# Effect of Water Content on Strength of Alluvial Silt in The Lower Yellow River

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{a}is net normal stress, χ is the effective stress parameter, u

_{a}− u

_{w}is matric suction, and φ′ is the effective internal friction angle of saturated soil. Due to the limitation of experimental methods and measurement means, it is difficult to measure the matric suction and determine the effective stress parameters [8]. It is difficult to use matric suction and effective stress parameters to directly express the strength of unsaturated soil under different water contents [9]. Therefore, it is of great significance for engineering practice to explore the corresponding matric suction under different moisture contents (degree of saturation), determine the effective stress parameters under the corresponding moisture contents [10], and then predict the strength of unsaturated Yellow River silt.

## 2. Test Equipment and Method

#### 2.1. SWCC Test

#### 2.2. Direct Shear Test of Unsaturated Soil

^{3}. For unsaturated and saturated soil samples, quick shear was imposed without controlling the pore water and pore air pressures [23]. In the shear testing, samples were divided into five groups based on the moisture content (20%, 40%, 60%, 80%, and 100%), while four samples of each group were tested under different normal stress conditions (25 kPa, 50 kPa, 75 kPa, and 100 kPa) with a standard strain rate of 0.8 mm/min.

## 3. Test Result and Analysis

#### 3.1. SWCC Test

#### 3.1.1. SWCC Test Results

_{1}= 4 kPa, the soil is in the boundary effect zone. In this region, the increase in matric suction barely impacts the corresponding degree of the soil saturation [24,25]. As the matric suction increased, the moisture content of soil samples decreased drastically and eventually reached the reverse bending point at where matric suction was 25 kPa. The reverse bending point can reflect the soil moisture state under the corresponding water content, which changes from capillary gravity water to capillary-suspended turbidity water. Later, as the matric suction increased, the degree of saturation decreased to less than 13.68%, with the dispersing of pore water and pore gas in the pore interior. According to the curve analysis, the slope of the soil sample at the reverse bending point is K

_{i}= 9.375 × 10

^{4}, and the specific water density of the soil sample represented the change in water content due to a change in until matric potential which is about 1.067 × 10

^{−3}(mL/bar g). Furthermore, an increase in matric suction resulted in the soil until it approached the residual degree of saturation at S

_{r}= 10%. Due to the equipment limitations, the maximum matric suction was set to 200 kPa, and the curve parameters were briefly determined by the method of brief drawing. In order to reduce the error caused by the traditional drawing method, the basic parameters of the curve are represented by the SWCC fitting parameters.

#### 3.1.2. SWCC Model Fitting

_{s}and θ

_{r}are the saturated volumetric and residual volumetric water content, respectively; S

_{r}and S

_{e}are the residual and effective degree of saturation, respectively; ψ is the suction pressure or matric suction; and a, m, n are the fitting parameters. The physical meaning of a, m, and n are the inverse of the air-entry pressure, the overall symmetry of the characteristics curve, and the pore size distribution of the soil, respectively, and it can be shown as m = 1 − 1/n [26,27,28,29].

#### 3.2. Direct Shear Test

#### 3.2.1. Direct Shear Test Results

_{f}is shear stress; σ is normal stress (here is the net normal stress σ − u

_{a}, where u

_{a}= 0); c

_{total}is the generalized cohesion; and φ

_{total}is the generalized friction angle.

#### 3.2.2. Effect of Moisture Content on Shear Strength Parameters

#### 3.3. Prediction of Shear Strength Parameters of Unsaturated Silt in the Lower Yellow River

#### 3.3.1. Study on the Effective Stress Parameters χ

#### 3.3.2. Prediction of Effective Stress Parameters χ of Unsaturated Silt in The Lower Yellow River

#### 3.3.3. Prediction of Shear Strength of Unsaturated Silt in The Lower Yellow River

_{a}− u

_{w}can be expressed in the function of saturation degree as shown below:

^{′}is the effective cohesion of saturated condition, φ

^{′}is the internal friction angle of saturated condition.

## 4. Conclusions

- The drying curve of silt samples from the lower Yellow River can be fitted by using the VG model, and the fitting parameters are as follows: a = 13.699 (kPa
^{−1}), m = 0.554, n = 2.241, and S_{r}= 9.965 (%); - As moisture content changes from a lower state to a higher state, the shear displacement and shear stress curves show shear softening and shear hardening behavior, respectively;
- Moisture content has a nonlinear inverse relationship with cohesion. The increase in moisture content results in a variation of friction angle and no clear law for this variation is defined. Furthermore, compared with the internal friction angle, moisture content has a greater influence on cohesion;
- The relationship between effective stress parameters and the degree of saturation of the silt in the lower Yellow River is proposed and validated by tests on the specific sample material in this study, which can be expressed as follows:

- 5.
- Based on the Bishop’s shear strength equation, this study suggests an empirical equation of shear strength for silt in the lower Yellow River channel, which includes the function of cohesion, friction angle and suction. The shear strength can be evaluated at the corresponding suction with a certain cohesion and friction angle, by using the equation below.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**The relationship between shear stress and shear displacement under different moisture contents. (

**a**) Moisture content 5.30% (degree of saturation 20%); (

**b**) Moisture content 10.60% (degree of saturation 40%); (

**c**) Moisture content 15.85% (degree of saturation 60%); (

**d**) Moisture content 21.10% (degree of saturation 80%); and (

**e**) Moisture content 37.86% (degree of saturation 100%).

**Figure 8.**The Relationship Between Shear Strength Parameters and Moisture Content. (

**a**) Cohesion of Yellow River silt under different moisture contents; and (

**b**) Internal friction angle of Yellow River silt under different moisture contents.

Yellow River Silt | Natural Moisture Content ω/% | Natural Gravity Gs/kN/m^{3} | Void Ratio e | Natural Saturation S′/% |

15.38 | 25.10 | 0.663 | 58.23 |

_{w}/m

_{s}, natural gravity, G

_{S}= ρg, void ratio, e = V

_{V}/V

_{S}, natural saturation, S′ = V

_{W}/V

_{V}.

Fitting Parameters | a/kPa^{−1} | m | n | Sr/% |
---|---|---|---|---|

VG model fitting values | 0.0730 | 0.554 | 2.241 | 9.965 |

Moisture Content ω (%) | Degree of Saturation S (%) | Normal Stress σ (kPa) | τ_{max} (kPa) | c_{total} (kPa) | φ_{total} (°) |
---|---|---|---|---|---|

5.30% | 20% | 25 | 48 | 30.5 | 37.52 |

50 | 73 | ||||

75 | 85 | ||||

100 | 108 | ||||

10.60% | 40% | 25 | 42 | 21.5 | 38.24 |

50 | 58 | ||||

75 | 84 | ||||

100 | 99 | ||||

15.85% | 60% | 25 | 37 | 17 | 37.67 |

50 | 53 | ||||

75 | 78 | ||||

100 | 93 | ||||

21.10% | 80% | 25 | 33 | 15.5 | 38.10 |

50 | 57 | ||||

75 | 76 | ||||

100 | 92 | ||||

37.86% | 100% | 25 | 24 | 7 | 39.21 |

50 | 52 | ||||

75 | 70 | ||||

100 | 86 |

Name | Unsaturated Soil Strength Equation is Commonly Used Currently | Meaning of Physical Quantity |
---|---|---|

The Effective Stress Parameters in the Shear Strength Equation Are Summarized | ||

Bishop’s shear strength equation [7] | ${\tau}_{{}_{f}}=c\prime +[(\sigma -{u}_{\mathrm{a}})+\chi ({u}_{a}-{u}_{w})]\mathrm{tan}\phi \prime $ | τ_{f} is shear stress at failure;c′ is effective cohesion of saturated soil; σ is net normal stress; u _{a} is the pore water pressure;u _{w} is the pore gas pressure;χ is effective stress parameters; φ′ is effective angle of internal friction of saturated soil. |

Khalili’s equation for predicting additional suction strength from soil–water characteristics curves [29] | ${\tau}_{{}_{f}}=c\prime +(\sigma -{u}_{a})\mathrm{tan}\phi \prime +({u}_{a}-{u}_{w}){\left[\frac{\theta (\psi )}{{\theta}_{s}}\right]}^{k}\mathrm{tan}\phi \prime $ | θ(ψ) is volumetric water content under different suction forces which is represented by the soil–water characteristics curve equation; θ _{s} is saturated volumetric water content;K is a fitting parameter for effective stress. |

$\chi ={\left[\frac{\theta (\psi )}{{\theta}_{s}}\right]}^{k}={S}^{k}$ | ||

Vanapalli and Fredlund’s equation for unsaturated soil strength at different moisture content [30] | ${\tau}_{{}_{f}}=c\prime +(\sigma -{u}_{a})\mathrm{tan}\phi \prime +({u}_{a}-{u}_{w})\left[\mathrm{tan}\phi \prime (\frac{\theta -{\theta}_{r}}{{\theta}_{s}-{\theta}_{r}})\right]$ | θ is volumetric water content; θ _{r} is residual volumetric water content;S _{e} is the effective degree of saturation;Sr is the residual degree of saturation. |

$\chi ={S}_{e}=\frac{S-{S}_{r}}{100-{S}_{r}}=\frac{\theta -{\theta}_{r}}{{\theta}_{s}-{\theta}_{r}}$ |

Degree of Saturation S/% | Matric Suction/kPa | Normal Stress /kPa | Shear Strength/kPa | Angle of Internal Friction/° | Cohesion/kPa | Effective Stress Parameters χ | Average Value of χ |
---|---|---|---|---|---|---|---|

0 | / | / | / | / | / | / | 0.000 |

20 | 79.52 | 25 | 48 | 37.52 | 30.5 | 0.087 | 0.115 |

50 | 73 | 0.182 | |||||

75 | 85 | 0.064 | |||||

100 | 108 | 0.126 | |||||

40 | 31.04 | 25 | 42 | 38.24 | 21.5 | 0.319 | 0.286 |

50 | 58 | 0.168 | |||||

75 | 84 | 0.425 | |||||

100 | 99 | 0.233 | |||||

60 | 18.19 | 25 | 37 | 37.67 | 17 | 0.548 | 0.498 |

50 | 53 | 0.313 | |||||

75 | 78 | 0.719 | |||||

100 | 93 | 0.413 | |||||

80 | 10.69 | 25 | 33 | 38.10 | 15.5 | 0.585 | 0.836 |

50 | 57 | 1.110 | |||||

75 | 76 | 1.038 | |||||

100 | 92 | 0.609 | |||||

100 | 0 | / | / | 39.21 | 7 | / | 1.000 |

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**MDPI and ACS Style**

Cheng, Y.-Y.; Gao, X.-G.; Liu, T.-H.; Li, L.-X.; Du, W.; Hamad, A.; Wang, J.-P.
Effect of Water Content on Strength of Alluvial Silt in The Lower Yellow River. *Water* **2022**, *14*, 3231.
https://doi.org/10.3390/w14203231

**AMA Style**

Cheng Y-Y, Gao X-G, Liu T-H, Li L-X, Du W, Hamad A, Wang J-P.
Effect of Water Content on Strength of Alluvial Silt in The Lower Yellow River. *Water*. 2022; 14(20):3231.
https://doi.org/10.3390/w14203231

**Chicago/Turabian Style**

Cheng, Yang-Yang, Xu-Guang Gao, Tai-Heng Liu, Lian-Xiang Li, Wei Du, Abu Hamad, and Ji-Peng Wang.
2022. "Effect of Water Content on Strength of Alluvial Silt in The Lower Yellow River" *Water* 14, no. 20: 3231.
https://doi.org/10.3390/w14203231