# Sand Transport with Cohesive Admixtures…—Laboratory Tests and Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−2}s

^{−1}] is quantified using the erosion threshold (Partheniades [4] and Winterwerp and van Kesteren [21]). Thresholds determine the proportion of shear stress $\tau $ [Nm

^{−2}] of the flow relative to the critical stress that causes erosion of the eroded surface ${\tau}_{ce}$ [Nm

^{−2}]. The above parameters are determined by experiments under laboratory conditions for sediment transport.

^{−6}[m]). For such conditions, the erosion threshold is greater than values that do not take into account inter-particle bonds resulting from the presence of cohesive agents (Migniot [5], Mehta [27,28], Parchure and Mehta [29]). In their studies, Sundborg [30] and Postma [31] wrote about a positive correlation between consolidation and critical shear stress. On the other hand, the research of Mitchener and Torfs [32] revealed the importance of an appropriate proportion of fine particles in mixtures of mud and sand in the initial erosion phases.

## 2. Materials and Methods

#### 2.1. Experimental Setup Gdańsk 2021 Measurements

- Outflow section 0.73 m long with a bottom inlet—supplying the channel with water;
- The launch section is 2.50 m long;
- Tray—a cavity across the channel width with a length of 1.00 m and a height of 0.08 m;
- Test section with a length of 2.50 m;
- Sediment trap in the form of another tray—a cavity in the channel with a length of 0.73 m and a height of 0.08 m with a bottom drain—drainage of water from the channel.

^{3}/h) with a system of closed water supply and drainage pipes (hoses with a nominal diameter of 7.5 cm) in a closed system and a set of control (Danfoss) and measurement apparatus (a set of Siemens flow meters with an accuracy of 0.25% of the measurement). The flow meter number 1 of the set was used in the study. An inverter was used to control the pump over the entire range.

#### 2.2. The Scope of Measurements

#### 2.3. Theoretical Model

#### 2.3.1. Basic Equations

#### 2.3.2. The Influence of Cohesion on Sand Transport

## 3. Comparison of Calculations with Measurements

## 4. Conclusions

- The results of experimental data were compared with the results of theoretical analysis based on the three-layer model by Kaczmarek et al. [55] for uniform sediments in steady flow, by Kaczmarek et al. [56] for non-uniform sediments in the wave motion and by Zawisza et al. [59] for non-uniform sediments in the steady flow. An extension of these models is proposed here in order to determine the inhibitory effect of cohesion admixtures on the transport of sand fractions. The present model assumes, that the presence of small amount of cohesive fractions in sediment causes an increase in the critical shear stress for the incipient sand motion and consequently a reduction in the magnitude of sand transport. Then, the cohesive fractions are released from the bottom and dispersed in the water. From then on they do not affect the transport of sand fractions.
- In the present model the shear stress at the top of the contact layer is identified as an input data with the value obtained for experiments. This value increases depending on the content of cohesive fractions in sediment. The greater the content of these fractions, the greater the resistance to movement. The difference between the values of shear velocity for sediments with and without cohesive admixtures is also identified here as an input data with the value from experiments. This value is related with the stresses due to cohesion.
- It can be seen from the model results the cohesion reduces the shear stress at the top of the dense layer and, as a result, reduces vertical concentration and velocity profiles of sand fractions inside the dense on contact layers. Thus, transport rate of these fractions is reduced.
- In order to verify the proposed extension of a three layer model the experiments in the laboratory of the Institute of Hydro-Engineering of the Polish Academy of Sciences in Gdańsk were carried out. The experiments were carried out for sand alone and with cohesive admixtures in the form of clay in an amount of 5, 10, 15 and 20% by weight. The amount of sand fractions retained in the trap and along the control area was measured.
- The experimental results were composed with the calculations by the present model. The other results from literature were also used for comparison. An agreement between transport calculations of sand fractions in a substrate with different content of cohesive fractions and the results of measurements was obtained within plus/minus a coefficient of two of the measurements.
- The present model is applicable to non-uniform non-cohesive sediments with small amount of cohesive fractions, while assuming the maximum cohesive fraction content limited by the porosity of the soil. Moreover, at present, the modeling requires experimentally determined shear velocity. Further model development activities will comprise the measurements of stresses due to cohesion and their comparison with the present model estimations based on the shear velocity measurements.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Results of transport rate measurements of sand fractions of sediments with cohesive admixtures obtained in Gdańsk 2021 experiment with the approximations of mean values of repeated tests by curves with a coefficients of determination.

**Figure 4.**Transport of sand fractions in the experiments by De Sutter et al. [48].

**Figure 5.**Vertical structure of: (

**a**) sediment transport profile with velocity and concentration of the i-th fraction of sediment; (

**b**) shear stress profile with cohesion stress ${\tau}_{coh}$.

**Figure 6.**Flow charts of numerical algorithms for calculations of sediment transport and the mobile-bed effect parameter ${\gamma}_{0c}$.

**Figure 7.**Influence of cohesive forces on calculations of the parameter ${\gamma}_{0c}$ depending on the content of clay in the sandy deposit data: ${{u}^{\prime}}_{f\ast}$, $u{\prime}_{f\ast c}$ and ${d}_{r}={d}_{50}=0.32$ mm from the experiment of De Sutter et al. [48].

**Figure 8.**Influence of cohesive forces of calculations of velocity profiles in: (

**a**) contact layer; (

**b**) in dense layer and concentration profiles in: (

**c**) contact layer, (

**d**) in dense layer; data: $u{\prime}_{f\ast}$ and $u{\prime}_{f\ast c}$ from the experiment of De Sutter et al. [48].

**Figure 9.**Influence of disregarding cohesion on transport rate calculations for De Sutter [48].

**Figure 11.**Comparison of sand transport calculations with Gdańsk 2021 measurements the approximation of mean values of repeated tests by linear curve with a coefficient of determination ${R}^{2}=0.9692$.

**Figure 12.**Comparison of sand transport calculations with measurements by De Sutter et al. [48] with the approximation of mean values of repeated tests by linear curve with a coefficient of determination ${R}^{2}=0.9145$.

**Figure 13.**Comparison of sand transport calculations with measurements by Torfs [63] the approximation of mean values of repeated tests by linear curve with a coefficient of determination ${R}^{2}=0.9873$.

**Figure 14.**Comparison of sand transport calculations with measurements by Alvarez -Hernandez [45] the approximation of mean values of repeated tests by linear curve with a coefficient of determination ${R}^{2}=0.9006$. Addition of 20% clay with two densities c = 24 g/L and 30 g/L.

Parameter | Symbol | Value | Unit |
---|---|---|---|

Water depth | H | 0.05 | m |

Test duration | T | 900–3600 | s |

Representative diameter of bottom sediment grains | ${d}_{50}$ | 0.23 | mm |

Diameter clay addition | ${d}_{50}$ | 0.19 | mm |

Sediment density | ${\rho}_{\mathrm{s}}$ | 2.65 | g/cm^{3} |

Liquid density | ${\rho}_{\mathrm{w}}$ | 1.00 | g/cm^{3} |

Porosity of sediment | ${N}_{\mathrm{p}}$ | 0.4 | - |

**Table 2.**Granulometric characteristics of the studied initial sand and sediments taken from the traps—IBW PAN Gdańsk 2021.

Type of Sediment | ${\mathit{d}}_{90}/{\mathit{d}}_{50}/{\mathit{d}}_{10}$ |
---|---|

Input sand | 0.23/0.22/0.14 |

Trap deposits | - |

TR_10_13 | 0.25/0.22/0.13 |

TR_15_11 | 0.43/0.24/0.13 |

TR_15_12 | 0.41/0.23/0.12 |

TR_15_13 | 0.40/0.23/0.12 |

TR_15_14 | 0.42/0.23/0.13 |

TR_20_12 | 0.44/0.24/0.13 |

TR_20_13 | 0.48/0.25/0.13 |

TR_20_15 | 0.41/0.23/0.12 |

Chemical Compound | Content |
---|---|

- SiO_{2} | 55.00–62.14% |

- Al_{2}O_{3} | 15.70–17.70% |

- TiO_{2} | 0.70–0.90% |

- Fe_{2}O_{3} | 6.09–7.90% |

- MnO | 0.04–0.17% |

- MgO | 2.20–3.20% |

- CaO | 0.33–1.81% |

- Na_{2}O | 0.06–0.26% |

- K_{2}O | 2.90–3.50% |

- P_{2}O_{5} | 0.05–0.18% |

- roasting losses | 7.04–13.40% |

Mineral | Content |
---|---|

- quartz | 17–25% |

- kaolinite | 3–10% |

- illit | 3–10% |

- hematite | 3–5% |

- plagioklaz | <3% |

- potassium feldspar | <3% |

- goethyt | <2% |

- anatase | <5% |

- mixed packet minerals (vermiculite/chlorite, smectite/illite) | 32–53% |

- amorphous phase | 15% |

Experiment | h [m] | Sand ${\mathit{d}}_{50}$ [mm] | ${{\mathit{u}}^{\prime}}_{\mathit{f}\ast}$ [m/s] | Additional Substance | Percentage Share of Additional Substance [%] | ${{\mathit{u}}^{\prime}}_{\mathit{f}\ast \mathit{c}}$ [m/s] |
---|---|---|---|---|---|---|

UNewcastle 1990 Alvarez-Hernandez [45] | 0.081–0.310 | 0.90 | clay gel c = 24 g/L clay gel c = 30 g/L | 20 20 | 0.0025 0.0050 | |

ULuven 1995 Torfs [63] | 0.053–0.195 | 0.21 | 0.028 ÷ 0.053 | montmorillonite | 7 9 | 0.0075 0.0900 |

UGhent 1998 De Sutter et al. [48] | 0.081–0.095 | 0.32 | 0.033 ÷ 0.055 | clay | 10 20 30 | 0.0040 0.0090 0.0125 |

IBW PAN Gdańsk 2021 | 0.05 | 0.22 | 0.031 ÷ 0.097 | clay | 5 10 20 | 0.0025 0.0035 0.0061 |

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## Share and Cite

**MDPI and ACS Style**

Zawisza, J.; Radosz, I.; Biegowski, J.; Kaczmarek, L.M.
Sand Transport with Cohesive Admixtures…—Laboratory Tests and Modeling. *Water* **2023**, *15*, 804.
https://doi.org/10.3390/w15040804

**AMA Style**

Zawisza J, Radosz I, Biegowski J, Kaczmarek LM.
Sand Transport with Cohesive Admixtures…—Laboratory Tests and Modeling. *Water*. 2023; 15(4):804.
https://doi.org/10.3390/w15040804

**Chicago/Turabian Style**

Zawisza, Jerzy, Iwona Radosz, Jarosław Biegowski, and Leszek M. Kaczmarek.
2023. "Sand Transport with Cohesive Admixtures…—Laboratory Tests and Modeling" *Water* 15, no. 4: 804.
https://doi.org/10.3390/w15040804