# Strength Model of Cemented Filling Body Based on a Neural Network Algorithm

Authors: Daiqiang Deng; Yihua Liang; Guodong Cao; Jinkuan Fan
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

As one of the key measures for comprehensive management of goaf in various mines, filling mining has been recognized by practitioners in recent years due to its functions (e.g., resource utilization of solid waste and thorough goaf treatment). The performance of the filling material is the core challenge of filling mining, and it is influenced by the settling speed, conveying characteristics, and filling body strength. To understand the strength characteristics of a cemented filling body composed of medium-fine tailings, in this study, filling material ratio tests under different content of cement, tailings, and water were conducted. A backpropagation (BP) neural network topology structure was established in this study. The strength after different curing times was used as the output variable to analyze the impact of the cement, tailings, and water content on the filling body. A 3-Hn-3 structural model was employed. When the number of hidden layers Hn was 7, the model achieved the best learning and training effect. The results show that the predicted value, which is close to the measured value (fitting accuracy of 92.43–99.92%; average error of 0.0792–7.5682%), satisfies the engineering requirements. The neural network model can be employed to predict the filling body’s strength and provide a good reference to analyze the change law in the filling body’s strength.


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## Body

## 1. Introduction

In the course of rapid industrialization, the environmental protection industry related to solid waste treatment in mines is also expanding quickly. In recent years, various environmental protection studies based on industrial projects have become more targeted, systematic, theoretical, and practical. Regarding the treatment of coal gangue in coal mines, researchers have conducted a number of performance studies to create conditions for its utilization as a resource [1, 2]. In goaf management in various mining projects, usual consideration is to use the solid waste products, such as coal gangue, and tailings are used to produce a filler slurry with a good homogeneity to fill the underground goaf [3, 4]. In view of the engineering conditions in some areas, some studies have investigated the properties of filling materials and have presented reasonable suggestions for the comprehensive treatment of goaf [5]. Since the use of coal gangue and tailings to fill the goaf can reduce the discharge of tailings and can control the goaf and ensure safe mining of the ore, the filling method performs well in the treatment of the goaf in mining projects [6, 7]. Research on filling techniques has become particularly important. There are a growing number of studies about filling systems, filling materials, and preparation processes. Many research results have achieved remarkable economic and environmental benefits in the application and production processes [8]. In terms of mine waste utilization, some researchers have systematically studied the waste cementation and filling, and some theoretical analyses have been implemented in engineering practice [9]. In the research on filling techniques, due to the different selection and preparation of filling materials in various mines and the different properties of the materials in different locations, it is necessary to perform a reasonable analysis based on the specific conditions [10, 11]. For example, the particle size distribution, particle size, density, bulk density, chemical composition, and output process of the various mine filling aggregates in different regions are different. In addition, the hydration process and cementation properties of the cement or other cementitious materials are also different. These differences could lead to different physical and chemical properties [12]. However, for specific mines, the determination of the filling aggregates and cementitious materials follows the same principle, that is, the supply of filling materials generally needs to meet the requirements of convenient transportation, low price, and good properties. The overall performance of the application of the filling body in the daily production process demonstrates its good competitiveness in terms of technical and economic costs.In the different stages of mine filling engineering design, it is necessary to conduct the investigation and analysis based on the on-site geological conditions of the mining enterprise to determine the most suitable filling process [13, 14]. For example, in mountainous areas, it is necessary to use the natural elevation difference of the mountain slopes to design different material conveying facilities, so that each link can make full use of the gravity of the materials to smoothly transport from the starting point to the endpoint. In this way, the filling materials required for the next process are continuously provided, and it reduces energy of transportation and cost [15].For the filling materials selected by mining enterprises, how to achieve a high strength has always been a goal pursued by researchers [16]. Regarding the microscopic characteristics of a cemented filling body, researchers have used advanced equipment to observe and describe the formation of the structure, analyze the material production and its development pattern, and provide good suggestions for improving the strength of the filling body [17]. For some goaf filling situations with long conveyance distances, the pump was adopted to deliver the filling slurry to the goaf [18]. The response surface method was adopted to design and conduct experiments to reveal the strength development pattern of the filling body with alkali-activated slag cementitious materials [19]. At present, methods analyzing the mechanical properties of filling materials and filling bodies, such as gray theory, fractal technology, computer science, and complex calculations, are developed to predict and optimize the strength performance of filling bodies [20]. Chang has sorted the test results and then applied the neural network method to predict the strength of the filling body [21]. Regarding the application of fractal mathematics to analyze the filling body strength, Liu adopted fractal mathematics to rigorously explore the internal mechanism of the influence of the tailings’ size on the filling body’s strength [22]. Yang has examined a variety of factors influencing on changes in the strength of the filling body [23].In terms of using fine-grained tailings as a filling material, the strength of the filling body composed of a combination of tailings and cement is low. According to the chemical composition and particle size distribution characteristics of tailings, researchers have carried out a development test for cementitious materials and have achieved good results in the laboratory [24]. To analyze the mechanical properties of the filling body under different field conditions, researchers have tested the strengths of filling bodies of different sizes and have explored the relationship between the strength of the cement paste and the specimen size [25]. In terms of optimizing the properties of the tailings filling materials, advanced mechanical equipment has been used to remove part of the fine particles in the tailings, or coarser filling aggregates have been added in order to obtain filling materials with a better permeability. The tailings, cement, and water were evenly mixed in a mixer. The filling body formed consolidated and hardened faster, and the strength of the filling body was greatly improved [26]. Regarding engineering applications of block stone cemented filling bodies, researchers have summarized some test processes and field applications and have analyzed the problems encountered in these applications [27]. The acoustic propagation of a block stone cemented filling body has a certain particularity, so it is different from other materials with good homogeneities. Based on the experimental analysis, researchers have determined the effects of the particle distribution and other factors on the mechanics and acoustic emission characteristics of filling bodies [28]. Regarding the resource utilization of the waste rock and tailings in the Anqing copper mine, researchers successfully applied the filling process model to engineering practice based on laboratory research [29, 30].For general beneficiation tailings, it is considered that tailings with average particle sizes of 20–80μm, 80–150 μm, and >150 μm are fine-grained, medium-fine-grained, and coarse-grained, respectively. In this study, the mechanical strengths of filling bodies composed of different medium-fine tailings, composite Portland cement, and water contents were analyzed. And then, a backpropagation (BP) neural network topology structure was developed to establish the mapping model between the strength of the filling body and cement, tailings as well as water content.


## 2. Test Materials and Methods

### 2.1. Tailings

The tailings used in the laboratory tests were obtained from a mining site and were sampled during the normal production period of the beneficiation workshop. To ensure that the sampling was representative, the sampling was conducted 5–7 times. The mine tailings dam is shown in Figure1(a). A small tailings pond with a volume of 5–7 m3 was set up, and the tailings pipe was introduced into the tailings pond for discharge, as shown in Figure 1(b). After the natural sedimentation of the low-concentration tailings mortar for 8–12 hours, the turbid tailings water in the upper part became clear and then flowed out. The process of discharging the water should not have resulted in the loss of fine particles. The tailings that were not completely dry were bagged and transported back to the laboratory in Changsha for further air-drying, and the completely dried tailings were stored in plastic buckets.Figure 1
Tailings sampling and natural sedimentation. (a) Mine tailings dam. (b) Tailpipe sampling.
(a)(b)Through chemical analysis and performance tests conducted in the laboratory, the SiO2, CaO, S, Al2O3, and MgO contents of the tailings were about 43%, 20%, 6%, and 3.13%, respectively. Compared with other mines, the SiO2 content of the tailings from this mine is relatively low. The contents of the different substances in the tailings are shown in Figure 2. The instrument used for particle size measurement is the CILAS-1064 laser particle size analyzer produced by the CILAS Company in France. The instrument integrates dry and wet methods and adopts DJD and multilaser technology. The particle size range measured by the wet method is from 0.04 μm to 500 μm. The cumulative contents of the 15.887 μm, 50.238 μm, 100.237 μm, and 1124.683 μm particles are 26.49%, 46.19%, 64.88%, and 100%, respectively. Compared with other mines, the tailings are slightly finer. The cumulative contents of the particles of different sizes in the tailings are presented in Figure 3. The tailings have a specific gravity of 2.998, a loose bulk density of 1.399 t/m3, a dense bulk density of 1.699 t/m3, and a natural angle of repose of 39.7°. The porosity corresponding to the dense bulk density is 43.33%, and the pore ratio is 0.765.Figure 2
Chemical composition of the tailings.Figure 3
Particle size distribution of the tailings.


### 2.2. Filling Cementitious Material

Combined with the actual production and filling material supply of the mining enterprises, the common Portland cementing material around the mine was cement produced by nearby cement plants. Therefore, the filling cementing material used in this ratio test was PC32.5 grade cement. A series of tests were conducted on the cement sample to obtain its relevant physical and mechanical properties. The PC32.5 grade cement had a specific gravity of 3.113, a loose bulk density of 1.233 t/m3, a dense bulk density of 1.705 t/m3, and a natural angle of repose of 40.1°. The porosity corresponding to the dense bulk density is 45.22%, and the pore ratio is 0.826.


### 2.3. Water

The mixing water of the filling materials used in the laboratory was ordinary tap water. According to the relevant test results, the specific gravity of the water was 1, the PH value was 6.9–7.1, and the temperature of the water was 16–21°C.


### 2.4. Preparation of Cement Filling Slurry

The tailings, PC32.5 grade cement, and tap water were mixed according to a certain proportion. Because of the fine tailings and cement particles, in order to fully mix the materials, the mixing time was set to 240–300 seconds. After achieving an evenly mixed filling slurry, it was transferred to a stainless steel bucket. The filling slurry was poured into a triple test mold with an iron spoon. The three test materials were summarized, and the ingredients were calculated. The consumption of the filling materials per unit volume is shown in Table1. The filling slurry preparation and perfusion test model are shown in Figures 4(a) and 4(b), respectively. The strength test and failure morphology of the filling body are presented in Figures 4(c) and 4(d), respectively.Table 1
Composition of filling materials per unit volume.
No.Filling slurry bulk density (t/m3)Tap water (kg/m3)Tailing (kg/m3)PC32.5Cement (kg/m3)11.931541104334822.091460130532632.034488123730941.980515117229351.929540111127862.089459139623372.032488132422181.978514125520991.9275401189198102.0874591447181112.0314871372171121.9775141300163131.9265391233154142.0864591502125152.0294871424119161.9765141350112171.9255391279107182.085459154977192.028487146873Figure 4
Sample preparation of and strength test on the filling body. (a) Mixing of cement tailings. (b) Filling slurry perfusion test model. (c) Filling body mechanics test. (d) Failure morphology of the filling body.
(a)(b)(c)(d)


## 2.1. Tailings

The tailings used in the laboratory tests were obtained from a mining site and were sampled during the normal production period of the beneficiation workshop. To ensure that the sampling was representative, the sampling was conducted 5–7 times. The mine tailings dam is shown in Figure1(a). A small tailings pond with a volume of 5–7 m3 was set up, and the tailings pipe was introduced into the tailings pond for discharge, as shown in Figure 1(b). After the natural sedimentation of the low-concentration tailings mortar for 8–12 hours, the turbid tailings water in the upper part became clear and then flowed out. The process of discharging the water should not have resulted in the loss of fine particles. The tailings that were not completely dry were bagged and transported back to the laboratory in Changsha for further air-drying, and the completely dried tailings were stored in plastic buckets.Figure 1
Tailings sampling and natural sedimentation. (a) Mine tailings dam. (b) Tailpipe sampling.
(a)(b)Through chemical analysis and performance tests conducted in the laboratory, the SiO2, CaO, S, Al2O3, and MgO contents of the tailings were about 43%, 20%, 6%, and 3.13%, respectively. Compared with other mines, the SiO2 content of the tailings from this mine is relatively low. The contents of the different substances in the tailings are shown in Figure 2. The instrument used for particle size measurement is the CILAS-1064 laser particle size analyzer produced by the CILAS Company in France. The instrument integrates dry and wet methods and adopts DJD and multilaser technology. The particle size range measured by the wet method is from 0.04 μm to 500 μm. The cumulative contents of the 15.887 μm, 50.238 μm, 100.237 μm, and 1124.683 μm particles are 26.49%, 46.19%, 64.88%, and 100%, respectively. Compared with other mines, the tailings are slightly finer. The cumulative contents of the particles of different sizes in the tailings are presented in Figure 3. The tailings have a specific gravity of 2.998, a loose bulk density of 1.399 t/m3, a dense bulk density of 1.699 t/m3, and a natural angle of repose of 39.7°. The porosity corresponding to the dense bulk density is 43.33%, and the pore ratio is 0.765.Figure 2
Chemical composition of the tailings.Figure 3
Particle size distribution of the tailings.


## 2.2. Filling Cementitious Material

Combined with the actual production and filling material supply of the mining enterprises, the common Portland cementing material around the mine was cement produced by nearby cement plants. Therefore, the filling cementing material used in this ratio test was PC32.5 grade cement. A series of tests were conducted on the cement sample to obtain its relevant physical and mechanical properties. The PC32.5 grade cement had a specific gravity of 3.113, a loose bulk density of 1.233 t/m3, a dense bulk density of 1.705 t/m3, and a natural angle of repose of 40.1°. The porosity corresponding to the dense bulk density is 45.22%, and the pore ratio is 0.826.


## 2.3. Water

The mixing water of the filling materials used in the laboratory was ordinary tap water. According to the relevant test results, the specific gravity of the water was 1, the PH value was 6.9–7.1, and the temperature of the water was 16–21°C.


## 2.4. Preparation of Cement Filling Slurry

The tailings, PC32.5 grade cement, and tap water were mixed according to a certain proportion. Because of the fine tailings and cement particles, in order to fully mix the materials, the mixing time was set to 240–300 seconds. After achieving an evenly mixed filling slurry, it was transferred to a stainless steel bucket. The filling slurry was poured into a triple test mold with an iron spoon. The three test materials were summarized, and the ingredients were calculated. The consumption of the filling materials per unit volume is shown in Table1. The filling slurry preparation and perfusion test model are shown in Figures 4(a) and 4(b), respectively. The strength test and failure morphology of the filling body are presented in Figures 4(c) and 4(d), respectively.Table 1
Composition of filling materials per unit volume.
No.Filling slurry bulk density (t/m3)Tap water (kg/m3)Tailing (kg/m3)PC32.5Cement (kg/m3)11.931541104334822.091460130532632.034488123730941.980515117229351.929540111127862.089459139623372.032488132422181.978514125520991.9275401189198102.0874591447181112.0314871372171121.9775141300163131.9265391233154142.0864591502125152.0294871424119161.9765141350112171.9255391279107182.085459154977192.028487146873Figure 4
Sample preparation of and strength test on the filling body. (a) Mixing of cement tailings. (b) Filling slurry perfusion test model. (c) Filling body mechanics test. (d) Failure morphology of the filling body.
(a)(b)(c)(d)


## 3. Determination of Test Data for the Samples

The strength performance of the filling body usually depends on the cement-to-tailings ratio and the filling slurry’s concentration. The higher the cement content and the concentration of the filling slurry, the higher the strength of the filling body. The factors that affect the filling body’s strength include the properties and types of the tailings and cementitious materials. The action process is often complex, so targeted research is needed. The ranges of the amounts of tailings, cement, and water used in the preparation of the filling slurry were 54–72.4%, 3.6–18%, and 22–28%, respectively. When the filling body test block reached the corresponding curing time, its strength was measured, and the strength data for curing times of 3 d, 7 d, and 28 d were analyzed. The various materials and strength data for each curing time are shown in Table2. In Table 2, datasets 1–19 were used as calculation samples, and datasets 6–9 were selected as test samples (in bold in the table) through arbitrary selection. The calculated values were compared with the test samples to analyze the model’s performance.Table 2
Material and strength data for each curing time for the filling body.
No.Percentage of each substanceCompressive strength of filling body (MPa)CementTailingsWater3 d7 d28 d10.1800.5400.281.441.753.0220.1560.6240.221.691.853.2730.1520.6080.241.361.532.9340.1480.5920.260.941.222.5050.1440.5760.280.871.092.4760.1110.6690.221.011.512.6170.1090.6510.240.951.352.2580.1060.6340.260.630.811.4890.1030.6170.280.610.881.46100.0870.6930.220.540.891.59110.0840.6760.240.380.691.39120.0820.6580.260.480.621.23130.0800.6400.280.300.380.89140.0600.7200.220.490.631.18150.0580.7020.240.350.440.79160.0570.6830.260.320.350.76170.0550.6650.280.310.350.73180.0370.7430.220.360.410.72190.0360.7240.240.340.310.56


## 4. Construction and Calculation Analysis of Network Model

### 4.1. Modeling Principle of the BP Neural Network

In recent years, with the deepening of complex scientific research, the use of mathematical methods to solve problems has become more extensive. Since neural network algorithms are convenient and efficient, related investigations have also become more popular [31, 32]. The learning process of the BP neural network is a combination of the forward propagation of the input signal and the reverse propagation of the error. The test samples are passed from the input layer to the hidden layer and then to the output layer. When the output value of the output layer exceeds the preset accuracy range and the calculation step does not reach the set value, it enters the reverse propagation mode of the error. Through repeating calculations and comparisons, this process keeps training and learning until the error value meets the accuracy requirements. Once the learning is completed, the operation is stopped after delivering the output [33, 34]. In studying the physical and mechanical properties of civil engineering materials, some researchers have modeled and carried out related calculations and analyses based on the key factors affecting the performance of concrete materials. For example, in studies of the mechanical properties of concrete materials, the common factors include the cement content, ambient temperature and humidity conditions, concrete admixture content, and engineering requirements. Some nonquantitative factors can also be properly quantified. After the analysis, the topological structure of the neural network model can be established; the written Matlab code statements can be input into the interface for calculation, and the calculation results can be analyzed depending on the requirements [35–37].In this study, during the construction of the filling body strength prediction model, the various factors affecting the strength of the full tailings cemented filling body were analyzed. Based on the modeling principle, a neural network model was constructed. The model is composed of a structure of three layers of 3-Hn-3, in which the hidden layer Hn is 7. In this model, the cement contentγ1, tailings content γ2, and water content γ3 are defined as the three input variables. The output layers are the strengths of the filling body at 3 days, 7 days, and 28 days (i.e., σ1, σ2, and σ3, respectively). In the network learning, the input layer uses the traindx() function for the training operations, the hidden layer is passed using the tansig tangent function, and the output layer is passed using the purelin linear function. To obtain a faster running speed and better results, the Levenberg-Marquardt optimization algorithm (trainlm) of the nonlinear least-squares calculation mode was used for the learning and training [38, 39]. The learning rate (net.trainParam.lr), the training accuracy (GOAL), and the number of iterations were set to 0.0001, 0.001, and 2000 steps, respectively.


### 4.2. Calculations and Result Analysis

After completing the modeling, the learning and training were carried out using the Matlab7.6 platform. The system stopped computing when the number of training steps reached 133, and the required results were delivered. The accuracy and error were controlled within a reasonable range. From the comparison data for the test samples and the predicted values of the model shown in Table3, it can be seen that the fitting degree between the measured and fitted values of the strength at each curing time is 92.43–99.92%. The calculation error of the network model is very small, the absolute value of the average error is 0.0792–7.5682% (much lower than 8%), and the absolute deviation is basically 0.0008–0.0666 MPa, which meets the engineering requirements. The fitting curve of the measured and predicted values of the filling body’s strength (Figure 5) shows that the difference between the two sets of data is small, and the correlation coefficient of the model is R = 0.99912. The threshold and weight of the calculation model obtained after the training and learning are shown in Tables 4 and 5. The convergence curve of the calculations (when the training reached the optimal value) is shown in Figure 6. Figure 6 shows that the thick solid line represents the calculation process accelerated to approach the set target value of 10–3 at the beginning. When the 20th step of the calculation process was reached, the calculation area was stable, and the final step, which approached the target value, was 133.Table 3
Comparison of the measured and predicted values.
Test sampleCompressive strength of filling body (MPa)Error (%)Absolute error (%)Goodness of fit (%)Measured valuePredicted valueAbsolute deviationσ6(3d)1.011.0108−0.0008−0.07920.079299.92σ7(3d)0.950.90750.04254.47374.473795.53σ8(3d)0.630.6607−0.0307−4.87304.873095.13σ9(3d)0.610.6223−0.0123−2.01642.016497.98σ6(7d)1.511.49840.01160.76820.768299.23σ7(7d)1.351.31840.03162.34072.340797.66σ8(7d)0.810.8282−0.0182−2.24692.246997.75σ9(7d)0.880.81340.06667.56827.568292.43σ6(28d)2.612.6185−0.0085−0.32570.325799.67σ7(28d)2.252.2829−0.0329−1.46221.462298.54σ8(28d)1.481.4831−0.0031−0.20950.209599.79σ9(28d)1.461.4653−0.0053−0.36300.363099.64Figure 5
Curve of measured versus simulated values (regression/plot regression).Table 4
Synaptic weights of the neural network model.
Unit1234567γ144.1089−30.2057−41.407213.1931−60.01775.1839−18.3355γ21.48671.402715.5618−25.9155−9.3966−16.912422.0916γ342.9247−47.205955.4194−59.134731.357564.569339.1561Threshold−19.794817.7550−18.139929.73704.5404−4.3056−21.3888Table 5
Bias of the forecast network model.
Unit1234567Thresholdσ1−6.4804−9.74062.10482.76871.9601−0.0269−2.08244.3262σ2−4.6311−7.15814.25337.56724.83980.0407−2.42053.6850σ3−1.9478−3.10037.351513.71308.80680.1279−3.93053.1902Figure 6
Curve of model operation convergence (performance/plot form).After 133 learning and training steps, the constructed BP neural network obtained the thresholds and weights of the prediction parameters from the uniaxial compressive strength data for the filling body. The corresponding thresholds and weights were brought into the calculation model. Analytical equations (1)–(3) for the filling body strengths (σ1, σ2, and σ3) for curing times of 3 d, 7 d, and 28 d for datasets 6–9 were obtained. These analytical formulas can be used to convert the changes in the different cement, tailings, and water contents (γ1, γ2, and γ3) into the corresponding strength of the filling body. Similarly, when the strength of the filling body and the amounts of the two materials added are known, the content of the third material can be calculated using these equations. Therefore, these equations have a wide applicability and a strong practicability.(1)σ1=−6.4804ξ1−9.7406ξ2+2.1048ξ3+2.7687ξ4+1.9601ξ5−0.0269ξ6−2.0824ξ7+4.3262,(2)σ2=−4.6311ξ1−7.1581ξ2+4.2533ξ3+7.5672ξ4+4.8398ξ5+0.0407ξ6−2.4205ξ7+3.6850,(3)σ3=−1.9478ξ1−3.1003ξ2+7.3515ξ3+13.7130ξ4+8.8068ξ5+0.1279ξ6−3.9305ξ7+3.1902.In the above equations,(4)ξ1=21−exp−244.1089γ1+1.4867γ2+42.9247γ3−19.7948−1;ξ2=21−exp−2−30.2057γ1+1.4027γ2−47.2059γ3+17.7550−1;ξ3=21−exp−2−41.4072γ1+15.5618γ2+55.4194γ3−18.1399−1;ξ4=21−exp−213.1931γ1−25.9155γ2−59.1347γ3+29.7370−1;ξ5=21−exp−2−60.0177γ1−9.3966γ2+31.3575γ3+4.5404−1;ξ6=21−exp−25.1839γ1−16.9124γ2+64.5693γ3−4.3056−1;ξ7=21−exp−2−18.3355γ1+22.0916γ2+39.1561γ3−21.3888−1.


## 4.1. Modeling Principle of the BP Neural Network

In recent years, with the deepening of complex scientific research, the use of mathematical methods to solve problems has become more extensive. Since neural network algorithms are convenient and efficient, related investigations have also become more popular [31, 32]. The learning process of the BP neural network is a combination of the forward propagation of the input signal and the reverse propagation of the error. The test samples are passed from the input layer to the hidden layer and then to the output layer. When the output value of the output layer exceeds the preset accuracy range and the calculation step does not reach the set value, it enters the reverse propagation mode of the error. Through repeating calculations and comparisons, this process keeps training and learning until the error value meets the accuracy requirements. Once the learning is completed, the operation is stopped after delivering the output [33, 34]. In studying the physical and mechanical properties of civil engineering materials, some researchers have modeled and carried out related calculations and analyses based on the key factors affecting the performance of concrete materials. For example, in studies of the mechanical properties of concrete materials, the common factors include the cement content, ambient temperature and humidity conditions, concrete admixture content, and engineering requirements. Some nonquantitative factors can also be properly quantified. After the analysis, the topological structure of the neural network model can be established; the written Matlab code statements can be input into the interface for calculation, and the calculation results can be analyzed depending on the requirements [35–37].In this study, during the construction of the filling body strength prediction model, the various factors affecting the strength of the full tailings cemented filling body were analyzed. Based on the modeling principle, a neural network model was constructed. The model is composed of a structure of three layers of 3-Hn-3, in which the hidden layer Hn is 7. In this model, the cement contentγ1, tailings content γ2, and water content γ3 are defined as the three input variables. The output layers are the strengths of the filling body at 3 days, 7 days, and 28 days (i.e., σ1, σ2, and σ3, respectively). In the network learning, the input layer uses the traindx() function for the training operations, the hidden layer is passed using the tansig tangent function, and the output layer is passed using the purelin linear function. To obtain a faster running speed and better results, the Levenberg-Marquardt optimization algorithm (trainlm) of the nonlinear least-squares calculation mode was used for the learning and training [38, 39]. The learning rate (net.trainParam.lr), the training accuracy (GOAL), and the number of iterations were set to 0.0001, 0.001, and 2000 steps, respectively.


## 4.2. Calculations and Result Analysis

After completing the modeling, the learning and training were carried out using the Matlab7.6 platform. The system stopped computing when the number of training steps reached 133, and the required results were delivered. The accuracy and error were controlled within a reasonable range. From the comparison data for the test samples and the predicted values of the model shown in Table3, it can be seen that the fitting degree between the measured and fitted values of the strength at each curing time is 92.43–99.92%. The calculation error of the network model is very small, the absolute value of the average error is 0.0792–7.5682% (much lower than 8%), and the absolute deviation is basically 0.0008–0.0666 MPa, which meets the engineering requirements. The fitting curve of the measured and predicted values of the filling body’s strength (Figure 5) shows that the difference between the two sets of data is small, and the correlation coefficient of the model is R = 0.99912. The threshold and weight of the calculation model obtained after the training and learning are shown in Tables 4 and 5. The convergence curve of the calculations (when the training reached the optimal value) is shown in Figure 6. Figure 6 shows that the thick solid line represents the calculation process accelerated to approach the set target value of 10–3 at the beginning. When the 20th step of the calculation process was reached, the calculation area was stable, and the final step, which approached the target value, was 133.Table 3
Comparison of the measured and predicted values.
Test sampleCompressive strength of filling body (MPa)Error (%)Absolute error (%)Goodness of fit (%)Measured valuePredicted valueAbsolute deviationσ6(3d)1.011.0108−0.0008−0.07920.079299.92σ7(3d)0.950.90750.04254.47374.473795.53σ8(3d)0.630.6607−0.0307−4.87304.873095.13σ9(3d)0.610.6223−0.0123−2.01642.016497.98σ6(7d)1.511.49840.01160.76820.768299.23σ7(7d)1.351.31840.03162.34072.340797.66σ8(7d)0.810.8282−0.0182−2.24692.246997.75σ9(7d)0.880.81340.06667.56827.568292.43σ6(28d)2.612.6185−0.0085−0.32570.325799.67σ7(28d)2.252.2829−0.0329−1.46221.462298.54σ8(28d)1.481.4831−0.0031−0.20950.209599.79σ9(28d)1.461.4653−0.0053−0.36300.363099.64Figure 5
Curve of measured versus simulated values (regression/plot regression).Table 4
Synaptic weights of the neural network model.
Unit1234567γ144.1089−30.2057−41.407213.1931−60.01775.1839−18.3355γ21.48671.402715.5618−25.9155−9.3966−16.912422.0916γ342.9247−47.205955.4194−59.134731.357564.569339.1561Threshold−19.794817.7550−18.139929.73704.5404−4.3056−21.3888Table 5
Bias of the forecast network model.
Unit1234567Thresholdσ1−6.4804−9.74062.10482.76871.9601−0.0269−2.08244.3262σ2−4.6311−7.15814.25337.56724.83980.0407−2.42053.6850σ3−1.9478−3.10037.351513.71308.80680.1279−3.93053.1902Figure 6
Curve of model operation convergence (performance/plot form).After 133 learning and training steps, the constructed BP neural network obtained the thresholds and weights of the prediction parameters from the uniaxial compressive strength data for the filling body. The corresponding thresholds and weights were brought into the calculation model. Analytical equations (1)–(3) for the filling body strengths (σ1, σ2, and σ3) for curing times of 3 d, 7 d, and 28 d for datasets 6–9 were obtained. These analytical formulas can be used to convert the changes in the different cement, tailings, and water contents (γ1, γ2, and γ3) into the corresponding strength of the filling body. Similarly, when the strength of the filling body and the amounts of the two materials added are known, the content of the third material can be calculated using these equations. Therefore, these equations have a wide applicability and a strong practicability.(1)σ1=−6.4804ξ1−9.7406ξ2+2.1048ξ3+2.7687ξ4+1.9601ξ5−0.0269ξ6−2.0824ξ7+4.3262,(2)σ2=−4.6311ξ1−7.1581ξ2+4.2533ξ3+7.5672ξ4+4.8398ξ5+0.0407ξ6−2.4205ξ7+3.6850,(3)σ3=−1.9478ξ1−3.1003ξ2+7.3515ξ3+13.7130ξ4+8.8068ξ5+0.1279ξ6−3.9305ξ7+3.1902.In the above equations,(4)ξ1=21−exp−244.1089γ1+1.4867γ2+42.9247γ3−19.7948−1;ξ2=21−exp−2−30.2057γ1+1.4027γ2−47.2059γ3+17.7550−1;ξ3=21−exp−2−41.4072γ1+15.5618γ2+55.4194γ3−18.1399−1;ξ4=21−exp−213.1931γ1−25.9155γ2−59.1347γ3+29.7370−1;ξ5=21−exp−2−60.0177γ1−9.3966γ2+31.3575γ3+4.5404−1;ξ6=21−exp−25.1839γ1−16.9124γ2+64.5693γ3−4.3056−1;ξ7=21−exp−2−18.3355γ1+22.0916γ2+39.1561γ3−21.3888−1.


## 5. Discussion

(1)
In studies of the properties of various geotechnical engineering materials, the software programs commonly used for the statistical analysis and calculations are SPSS, Excel, Matlab, and SAS. When using these software programs to analyze the test data, it is necessary to design the topological structure according to the actual situation. Then, a reasonable method should be implemented to solve the problem. This process requires strong logic. The macroscopic properties of geotechnical engineering materials are usually a concrete manifestation of the effects of multiple factors. For example, the strength performance of red clay is often related to the soil properties (e.g., porosity, void ratio, bulk density, boundary moisture content, and chemical mineral composition). Thus, the strengths of the cemented filling bodies used in this study also needed to be studied in conjunction with the material properties.(2)
In this study, the filling bodies were composed of uniformly mixed full tailings, cement, and water, and the distribution of the particles was closely related to the water content. Due to the presence of water in the preparation of the filling slurry, the slurry produced had a certain solid material buoyancy, and the buoyancy varied with the density of the slurry. In the natural sedimentation of the materials with different water contents, the different buoyancies resulted in different sedimentation speeds. This led to differences in the porosities of the consolidated and hardened filling bodies. For filling materials with the same tailings-to-cement ratio, the strength was different due to the differences in the compactness of the filling bodies. The proposed BP neural network model for the filling body’s strength provides a reference for the quantitative analysis of the changes in the filling body’s strength.


## 6. Conclusions

(1)
In this study, the statistical calculation function of Matlab was used to develop a prediction model of backfill strength variation law. For the diversity and complexity of the composition of the filling materials, a BP neural network was used to establish the mapping relationship model between the filling body strength and cement, tailings, and water contents. During the training and learning process, the model was demonstrated to have a fast convergence and strong applicability. It can be used to analyze the changes in a filling body’s strength.(2)
After comparing multiple schemes of geotechnical engineering materials and analyzing the related influencing factors, the established neural network model’s structure was determined to be 3-Hn-3. Once the number of hidden layers was selected as 5–9, a trial calculation using code was performed. When Hn = 5, 6, 8, and 9, there were problems with the convergence effect. When Hn = 7, the calculation was the best and met the normal requirements. Therefore, the appropriate model structure identified in this study was 3-7-3.(3)
By combining the effects of the various factors on the filling body’s strength, we trained the established neural network model by setting the number of iterations of the learning rate to 2000 steps and the training accuracy to 0.001. A good training effect was achieved after 133 iterations. The predicted value fits well with the measured value, and the error was small. The correlation coefficient R reached 0.99912.



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*Source: 2566960-2022-04-29.xml*