), it is transformed to the following form:

_{1}can be expressed as:

_{1}, ρ

_{2}, and ρ

_{w}have been determined from an analysis of the in situ collected soil samples; S

_{0}, T

_{N}, and A

_{r}vary with soil structure and plant species on the failed surface, which can be measured in situ; A

_{s}, d

_{1}, d

_{2}, and b

_{c}can also be measured in the field. d

_{2}= 0 when water scour reaches the soil-root composite. In this case, Equation (10) can be further simplified as follows:

_{c}can be obtained from Equation (11) as follows:

## 5. Results

#### 5.1. Characteristics of Vegetation, Its Roots, Soil, and River

_{root}(Figure 4). This relationship can be expressed as:

_{root}

^{−1.297}(R

^{2}= 0.713)

^{−1}to 1.9 m∙s

^{−1 }(Table 3).

#### 5.2. Impact of Plant Roots on Bank Failure

^{2}= 0.289) between the length and width of critical blocks. However, the correlation is slightly looser for slump blocks (r = 0.531, R

^{2}= 0.282 with a linear relationship); R-squared values showed a lack of correlation between the length and width of collapsed blocks.

_{r}of both slump and critical blocks was in good agreement with the thickness d

_{1}of the failed blocks after natural logarithmic transformation (Figure 6b). This relationship can be expressed as Equation (13) for slump blocks and Equation (14) for critical blocks:

_{1}= 0.4965 lnL

_{r}+ 1.1816 (R

^{2 }= 0.892, n = 63)

_{1}= 0.4637 lnL

_{r}+ 1.1342 (R

^{2}= 0.757, n = 15)

_{s}= 0.3298 L

_{r}

^{1.3165}(R

^{2}= 0.527)

^{2}= 0.5271) derived for the slump blocks is closer than that for the critical blocks (r = 0.603, R

^{2}= 0.3633), like attributable to the role of plant roots. However, this relationship does suggest that the volume of the failed blocks is associated with the root length of riparian vegetation. It demonstrates that the root system of the soil-root composite has a strong reinforcing and binding effect on vertical bank deposits.

#### 5.3. Predicted Width of the Failed Blocks

_{c}) of the failed blocks using Equation (12) that has been transformed to Equation (17) after the root area ratio A

_{r}/A

_{s}was expressed in terms of root diameter.

_{i}is the diameter of root i; n stands for the total number of roots on a collapsed surface (0.20 m × 0.20 m in size); the root area ratio A

_{r}/A

_{s}of the study area ranges from 0.11% to 0.13% with an average of 0.12% (Table 2, column 7); d

_{1}is the thickness of the collapsed block at the four study sites. It was measured at 0.65–1.22 m from the field samples; the average d

_{1}was calculated from weighted averaging of the thickness of both critical and slump blocks (Table 4, column 5). Notably, the overall slump blocks and critical blocks in each of the sites were used to derive the average thickness of the riverbank soil-root composite (Table 5, column 2). The average thickness of the collapsed block was calculated to be 0.81 m; S

_{0}was the average shear strength of the soil, with a mean of S

_{0}= 4.11 kPa (Table 2, column 9); T

_{N}was the tensile strength of plant roots within the collapsed riparian blocks at the four sites (Table 2, column 8). The average soil-root composite density ρ

_{1}was calculated as 1536 kg/m

^{3}from in situ measurements (Table 2, column 2).

_{r}is the tensile strength of plant roots per unit area, θ is the angle of tensile distortion, and φ is the angle of friction. According to the results of in situ shear strength tests, θ and φ were found to vary from 40° < θ < 80° and 10° < φ < 25°, resulting in ΔS varying from 0.61 to 1.15. Thus, a middle value of 0.85 was used in this study to calibrate the predicted width of blocks.

_{c}of the collapsed block at each of the four study sites was predicted by applying all the above relevant values into Equation (17). It ranged from 0.989 m at site B to 1.158 m at site D, with an average of 1.056 m (Table 5, column 4). The four in situ measured widths of the collapsed slump and critical blocks had an average of 0.865 m (see Table 5, column 3), which was slightly smaller than the predicted b

_{c}of 1.056 m, resulting in an overall relative error of 22.1%. Furthermore, all four predicted widths were larger than their in situ measured counterparts because Equation (17) was underpinned by the assumption that all the roots passing through the collapsed surface snapped simultaneously at the moment of failure. In reality, the plant roots were entangled with one another in the soil. In the case of bank failure, the roots on the collapsed surface are gradually pulled away under gravity. Some are also connected to other fibrous roots that do not pass through the collapsed surface. Their tensile effect has been ignored in the prediction, resulting in an average overestimated value of 22.1%.

## 6. Discussion

_{c}(Table 5, column 6) was much closer to the in situ measured counterparts, resulting in an average overestimation of only 2.7% (Table 5, column 7).

## 7. Conclusions

^{2}= 0.26 to 0.29). The dimension of the failed blocks varies according to site. Such variations in the morphology of the failed blocks are linked closely to plant root length. In particular, block thickness can be accurately predicted from root length (R

^{2}≥ 0.76) but not block width. The thickness of slump blocks is logarithmically related to root length. Similarly, the volume of the displaced blocks is also closely related to root length for slump blocks (R

^{2}= 0.527) but not for critical blocks, attributable to the action of plant roots. The block width predicted from the proposed equilibrium equation differed from the in situ measured width by an average of 22.1% among the four sites. The constrained equilibrium formula for predicting the width of blocks suggests that alpine meadow vegetation can increase the amount of time required to undermine, detach, and remove bank failure blocks. It can be concluded that the proposed equilibrium equation is reliable for predicting the width of collapsed blocks from in situ measured soil and vegetation properties. It facilitates the understanding of the mechanism of cantilever bank collapse. However, its applicability to other study areas requires further investigation, where bank deposits may comprise different materials.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Thorne, C.R.; Tovey, N.K. Stability of composite river banks. Earth Surf. Process. Landf.
**1981**, 6, 469–484. [Google Scholar] [CrossRef] - Hickin, E.J. Vegetation and river channel dynamics. Can. Geogr.
**1984**, 28, 111–126. [Google Scholar] [CrossRef] - Abernethy, B.; Rutherfurd, I.D. Where along a river’s length will vegetation most effectively stabilise stream banks? Geomorphology
**1998**, 23, 55–75. [Google Scholar] [CrossRef] - 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] - Gray, D.H.; Barker, D. Root-soil mechanics and interactions. In Riparian Vegetation and Fluvial Geomorphology; American Geophysical Union: Washington, DC, USA, 2004; pp. 113–123. [Google Scholar]
- Wiel, M.J.; Darby, S.E. A new model to analyse the impact of woody riparian vegetation on the geotechnical stability of riverbanks. Earth Surf. Process. Landf.
**2007**, 32, 2185–2198. [Google Scholar] [CrossRef] - Pollen, N. Temporal and spatial variability in root reinforcement of streambanks: Accounting for soil shear strength and moisture. Catena
**2007**, 69, 197–205. [Google Scholar] [CrossRef] - Eaton, B.; Millar, R. Predicting gravel bed river response to environmental change: The strengths and limitations of a regime-based approach. Earth Surf. Process. Landf.
**2017**, 42, 994–1008. [Google Scholar] [CrossRef] - Abernethy, B.; Rutherfurd, I.D. The effect of riparian tree roots on the mass-stability of riverbanks. Earth Surf. Process. Landf.
**2000**, 25, 921–937. [Google Scholar] [CrossRef] - Kirchner, J.W.; Micheli, L.; Farrington, J.D. Effects of Herbaceous Riparian Vegetation on Streambank Stability; University of California Water Resources Center: Berkeley, CA, USA, 1998. [Google Scholar]
- Langendoen, E.J.; Simon, A. Modeling the evolution of incised streams. II: Streambank erosion. J. Hydraul. Eng.
**2008**, 134, 905–915. [Google Scholar] [CrossRef] - Perucca, E.; Camporeale, C.; Ridolfi, L. Significance of the riparian vegetation dynamics on meandering river morphodynamics. Water Resour. Res.
**2007**, 43, W03430-1–W03430-10. [Google Scholar] [CrossRef] - Thorne, C. Processes and mechanisms of river bank erosion. In Gravel-bed Rivers; Hey, J.B., Thorne, R.D., Eds.; John, Wiley and Sons: Chichester, UK, 1982; pp. 227–272. [Google Scholar]
- Page, K.; Nanson, G. Concave-bank benches and associated floodplain formation. Earth Surf. Process. Landf.
**1982**, 7, 529–543. [Google Scholar] [CrossRef] - Huang, B.; Bai, Y.; Wan, Y. Model for dilapidation mechanism of riverbank. J. Hydraul. Eng.
**2002**, 33, 49–54. [Google Scholar] - Wang, Y.G.; Kuang, S.F. Critical height of bank collapse. J. Hydraul. Eng.
**2007**, 38, 1158–1165. [Google Scholar] - Osman, A.M.; Thorne, C.R. Riverbank stability analysis. I: Theory. J. Hydraul. Eng.
**1988**, 114, 134–150. [Google Scholar] [CrossRef] - Wang, Y.G.; Kuang, S.F.; Su, J.L. Critical caving erosion width for cantilever failures of river bank. Int. J. Sediment Res.
**2016**, 31, 220–225. [Google Scholar] [CrossRef] - Gregory, K.J.; Gurnell, A.M. Vegetation and river channel form and process. In Biogeomorphology; Basil Blackwell: Oxford, UK, 1988; pp. 11–42. [Google Scholar]
- Wynn, T.M.; Mostaghimi, S.; Burger, J.A.; Harpold, A.A.; Henderson, M.B.; Henry, L.A. Variation in root density along stream banks. J. Environ. Qual.
**2004**, 33, 2030–2039. [Google Scholar] [CrossRef] [PubMed] - Konsoer, K.M.; Rhoads, B.L.; Langendoen, E.J.; Best, J.L.; Ursic, M.E.; Abad, J.D.; Garcia, M.H. Spatial variability in bank resistance to erosion on a large meandering, mixed bedrock-alluvial river. Geomorphology
**2016**, 252, 80–97. [Google Scholar] [CrossRef] - Fukuoka, S. Erosion processes of natural riverbank. In Proceedings of the 1st International Symposium on Hydraulic Measurement (CHES and IAHR), Beijing, China, 15 September 1994; pp. 222–229. [Google Scholar]
- Samadi, A.; Amiri-Tokaldany, E.; Davoudi, M.H.; Darby, S.E. Experimental and numerical investigation of the stability of overhanging riverbanks. Geomorphology
**2013**, 184, 1–19. [Google Scholar] [CrossRef] - Pollen-Bankhead, N.; Simon, A. Hydrologic and hydraulic effects of riparian root networks on streambank stability: Is mechanical root-reinforcement the whole story? Geomorphology
**2010**, 116, 353–362. [Google Scholar] [CrossRef] - Simon, A.; Collison, A.J. Quantifying the mechanical and hydrologic effects of riparian vegetation on streambank stability. Earth Surf. Process. Landf.
**2002**, 27, 527–546. [Google Scholar] [CrossRef] - Xia, J.Q.; Wu, B.S.; Wang, Y.P.; Zhao, S.G. An analysis of soil composition and mechanical properties of riverbanks in a braided reach of the Lower Yellow River. Chin. Sci. Bull.
**2008**, 53, 2400–2409. [Google Scholar] [CrossRef] - Lin, C.Y.; Li, X.L.; Liu, K.; Xue, Z.P. Vegetation change characteristics during degradation succession in floodplain wetlands of the Yellow River Source Zone. Chin. Agric. Sci. Bull.
**2016**, 32, 115–119. [Google Scholar] - Zhu, H.L.; Wang, Z.Y.; Li, Z.W. Influence of riparian meadow to the meandering rivers evolution in the yellow river source region. Yellow River
**2013**, 35, 41–44. [Google Scholar] - Fu, J.T.; Hu, X.S.; Brierley, G.; Qiao, N.; Yu, Q.Q.; Lu, H.J.; Li, G.R.; Zhu, H.L. The influence of plant root system architectural properties upon the stability of loess hillslopes, Northeast Qinghai, China. J. Mt. Sci.
**2016**, 13, 785–801. [Google Scholar] [CrossRef] - Li, Z.W. Fluvial Processes and Wetland Degradation Mechanism of the Sanjiangyuan Source. Ph.D. Thesis, Tsinghua University, Beijing, China, 1 November 2013. [Google Scholar]
- Wu, T.H.; McKinnell, W.P., III; Swanston, D.N. Strength of tree roots and landslides on Prince of Wales Island, Alaska. Can. Geotech. J.
**1979**, 16, 19–33. [Google Scholar] [CrossRef] - Liu, S.W. Qinghai Flora; People’s Publishing House of Qinghai: Xining, China, 1996. [Google Scholar]
- Gray, D.H.; Leiser, A.T. Biotechnical Slope Protection and Erosion Control; Nostrand Reinhold Co.: New York, NY, USA, 2001; p. 40. [Google Scholar]
- Xia, J.Q.; Zong, Q.L.; Xu, Q.X.; Deng, C.Y. Soil properties and erosion mechanisms of composite riverbanks in lower Jingjiang reach. Adv. Water Sci.
**2013**, 24, 810–820. [Google Scholar] - Juez, C.; Murillo, J.; García-Navarro, P. Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations. J. Hydroinform.
**2013**, 15, 1234–1257. [Google Scholar] [CrossRef] - Abernethy, B.; Rutherfurd, I.D. The distribution and strength of riparian tree roots in relation to riverbank reinforcement. Hydrol. Process.
**2001**, 15, 63–79. [Google Scholar] [CrossRef] - Loades, K.W.; Bengough, A.G.; Bransby, M.F.; Hallett, P.D.; Stokes, A. Planting density influence on fibrous root reinforcement of soils. Ecol. Eng.
**2010**, 36, 276–284. [Google Scholar] [CrossRef] - Zhu, J.Q.; Wang, Y.Q.; Wang, Y.J.; Zhang, H.L.; Li, Y.P.; Li, Y. Analysis of root system enhancing shear strength based on experiment and model. Rock Soil Mech.
**2014**, 35, 449–458. [Google Scholar] - Zhu, J.Q.; Wang, Y.Q.; Wang, Y.J.; Zhang, H.L.; Li, Y.P.; Li, Y. An analysis on soil physical enhancement effects of root system of Pinus Tabulae formis and Acer Truncatum based on two models. Bull. Soil Water Conserv.
**2015**, 35, 277–282. [Google Scholar]

**Figure 1.**Location of the Lanmucuo River and its highly sinuous bends. (

**a**) location of the study site; (

**b**) the channel stretch within which bank failures were inspected and measured; (

**c**) A, B, C, and D: sites from where soil samples were collected and in situ soil and root properties tests were carried out.

**Figure 2.**The outer bank of the meandering bend. (

**a**) The exposed soil-root layer after bank failure; (

**b**) the cantilever slump blocks and critical blocks.

**Figure 3.**A schematic diagram illustrating the failure of the outer bank as a slump block in the presence of plant roots (green) (refer to section 4 for the meaning of the symbols).

**Figure 4.**Relationship between root tensile strength and root diameter of Blysmus sinocompressus Tang et Wang.

**Figure 6.**Relationship between root length and corresponding dimensions and volume of failed blocks. (

**a**) block width; (

**b**) block thickness; and (

**c**) block volume.

**Figure 7.**Root reinforcement model with a flexible elastic root aligned horizontally to the shear zone prior to bank failure [33] (adapted from Gray and Leiser (1982) (z: Thickness of shear zone; x: Deflection of root; τ

_{r}: Interface friction between root and soil).

Species | Coverage (%) | Mean Height (cm) | Root Diameter (mm) | Root Length (cm) |
---|---|---|---|---|

Blysmus sinocompressus Tang et Wang | 16–20 | 14 | 0.79 | 62 |

Kobresia capillifolia (Decne.) C. B. Clarke | 11–14 | 26 | 0.46 | 55 |

Kobresia tibetica Maxim | 8–10 | 13 | 0.52 | 57 |

Poa annua L. | 5–8 | 47 | 0.41 | 45 |

Elymus nutans Griseb. | 4–7 | 53 | 0.49 | 47 |

Carex moorcroftii Falc. ex Boott | 4–7 | 11 | 0.55 | 68 |

Potentilla fruticosa L. | 7–9 | 28 | 1.57 | 90 |

Potentilla glabra Lodd. | 4–7 | 25 | 1.33 | 86 |

Hippophae thibetana Schlechtend. | 3–5 | 17 | 1.36 | 49 |

Polygonum viviparum L. | 8–12 | 9 | 0.29 | The root system is sparse,<22 cm |

Ligularia virgaurea Mattf | 35 | |||

Nardostachys chinensis Batal. | 8 | |||

Oxytropis ochrocephala Bunge | 6.5 | |||

Cremanthodium lineare Maxim. | 5 | |||

Geranium pylzowianum Maxim. | 6 | |||

Dxytropis coerulea | 4.5 |

**Table 2.**Physical parameters of soil-root composite (SRC), soil, and roots in the undisturbed samples.

Site | SRC Density ρ_{I} (kg/m^{3}) | SRC Moisture Content (%) | Root Diameter d_{i} (m) | Particle Size (%) | A_{r}/A_{s} (%) | Root Tensile Strength T_{N} (kPa) | Soil Shear Strength S_{0} (kPa) | |
---|---|---|---|---|---|---|---|---|

d ≤ 0.075 | 0.005 < d ≤ 0.075 | |||||||

A | 1542 | 53.09 | 5.8 × 10^{−4} | 65.56 | 54.79 | 0.11 | 15,480 | 4.02 |

B | 1516 | 49.88 | 6.8 × 10^{−4} | 81.85 | 59.86 | 0.12 | 15,240 | 5.03 |

C | 1559 | 42.78 | 8.7 × 10^{−4} | 79.6 | 61.22 | 0.11 | 14,920 | 3.98 |

D | 1528 | 43.69 | 11.6 × 10^{−4} | 68.84 | 57.44 | 0.13 | 13,530 | 3.41 |

Average | 1536 | 47.36 | 8.2 × 10^{−4} | 73.96 | 58.33 | 0.12 | 14,792 | 4.11 ± 0.58 |

Mean Water Depth (m) | Mean Velocity (m∙s^{−1}) | Bottom Roughness | Channel Width (m) | Median Size (mm) | |
---|---|---|---|---|---|

Cantilever Slump Blocks | River Bed | ||||

0.59 | 1.26 | 0.025–0.03 | 6–13 | 0.018 | 9.83 |

**Table 4.**In situ measured average dimensions of failed blocks by failure manner in comparison with root length.

Types | Quantity | Length (m) | Width b_{c} (m) | Thickness d_{1} (m) | Primary Root Length * (m) |
---|---|---|---|---|---|

Slump block | 63 | 2.270 ± 1.06 | 0.881 ± 0.23 | 0.845 ± 0.25 | 0.571 ± 0.28 |

Critical block | 15 | 2.053 ± 1.33 | 0.799 ± 0.26 | 0.699 ± 0.18 | 0.416 ± 0.42 |

Overall | 78 | 2.228 ± 0.15 | 0.865 ± 0.06 | 0.817 ± 0.10 | 0.541 ± 0.11 |

Site | Measured Value d_{1} (m) | Measured Value b_{c} (m) | Predicted b_{c} (m) | Relative Error(%) | Calibrated b_{c} * (m) | Relative Error (%) |
---|---|---|---|---|---|---|

A | 0.77 | 0.85 | 1.021 | 20.16 | 0.860 | 1.17 |

B | 0.66 | 0.79 | 0.989 | 25.13 | 0.832 | 5.36 |

C | 0.86 | 0.89 | 1.054 | 18.42 | 0.887 | 0.29 |

D | 0.95 | 0.93 | 1.158 | 24.53 | 0.975 | 4.84 |

Overall | 0.81 | 0.865 | 1.056 | 22.06 | 0.888 | 2.74 |

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**MDPI and ACS Style**

Zhu, H.; Hu, X.; Li, Z.; Song, L.; Li, K.; Li, X.; Li, G.
The Influences of Riparian Vegetation on Bank Failures of a Small Meadow-Type Meandering River. *Water* **2018**, *10*, 692.
https://doi.org/10.3390/w10060692

**AMA Style**

Zhu H, Hu X, Li Z, Song L, Li K, Li X, Li G.
The Influences of Riparian Vegetation on Bank Failures of a Small Meadow-Type Meandering River. *Water*. 2018; 10(6):692.
https://doi.org/10.3390/w10060692

**Chicago/Turabian Style**

Zhu, Haili, Xiasong Hu, Zhiwei Li, Lu Song, Ke Li, Xilai Li, and Guorong Li.
2018. "The Influences of Riparian Vegetation on Bank Failures of a Small Meadow-Type Meandering River" *Water* 10, no. 6: 692.
https://doi.org/10.3390/w10060692