# Time-Dependent Rheological Properties of Cemented Aeolian Sand-Fly Ash Backfill Vary with Particles Size and Plasticizer

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Rheological Model

#### 2.1. Rheological Parameters Analysis

#### 2.2. The Rheological Model

^{−1}, $\mu $ is the viscosity, Pa·s; ${\tau}_{0}$ is the initial yield stress, Pa; n is the fluidity index. When n = 1, ${\tau}_{0}$ = 0, it is a Newtonian body; when n = 1, ${\tau}_{0}>$ 0, it is the Bingham body; when n > 1, it is the swelling body; when n < 1, it is pseudoplastic body [33].

#### 2.3. The Properties and Characteristics of Materials

#### 2.3.1. Aeolian Sand

#### 2.3.2. Coal Gangue

#### 2.3.3. Fly Ash

#### 2.3.4. Cement

^{3}, and the initial and final setting times were 165 min and 231 min, respectively. The compressive strengths at 3d and 28d were 18.4 MPa and 46.4 MPa, respectively. The mineralogical analysis of the cement was carried out using an XRD spectrometer (Japan Rigaku Smartlab), as shown in Figure 8. The particle size analysis was performed using a particle size analyzer (NKT5200-HF), and the results showed that the cement particle size was mainly below 100 μm in Figure 9. The chemical composition of the cement was analyzed using an XRF spectrometer, as shown in Table 4.

#### 2.3.5. Chemical Admixture

#### 2.4. Instructions for Rheometer and Vane Spindle

^{−3}s

^{−1}to 4 $\times $ 10

^{3}s

^{−1}, shear stress from 0.5 Pa to 3 $\times $ 10

^{4}Pa, depending on the measurement system, and viscosity from 1 Pa·s to 1 $\times $ 10

^{9}Pa·s. The accuracy of the rheometer is 0.1%. The rheometer works on the principle of Searle. The vane spindle has an aspect ratio (height/diameter) 1.8. The geometry of the blade spindle effectively eliminates any wall slip effects, suppressing any significant interference with the sample that may result during the immersion of the blade into the sample before any measurement, thus allowing the paste to yield under the static conditions of the material itself. It will be very important that the suspension is thixotropic. In the wall slip phenomenon, an extremely thin film of low-concentration solid lubricant is formed in the material near the rotating surface of a concentric cylindrical or conical plate rheometer. As a result, the shear stress and viscosity in the film are much lower relative to the remaining dense, concentrated material. Therefore the true rheological behavior of the concentrated material may not be captured. Therefore, the vane is best suited for the thixotropic behavior of highly concentrated suspensions. It is important to note that the depth of the CAFB suspension and the diameter of the sample container (beaker or cup) should be at least twice the length and diameter of the vane to minimize the effects caused by rigid boundaries. For satisfactory measurements with the vane spindle, the following criteria are followed:$H/D3.5$, ${D}_{T}/D>2.0$, ${Z}_{1}/D>1.0$, and ${Z}_{2}/D0.5$ (Figure 7). The submerged depth of the vane is described by the distances ${Z}_{1}$ and ${Z}_{2}$, while H is the height of vane blades, as shown in Figure 10. Here, the diameters of the vane spindle and the sample container are calculated, respectively.

#### 2.5. Specimen Preparation and Experimental Methods

_{wt.%}, aeolian sand dosage B

_{wt.%}, coal gangue dosage D

_{wt.%}, fly ash dosage E

_{wt.%}, cement dosage F

_{wt.%}, plasticizer dosage SP(%) and water content G

_{wt.%}which are used in subsequent sections of this paper are calculated from the following equations (Equation (2a)–(2g)):

_{water}is the mass of water in the paste fill; M

_{dry-solid}is the mass of aeolian sand, coal sand, Portland cement, and fly ash. M

_{aeolian-sand}is the mass of aeolian sand, M

_{cement}is the mass of Portland cement, M

_{coal-gangue}is the mass of coal gangue, M

_{fly-ash}is the mass of fly ash, and M

_{sp}is the mass of plasticizer. The amount of aeolian sand and coal gangue are varied to prepare different mix compositions, as shown in Table 5.

#### 2.5.1. Vane Test to Determine Yield Stress and Viscosity

**Step 1. Initial mixing:**The air-dried coal gangue is thoroughly mixed with a certain proportion of aeolian sand, cement, and fly ash using a spatula in a mixing container. Then specified amount of tap water followed by a certain proportion of SP is added and homogenized thoroughly using the electric blender at high shear (+1000 rpm) for 5 min.

**Step 2. Final mixing:**The slurry was then loaded into a 500 mL beaker, and finally, the container loaded with the slurry was assembled with the rheometer for subsequent rheological tests, with a four-blade rotor gradually entering the middle of the beaker and inserted with the slurry sample undisturbed for 30 s to allow the mixed slurry to reach its structural balance and at least partially recover its initial structure and strain state.

**Step 3. Determination of yield stress and viscosity**: Rheological curves describing the correlation between shear stress and shear rate were obtained experimentally for each sample. The rheological parameters describing the rheological properties of the slurry included yield stress and viscosity. The yield stress is the stress value at which the material starts to yield to a state transition, and the shear rate of the rheological curve is from 0.01 s

^{−1}to 150 s

^{−1}with an interval of 0.05 s

^{−1}. The Herschel-Bulkley rheological model was used to fit the measured rheological curves. In the fitted curves, the intersection of the shear stress curve with the longitudinal coordinate (longitudinal intercept) is the yield stress, the viscosity is the slope of the fitted curve, and the viscosity is the ratio of shear stress to shear rate.

**Step 4.**The above process was repeated for samples from the same slurry batch to obtain different parameters, i.e., 3 min, 30 min, and 60 min after sample preparation. The hydration age was chosen to cover various transport times encountered during the slurry backfill tests. The shear test was performed using a controlled shear rate by placing the rotor in a 500 mL beaker for rheological testing, rotating it at a variable shear rate, dispensing the slurry several times and taking the average value for multiple measurements to eliminate experimental errors, and recording the corresponding shear stress and viscosity in real-time. The test is repeated three times for each slurry sample to ensure reproducible results.

#### 2.5.2. Differential Thermogravimetric Analysis Test

#### 2.5.3. Zeta Potential Test

#### 2.5.4. Monitoring through Electrical Conductivity

#### 2.5.5. Scanning Electron Microscopy Morphological Analysis

## 3. Results and Discussion

#### 3.1. Fitting and Analysis of Rheological Parameters

#### 3.2. The Influence of the Amount of Coal Gangue Added on the Rheological Properties of the Slurry

_{10}particle size value is becoming smaller. The D

_{90}particle size value is in becoming larger, which indicates that the particle size distribution of the material is more uniform, but, with the increase of coal gangue, the initial shear stress of the slurry is getting bigger and bigger, the reasonable particle gradation should not only ensure that the slurry has good rheology but also make the yield stress of slurry to be in a reasonable range, so that the pipeline’s conveying resistance runs in a reasonable range and reduce the energy loss [26,36].

#### 3.3. Correlation between Rheological Parameters and Particles Size

_{1}and the particle gradation parameter X

_{2}for different slurries, the correlation is expressed by the following equation.

_{1}and X

_{2}can be derived. In general, when r < 0.4, there is no or weak correlation between the variables; when 0.4 < r < 0.6, there is a moderate correlation between the variables; when 0.6 < r < 0.8, there is a strong correlation (significant correlation) between the variables; and when 0.8 < r < 1.0, there is a very strong correlation between the variables.

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size after 3 min of standing are above 0.98, which indicates that there is a strong correlation between them because the mass fraction of the slurry with yield stress is related to the content of fine particles, and the smaller the particle size or, the higher the content, the lower the mass fraction of the slurry with yield stress. with the growth of coal gangue particle content, 1#, 2#, 3#, 4# and 5# of mixed slurry fine particles are increasing, and the proportion of coarse particles is also increasing, which shows that there is a strong correlation between the yield stress of the slurry and the slurry particle size. with the slurry in the rest 3 min, the correlation coefficient of viscosity and D

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size is above 0.75. This shows that there is a strong correlation between the two, which indicates that there is also a strong correlation between the particle gradation and the viscosity of the slurry.

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size is above 0.86 or more, which indicates that there is a strong correlation between the two, because the mass fraction of the slurry with yield stress is related to the content of fine particles, the smaller the particle size or the higher the content, the slurry mass fraction of yield stress is lower. with the growth of coal gangue particle content, 1#, 2#, 3#, 4# and 5# of mixed slurry fine particles are increasing, and the proportion of coarse particles is also increasing, which shows that there is a strong correlation between the yield stress of the slurry and the slurry particle size. With the slurry in the resting 30 min, the correlation coefficient between viscosity and D

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size reached 0.20, indicating no correlation between them.

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size are about 0.93 or more, indicating that there is a strong correlation between the two because the mass fraction of the slurry with yield stress is related to the content of fine particles, the smaller the particle size or, the higher the content, the slurry mass fraction of yield stress is lower. with the growth of coal gangue particle content, 1#, 2#, 3#, 4# and 5# of mixed slurry, fine particles are increasing, and the proportion of coarse particles is also increasing, which shows that there is a strong correlation between the yield stress of the slurry and the slurry particle size. with the slurry in the resting 60 min, the correlation coefficient of viscosity and D

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}of particle size are 0.39 or more, indicating a weak correlation between the two.

_{10}, D

_{30}, D

_{50}, D

_{60}and D

_{90}greatly influence the relationship with the initial shear stress of the slurry. At 3 min, the viscosity of each particle size with the slurry has a greater influence.

#### 3.4. Time-Dependent Evolution of the Rheological Properties of CAFB with the Ratio of Aeolian Sand/Coal Gangue

^{3}.

#### 3.5. Time-Dependent Evolution of the Rheological Properties of CAFB with Plasticizer

## 4. Conclusions

- The 3#, 4# and 5# slurry flow index change patterns are the same. The index n, which characterizes the flow property as greater than 1 after 3 min resting, belongs to the swelling body; n is close to 1 after 30 min resting, belongs to Bingham body; n is less than 1 after 60 min resting, belongs to the pseudoplastic body; 1# and 2# slurry in 3–30 min flow index is greater than 1, belongs to the swelling body, After 60 min of resting, the flow pattern of slurry changes n is less than 1, which belongs to the pseudoplastic body.
- With the increase of shear rate and shear time, the viscosity first gradually decreases and then stabilizes, i.e., the rheological properties of the slurry have the characteristic of “shear thinning”; the rheological properties of the slurry process is the comprehensive embodiment of a variety of model composite properties, with the increase of shear rate, the rheological curve of the slurry shows an upward convex shape, showing a pseudoplastic body-Bingham body-Pseudoplastic body (swelling body).
- According to 2# and 3# mixed material, it will be grading configuration aeolian sand, coal gangue, and fly ash filling slurry to ensure long-distance pipeline conveying process slurry flow stability, to ensure smooth pipeline transport.
- Curing time (0–0.5 h) results in higher yield stress of the CAFB. A longer curing time is associated with a greater degree of cement hydration products. Curing time (0.5–1 h) results in lower yield stress of the CAFB. It is because more hydration products are associated with a decrease in the aeolian sand inter-particle frictional resistance of the CAFB.
- The addition of plasticizer to the CAFB significantly reduces the yield stress and viscosity of CAFB. Adding 0.05% of the admixture results in over 65% reduction in yield stress at the time of preparation and after 1 h. A similar reduction was observed in the improvement of viscosity. The marginal reduction upon increasing the admixture to 0.1% is much less, indicating that an optimum percentage is around 0.05.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**Distribution diagram of shear stress (

**a**), viscosity (

**b**) and shear rate after standing for 60 min.

**Figure 12.**Distribution diagram of shear stress (

**a**), viscosity (

**b**) and shear rate after standing for 30 min.

**Figure 13.**Distribution diagram of shear stress (

**a**), viscosity (

**b**) and shear rate after standing for 3 min.

**Figure 16.**Time-dependent evolution of yield stress of CAFB containing different dosages of plasticizer.

**Figure 17.**Time-dependent evolution of viscosity of CAFB containing different dosages of plasticizer.

**Figure 18.**Effect of the plasticizer on the zeta potential of fresh CAFB made with different admixture content.

**Figure 19.**Development of electrical conductivity in CAFB containing different dosages of plasticizer.

Chemical Composition | Al_{2}O_{3} | SiO_{2} | Na_{2}O | CaO | K_{2}O_{4} | Fe_{2}O_{3} | Other | Total |
---|---|---|---|---|---|---|---|---|

Mass percentage (%) | 9.78 | 68.94 | 2.34 | 6.65 | 2.13 | 2.24 | 7.92 | 100 |

Chemical Composition | Al_{2}O_{3} | SiO_{2} | P_{2}O_{5} | K_{2}O | CaO | TiO_{2} | Fe_{2}O_{3} | Total |
---|---|---|---|---|---|---|---|---|

Mass percentage (%) | 22.23 | 62.06 | 0.65 | 2.95 | 3.11 | 0.99 | 8.01 | 100 |

Chemical Composition | Al_{2}O_{3} | SiO_{2} | S | K_{2}O | CaO | TiO_{2} | Fe_{2}O_{3} | Total |
---|---|---|---|---|---|---|---|---|

Mass percentage (%) | 31.89 | 56.89 | 0.66 | 1.39 | 1.84 | 1.95 | 5.38 | 100 |

Chemical Composition | CaO | SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | MgO | Other | Total |
---|---|---|---|---|---|---|---|

Mass percentage (%) | 65.08 | 22.36 | 5.53 | 3.46 | 1.27 | 2.30 | 100 |

CAFB Code | ${\mathit{B}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ | ${\mathit{D}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ | ${\mathit{E}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ | ${\mathit{F}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ | $\mathit{S}\mathit{P}\mathit{\%}$ | ${\mathit{G}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ | ${\mathit{C}}_{\mathit{w}\mathit{t}.\mathit{\%}}$ |
---|---|---|---|---|---|---|---|

1# | 46 | 5 | 17.5 | 9 | 0 | 22.5 | 77.5 |

2# | 43 | 8 | 17.5 | 9 | 0 | 22.5 | 77.5 |

3# | 40 | 11 | 17.5 | 9 | 0 | 22.5 | 77.5 |

4# | 37 | 14 | 17.5 | 9 | 0 | 22.5 | 77.5 |

5# | 34 | 17 | 17.5 | 9 | 0 | 22.5 | 77.5 |

6# | 40 | 11 | 17.5 | 9 | 0.05 | 22.5 | 77.5 |

7# | 40 | 11 | 17.5 | 9 | 0.1 | 22.5 | 77.5 |

Time/min | Rheology Index | 1# | 2# | 3# | 4# | 5# |
---|---|---|---|---|---|---|

60 | μ (Pa·s) | 0.052 | 0.038 | 0.115 | 0.017 | 0.0104 |

τ_{0}/Pa | 410.891 | 537.44 | 652.84 | 725.24 | 705.04 | |

n | 0.788 | 1.636 | 1.359 | 1.682 | 0.121 | |

R^{2} | 0.954 | 0.972 | 0.852 | 0.831 | 0.409 | |

30 | μ (Pa·s) | 1.12 | 0.385 | 0.989 | 1.781 | 0.384 |

τ_{0}/Pa | 611.650 | 543.827 | 600.575 | 779.76 | 919.08 | |

n | 3.048 | 1.452 | 1.024 | 0.997 | 1.085 | |

R^{2} | 0.956 | 0.989 | 0.964 | 0.953 | 0.626 | |

3 | μ (Pa·s) | 1.166 | 1.763 | 0.148 | 0.563 | 0.041 |

τ_{0}/Pa | 415.16 | 457.91 | 629.84 | 728.86 | 931.98 | |

n | 1.210 | 1.080 | 1.496 | 1.269 | 1.621 | |

R^{2} | 0.982 | 0.978 | 0.981 | 0.961 | 0.802 |

CAFB Code | D_{10}/μm | D_{30}/μm | D_{60}/μm | D_{90}/μm | D_{50}/μm |
---|---|---|---|---|---|

1# | 53.771 | 80.586 | 179.465 | 361.146 | 138.018 |

2# | 51.263 | 78.586 | 207.453 | 449.321 | 151.538 |

3# | 48.755 | 76.587 | 235.442 | 533.496 | 165.059 |

4# | 46.247 | 74.587 | 263.43 | 617.671 | 178.579 |

5# | 43.74 | 72.594 | 291.507 | 702.089 | 192.149 |

I 6# | 48.755 | 76.587 | 235.442 | 533.496 | 165.059 |

7# | 48.755 | 76.587 | 235.442 | 533.496 | 165.059 |

_{10}, D

_{30}, D

_{60}, and D

_{90}are the corresponding particle sizes when the cumulative particle size content reaches 10%, 30%, 60%, and 90%, respectively.

**Table 8.**The correlation between the rheological parameters of the slurry and the particle size gradation after standing for 3 min.

Correlation Model | a | b | $\left|\mathit{r}\right|$ | $\left|{\mathit{r}}^{2}\right|$ |
---|---|---|---|---|

$\mu =a+b{d}_{10}$ | −5.971 | 0.138 | 0.753 | 0.423 |

$\mu =a+b{d}_{30}$ | −12.486 | 0.173 | 0.753 | 0.423 |

$\mu =a+b{d}_{50}$ | 4.945 | −0.026 | 0.753 | 0.423 |

$\mu =a+b{d}_{60}$ | 3.637 | −0.012 | 0.753 | 0.423 |

$\mu =a+b{d}_{90}$ | 2.890 | −0.004 | 0.750 | 0.417 |

$\tau =a+b{d}_{10}$ | 3169.028 | −52.021 | 0.981 | 0.951 |

$\tau =a+b{d}_{30}$ | 5632.278 | −65.278 | 0.981 | 0.951 |

$\tau =a+b{d}_{50}$ | −959.012 | 9.643 | 0.981 | 0.951 |

$\tau =a+b{d}_{60}$ | −464.177 | 4.659 | 0.981 | 0.951 |

$\tau =a+b{d}_{90}$ | −183.410 | 1.532 | 0.980 | 0.947 |

**Table 9.**The correlation between the rheological parameters of the slurry and the particle size gradation after standing for 30 min.

Correlation Model | a | b | $\left|\mathit{r}\right|$ | $\left|{\mathit{r}}^{2}\right|$ |
---|---|---|---|---|

$\mu =a+b{d}_{10}$ | 0.784 | 0.003 | 0.021 | 0.333 |

$\mu =a+b{d}_{30}$ | 0.647 | 0.004 | 0.020 | 0.333 |

$\mu =a+b{d}_{50}$ | 1.027 | −0.0005 | 0.021 | 0.333 |

$\mu =a+b{d}_{60}$ | 0.997 | −0.0002 | 0.021 | 0.333 |

$\mu =a+b{d}_{90}$ | 0.985 | −0.0001 | 0.023 | 0.333 |

$\tau =a+b{d}_{10}$ | 2344.996 | −33.924 | 0.868 | 0.672 |

$\tau =a+b{d}_{30}$ | 3951.053 | −42.566 | 0.868 | 0.671 |

$\tau =a+b{d}_{50}$ | −347.240 | 6.290 | 0.868 | 0.672 |

$\tau =a+b{d}_{60}$ | −24.474 | 3.038 | 0.868 | 0.672 |

$\tau =a+b{d}_{90}$ | 160.503 | 0.996 | 0.864 | 0.662 |

**Table 10.**The correlation between the rheological parameters of the slurry and the particle size gradation after standing for 60 min.

Correlation Model | a | b | $\left|\mathit{r}\right|$ | $\left|{\mathit{r}}^{2}\right|$ |
---|---|---|---|---|

$\mu =a+b{d}_{10}$ | −0.156 | 0.004 | 0.395 | 0.126 |

$\mu =a+b{d}_{30}$ | −0.353 | 0.005 | 0.395 | 0.126 |

$\mu =a+b{d}_{50}$ | 0.174 | −0.0007 | 0.395 | 0.126 |

$\mu =a+b{d}_{60}$ | 0.134 | −0.0004 | 0.395 | 0.126 |

$\mu =a+b{d}_{90}$ | 0.111 | −0.0001 | 0.392 | 0.128 |

$\tau =a+b{d}_{10}$ | 2115.179 | −30.948 | 0.934 | 0.831 |

$\tau =a+b{d}_{30}$ | 3581.505 | −38.847 | 0.935 | 0.831 |

$\tau =a+b{d}_{50}$ | −340.291 | 5.734 | 0.934 | 0.830 |

$\tau =a+b{d}_{60}$ | −46.059 | 2.770 | 0.934 | 0.830 |

$\tau =a+b{d}_{90}$ | 118.957 | 0.915 | 0.936 | 0.836 |

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## Share and Cite

**MDPI and ACS Style**

Yang, B.; Zheng, Z.; Jin, J.; Wang, X.
Time-Dependent Rheological Properties of Cemented Aeolian Sand-Fly Ash Backfill Vary with Particles Size and Plasticizer. *Materials* **2023**, *16*, 5295.
https://doi.org/10.3390/ma16155295

**AMA Style**

Yang B, Zheng Z, Jin J, Wang X.
Time-Dependent Rheological Properties of Cemented Aeolian Sand-Fly Ash Backfill Vary with Particles Size and Plasticizer. *Materials*. 2023; 16(15):5295.
https://doi.org/10.3390/ma16155295

**Chicago/Turabian Style**

Yang, Baogui, Zhijun Zheng, Junyu Jin, and Xiaolong Wang.
2023. "Time-Dependent Rheological Properties of Cemented Aeolian Sand-Fly Ash Backfill Vary with Particles Size and Plasticizer" *Materials* 16, no. 15: 5295.
https://doi.org/10.3390/ma16155295