The Mechanical Properties of Gangue Paste Material for Deep Mines: An Experimental and Model Study

Gangue paste material is mainly composed of coal gangue with particle size, which is mixed with cement. Fly ash and additives can be added to change its performance. In this paper, the influence of each component on the mechanical properties of gangue paste material was studied by an orthogonal experiment. The conversion relationship among various indexes of mechanical properties of gangue paste material and the response surface prediction model were discussed. The results show that the mechanical properties of gangue paste materials are positively correlated with the content of cement, the content of fly ash and the mass concentration, which increase with the increase of the three factors, and show the primary and secondary relationship of the content of cement > the content of fly ash > the mass concentration. A response surface prediction model of mechanical property parameters is established, which includes the first order term of the influencing factors of gangue paste material and the first order interaction term between any two factors. In the response surface prediction model of uniaxial compressive strength, splitting tensile strength, cohesion and elastic modulus, the goodness of fit test coefficients are 0.998, 0.957, 0.970 and 0.997, respectively, which proves that the model has good goodness of fit. The research results provide basic parameters for paste filling mining practice, and also provide the basis for numerical simulation of filling body value.


Introduction
In the early 21st century, paste filling materials developed rapidly with unique characteristics. The gangue paste has excellent pipeline transportation performance such as high concentration, no critical flow rate, and plunger structure flow. There is no bleeding, segregation, and precipitation in the process of transportation and solidification, and the compression ratio is extremely low after solidification, which accounts for its favourable reception in markets, especially in backfill mining technology [1,2]. The mechanical properties of paste filling materials are closely related to the control effect of surface subsidence deformation. In addition, many scholars have carried out a lot of research on it [3][4][5][6][7][8][9]. The mechanical properties of paste materials are mainly affected by the amount of cement, curing conditions, the ratio of binder to aggregates, and particle size distribution [10][11][12][13][14][15][16]. Through uniaxial compression and triaxial tests, the characteristic information of backfill before loading failure is studied, and four stages of deformation and failure of the stress-strain curve are proposed. The internal relationship of energy dissipation, confining pressure, and stress-strain under different confining pressure loading conditions, as well as crack propagation, macro failure, and fracture surface distribution were analyzed [17][18][19][20][21]. Through response surface analysis, Ensemble Learner Algorithms, or BP neural network, the strength of paste filling material can be obtained by using the mixture ratio of paste filling material [15,18,[22][23][24]. Most of the studies only focus on the uniaxial compressive the strength of paste filling material can be obtained by using the mixture ratio of paste filling material [15,18,[22][23][24]. Most of the studies only focus on the uniaxial compressive strength and elastic modulus, but few on the tensile strength, cohesion, internal friction angle, and Poisson's ratio [25][26][27]. Therefore, through the method of orthogonal test, the basic mechanical properties of gangue gypsum body material were comprehensively analyzed. The results are of great significance to the understanding of the strength characteristics of gangue paste filling materials, and also provide a theoretical basis for the selection of filling body parameters in the numerical simulation of gangue gypsum body filling mining.

Materials
The test gangue was taken from the Gaohe coal mine of Shanxi Lu'an Group. Coal gangue is mainly composed of SiO2, Al2O3, and some trace elements. It is a combination of argillaceous, carbonaceous, and sandy shale. Coal gangue is a kind of rock associated with the formation of coal, and its hardness is harder than coal The main components of the fly ash are shown in Table 1; The cement is an SL cement developed by Professor Zhou Huaqiang's research group of China University of mining and technology ( Figure 1). Its physical and mechanical properties are shown in Tables 2 and 3; The particle size distribution of coal gangue water-screen gradation is shown in Figure 2.The mechanical and working properties of the paste material can be improved by adding the same dosage of bFGF in each group, PA is 3 kg/m 3 , HA is 5 kg/m 3 .        To better study, the influence law of each component of paste material on the mechanical properties of gangue paste material and the conversion relationship and prediction model among parameters, this paper adopts an orthogonal test to set 9 groups of proportion, which can not only consider the interaction of single factor and various factors, but also easily set up multiple groups of the reasonable proportioning scheme. The experimental design was three factors and three levels, and the orthogonal factor levels are shown in Table 4, and the L9 (3 3 ) orthogonal experimental table was selected. The orthogonal test scheme is shown in Table 5. To better study, the influence law of each component of paste material on the mechanical properties of gangue paste material and the conversion relationship and prediction model among parameters, this paper adopts an orthogonal test to set 9 groups of proportion, which can not only consider the interaction of single factor and various factors, but also easily set up multiple groups of the reasonable proportioning scheme. The experimental design was three factors and three levels, and the orthogonal factor levels are shown in Table 4, and the L9 (3 3 ) orthogonal experimental table was selected. The orthogonal test scheme is shown in Table 5.  1  83  125  0  3  5  240  500  GH-2  83  175  50  3  5  260  580  GH-3  83  225  100  3  5  265  620  GH-4  84  125  50  3  5  255  590  GH-5  84  175  100  3  5  265  550  GH-6  84  225  0  3  5  268  610  GH-7  85  125  100  3  5  255  595  GH-8  85  175  0  3  5  250  510  GH-9  85  225  50  3  5  236  410 Materials 2022, 15, 5904

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The paste filling material is transported to the downhole through the pipeline, and the low fluidity easily leads to pipe plugging and cannot be pumped. Therefore, good fluidity is very important. Fluidity is usually expressed by slump and expansion in engineering. It is generally considered that when the slump of gangue gypsum body material is ≥240 mm, it has pumpability and can be transported through pipes. The slump and expansion of each proportioned material in Table 5 were tested. In addition, the results show that the slump and expansion of the 9 proportions are 240~268 mm and 410~620 mm, respectively [28]. The flow performance can meet the requirements of engineering practice. The proportion has reference significance for engineering practice.

Experiments
In this paper, 81 samples of gangue paste were made. Since there is no standard for mechanical property test of paste materials at present, the sample size and test method shall be determined according to The National Standards of China, The Standard for test method of mechanical properties on ordinary concrete and The Methods for Determining the Physical and Mechanical Properties of Coal and Rock. Among them, there are a total of 54 cubic specimens with a size of 100 mm × 100 mm × 100 mm, and a total of 27 cylindrical specimens with a diameter of 50 mm and a height of 100 mm. After the specimens are made, they are put into the curing box for 28 days, and the corresponding tests are carried out. The prepared samples is given in Figure 3, the purpose of the test piece is shown in Table 6. During the test, the loading speed is controlled as 0.5 mm/min.

Experimental Results
The compression failure process of gangue paste material specimen is shown in Fig  ure 4. At the beginning of pressurization, there is no obvious change on the outer surfac and the compression amount in this process is about 2%, and then there are visible crack The difference between the cube test piece and the cylinder test piece is the final failur form. After cracks appear in the cube specimen with loading, the four walls protrude ou

Experimental Results
The compression failure process of gangue paste material specimen is shown in Figure 4. At the beginning of pressurization, there is no obvious change on the outer surface, and the compression amount in this process is about 2%, and then there are visible cracks. The difference between the cube test piece and the cylinder test piece is the final failure form. After cracks appear in the cube specimen with loading, the four walls protrude outward, and finally show "X" failure characteristics. This is because the cubic gangue gypsum material specimen is affected by the "hoop effect" of the upper and lower pressure plates in the uniaxial compression process. The stress concentration in the middle position is large, and the surface is broken and falls off. It is a typical crushing failure and the compressibility is small. After the cracks appear in the cylindrical specimen with loading, the cracks develop obliquely, and finally penetrate the failure. There are obvious sliding traces on the failure surface, and the failure surface is a small particle cementitious layer, and the large particles are not obviously damaged. This indicates that the cylindrical gangue gypsum body material specimen has a typical shear failure of the cementitious layer during uniaxial compression [29,30].

Experimental Results
The compression failure process of gangue paste material specimen is shown in Figure 4. At the beginning of pressurization, there is no obvious change on the outer surface, and the compression amount in this process is about 2%, and then there are visible cracks. The difference between the cube test piece and the cylinder test piece is the final failure form. After cracks appear in the cube specimen with loading, the four walls protrude outward, and finally show "X" failure characteristics. This is because the cubic gangue gypsum material specimen is affected by the "hoop effect" of the upper and lower pressure plates in the uniaxial compression process. The stress concentration in the middle position is large, and the surface is broken and falls off. It is a typical crushing failure and the compressibility is small. After the cracks appear in the cylindrical specimen with loading, the cracks develop obliquely, and finally penetrate the failure. There are obvious sliding traces on the failure surface, and the failure surface is a small particle cementitious layer, and the large particles are not obviously damaged. This indicates that the cylindrical gangue gypsum body material specimen has a typical shear failure of the cementitious layer during uniaxial compression [29,30].   Table 7.   Table 7.

Range Analysis
Range analysis [31,32], also known as intuitive analysis method, is a fast and simple analysis process. It only needs to calculate the average response value K ij (j represents factor, i represents level) of different levels of each influencing factor, and calculate the range (R) of corresponding index of each influencing factor level according to the average response value K ij , and determine the primary and secondary relationship of influencing factors according to the value of R.
It can be seen from Table 8 that in the range analysis of influencing factors of uniaxial compressive strength, splitting tensile strength, cohesion, internal friction angle, and elastic modulus, R Cement content > R Fly ash content > R Mass concentration , so the order of influencing factors of the above five indexes of gangue paste material is: cement content, fly ash content, and mass concentration. However, in the Poisson's ratio range analysis, R Cement content > R Mass concentration > R Fly ash content , that is, the primary and secondary factors affecting the Poisson's ratio of gangue paste material are: cement content, mass concentration and fly ash content. Uniaxial compressive strength, splitting tensile strength, and elastic modulus increase with the increase of cement content, fly ash content, and mass concentration; The cohesive force increases with the increase of mass concentration and cement content, and increases first and then decreases with the increase of fly ash content, which indicates that fly ash can promote the cohesive force to a certain extent, and the cohesive force of gangue paste material will be reduced if too much fly ash is added; The results show that the influence of cement content, fly ash content, and mass concentration on internal friction angle and Poisson's ratio is not consistent In the range analysis of this test, the internal friction angle first decreases and then increases with the increase of mass concentration and fly ash content, first increases and then decreases with the increase of cement content, Poisson's ratio increases first and then decreases with the increase of mass concentration, and decreases with the increase of cement and fly ash.
In the range analysis of the influencing factors of the mechanical properties of gangue paste material, the single factor of cement content, fly ash content, and mass concentration has a positive correlation on most of the mechanical properties, which increases with the increase of the three factors, and shows the primary and secondary relationship of cement content > fly ash content > mass concentration. The influence law of internal friction angle and Poisson's ratio is not clear in range analysis, which needs further analysis.

Analysis of Variance
The influence of mass concentration [33], cement content and fly ash content on the mechanical properties of gangue paste was discussed by orthogonal test range analysis, and the trend of mechanical properties changing with the level of various factors was analyzed. Since range analysis can not distinguish whether the test results are caused by different levels of factors or by test errors, and can not determine the significance of the influencing factors, and the influence law of internal friction angle and Poisson's ratio is not clear in range analysis, consequently, variance analysis is carried out for the test results.
According to Table 9, in the variance analysis of factors influencing uniaxial compressive strength, split tensile strength, cohesion, internal friction angle, and elastic modulus, SS cement material > SS fly ash content > SS mass concentration , so the main and secondary order of the influencing factors of the above five indexes is: Cement content, fly ash content, and mass concentration, which is consistent with the results of extreme difference analysis. In Poisson ratio extreme difference analysis, SS cement material > SS mass concentration > SS fly ash content , that is, the main and secondary order of factors affecting Poisson ratio of gangue gypsum material is: cement content, mass concentration and fly ash content, which is consistent with the results of extreme analysis.
For uniaxial compressive strength, splitting tensile strength, cohesion, and elastic modulus, the F cement content is more than F 0.05 (2, 8) = 8.65, that is, the change of cement content factor has significant influence on the above four indexes; For internal friction angle and Poisson ratio, the F mass concentration is less than F 0.05 (2, 8) = 4.46, F cement content is less than F 0.01 (2, 8) = 8.65, F fly ash content is less than F 0.1 (2, 8) = 3.11, that is, the change of the three factors of the quality concentration, cement content, and fly ash content has no significant influence on the internal friction angle and Poisson ratio; In internal friction angle, SS error > SS mass concentration indicates that the influence of mass concentration on internal friction angle of material is caused by the error. In Poisson ratio, SS error > SS cement content > SS mass concentration > SS fly ash content , which indicates that the influence of mass concentration, cement content, and fly ash content on Poisson ratio of material is also caused by error. Therefore, it can be considered that the influence of cement content, fly ash content, and mass concentration on Poisson's ratio is positively correlated, and increases with the increase of the three factors, and shows the primary and secondary relationship of cement content > fly ash content > mass concentration.
In the variance analysis of the factors influencing the mechanical properties of gangue paste, it can be seen that the cement content has the most significant influence on the properties; Combined with the analysis of extreme difference, it can be concluded that the factors of cement content, fly ash content, and mass concentration have positive correlation with the mechanical properties of gangue paste, and increases with the increase of the three factors, and shows the primary and secondary relationship of cement content > fly ash content > mass concentration.

Conversion Relationship of Each Index
The quantitative fitting relationship of the compressive strength of the cube and the tensile strength, cohesion, and elastic modulus is statistically analyzed.
(1) Relationship between splitting tensile strength and cube compressive strength.
As shown in Figure 5, the relationship (1) is obtained by fitting the splitting tensile strength and cube compressive strength of gangue paste material with power function by origin.
where f t is Tensile strength (MPa); f cu is Cube Strength (MPa).

Materials 2022, 15, x FOR PEER REVIEW
As shown in Figure 5, the relationship (1) is obtained by fitting the split strength and cube compressive strength of gangue paste material with power origin. .
Fitting Formula (1) residual sum of squares is 0.030, the goodness of fit R 2 fitting effect is better. It can be seen that the uniaxial compressive strength can predict the splitting tensile strength accurately through Formula (1).
(2) Relationship between cohesion and cube compressive strength.
As shown in Figure 6, the relationship (2) is obtained by fitting the split strength and cube compressive strength of gangue paste material with origin.  Fitting Formula (1) residual sum of squares is 0.030, the goodness of fit R 2 = 0.966, the fitting effect is better. It can be seen that the uniaxial compressive strength can be used to predict the splitting tensile strength accurately through Formula (1).
(2) Relationship between cohesion and cube compressive strength.
As shown in Figure 6, the relationship (2) is obtained by fitting the splitting tensile strength and cube compressive strength of gangue paste material with origin.
where C is cohesion (MPa); f cu is Cube Strength (MPa).
Fitting Formula (2) residual sum of squares is 0.030, goodness of fit R 2 = 0.971, the fitting effect is better. It can be seen that the cohesive strength value can be accurately predicted by the uniaxial compressive strength value in Formula (2).
(3) Relationship between elastic modulus and cube compressive strength.
As shown in Figure 7, the relationship (3)  Fitting Formula (1) residual sum of squares is 0.030, the goodness of fit R 2 = fitting effect is better. It can be seen that the uniaxial compressive strength can predict the splitting tensile strength accurately through Formula (1).
(2) Relationship between cohesion and cube compressive strength.
As shown in Figure 6, the relationship (2) is obtained by fitting the splitt strength and cube compressive strength of gangue paste material with origin.
Fitting Formula (2) residual sum of squares is 0.030, goodness of fit R 2 = fitting effect is better. It can be seen that the cohesive strength value can be predicted by the uniaxial compressive strength value in Formula (2).
(3) Relationship between elastic modulus and cube compressive strength.
As shown in Figure 7, the relationship (3) is obtained by fitting the elasti and cube compressive strength of gangue gypsum body material with origin.  The square sum of residual error of fitting Formula (3) is 25,707.028, and the value is too large. It can be seen that the fitting is not convergent, and the error is large, but the goodness of fit R 2 = 0.966. Combined with Figure 4, it can be seen that the fitting result has high accuracy, and the value of elastic modulus can be predicted by the uniaxial compressive strength value of Formula (3).

Prediction Model
In this section, based on the data of orthogonal test and response surface analysis by design expert software, a response surface prediction model of mechanical properties parameters is established, which includes the first-order term of the influencing factors of gangue paste material and the first-order interaction term between any two factors. The expressions are shown in (4) to (9).
where f cu is Uniaxial compressive strength (MPa); f t is Splitting tensile strength (MPa); C is Cohesive force (MPa); ϕ is Internal friction angle ( • ); E is Elastic modulus (MPa); µ is Poisson's ratio; x 1 is Mass concentration; x 2 is Cement content (kg/m 3 ); x 3 is Fly ash content (kg/m 3 ). Design expert software is used to draw the 3D response surface diagram of the three influencing factors of binder content, fly ash content and mass concentration for each response value. The influence results of different factors on uniaxial compressive strength, splitting tensile strength, cohesion, internal friction angle, elastic modulus and Poisson's ratio are shown in Figure 8. With the help of 3D response surface diagram, we can more intuitively understand the interaction between various influencing factors, and effectively determine the optimal range of different influencing factors.  . 17  x is Fly ash content (kg/m 3 ).
Design expert software is used to draw the 3D response surface diagram of the three influencing factors of binder content, fly ash content and mass concentration for each response value. The influence results of different factors on uniaxial compressive strength, splitting tensile strength, cohesion, internal friction angle, elastic modulus and Poisson's ratio are shown in Figure 8. With the help of 3D response surface diagram, we can more intuitively understand the interaction between various influencing factors, and effectively determine the optimal range of different influencing factors. The results of variance analysis of the response surface prediction model are shown in Table 10 The judgment coefficient R 2 is the goodness of fit test, which indicates the difference between the measured value and the predicted value. The closer the R 2 value is to 1, the better the fitting degree is; F is the significance test of the regression equation, which indicates the significance of the fitting equation. The larger the value is, the more significant the equation is; When p < 0.05, the factor is significant, when p > 0.05, the factor is not significant. R 2 = 0.998 in response surface prediction model of uniaxial compressive strength, which proves that the model fits well. P model < 0.05 shows that the whole model is significant, PX2 < PX3 < 0.05 shows that the amount of cement and fly ash has a significant impact on the prediction model of uniaxial compressive strength, and the cement is the most prominent. The R 2 = 0.957 in the variance analysis of the response surface prediction model of splitting tensile strength proves that the model has a good fitting degree. R 2 = 0.970 in variance analysis of cohesive strength response surface prediction model, which proves that the model has a good fitting degree. In the analysis of variance, R 2 = 0.735, which indicates that the model fitting is low; P model > 0.05, indicating that the overall model is not significant. R 2 = 0.997 in variance analysis of elastic modulus response surface prediction model, which proves that the model has a good fit; P model < 0.05 shows that the model as a whole is significant, PX2 < PX3 < PX1 < px1x2 < 0.05, indicating that cementitious materials, fly ash content, mass concentration, and the interaction between mass concentration and cementitious materials have significant effects on the prediction model of elastic modulus, The results of variance analysis of the response surface prediction model are shown in Table 10 The judgment coefficient R 2 is the goodness of fit test, which indicates the difference between the measured value and the predicted value. The closer the R 2 value is to 1, the better the fitting degree is; F is the significance test of the regression equation, which indicates the significance of the fitting equation. The larger the value is, the more significant the equation is; When p < 0.05, the factor is significant, when p > 0.05, the factor is not significant. 88.700 6.083 × 10 5 0.020 R 2 = 0.998 in response surface prediction model of uniaxial compressive strength, which proves that the model fits well. P model < 0.05 shows that the whole model is significant, P X2 < P X3 < 0.05 shows that the amount of cement and fly ash has a significant impact on the prediction model of uniaxial compressive strength, and the cement is the most prominent. The R 2 = 0.957 in the variance analysis of the response surface prediction model of splitting tensile strength proves that the model has a good fitting degree. R 2 = 0.970 in variance analysis of cohesive strength response surface prediction model, which proves that the model has a good fitting degree. In the analysis of variance, R 2 = 0.735, which indicates that the model fitting is low; P model > 0.05, indicating that the overall model is not significant. R 2 = 0.997 in variance analysis of elastic modulus response surface prediction model, which proves that the model has a good fit; P model < 0.05 shows that the model as a whole is significant, P X2 < P X3 < P X1 < p x1x2 < 0.05, indicating that cementitious materials, fly ash content, mass concentration, and the interaction between mass concentration and cementitious materials have significant effects on the prediction model of elastic modulus, and cementitious materials are the most prominent. In the analysis of variance of Poisson's ratio response surface prediction model, R 2 = 0.875, which proves that the model fitting is low; P model > 0.05, indicating that the overall model is not significant

Conclusions
(1) According to the range analysis and variance analysis of the orthogonal experimental results of gangue paste filling material, it can be seen that the influence of single factor of cement content, fly ash content, and mass concentration on each performance index increases with the increase of the three-factor levels, and shows the primary and secondary relationship of cement content > fly ash content > mass concentration. (2) The uniaxial compressive strength, splitting tensile strength, cohesive force, and elastic modulus of gangue paste material can be fitted by origin, which has a good functional relationship, and this relationship is less affected by mass concentration, fly ash content, and cement content. (3) Through response surface analysis, the mathematical prediction model of the firstorder interaction term between any two factors and the first-order interaction term of the influencing factors of the mechanical and deformation properties of gangue gypsum material is established, and it has high accuracy. (4) In this paper, the orthogonal experiment is selected in the experiment, and the number of experiments is reduced, which may lead to some shortcomings in the test results. Therefore, more experiments need to be carried out in the future, and the artificial intelligence prediction will be combined to acquire a better model. (5) The mechanical property prediction model of gangue gypsum body material is used to guide the determination of the proportion parameters of the filling body material in Gaohe coal mine. Through filling mining, a large amount of solid wastes in Gaohe coal mine are treated, and the problems of coal pressing under buildings are also solved.