# Basic Experimental Study of Plasticity Material for Coal Rock Fracture Grouting Based on RSM-PCA Technology

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Experimental Design

_{1}, X

_{2}, and X

_{3}, and the corresponding levels were −1, 0, and 1. According to the research results of some scholars on the proportion of grouting materials [18,19,20], it was determined that the initial value of the cement content is 25–50% of all the slurry and the value of sand is 0–15%. According to the experience of crack closure [21], the W/C range is 0.4–0.6. Table 5 and Table 6 show the specific scheme design.

#### 2.3. Experiment Procedures

#### 2.4. Numerical

#### 2.4.1. PCA of Basic Performance Indexes

#### 2.4.2. Analysis of RSM

## 3. Results

#### 3.1. Basic Performance of Grouting

#### 3.1.1. Bleeding Rate and Setting Time

_{3}S clinker particles release a large amount of Ca

^{2+}and OH

^{−}, and the slurry is alkaline. The reaction formula is as follows [28]:

#### 3.1.2. Viscosity

#### 3.1.3. Unconfined Compressive Strength

_{3}A and C

_{4}AF improved the early strength of the specimen [34]. When the specimens were cured for 7 to 28 days, the strength of the stone body increased relatively slowly, with an average growth rate of 30.5%. The main reason for the further increase of the strength of the stone body was that the C-S-H gel formed by the reaction of C

_{3}S and water filled the pore structure of the consolidated clay. As can be seen from Figure 6a, when the W/C is 0.4, the amount of cement has a greater influence on the compressive strength. This result is also revealed in Figure 6b,c. It is noted that, when the cement content is 50%, the fine sand content is 7% and the W/C is 0.4; the maximum 28 days of compressive strength of the specimen is 8.45 Mpa. In the parallel experiment, there was a small gap in the compressive strength of the specimen, which is displayed in Figure 6d. In short, the cement content and W/C have great influence on the strength.

#### 3.2. PCA of Slurry Performance Index

#### 3.3. RSM Analysis

^{2}of the regression equation about Z was 0.9884, which showed that the regression model was in good agreement with the actual situation and can be used to predict the value of Z. The variance analysis of regression items shows that the linear effect of W/C on Z was significant.

#### 3.4. Mixing Optimization and Verification

#### 3.5. Microanalysis

#### 3.5.1. Microstructure of Solidified Slurry

#### 3.5.2. Phase Composition Analysis of Curing System

_{2}diffraction peak was found in the phase analysis, and the Ca(OH)

_{2}substance was also observed in the SEM diagram, which can indicate that the cement hydration reaction after curing 28 is not complete. Due to the lean cement, the gel material produced by the reaction is also less [46]. The diffraction peak of the hydration product is weak, which is also the main reason for the decrease in the strength of the consolidated body. The chemical reaction that occurs in the composite material is mainly a cement hydration reaction, and the new phases are mainly cement hydration reaction products, including C-S-H, C-A-H, ettringite, calcium hydroxide, etc. The consolidation of clay with water is a physical reaction, and the XRD spectrum shows that no new clay mineral phase is formed.

## 4. Conclusions

_{2}is 0.9884, which is consistent with the actual situation. The linear effect of W/C on the Z value is significant.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PCA | Principal Component Analysis |

RSM | Response Surface Method |

RSM-PCA | Combining of response surface method and principal component analysis |

SEM | Scanning Electron Microscope |

W/C | Water-Cement ratio |

XRD | X-Ray Diffraction |

C_{3}A | Tricalcium Aluminate |

C_{3}S | Tricalcium Silicate |

C_{4}AF | Tetracalcium Aluminoferrite |

C-S-H | Calcium Silicate Hydrate |

KMO | Kaiser Meyer Olkin |

C | The cumulative characteristic value |

F | The comprehensive score |

F_{max} | The maximum value in the comprehensive score |

F_{min} | The minimum value in the comprehensive score. |

F_{i} | The score of the main component |

i | Index |

X_{i} | The value of the influencing factors |

X_{j} | The value of the influencing factors |

Y | The response prediction value |

Y_{i} | The characteristic value of the main component |

Z | A standardized comprehensive score |

α_{0} | Constant |

α_{i} | A linear coefficient |

α_{ii} | A square coefficient |

α_{ij} | An interaction coefficient |

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**Figure 3.**Bleeding rate of slurry with different components. (

**a**) Bleeding rate of groups 1, 3, 11, and 13; (

**b**) Bleeding rate of groups 2, 4, 8, and 14; (

**c**) Bleeding rate of groups 5, 9, 10, and 16; (

**d**) Bleeding rate of groups 6, 7, 12, 15, and 17.

**Figure 4.**Setting time of the slurry with different components. (

**a**) Setting time of groups 1, 3, 11, and 13; (

**b**) Setting time of groups 2, 4, 8, and 14; (

**c**) Setting time of groups 5, 9, 10, and 16; (

**d**) Setting time of 6, 7, 12, 15, and 17.

**Figure 5.**Viscosity of the slurry with different components. (

**a**) Viscosity of groups 1, 3, 11, and 13; (

**b**) Viscosity of groups 2, 4, 8, and 14; (

**c**) Viscosity of groups 5, 9, 10, and 16; (

**d**) Viscosity of 6, 7, 12, 15, and 17.

**Figure 6.**The strength of grout stones in different curing periods. (

**a**) 3, 7, and 28 days of groups 1, 3, 11, and 13; (

**b**) 3, 7, and 28 days of groups 2, 4, 8, and 14; (

**c**) 3, 7, and 28 days of groups 5, 9, 10, and 16; (

**d**) 3, 7, and 28 days of 6, 7, 12, 15, and 17.

**Figure 10.**SEM of the test specimen. (

**a**) The crack is magnified 1000 times; (

**b**) The crack is magnified 4000 times; (

**c**) The crack is magnified 15,000 times; (

**d**) The pore is magnified 1000 times; (

**e**) The pore is magnified 4000 times; (

**f**) The pore is magnified 15,000 times; (

**g**) The transition zone of interface are magnified 1000 times; (

**h**) The transition zone of interface are magnified 4000 times; (

**i**) The transition zone of interface are magnified 15,000 times.

Water Content/% | Average Specific Gravity | Natural Density /(g/cm ^{3}) | Porosity | Plastic Limit/% | liquid Limit/% | Cohesion/(KPa) | Internal Friction Angle/(°) | Impurity/(%) |
---|---|---|---|---|---|---|---|---|

10.29 | 2.65 | 1.30 | 2.24 | 27.3 | 56.4 | 15 | 16 | 9.54 |

SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | K_{2}O | CaO | MgO | Miscellaneous |
---|---|---|---|---|---|---|

47.21% | 32.46% | 3.05% | 1.28% | 2.35% | 1.14% | 12.51% |

Fineness/% | Water Consumption for Standard Consistency/% | Reliability | Setting Times/ (min) | Flexural Strength/(KPa) | Compressive Strength/(MPa) | |||
---|---|---|---|---|---|---|---|---|

Initial | Final | 3 d | 28 d | 3 d | 28 d | |||

4.1 | 31% | qualified | 124 | 184 | 6.1 | 8.6 | 34.5 | 55.9 |

CaO | SiO_{2} | Fe_{2}O_{3} | Al_{2}O_{3} | TiO_{2} | MgO | SO_{3} | Na_{2}O | K_{2}O | Ignition Loss |
---|---|---|---|---|---|---|---|---|---|

56.78% | 23.15% | 3.89% | 7.41% | 0.24% | 1.98% | 2.45% | 0.25% | 0.26% | 3.54% |

Independent Variable | Variable Level | ||
---|---|---|---|

Low (−1) | Middle (0) | High (+1) | |

Cement content (%) | 25 | 38 | 50 |

Sand content (%) | 0 | 7 | 15 |

W/C | 0.4 | 0.5 | 0.6 |

Number | Cement Content/% | Sand Content/% | W/C | Number | Cement Content/% | Sand Content/% | W/C |
---|---|---|---|---|---|---|---|

1 | 25 | 7 | 0.4 | 10 | 25 | 7 | 0.6 |

2 | 25 | 0 | 0.5 | 11 | 38 | 0 | 0.4 |

3 | 38 | 15 | 0.4 | 12 | 38 | 7 | 0.5 |

4 | 50 | 15 | 0.5 | 13 | 50 | 7 | 0.4 |

5 | 38 | 0 | 0.6 | 14 | 25 | 15 | 0.5 |

6 | 38 | 7 | 0.5 | 15 | 38 | 7 | 0.5 |

7 | 38 | 7 | 0.5 | 16 | 38 | 15 | 0.6 |

8 | 50 | 0 | 0.5 | 17 | 38 | 7 | 0.5 |

9 | 50 | 7 | 0.6 |

Number | Viscosity /(mPa·s) | Setting Time/(min) | Compressive Strength/(MPa) | Bleeding Rate /% | |||
---|---|---|---|---|---|---|---|

Initial | Final | 3 days | 7 days | 28 days | |||

1 | 390 | 130 | 260 | 0.75 | 1.61 | 2.31 | 2.1 |

2 | 230 | 275 | 375 | 0.63 | 1.33 | 1.82 | 5.1 |

3 | 440 | 125 | 245 | 1.21 | 3.24 | 4.26 | 1.4 |

4 | 280 | 305 | 455 | 1.55 | 3.56 | 4.51 | 3.5 |

5 | 120 | 325 | 505 | 1.47 | 3.17 | 3.68 | 10.3 |

6 | 230 | 280 | 445 | 1.13 | 3.48 | 4.86 | 4.3 |

7 | 240 | 290 | 450 | 1.35 | 3.66 | 5.02 | 4.2 |

8 | 270 | 270 | 425 | 2.14 | 5.22 | 6.13 | 3.1 |

9 | 140 | 330 | 535 | 3.37 | 5.74 | 6.87 | 9.5 |

10 | 180 | 375 | 555 | 0.69 | 1.97 | 2.46 | 9.8 |

11 | 360 | 150 | 255 | 1.86 | 3.93 | 5.41 | 1.6 |

12 | 260 | 275 | 425 | 1.46 | 3.87 | 4.97 | 4.1 |

13 | 380 | 135 | 265 | 2.01 | 7.71 | 8.45 | 1.1 |

14 | 330 | 290 | 400 | 0.88 | 2.12 | 3.24 | 4.8 |

15 | 220 | 250 | 435 | 1.26 | 3.62 | 4.68 | 4.6 |

16 | 240 | 295 | 525 | 1.42 | 3.43 | 4.14 | 8.6 |

17 | 220 | 260 | 415 | 1.14 | 3.68 | 5.13 | 4.3 |

Index | Eigenvector Values | |
---|---|---|

First Principal Component | Second Principal Component | |

Initial setting time | 0.978 | 0.100 |

Bleeding rate | 0.944 | 0.058 |

Final setting time | 0.943 | 0.170 |

Viscosity | −0.922 | −0.206 |

Compressive strength (3 d) | −0199 | 0.969 |

Compressive strength (7 d) | 0.023 | 0.926 |

Compressive strength (28 d) | −0.379 | 0.877 |

Group | First Principal Component Score | Second Principal Component Score | Comprehensive Score | Standardized Comprehensive Score |
---|---|---|---|---|

1 | −1.11938 | −1.54969 | −1.18941 | 0 |

2 | 0.29447 | −1.48413 | −0.40306 | −0.70929 |

3 | −1.60096 | −0.61966 | −1.09684 | −0.40549 |

4 | 0.08313 | 0.06118 | 0.06793 | −0.97489 |

5 | 1.45919 | 0.00512 | 0.787901 | 0.29128 |

6 | 0.18470 | −0.07001 | 0.07299 | 0.026984 |

7 | 0.14769 | 0.11452 | 0.12289 | 0.045432 |

8 | −0.24972 | 1.04569 | 0.261235 | 0.096576 |

9 | 1.23223 | 2.25084 | 1.515546 | 0.560285 |

10 | 1.65978 | −0.91817 | 0.546526 | 0.202046 |

11 | −1.34704 | 0.20555 | −0.64777 | −0.23947 |

12 | −0.01060 | 0.16799 | 0.057866 | 0.021393 |

13 | −1.73359 | 1.73861 | −0.27579 | −0.10196 |

14 | 0.00320 | −0.94535 | −0.35604 | −0.13163 |

15 | 0.12886 | −0.01599 | 0.063356 | 0.023422 |

16 | 0.85603 | 0.00345 | 0.462389 | 0.170941 |

17 | 0.01202 | 0.01006 | 0.010282 | 0.003801 |

Source | Sum of Squares | df | Mean Square | F Value | p-Value Prob > F |
---|---|---|---|---|---|

Model | 2.09 | 9 | 0.23 | 66.47 | <0.0001 |

A | 0.058 | 1 | 0.058 | 16.67 | 0.0047 |

B | 0.0094 | 1 | 0.0094 | 2.69 | 0.1447 |

C | 0.47 | 1 | 0.47 | 135.4 | <0.001 |

AB | 0.68 | 1 | 0.68 | 194.92 | <0.001 |

AC | 0.053 | 1 | 0.053 | 15.18 | 0.0059 |

BC | 0.00052 | 1 | 0.00052 | 0.15 | 0.7104 |

A^{2} | 0.062 | 1 | 0.062 | 17.85 | 0.0039 |

B^{2} | 0.47 | 1 | 0.47 | 0.15 | <0.0001 |

C^{2} | 0.29 | 1 | 0.29 | 17.85 | <0.0001 |

Residual | 0.024 | 7 | 0.003488 | 133.37 | |

Lack of Fit | 0.024 | 3 | 0.007845 | 83.18 | 0.0024 |

Pure Error | 0.0008892 | 4 | 0.0002208 | ||

Cor Total | 2.11 | 16 | 35.53 | ||

Notice: R^{2} = 0.9884 |

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**MDPI and ACS Style**

Liu, W.; Qin, Y.; Meng, X.; Pang, L.; Han, M.; Song, Z.
Basic Experimental Study of Plasticity Material for Coal Rock Fracture Grouting Based on RSM-PCA Technology. *Energies* **2021**, *14*, 4516.
https://doi.org/10.3390/en14154516

**AMA Style**

Liu W, Qin Y, Meng X, Pang L, Han M, Song Z.
Basic Experimental Study of Plasticity Material for Coal Rock Fracture Grouting Based on RSM-PCA Technology. *Energies*. 2021; 14(15):4516.
https://doi.org/10.3390/en14154516

**Chicago/Turabian Style**

Liu, Weitao, Yueyun Qin, Xiangxi Meng, Lifu Pang, Mengke Han, and Zengmou Song.
2021. "Basic Experimental Study of Plasticity Material for Coal Rock Fracture Grouting Based on RSM-PCA Technology" *Energies* 14, no. 15: 4516.
https://doi.org/10.3390/en14154516