# Intelligent Control of Smooth Blasting Quality in Rock Tunnels Using BP-ANN, ENN, and ANFIS

Authors: Baoping Zou; Jianxiu Wang; Zhanyou Luo; Lisheng Hu
Journal: Geofluids
 (2021)

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## Abstract

The construction quality of tunnel smooth blasting is difficult to control and fluctuates greatly. Moreover, the existing technology, which relies on the visual observation, empirical judgment, and artificial control, has difficulty meeting the requirements of tunnel smooth blasting construction quality control. This paper presents the construction principle of a tunnel smooth blasting quality control system, introduces a process quality control technology into quality control of tunnel smooth blasting construction, designs a framework for the tunnel smooth blasting quality control system, and collects control index data based on field investigation, expert consultation, and experimental research. By using the methods of index utilization rate statistics, gray correlation analysis, and principal component analysis, this paper primarily elects and selects the control indexes; establishes the tunnel smooth blasting quality control index system; constructs a comprehensive optimization control model of tunnel smooth blasting quality using back propagation artificial neural network (BP-ANN), Elman neural network (ENN), and adaptive neuro fuzzy inference systems (ANFIS); and studies the tunnel smooth blasting quality control system. The following are the conclusions of this study: (1) This paper presented a method of constructing a tunnel smooth blasting quality control index system and established this system with seven criteria layers, namely, geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, as well as a total of nine indexes. (2) The comprehensive optimization control model of BP-ANN, ANFIS, and ENN for tunnel smooth blasting quality was established. (3) The uniform design method was used to optimize the blasting parameters of the tunnel section, which needs to be controlled, and verify that the construction of these comprehensive optimization control models can change the focus of tunnel smooth blasting quality control from the traditional single index control method into a dynamic, intelligent, pluralistic, and integrated control technology.


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## Body

## 1. Introduction

Tunnel smooth blasting quality control is a general term in engineering practice in which the construction side of the employer, the construction side of the contractor, and other participating units identify, assess, and prevent all problems at all stages of the tunnel engineering blasting construction and control the whole process, work through the tunnel blasting construction through professional technology and construction management work, and obtain optimal economic benefits and safety guarantee with minimum engineering cost. The tunnel smooth blasting construction process is complex. After blasting, the unlined tunnel molding must be regular and has a smooth surface. The molded contour outside the rock is not subject to artillery disturbance and destruction. The contour inside the rock should be well broken, with high requirements for construction accuracy. However, given the many factors that influence the tunnel smooth blasting quality, the tunnel smooth blasting construction quality is difficult to control and fluctuates greatly. In ensuring the construction quality of tunnel smooth blasting control, the existing technology, which relies on the method of visual observation, empirical judgment, and artificial control, has difficulty meeting the requirements of tunnel smooth blasting construction quality control. To ensure the quality of tunnel smooth blasting construction, the focus of quality control should change from the traditional single index control method to a dynamic, intelligent, pluralistic, and integrated control technology.Many factors influence the quality of tunnel smooth blasting, which is difficult to control and fluctuates greatly. Determining how to control the quality of tunnel smooth blasting correctly and reasonably has attracted the attention of researchers at home and abroad, and many promising studies have been conducted on the subject. Research on tunnel smooth blasting quality control in China has obtained productive results, such as the Railway Tunnel Construction Specifications, the Railway Tunnel Construction Technical Guide, and the Highway Tunnel Construction Technical Specifications. All these guidelines provide a control index for tunnel smooth blasting. However, the proposed control index does not form a system, the actual smooth blasting control process is greatly influenced by human subjectivity, and the accuracy and reliability of the control is poor. Numerous domestic scholars have also conducted extensive research on the tunnel smooth blasting quality control, which mainly involves the repeated test and optimization of blasting parameters [1–12], neural network models [13, 14], mutation comprehensive evaluation theory [15], computer simulation [16, 17], information construction [18, 19], three-dimensional laser scanning [20], and other technologies, thereby proposing a reasonable control technology. However, no unified system exists for studying the tunnel smooth blasting control index, control criterion, and control method. Moreover, the scholars did not present a quantitative grading and classification, provided no control on the whole process of tunnel smooth blasting construction, and did not develop a dynamic, intelligent, pluralistic, and integrated tunnel smooth blasting quality control technology.Therefore, the following steps are necessary: process quality control technology needs to be introduced into tunnel smooth blasting construction quality control, a set of tunnel smooth blasting quality control index system should be established, a tunnel smooth blasting quality control model must be constructed, and the quality of tunnel smooth blasting should be ensured by focusing on controlling the quality of the tunnel smooth blasting construction process. Thus, in accordance with the evaluation level of tunnel smooth blasting quality, tunnel smooth blasting parameters are optimized and adjusted, with the postcontrol of smooth blasting quality being changed to precontrol, which is beneficial to the construction side of the employer, the construction side of the contractor, and other participating units in formulating the appropriate control range for the key links of tunnel smooth blasting construction and to monitor and effectively control it in real time.


## 2. Materials and Methods

### 2.1. Principle of the Model

#### 2.1.1. Back Propagation Artificial Neural Network (BP-ANN)

A back propagation artificial neural network (BP-ANN), one of the most popular neural network algorithms, processes information by imitating the structure and function of the human central nervous system [21]. The structure of a BP-ANN is shown in Figure 1.Figure 1
The structure of the BP-ANN.Each node in the network is a neuron whose function is to calculate the inner product of the input vector and weight vector by a nonlinear transfer function to get a scalar result. This particular network is a three-layer network: the input layer, the hidden layer, and the output layer. The mathematical model [21, 22] of the three-layer BP-ANN is expressed as the output of the hidden layer neurons for:
(1)Hj=f∑i=1nwijxi−ajj=1,2,⋯l,where Hj and xi are the output values of the hidden layer and input value of the network, respectively. n and l are the numbers of input and hidden layer neurons. Respectively, i, k, and wij are the input neurons, hidden neurons, and weighting of inputs to the hidden layer neuron. aj denotes the threshold of the hidden layer neurons. f is the activation function of a node.The output of the output layer neurons is expressed as:(2)yj=f∑k=1lwkjHk−bjj=1,2,⋯m,where yj and Hk are the actual output values of the output layer and the output values of the hidden layer, respectively. l and m are the numbers of hidden and output layer neurons. Respectively, k, j, and wkj represent the hidden neurons, output neurons, and the weighting of the hidden neurons to the output layer neurons. bj denotes the threshold of the output layer neurons.Minimize the global errorE via the training algorithm is expressed as:
(3)E=12∑yj−Rt2,where Rt is the real output of training data.


#### 2.1.2. Elman Neural Network (ENN)

Elman neural network (ENN) is a local-feedback recursive neural network, which belongs to a nonlinear state space model. The ENN includes 4 main layers: the input layer, the context layer, the hidden layer, and the output layer. The function of the connecting layer is to receive the output of the hidden layer and transmit the information corresponding to the previous time to the hidden layer in the form of feedback to establish a local ring structure. As the connecting layer unit has a delayed memory effect on the characteristics contained in historical data, the output value of the neural network is more in line with the actual development trend of data [23, 24]. The ENN structure is shown in Figure 2.Figure 2
The structure of the ENN.State space equation of ENN [23] is shown in Eqs. (4)–(6):
(4)xk=fw1xck+w2uk−1+b1,(5)yk=gw3xk+b2,(6)xck=xk−1,where xk and xck represent output vectors of hidden layer and connecting layer at time k, respectively, uk−1 is input layer vector at time k−1, and yk is output vector at time k. w1 denotes the weight vectors θ between hidden layer and hidden layer, w2 denotes the weight vectors between input layer and hidden layer, and w3 denotes the weights matrix between hidden layer and output layer. b1 and b2 are threshold vectors φ of hidden layer and output layer, respectively. f· and g· represent the transfer function of neurons in hidden layer and output layer, respectively.The weights of ENN are adjusted by minimizing the RMSE (root mean square error), which is estimated by Eq. (7):
(7)RMSE=1M−1∑n=1Myk−yek2,where yek denotes the expected value at time k and M is total time.


#### 2.1.3. Adaptive Neuro Fuzzy Inference Systems (ANFIS)

The adaptive neuro fuzzy inference system (ANFIS) is a fuzzy Sugeno model entered in the framework of adaptive systems to facilitate learning and adaptation. To present the ANFIS architecture [25, 26], two fuzzy if-then rules based on a first-order Sugeno model are considered:
(8)Rule1:ifxisA1andyisB1,thenf1=p1x+q1y+r1,(9)Rule2:ifxisA2andyisB2,thenf2=p2x+q2y+r2,where x and y are the inputs, Ai and Bi are the fuzzy sets, fi is the outputs within the fuzzy region specified by the fuzzy rule, and pi, qi, and ri are the design parameters that are determined during the training process. Figure 3 shows the corresponding equivalent ANFIS architecture. The five layers comprising the ANFIS structure are briefly described as follows:Figure 3
The structure of the ANFIS.Layer 1: every node i in this layer is an adaptive node, whose output is defined as follows:
(10)oi1=μAix,fori=1,2or,oi1=μBi−2y,fori=3,4,where x or y is the input to the ith node and Ai or Bi−2 is a fuzzy label.Layer 2: in the second layer, the nodes are fixed nodes, labeled M, indicating that they perform as a simple multiplier. For example,
(11)oi2=wi=μAixμBiy,i=1,2.Layer 3: every node in this layer is a fixed node labeled N. The ith node calculates the ratio of the rule’s firing strength to the sum of all rules’ firing strengths:
(12)oi3=w¯i=wiw1+w2,i=1,2.Layer 4: every node i in this layer is an adaptive node with a node function as
(13)oi4=w¯ifi=w¯ipix+qiy+ri,i=1,2,where w¯i is a normalized firing strength from layer 3 and pi,qi,ri is the parameter set of this node.Layer 5: as the last layer, layer 5 includes a stable and single node, labeled ∑, which sums all the signals to calculate the total output:
(14)oi5=∑w¯ifi=∑iwifi∑iwi.


### 2.2. Methodological Framework

#### 2.2.1. Construction Principle and Frame Structure Design

The selection of tunnel smooth blasting quality control index should follow the principles of comprehensiveness and representativeness, innovation and science, systematicness and hierarchy, maneuverability, dynamics, and scientific quantification. On the basis of these control principles and taking the Pressure-State-Response (PSR) concept model [27–29] proposed by the United Nations Economic Cooperation and Development Agency as a reference, this paper establishes the PSR concept model of a quality control index system of tunnel smooth blasting construction (see Figure 4) based on the actual situation of the tunnel smooth blasting construction process. The PSR model separates the indicators into three groups of categories: (1) the “pressure” indicator has an impact factor that reflects the human activities and leads to unreasonable blasting quality of the rock tunnel; (2) the “state” indicator, which illustrates the quality state and control process of smooth blasting; and (3) the “response” indicator, which measures its smooth blasting quality evaluation service. Thus, it can clearly reflect the relationship between the relevant factors of tunnel smooth blasting quality, thereby enabling decision-makers to address the primary and secondary relations in the complex smooth blasting quality control index and then compare and judge one by one, optimize the best control index, feed the control results back to the control system, reverse the performance of the optimal tunnel smooth blasting quality control index, and obtain the optimal index quality control range to ensure the integrity and effectiveness of the final control index system.Figure 4
PSR concept model of a quality control index system.


#### 2.2.2. Construction Method

The main process of establishing the quality control index system for tunnel smooth blasting is shown in Figure5. The primary theoretical methods used in the construction of the control index system are gray correlation [30] and principal component analyses [31].Figure 5
Construction process of quality control index system for tunnel smooth blasting.To perform the gray correlation analysis, the reference sequence can be defined asx0=x01,x02,⋯,x0m while the comparative sequence can be xi=xi1,xi2,⋯,xim, and i=1,2,⋯,n. The reference sequence denoted as x0′ can be expressed as Eq. (15) while the comparative sequence indicated as xi′ can be described as Eq. (16).
(15)x0′=x0′1,x0′2,⋯,x0′m=x01∑j=1mx0j/m,x02∑j=1mx0j/m,⋯,x0m∑j=1nx0j/m,(16)xi′=xi′1,xi′2,⋯,xi′m=xi1∑j=1mxij/m,xi2∑j=1mxij/m,⋯,xim∑j=1mxij/m.The correlation coefficient is defined as:(17)η0ij=∆min+w∆maxxoj−xij+w∆max,in which w is the resolution coefficient, ∆min is the minimum difference between the two sequences, and ∆max is the maximum difference between the two sequences.The principal component analyses model is:(18)X=TET+F,in which X is the input matrix m×e which represents original parameters, T is the score matrix m×k which represents the relationship between original parameters, E is the loading matrix e×j which represents the contribution of original parameters, and F is the residual matrix m×e which represents the uncaptured variance. m is the number of time steps, e is the number of original parameters, and j is the number of principal components.


### 2.3. Control Index Data Collection

Field investigation, expert consultation, experimental research, existing engineering case data collection, and other methods were used to collect the control index data.


#### 2.3.1. On-Site Investigation and Expert Consultation

In accordance with the influencing factors of tunnel smooth blasting quality control, field investigation and expert consultation method are conducted with seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors and a total of 43 influencing factors to evaluate the importance level of qualitative and quantitative indexes, which are divided into five levels: 1 represents very important (5 points), 2 represents more important (4 points), 3 represents generally important (3 points), 4 represents less important (2 points), and 5 represents very unimportant (1 point). The statistical results of field investigation and expert consultation show that the adoption rate of the indicators below level-1 subsection-5 is less than 60%. In accordance with the maneuverability, science, and effectiveness of tunnel smooth blasting quality control, this paper lists only the (very important) adoption rate that impacts the tunnel smooth blasting quality at level-1 subsection-5 because of space limitations; see Figures6–12.Figure 6
Geological conditions.Figure 7
Explosive properties.Figure 8
Borehole parameters.Figure 9
Charge parameters.Figure 10
Method of initiation.Figure 11
Tunnel parameters.Figure 12
Construction factors.Figure6 shows that the index adoption rate of rock category is 86%, the index adoption rate of joint fracture is 64%, the index adoption rate of groundwater is 64%, and the adoption rate of other indexes is less than 60%.Figure7 shows that the index adoption rate of explosive components is 64%, the index adoption rate of blasting force is 64%, the index adoption rate of blasting speed is 64%, and the adoption rate of other indexes is less than 60%.Figure8 shows that the index adoption rate of borehole depth is 71%, the index adoption rate of neighboring eyes spacing is 64%, the index adoption rate of minimum resistance line is 79%, the index adoption rate of neighboring eyes dense factor is 64%, and the adoption rate of other indexes is less than 60%.Figure9 shows that the index adoption rate of linear charge density is 64%, the index adoption rate of noncoupling coefficient is 60%, the index adoption rate of plugging quality is 71%, and the adoption rate of other indexes is less than 60%.Figure10 shows that the index adoption rate of sequence of initiation is 93%, the index adoption rate of time difference of initiation is 64%, the index adoption rate of method of initiation is 71%, and the adoption rate of other indexes is less than 60%.Figure11 shows that the index adoption rate of the excavation method is 71%, the index adoption rate of blasting method is 64%, the index adoption rate of excavation section is 64%, and the adoption rate of other indexes is less than 60%.Figure12 shows that the index adoption rate of drilling accuracy is 67%, the index adoption rate of measuring and setting out (including midline or elevation deviation) is 64%, the index adoption rate of on-site management system is 71%, and the adoption rate of other indexes is less than 60%.


#### 2.3.2. Experimental Research

The experimental study is mainly based on the Chengdu–Chongqing high-speed rail Da’an Tunnel [32]. Total length of the tunnel is about 5050 m, while the excavated radius and height are 7.45 m and 11.08 m, respectively. The lithology exposed on both sides of the syncline includes mudstone and sandstone with age of Jurassic (J). Overlying formations consist of soft silty clay with ages of Holocene series in Quaternary system (Q4d1+p1), soft-flowing plastic silty clay, silty clay, slope residual (Q4d1+e1) silty clay, and colluvial deposits (Q4d1+co1). Moreover, the underlying formations are Shaxi group of middle Jurassic (J), including sandstone, mudstone, sandstone, and argillaceous sandstone. Field and numerical tests were conducted to collect quantitative data, and the main indicators collected in the field test include eight indicators: rock category, neighboring eyes spacing, borehole depth, number of boreholes, charge quantity, minimum resistance line, maximum infrared temperature, and minimum infrared temperature. Field data acquisition test is shown in Figure 13. The numerical test collected seven main indexes [32]: neighboring eyes spacing, minimum resistance line, relative distance, linear charge density, rock category, blasting speed, and measuring and setting out.Figure 13
Field data acquisition tests.


#### 2.3.3. Collection of Existing Engineering Case Data

The existing engineering case data collection is mainly aimed at collecting the control indexes used in blasting construction of all kinds of tunnels and underground engineering reported in the existing literature to obtain the most sample data and provide more information for tunnel smooth blasting quality control. Seventy-seven tunnel and underground engineering cases were collected, and the collected control indexes mainly include 23 indexes, such as rock category, borehole depth, and neighboring eyes spacing, as shown in Table1.Table 1
Collection of existing engineering case data.
No.IndexNo.IndexNo.Index1Rock category9Minimum resistance line17Excavation method2Joint fracture10Relative distance18Blasting method3Groundwater11Linear charge density19Buried depth of tunnel4Explosive components12Noncoupling coefficient20Excavation section5Blasting force13Plugging quality21Drilling accuracy6Blasting speed14Sequence of initiation22Measuring and setting out7Borehole depth15Time difference of initiation23On-site management system8Neighboring eyes spacing16Method of initiation


### 2.4. Establishment of Quality Control Index System

#### 2.4.1. Primary Election of Quality Control Index System

On the basis of the factors that influence the quality of tunnel smooth blasting, this paper analyzes the index adoption rate of the control indexes involved in a domestic tunnel and underground project from three aspects, namely, domestic project case statistics, standard statistics, and foreign project case statistics. A total of 210 cases and 43 indicators were counted in domestic project cases, as shown in Figures14–20.Figure 14
Geological conditions.Figure 15
Explosive properties.Figure 16
Borehole parameters.Figure 17
Charge parameters.Figure 18
Method of initiation.Figure 19
Tunnel parameters.Figure 20
Construction factors.To ensure the validity, feasibility, and scientificity of the control index while analyzing the above figures, only the index with the indicatoradoptionrate≥60% is analyzed. Therefore, for geological conditions, the index adoption rate of rock category is 89%; for the borehole blasting design, the index adoption rate of neighboring eyes spacing is 92.4%, the index adoption rate of minimum resistance line is 86.2%, the index adoption rate of relative distance is 66.2%, and the adoption rate of linear charge density is 77.1%. The adoption rates of construction factors, drilling accuracy, measuring and setting out, personnel quality, on-site management system, and other indicators are low.The statistics on the adoption rate of control indicators in various current regulations in China mainly include nine specifications, such as Technical Specifications for Construction of Highway Tunnel (JTG/T 3660-2020), Code for construction and acceptance of metro engineering (2012 version) (GB 50299-1999), and Code for construction on tunnel of railway (TB 10204-2002), as shown in Figure21. The figure shows that, in the current specification, the index adoption rate of charge noncoupling coefficient is 44%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of minimum resistance line is 100%, the index adoption rate of relative distance is 67%, the adoption rate of linear charge density is 100%, the adoption rate of rock category is 100%, and the adoption rate of borehole depth is 11%.Figure 21
Statistics on the adoption rate of quality control index of tunnel blasting in current specification.The quality control index of tunnel smooth blasting used in foreign engineering cases is analyzed statistically [5, 6, 33–48], as shown in Figure 22. The figure shows that the index adoption rate of charge noncoupling coefficient is 10%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of neighboring eyes minimum resistance line is 100%, the index adoption rate of relative distance is 30%, the adoption rate of linear charge density is 100%, the adoption rate of borehole depth is 40%, the adoption rate of rock category is 100%, and the adoption rate of measuring and setting out is 30%.Figure 22
Foreign engineering case statistics.Therefore, combined with the domestic engineering case statistics, standard statistics, foreign engineering case statistics, and tunnel smooth blasting quality control index data collection, from the seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, the tunnel smooth blasting quality control index system was primarily established, with a total of 22 indicators, as seen in Table2.Table 2
Primary election of quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layerQuality control index system for tunnel smooth blastingGeological conditionsRock categoryJoint fractureGroundwaterExplosive propertiesExplosive componentsBlasting forceBlasting speedBorehole parametersBorehole depthNeighboring eyes spacingMinimum resistance lineRelative distanceCharge parametersLinear charge densityNoncoupling coefficientPlugging qualityMethod of initiationSequence of initiationTime difference of initiationMethod of initiationTunnel parametersExcavation methodBlasting methodExcavation sectionConstruction factorsDrilling accuracyMeasuring and setting outOn-site management system


#### 2.4.2. Selection of Quality Control Index System

In accordance with the principle of constructing the quality control index system of tunnel smooth blasting, the control index needs to be screened and modified, and the modified method mainly adopts gray correlation [30] and principal component analyses [31].(1) Geological conditions. X1–X3 represent the rock category, joint fracture, and groundwater, respectively. The correlation degree of geological condition index calculated by gray correlation analysis is shown in Table 3Table 3
Correlation degree of geological condition index.
Control indexCorrelation degreeRock category0.6493Joint fracture0.6423Groundwater0.5008The above analysis indicates that in each control index, the rock category has the highest correlation degree, followed by the joint fracture and the groundwater.The normalized eigenvectors of geological condition indexes calculated by principal component analysis are shown in Table4, and the eigenvalues are shown in Table 5.Table 4
Normalized eigenvectors of geological condition index.
Control indexControl index 1Control index 2Control index 3X10.64620.25770.7183X20.63350.3438-0.6932X3-0.42560.9030.0589Table 5
Eigenvalues of geological condition index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.14571.5071.5020.749524.9896.4830.10553.51100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 96.48% of the total amount of information, and the first principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of geological conditions is the rock category.(2) Explosive properties. X1–X3 represent the explosive components, blasting force, and blasting speed, respectively. The correlation degree of the explosive property index calculated by gray correlation analysis is shown in Table 6Table 6
Correlation degree of the explosive property index.
Control indexCorrelation degreeExplosive components0.487Blasting force0.544Blasting speed0.544The above analysis shows that the most significant influencing factors of correlation degree are blasting force and blasting speed.The normalized eigenvectors of explosive property indexes calculated by principal component analysis are shown in Table7, and the eigenvalues are shown in Table 8.Table 7
Normalized eigenvectors of explosive property index.
Control indexControl index 1Control index 2Control index 3X1-0.57520.59050.5661X20.53420.7952-0.2868X30.6195-0.13740.7729Table 8
Eigenvalues of explosive property index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.318977.2977.2920.51317.1094.3930.1685.60100The above analysis shows that the amount of information contained in the first main component is 77.29% of the total amount of information, and the first principal component represents X3. Combined with the gray correlation and principal component analyses, findings indicate that the optimal characteristic index of explosive properties is the blasting speed.(3) Borehole parameters. X1–X4 represent the borehole depth, neighboring eyes spacing, minimum resistance line, and relative distance, respectively. The correlation degree of the borehole parameter index calculated by gray correlation analysis is shown in Table 9Table 9
Correlation degree of the borehole parameter index.
Control indexCorrelation degreeBorehole depth0.5787Neighboring eyes spacing0.6063Minimum resistance line0.6655Relative distance0.6473The above analysis shows that the most significant influencing factor of correlation degree is the minimum resistance line.The normalized eigenvectors of borehole parameter indexes calculated by principal component analysis are shown in Table10, and the eigenvalues are shown in Table 11.Table 10
Normalized eigenvectors of borehole parameter index.
Control indexControl index 1Control index 2Control index 3Control index 4X10.4328-0.28730.8544-0.0101X20.65360.1733-0.2809-0.6811X30.5135-0.5147-0.42690.5377X40.3490.78890.09440.4968Table 11
Eigenvalues of borehole parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.117652.9452.9421.177629.4382.3730.693217.3399.7140.01160.28100Combined with the above analyses, findings indicate that the amount of information contained in the first two main components is 82.37% of the total amount of information, the first principal component represents X2, and the second principal component represents X4.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic indicators of borehole parameters are the rock category, minimum resistance line, and relative distance.(4) Charge parameters. X1–X3 represent the linear charge density, noncoupling coefficient, and plugging quality, respectively. The correlation degree of charge parameter index calculated by gray correlation analysis is shown in Table 12Table 12
Correlation degree of the charge parameter index.
Control indexCorrelation degreeLinear charge density0.6502Noncoupling coefficient0.6109Plugging quality0.6383The above analysis shows that the first influencing factor of correlation degree is linear charge density, the second influencing factor is plugging quality, and the third is noncoupling coefficient.The normalized eigenvectors of charge parameter indexes calculated by principal component analysis are shown in Table13, and the eigenvalues are shown in Table 14.Table 13
Normalized eigenvectors of charge parameter index.
Control indexControl index 1Control index 2Control index 3X10.20760.90610.3687X20.6577-0.40830.6331X3-0.7241-0.11110.6806Table 14
Eigenvalues of charge parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.26542.1642.1621.035934.5376.6930.699123.30100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 76.69% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of charge parameters is the linear charge density.(5) Method of initiation. X1–X3 represent the sequence of initiation, time difference of initiation, and method of initiation, respectively. The correlation degree of the method of initiation index calculated by gray correlation analysis is shown in Table 15.Table 15
Correlation degree of the method of initiation index.
Control indexCorrelation degreeSequence of initiation0.7904Time difference of initiation0.7885Method of initiation0.6664The above analysis shows that the first influencing factor of correlation degree is the sequence of initiation, the second is the time difference of initiation, and the third is the method of initiation.The normalized eigenvectors of the method of initiation index calculated by principal component analysis are shown in Table16, and the eigenvalues are shown in Table 17.Table 16
Normalized eigenvectors of method of initiation index.
Control indexControl index 1Control index 2Control index 3X10.69890.06080.7126X20.67320.2805-0.6842X3-0.24150.95790.1551Table 17
Eigenvalues of method of initiation index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.355545.1845.1820.986432.8778.0630.658121.93100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 78.06% of the total amount of information, the first principal component represents X1, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of the method of initiation is the sequence of initiation.(6) Tunnel parameters. X1–X3 represent the excavation method, blasting method, and excavation section, respectively. The correlation degree of tunnel parameter index calculated by gray correlation analysis is shown in Table 18.Table 18
Correlation degree of the tunnel parameter index.
Control indexCorrelation degreeExcavation method0.6639Blasting method0.5711Excavation section0.6261The above analysis shows that the first influencing factor of correlation degree is the excavation method, the second is the blasting method, and the third is the excavation section.The normalized eigenvectors of the tunnel parameter indexes calculated by principal component analysis are shown in Table19, and the eigenvalues are shown in Table 20.Table 19
Normalized eigenvectors of tunnel parameter index.
Control indexControl index 1Control index 2Control index 3X10.52010.7564-0.3967X2-0.55590.65240.5151X30.6484-0.04740.7598Table 20
Eigenvalues of tunnel parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.892963.0963.0920.756525.2188.3130.350611.68100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 88.31% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of tunnel parameters is the excavation method.(7) Construction factors. X1–X3 represent the drilling accuracy, measuring and setting out, and on-site management system, respectively. The correlation degree of the construction factor index calculated by gray correlation analysis is shown in Table 21.Table 21
Correlation degree of the construction factor index.
Control indexCorrelation degreeDrilling accuracy0.5910Measuring and setting out0.6499On-site management system0.6012The above analysis shows that the first influencing factor of correlation degree is the measuring and setting out, the second is on-site management system, and the third is drilling accuracy.The normalized eigenvectors of construction factor indexes calculated by principal component analysis are shown in Table22, and the eigenvalues are shown in Table 23.Table 22
Normalized eigenvectors of construction factor index.
Control indexControl index 1Control index 2Control index 3X10.5837-0.53050.6147X20.6117-0.2105-0.7625X30.53390.82110.2017Table 23
Eigenvalues of construction factor index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.654855.1555.1520.747424.9180.0730.597819.92100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 80.07% of the total amount of information, the first principal component represents X2, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of construction factor is the measuring and setting out.


#### 2.4.3. Establishment of Quality Control Index System

In accordance with the primary selection and screening of the control index, abandoning the noncompliant index, the retaining control index is established according to the designed frame structure of the control system, and the tunnel smooth blasting quality control index system, which includes the seven criteria layers of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, and a total of nine indexes, is established, as shown in Table24.Table 24
Establishment of the quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layer (unit)Quality control index system for tunnel smooth blastingAGeological conditionsB1Rock categoryC11Explosive propertiesB2Blasting speedC21 (m/s)Borehole parametersB3Neighboring eyes spacingC31 (mm)Minimum resistance lineC32 (m)Relative distanceC33Charge parametersB4Linear charge densityC41 (kg/m)Method of initiationB5Sequence of initiationC51Tunnel parametersB6Excavation methodC61Construction factorsB7Measuring and setting outC71


## 2.1. Principle of the Model

### 2.1.1. Back Propagation Artificial Neural Network (BP-ANN)

A back propagation artificial neural network (BP-ANN), one of the most popular neural network algorithms, processes information by imitating the structure and function of the human central nervous system [21]. The structure of a BP-ANN is shown in Figure 1.Figure 1
The structure of the BP-ANN.Each node in the network is a neuron whose function is to calculate the inner product of the input vector and weight vector by a nonlinear transfer function to get a scalar result. This particular network is a three-layer network: the input layer, the hidden layer, and the output layer. The mathematical model [21, 22] of the three-layer BP-ANN is expressed as the output of the hidden layer neurons for:
(1)Hj=f∑i=1nwijxi−ajj=1,2,⋯l,where Hj and xi are the output values of the hidden layer and input value of the network, respectively. n and l are the numbers of input and hidden layer neurons. Respectively, i, k, and wij are the input neurons, hidden neurons, and weighting of inputs to the hidden layer neuron. aj denotes the threshold of the hidden layer neurons. f is the activation function of a node.The output of the output layer neurons is expressed as:(2)yj=f∑k=1lwkjHk−bjj=1,2,⋯m,where yj and Hk are the actual output values of the output layer and the output values of the hidden layer, respectively. l and m are the numbers of hidden and output layer neurons. Respectively, k, j, and wkj represent the hidden neurons, output neurons, and the weighting of the hidden neurons to the output layer neurons. bj denotes the threshold of the output layer neurons.Minimize the global errorE via the training algorithm is expressed as:
(3)E=12∑yj−Rt2,where Rt is the real output of training data.


### 2.1.2. Elman Neural Network (ENN)

Elman neural network (ENN) is a local-feedback recursive neural network, which belongs to a nonlinear state space model. The ENN includes 4 main layers: the input layer, the context layer, the hidden layer, and the output layer. The function of the connecting layer is to receive the output of the hidden layer and transmit the information corresponding to the previous time to the hidden layer in the form of feedback to establish a local ring structure. As the connecting layer unit has a delayed memory effect on the characteristics contained in historical data, the output value of the neural network is more in line with the actual development trend of data [23, 24]. The ENN structure is shown in Figure 2.Figure 2
The structure of the ENN.State space equation of ENN [23] is shown in Eqs. (4)–(6):
(4)xk=fw1xck+w2uk−1+b1,(5)yk=gw3xk+b2,(6)xck=xk−1,where xk and xck represent output vectors of hidden layer and connecting layer at time k, respectively, uk−1 is input layer vector at time k−1, and yk is output vector at time k. w1 denotes the weight vectors θ between hidden layer and hidden layer, w2 denotes the weight vectors between input layer and hidden layer, and w3 denotes the weights matrix between hidden layer and output layer. b1 and b2 are threshold vectors φ of hidden layer and output layer, respectively. f· and g· represent the transfer function of neurons in hidden layer and output layer, respectively.The weights of ENN are adjusted by minimizing the RMSE (root mean square error), which is estimated by Eq. (7):
(7)RMSE=1M−1∑n=1Myk−yek2,where yek denotes the expected value at time k and M is total time.


### 2.1.3. Adaptive Neuro Fuzzy Inference Systems (ANFIS)

The adaptive neuro fuzzy inference system (ANFIS) is a fuzzy Sugeno model entered in the framework of adaptive systems to facilitate learning and adaptation. To present the ANFIS architecture [25, 26], two fuzzy if-then rules based on a first-order Sugeno model are considered:
(8)Rule1:ifxisA1andyisB1,thenf1=p1x+q1y+r1,(9)Rule2:ifxisA2andyisB2,thenf2=p2x+q2y+r2,where x and y are the inputs, Ai and Bi are the fuzzy sets, fi is the outputs within the fuzzy region specified by the fuzzy rule, and pi, qi, and ri are the design parameters that are determined during the training process. Figure 3 shows the corresponding equivalent ANFIS architecture. The five layers comprising the ANFIS structure are briefly described as follows:Figure 3
The structure of the ANFIS.Layer 1: every node i in this layer is an adaptive node, whose output is defined as follows:
(10)oi1=μAix,fori=1,2or,oi1=μBi−2y,fori=3,4,where x or y is the input to the ith node and Ai or Bi−2 is a fuzzy label.Layer 2: in the second layer, the nodes are fixed nodes, labeled M, indicating that they perform as a simple multiplier. For example,
(11)oi2=wi=μAixμBiy,i=1,2.Layer 3: every node in this layer is a fixed node labeled N. The ith node calculates the ratio of the rule’s firing strength to the sum of all rules’ firing strengths:
(12)oi3=w¯i=wiw1+w2,i=1,2.Layer 4: every node i in this layer is an adaptive node with a node function as
(13)oi4=w¯ifi=w¯ipix+qiy+ri,i=1,2,where w¯i is a normalized firing strength from layer 3 and pi,qi,ri is the parameter set of this node.Layer 5: as the last layer, layer 5 includes a stable and single node, labeled ∑, which sums all the signals to calculate the total output:
(14)oi5=∑w¯ifi=∑iwifi∑iwi.


## 2.1.1. Back Propagation Artificial Neural Network (BP-ANN)

A back propagation artificial neural network (BP-ANN), one of the most popular neural network algorithms, processes information by imitating the structure and function of the human central nervous system [21]. The structure of a BP-ANN is shown in Figure 1.Figure 1
The structure of the BP-ANN.Each node in the network is a neuron whose function is to calculate the inner product of the input vector and weight vector by a nonlinear transfer function to get a scalar result. This particular network is a three-layer network: the input layer, the hidden layer, and the output layer. The mathematical model [21, 22] of the three-layer BP-ANN is expressed as the output of the hidden layer neurons for:
(1)Hj=f∑i=1nwijxi−ajj=1,2,⋯l,where Hj and xi are the output values of the hidden layer and input value of the network, respectively. n and l are the numbers of input and hidden layer neurons. Respectively, i, k, and wij are the input neurons, hidden neurons, and weighting of inputs to the hidden layer neuron. aj denotes the threshold of the hidden layer neurons. f is the activation function of a node.The output of the output layer neurons is expressed as:(2)yj=f∑k=1lwkjHk−bjj=1,2,⋯m,where yj and Hk are the actual output values of the output layer and the output values of the hidden layer, respectively. l and m are the numbers of hidden and output layer neurons. Respectively, k, j, and wkj represent the hidden neurons, output neurons, and the weighting of the hidden neurons to the output layer neurons. bj denotes the threshold of the output layer neurons.Minimize the global errorE via the training algorithm is expressed as:
(3)E=12∑yj−Rt2,where Rt is the real output of training data.


## 2.1.2. Elman Neural Network (ENN)

Elman neural network (ENN) is a local-feedback recursive neural network, which belongs to a nonlinear state space model. The ENN includes 4 main layers: the input layer, the context layer, the hidden layer, and the output layer. The function of the connecting layer is to receive the output of the hidden layer and transmit the information corresponding to the previous time to the hidden layer in the form of feedback to establish a local ring structure. As the connecting layer unit has a delayed memory effect on the characteristics contained in historical data, the output value of the neural network is more in line with the actual development trend of data [23, 24]. The ENN structure is shown in Figure 2.Figure 2
The structure of the ENN.State space equation of ENN [23] is shown in Eqs. (4)–(6):
(4)xk=fw1xck+w2uk−1+b1,(5)yk=gw3xk+b2,(6)xck=xk−1,where xk and xck represent output vectors of hidden layer and connecting layer at time k, respectively, uk−1 is input layer vector at time k−1, and yk is output vector at time k. w1 denotes the weight vectors θ between hidden layer and hidden layer, w2 denotes the weight vectors between input layer and hidden layer, and w3 denotes the weights matrix between hidden layer and output layer. b1 and b2 are threshold vectors φ of hidden layer and output layer, respectively. f· and g· represent the transfer function of neurons in hidden layer and output layer, respectively.The weights of ENN are adjusted by minimizing the RMSE (root mean square error), which is estimated by Eq. (7):
(7)RMSE=1M−1∑n=1Myk−yek2,where yek denotes the expected value at time k and M is total time.


## 2.1.3. Adaptive Neuro Fuzzy Inference Systems (ANFIS)

The adaptive neuro fuzzy inference system (ANFIS) is a fuzzy Sugeno model entered in the framework of adaptive systems to facilitate learning and adaptation. To present the ANFIS architecture [25, 26], two fuzzy if-then rules based on a first-order Sugeno model are considered:
(8)Rule1:ifxisA1andyisB1,thenf1=p1x+q1y+r1,(9)Rule2:ifxisA2andyisB2,thenf2=p2x+q2y+r2,where x and y are the inputs, Ai and Bi are the fuzzy sets, fi is the outputs within the fuzzy region specified by the fuzzy rule, and pi, qi, and ri are the design parameters that are determined during the training process. Figure 3 shows the corresponding equivalent ANFIS architecture. The five layers comprising the ANFIS structure are briefly described as follows:Figure 3
The structure of the ANFIS.Layer 1: every node i in this layer is an adaptive node, whose output is defined as follows:
(10)oi1=μAix,fori=1,2or,oi1=μBi−2y,fori=3,4,where x or y is the input to the ith node and Ai or Bi−2 is a fuzzy label.Layer 2: in the second layer, the nodes are fixed nodes, labeled M, indicating that they perform as a simple multiplier. For example,
(11)oi2=wi=μAixμBiy,i=1,2.Layer 3: every node in this layer is a fixed node labeled N. The ith node calculates the ratio of the rule’s firing strength to the sum of all rules’ firing strengths:
(12)oi3=w¯i=wiw1+w2,i=1,2.Layer 4: every node i in this layer is an adaptive node with a node function as
(13)oi4=w¯ifi=w¯ipix+qiy+ri,i=1,2,where w¯i is a normalized firing strength from layer 3 and pi,qi,ri is the parameter set of this node.Layer 5: as the last layer, layer 5 includes a stable and single node, labeled ∑, which sums all the signals to calculate the total output:
(14)oi5=∑w¯ifi=∑iwifi∑iwi.


## 2.2. Methodological Framework

### 2.2.1. Construction Principle and Frame Structure Design

The selection of tunnel smooth blasting quality control index should follow the principles of comprehensiveness and representativeness, innovation and science, systematicness and hierarchy, maneuverability, dynamics, and scientific quantification. On the basis of these control principles and taking the Pressure-State-Response (PSR) concept model [27–29] proposed by the United Nations Economic Cooperation and Development Agency as a reference, this paper establishes the PSR concept model of a quality control index system of tunnel smooth blasting construction (see Figure 4) based on the actual situation of the tunnel smooth blasting construction process. The PSR model separates the indicators into three groups of categories: (1) the “pressure” indicator has an impact factor that reflects the human activities and leads to unreasonable blasting quality of the rock tunnel; (2) the “state” indicator, which illustrates the quality state and control process of smooth blasting; and (3) the “response” indicator, which measures its smooth blasting quality evaluation service. Thus, it can clearly reflect the relationship between the relevant factors of tunnel smooth blasting quality, thereby enabling decision-makers to address the primary and secondary relations in the complex smooth blasting quality control index and then compare and judge one by one, optimize the best control index, feed the control results back to the control system, reverse the performance of the optimal tunnel smooth blasting quality control index, and obtain the optimal index quality control range to ensure the integrity and effectiveness of the final control index system.Figure 4
PSR concept model of a quality control index system.


### 2.2.2. Construction Method

The main process of establishing the quality control index system for tunnel smooth blasting is shown in Figure5. The primary theoretical methods used in the construction of the control index system are gray correlation [30] and principal component analyses [31].Figure 5
Construction process of quality control index system for tunnel smooth blasting.To perform the gray correlation analysis, the reference sequence can be defined asx0=x01,x02,⋯,x0m while the comparative sequence can be xi=xi1,xi2,⋯,xim, and i=1,2,⋯,n. The reference sequence denoted as x0′ can be expressed as Eq. (15) while the comparative sequence indicated as xi′ can be described as Eq. (16).
(15)x0′=x0′1,x0′2,⋯,x0′m=x01∑j=1mx0j/m,x02∑j=1mx0j/m,⋯,x0m∑j=1nx0j/m,(16)xi′=xi′1,xi′2,⋯,xi′m=xi1∑j=1mxij/m,xi2∑j=1mxij/m,⋯,xim∑j=1mxij/m.The correlation coefficient is defined as:(17)η0ij=∆min+w∆maxxoj−xij+w∆max,in which w is the resolution coefficient, ∆min is the minimum difference between the two sequences, and ∆max is the maximum difference between the two sequences.The principal component analyses model is:(18)X=TET+F,in which X is the input matrix m×e which represents original parameters, T is the score matrix m×k which represents the relationship between original parameters, E is the loading matrix e×j which represents the contribution of original parameters, and F is the residual matrix m×e which represents the uncaptured variance. m is the number of time steps, e is the number of original parameters, and j is the number of principal components.


## 2.2.1. Construction Principle and Frame Structure Design

The selection of tunnel smooth blasting quality control index should follow the principles of comprehensiveness and representativeness, innovation and science, systematicness and hierarchy, maneuverability, dynamics, and scientific quantification. On the basis of these control principles and taking the Pressure-State-Response (PSR) concept model [27–29] proposed by the United Nations Economic Cooperation and Development Agency as a reference, this paper establishes the PSR concept model of a quality control index system of tunnel smooth blasting construction (see Figure 4) based on the actual situation of the tunnel smooth blasting construction process. The PSR model separates the indicators into three groups of categories: (1) the “pressure” indicator has an impact factor that reflects the human activities and leads to unreasonable blasting quality of the rock tunnel; (2) the “state” indicator, which illustrates the quality state and control process of smooth blasting; and (3) the “response” indicator, which measures its smooth blasting quality evaluation service. Thus, it can clearly reflect the relationship between the relevant factors of tunnel smooth blasting quality, thereby enabling decision-makers to address the primary and secondary relations in the complex smooth blasting quality control index and then compare and judge one by one, optimize the best control index, feed the control results back to the control system, reverse the performance of the optimal tunnel smooth blasting quality control index, and obtain the optimal index quality control range to ensure the integrity and effectiveness of the final control index system.Figure 4
PSR concept model of a quality control index system.


## 2.2.2. Construction Method

The main process of establishing the quality control index system for tunnel smooth blasting is shown in Figure5. The primary theoretical methods used in the construction of the control index system are gray correlation [30] and principal component analyses [31].Figure 5
Construction process of quality control index system for tunnel smooth blasting.To perform the gray correlation analysis, the reference sequence can be defined asx0=x01,x02,⋯,x0m while the comparative sequence can be xi=xi1,xi2,⋯,xim, and i=1,2,⋯,n. The reference sequence denoted as x0′ can be expressed as Eq. (15) while the comparative sequence indicated as xi′ can be described as Eq. (16).
(15)x0′=x0′1,x0′2,⋯,x0′m=x01∑j=1mx0j/m,x02∑j=1mx0j/m,⋯,x0m∑j=1nx0j/m,(16)xi′=xi′1,xi′2,⋯,xi′m=xi1∑j=1mxij/m,xi2∑j=1mxij/m,⋯,xim∑j=1mxij/m.The correlation coefficient is defined as:(17)η0ij=∆min+w∆maxxoj−xij+w∆max,in which w is the resolution coefficient, ∆min is the minimum difference between the two sequences, and ∆max is the maximum difference between the two sequences.The principal component analyses model is:(18)X=TET+F,in which X is the input matrix m×e which represents original parameters, T is the score matrix m×k which represents the relationship between original parameters, E is the loading matrix e×j which represents the contribution of original parameters, and F is the residual matrix m×e which represents the uncaptured variance. m is the number of time steps, e is the number of original parameters, and j is the number of principal components.


## 2.3. Control Index Data Collection

Field investigation, expert consultation, experimental research, existing engineering case data collection, and other methods were used to collect the control index data.


### 2.3.1. On-Site Investigation and Expert Consultation

In accordance with the influencing factors of tunnel smooth blasting quality control, field investigation and expert consultation method are conducted with seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors and a total of 43 influencing factors to evaluate the importance level of qualitative and quantitative indexes, which are divided into five levels: 1 represents very important (5 points), 2 represents more important (4 points), 3 represents generally important (3 points), 4 represents less important (2 points), and 5 represents very unimportant (1 point). The statistical results of field investigation and expert consultation show that the adoption rate of the indicators below level-1 subsection-5 is less than 60%. In accordance with the maneuverability, science, and effectiveness of tunnel smooth blasting quality control, this paper lists only the (very important) adoption rate that impacts the tunnel smooth blasting quality at level-1 subsection-5 because of space limitations; see Figures6–12.Figure 6
Geological conditions.Figure 7
Explosive properties.Figure 8
Borehole parameters.Figure 9
Charge parameters.Figure 10
Method of initiation.Figure 11
Tunnel parameters.Figure 12
Construction factors.Figure6 shows that the index adoption rate of rock category is 86%, the index adoption rate of joint fracture is 64%, the index adoption rate of groundwater is 64%, and the adoption rate of other indexes is less than 60%.Figure7 shows that the index adoption rate of explosive components is 64%, the index adoption rate of blasting force is 64%, the index adoption rate of blasting speed is 64%, and the adoption rate of other indexes is less than 60%.Figure8 shows that the index adoption rate of borehole depth is 71%, the index adoption rate of neighboring eyes spacing is 64%, the index adoption rate of minimum resistance line is 79%, the index adoption rate of neighboring eyes dense factor is 64%, and the adoption rate of other indexes is less than 60%.Figure9 shows that the index adoption rate of linear charge density is 64%, the index adoption rate of noncoupling coefficient is 60%, the index adoption rate of plugging quality is 71%, and the adoption rate of other indexes is less than 60%.Figure10 shows that the index adoption rate of sequence of initiation is 93%, the index adoption rate of time difference of initiation is 64%, the index adoption rate of method of initiation is 71%, and the adoption rate of other indexes is less than 60%.Figure11 shows that the index adoption rate of the excavation method is 71%, the index adoption rate of blasting method is 64%, the index adoption rate of excavation section is 64%, and the adoption rate of other indexes is less than 60%.Figure12 shows that the index adoption rate of drilling accuracy is 67%, the index adoption rate of measuring and setting out (including midline or elevation deviation) is 64%, the index adoption rate of on-site management system is 71%, and the adoption rate of other indexes is less than 60%.


### 2.3.2. Experimental Research

The experimental study is mainly based on the Chengdu–Chongqing high-speed rail Da’an Tunnel [32]. Total length of the tunnel is about 5050 m, while the excavated radius and height are 7.45 m and 11.08 m, respectively. The lithology exposed on both sides of the syncline includes mudstone and sandstone with age of Jurassic (J). Overlying formations consist of soft silty clay with ages of Holocene series in Quaternary system (Q4d1+p1), soft-flowing plastic silty clay, silty clay, slope residual (Q4d1+e1) silty clay, and colluvial deposits (Q4d1+co1). Moreover, the underlying formations are Shaxi group of middle Jurassic (J), including sandstone, mudstone, sandstone, and argillaceous sandstone. Field and numerical tests were conducted to collect quantitative data, and the main indicators collected in the field test include eight indicators: rock category, neighboring eyes spacing, borehole depth, number of boreholes, charge quantity, minimum resistance line, maximum infrared temperature, and minimum infrared temperature. Field data acquisition test is shown in Figure 13. The numerical test collected seven main indexes [32]: neighboring eyes spacing, minimum resistance line, relative distance, linear charge density, rock category, blasting speed, and measuring and setting out.Figure 13
Field data acquisition tests.


### 2.3.3. Collection of Existing Engineering Case Data

The existing engineering case data collection is mainly aimed at collecting the control indexes used in blasting construction of all kinds of tunnels and underground engineering reported in the existing literature to obtain the most sample data and provide more information for tunnel smooth blasting quality control. Seventy-seven tunnel and underground engineering cases were collected, and the collected control indexes mainly include 23 indexes, such as rock category, borehole depth, and neighboring eyes spacing, as shown in Table1.Table 1
Collection of existing engineering case data.
No.IndexNo.IndexNo.Index1Rock category9Minimum resistance line17Excavation method2Joint fracture10Relative distance18Blasting method3Groundwater11Linear charge density19Buried depth of tunnel4Explosive components12Noncoupling coefficient20Excavation section5Blasting force13Plugging quality21Drilling accuracy6Blasting speed14Sequence of initiation22Measuring and setting out7Borehole depth15Time difference of initiation23On-site management system8Neighboring eyes spacing16Method of initiation


## 2.3.1. On-Site Investigation and Expert Consultation

In accordance with the influencing factors of tunnel smooth blasting quality control, field investigation and expert consultation method are conducted with seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors and a total of 43 influencing factors to evaluate the importance level of qualitative and quantitative indexes, which are divided into five levels: 1 represents very important (5 points), 2 represents more important (4 points), 3 represents generally important (3 points), 4 represents less important (2 points), and 5 represents very unimportant (1 point). The statistical results of field investigation and expert consultation show that the adoption rate of the indicators below level-1 subsection-5 is less than 60%. In accordance with the maneuverability, science, and effectiveness of tunnel smooth blasting quality control, this paper lists only the (very important) adoption rate that impacts the tunnel smooth blasting quality at level-1 subsection-5 because of space limitations; see Figures6–12.Figure 6
Geological conditions.Figure 7
Explosive properties.Figure 8
Borehole parameters.Figure 9
Charge parameters.Figure 10
Method of initiation.Figure 11
Tunnel parameters.Figure 12
Construction factors.Figure6 shows that the index adoption rate of rock category is 86%, the index adoption rate of joint fracture is 64%, the index adoption rate of groundwater is 64%, and the adoption rate of other indexes is less than 60%.Figure7 shows that the index adoption rate of explosive components is 64%, the index adoption rate of blasting force is 64%, the index adoption rate of blasting speed is 64%, and the adoption rate of other indexes is less than 60%.Figure8 shows that the index adoption rate of borehole depth is 71%, the index adoption rate of neighboring eyes spacing is 64%, the index adoption rate of minimum resistance line is 79%, the index adoption rate of neighboring eyes dense factor is 64%, and the adoption rate of other indexes is less than 60%.Figure9 shows that the index adoption rate of linear charge density is 64%, the index adoption rate of noncoupling coefficient is 60%, the index adoption rate of plugging quality is 71%, and the adoption rate of other indexes is less than 60%.Figure10 shows that the index adoption rate of sequence of initiation is 93%, the index adoption rate of time difference of initiation is 64%, the index adoption rate of method of initiation is 71%, and the adoption rate of other indexes is less than 60%.Figure11 shows that the index adoption rate of the excavation method is 71%, the index adoption rate of blasting method is 64%, the index adoption rate of excavation section is 64%, and the adoption rate of other indexes is less than 60%.Figure12 shows that the index adoption rate of drilling accuracy is 67%, the index adoption rate of measuring and setting out (including midline or elevation deviation) is 64%, the index adoption rate of on-site management system is 71%, and the adoption rate of other indexes is less than 60%.


## 2.3.2. Experimental Research

The experimental study is mainly based on the Chengdu–Chongqing high-speed rail Da’an Tunnel [32]. Total length of the tunnel is about 5050 m, while the excavated radius and height are 7.45 m and 11.08 m, respectively. The lithology exposed on both sides of the syncline includes mudstone and sandstone with age of Jurassic (J). Overlying formations consist of soft silty clay with ages of Holocene series in Quaternary system (Q4d1+p1), soft-flowing plastic silty clay, silty clay, slope residual (Q4d1+e1) silty clay, and colluvial deposits (Q4d1+co1). Moreover, the underlying formations are Shaxi group of middle Jurassic (J), including sandstone, mudstone, sandstone, and argillaceous sandstone. Field and numerical tests were conducted to collect quantitative data, and the main indicators collected in the field test include eight indicators: rock category, neighboring eyes spacing, borehole depth, number of boreholes, charge quantity, minimum resistance line, maximum infrared temperature, and minimum infrared temperature. Field data acquisition test is shown in Figure 13. The numerical test collected seven main indexes [32]: neighboring eyes spacing, minimum resistance line, relative distance, linear charge density, rock category, blasting speed, and measuring and setting out.Figure 13
Field data acquisition tests.


## 2.3.3. Collection of Existing Engineering Case Data

The existing engineering case data collection is mainly aimed at collecting the control indexes used in blasting construction of all kinds of tunnels and underground engineering reported in the existing literature to obtain the most sample data and provide more information for tunnel smooth blasting quality control. Seventy-seven tunnel and underground engineering cases were collected, and the collected control indexes mainly include 23 indexes, such as rock category, borehole depth, and neighboring eyes spacing, as shown in Table1.Table 1
Collection of existing engineering case data.
No.IndexNo.IndexNo.Index1Rock category9Minimum resistance line17Excavation method2Joint fracture10Relative distance18Blasting method3Groundwater11Linear charge density19Buried depth of tunnel4Explosive components12Noncoupling coefficient20Excavation section5Blasting force13Plugging quality21Drilling accuracy6Blasting speed14Sequence of initiation22Measuring and setting out7Borehole depth15Time difference of initiation23On-site management system8Neighboring eyes spacing16Method of initiation


## 2.4. Establishment of Quality Control Index System

### 2.4.1. Primary Election of Quality Control Index System

On the basis of the factors that influence the quality of tunnel smooth blasting, this paper analyzes the index adoption rate of the control indexes involved in a domestic tunnel and underground project from three aspects, namely, domestic project case statistics, standard statistics, and foreign project case statistics. A total of 210 cases and 43 indicators were counted in domestic project cases, as shown in Figures14–20.Figure 14
Geological conditions.Figure 15
Explosive properties.Figure 16
Borehole parameters.Figure 17
Charge parameters.Figure 18
Method of initiation.Figure 19
Tunnel parameters.Figure 20
Construction factors.To ensure the validity, feasibility, and scientificity of the control index while analyzing the above figures, only the index with the indicatoradoptionrate≥60% is analyzed. Therefore, for geological conditions, the index adoption rate of rock category is 89%; for the borehole blasting design, the index adoption rate of neighboring eyes spacing is 92.4%, the index adoption rate of minimum resistance line is 86.2%, the index adoption rate of relative distance is 66.2%, and the adoption rate of linear charge density is 77.1%. The adoption rates of construction factors, drilling accuracy, measuring and setting out, personnel quality, on-site management system, and other indicators are low.The statistics on the adoption rate of control indicators in various current regulations in China mainly include nine specifications, such as Technical Specifications for Construction of Highway Tunnel (JTG/T 3660-2020), Code for construction and acceptance of metro engineering (2012 version) (GB 50299-1999), and Code for construction on tunnel of railway (TB 10204-2002), as shown in Figure21. The figure shows that, in the current specification, the index adoption rate of charge noncoupling coefficient is 44%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of minimum resistance line is 100%, the index adoption rate of relative distance is 67%, the adoption rate of linear charge density is 100%, the adoption rate of rock category is 100%, and the adoption rate of borehole depth is 11%.Figure 21
Statistics on the adoption rate of quality control index of tunnel blasting in current specification.The quality control index of tunnel smooth blasting used in foreign engineering cases is analyzed statistically [5, 6, 33–48], as shown in Figure 22. The figure shows that the index adoption rate of charge noncoupling coefficient is 10%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of neighboring eyes minimum resistance line is 100%, the index adoption rate of relative distance is 30%, the adoption rate of linear charge density is 100%, the adoption rate of borehole depth is 40%, the adoption rate of rock category is 100%, and the adoption rate of measuring and setting out is 30%.Figure 22
Foreign engineering case statistics.Therefore, combined with the domestic engineering case statistics, standard statistics, foreign engineering case statistics, and tunnel smooth blasting quality control index data collection, from the seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, the tunnel smooth blasting quality control index system was primarily established, with a total of 22 indicators, as seen in Table2.Table 2
Primary election of quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layerQuality control index system for tunnel smooth blastingGeological conditionsRock categoryJoint fractureGroundwaterExplosive propertiesExplosive componentsBlasting forceBlasting speedBorehole parametersBorehole depthNeighboring eyes spacingMinimum resistance lineRelative distanceCharge parametersLinear charge densityNoncoupling coefficientPlugging qualityMethod of initiationSequence of initiationTime difference of initiationMethod of initiationTunnel parametersExcavation methodBlasting methodExcavation sectionConstruction factorsDrilling accuracyMeasuring and setting outOn-site management system


### 2.4.2. Selection of Quality Control Index System

In accordance with the principle of constructing the quality control index system of tunnel smooth blasting, the control index needs to be screened and modified, and the modified method mainly adopts gray correlation [30] and principal component analyses [31].(1) Geological conditions. X1–X3 represent the rock category, joint fracture, and groundwater, respectively. The correlation degree of geological condition index calculated by gray correlation analysis is shown in Table 3Table 3
Correlation degree of geological condition index.
Control indexCorrelation degreeRock category0.6493Joint fracture0.6423Groundwater0.5008The above analysis indicates that in each control index, the rock category has the highest correlation degree, followed by the joint fracture and the groundwater.The normalized eigenvectors of geological condition indexes calculated by principal component analysis are shown in Table4, and the eigenvalues are shown in Table 5.Table 4
Normalized eigenvectors of geological condition index.
Control indexControl index 1Control index 2Control index 3X10.64620.25770.7183X20.63350.3438-0.6932X3-0.42560.9030.0589Table 5
Eigenvalues of geological condition index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.14571.5071.5020.749524.9896.4830.10553.51100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 96.48% of the total amount of information, and the first principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of geological conditions is the rock category.(2) Explosive properties. X1–X3 represent the explosive components, blasting force, and blasting speed, respectively. The correlation degree of the explosive property index calculated by gray correlation analysis is shown in Table 6Table 6
Correlation degree of the explosive property index.
Control indexCorrelation degreeExplosive components0.487Blasting force0.544Blasting speed0.544The above analysis shows that the most significant influencing factors of correlation degree are blasting force and blasting speed.The normalized eigenvectors of explosive property indexes calculated by principal component analysis are shown in Table7, and the eigenvalues are shown in Table 8.Table 7
Normalized eigenvectors of explosive property index.
Control indexControl index 1Control index 2Control index 3X1-0.57520.59050.5661X20.53420.7952-0.2868X30.6195-0.13740.7729Table 8
Eigenvalues of explosive property index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.318977.2977.2920.51317.1094.3930.1685.60100The above analysis shows that the amount of information contained in the first main component is 77.29% of the total amount of information, and the first principal component represents X3. Combined with the gray correlation and principal component analyses, findings indicate that the optimal characteristic index of explosive properties is the blasting speed.(3) Borehole parameters. X1–X4 represent the borehole depth, neighboring eyes spacing, minimum resistance line, and relative distance, respectively. The correlation degree of the borehole parameter index calculated by gray correlation analysis is shown in Table 9Table 9
Correlation degree of the borehole parameter index.
Control indexCorrelation degreeBorehole depth0.5787Neighboring eyes spacing0.6063Minimum resistance line0.6655Relative distance0.6473The above analysis shows that the most significant influencing factor of correlation degree is the minimum resistance line.The normalized eigenvectors of borehole parameter indexes calculated by principal component analysis are shown in Table10, and the eigenvalues are shown in Table 11.Table 10
Normalized eigenvectors of borehole parameter index.
Control indexControl index 1Control index 2Control index 3Control index 4X10.4328-0.28730.8544-0.0101X20.65360.1733-0.2809-0.6811X30.5135-0.5147-0.42690.5377X40.3490.78890.09440.4968Table 11
Eigenvalues of borehole parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.117652.9452.9421.177629.4382.3730.693217.3399.7140.01160.28100Combined with the above analyses, findings indicate that the amount of information contained in the first two main components is 82.37% of the total amount of information, the first principal component represents X2, and the second principal component represents X4.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic indicators of borehole parameters are the rock category, minimum resistance line, and relative distance.(4) Charge parameters. X1–X3 represent the linear charge density, noncoupling coefficient, and plugging quality, respectively. The correlation degree of charge parameter index calculated by gray correlation analysis is shown in Table 12Table 12
Correlation degree of the charge parameter index.
Control indexCorrelation degreeLinear charge density0.6502Noncoupling coefficient0.6109Plugging quality0.6383The above analysis shows that the first influencing factor of correlation degree is linear charge density, the second influencing factor is plugging quality, and the third is noncoupling coefficient.The normalized eigenvectors of charge parameter indexes calculated by principal component analysis are shown in Table13, and the eigenvalues are shown in Table 14.Table 13
Normalized eigenvectors of charge parameter index.
Control indexControl index 1Control index 2Control index 3X10.20760.90610.3687X20.6577-0.40830.6331X3-0.7241-0.11110.6806Table 14
Eigenvalues of charge parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.26542.1642.1621.035934.5376.6930.699123.30100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 76.69% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of charge parameters is the linear charge density.(5) Method of initiation. X1–X3 represent the sequence of initiation, time difference of initiation, and method of initiation, respectively. The correlation degree of the method of initiation index calculated by gray correlation analysis is shown in Table 15.Table 15
Correlation degree of the method of initiation index.
Control indexCorrelation degreeSequence of initiation0.7904Time difference of initiation0.7885Method of initiation0.6664The above analysis shows that the first influencing factor of correlation degree is the sequence of initiation, the second is the time difference of initiation, and the third is the method of initiation.The normalized eigenvectors of the method of initiation index calculated by principal component analysis are shown in Table16, and the eigenvalues are shown in Table 17.Table 16
Normalized eigenvectors of method of initiation index.
Control indexControl index 1Control index 2Control index 3X10.69890.06080.7126X20.67320.2805-0.6842X3-0.24150.95790.1551Table 17
Eigenvalues of method of initiation index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.355545.1845.1820.986432.8778.0630.658121.93100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 78.06% of the total amount of information, the first principal component represents X1, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of the method of initiation is the sequence of initiation.(6) Tunnel parameters. X1–X3 represent the excavation method, blasting method, and excavation section, respectively. The correlation degree of tunnel parameter index calculated by gray correlation analysis is shown in Table 18.Table 18
Correlation degree of the tunnel parameter index.
Control indexCorrelation degreeExcavation method0.6639Blasting method0.5711Excavation section0.6261The above analysis shows that the first influencing factor of correlation degree is the excavation method, the second is the blasting method, and the third is the excavation section.The normalized eigenvectors of the tunnel parameter indexes calculated by principal component analysis are shown in Table19, and the eigenvalues are shown in Table 20.Table 19
Normalized eigenvectors of tunnel parameter index.
Control indexControl index 1Control index 2Control index 3X10.52010.7564-0.3967X2-0.55590.65240.5151X30.6484-0.04740.7598Table 20
Eigenvalues of tunnel parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.892963.0963.0920.756525.2188.3130.350611.68100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 88.31% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of tunnel parameters is the excavation method.(7) Construction factors. X1–X3 represent the drilling accuracy, measuring and setting out, and on-site management system, respectively. The correlation degree of the construction factor index calculated by gray correlation analysis is shown in Table 21.Table 21
Correlation degree of the construction factor index.
Control indexCorrelation degreeDrilling accuracy0.5910Measuring and setting out0.6499On-site management system0.6012The above analysis shows that the first influencing factor of correlation degree is the measuring and setting out, the second is on-site management system, and the third is drilling accuracy.The normalized eigenvectors of construction factor indexes calculated by principal component analysis are shown in Table22, and the eigenvalues are shown in Table 23.Table 22
Normalized eigenvectors of construction factor index.
Control indexControl index 1Control index 2Control index 3X10.5837-0.53050.6147X20.6117-0.2105-0.7625X30.53390.82110.2017Table 23
Eigenvalues of construction factor index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.654855.1555.1520.747424.9180.0730.597819.92100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 80.07% of the total amount of information, the first principal component represents X2, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of construction factor is the measuring and setting out.


### 2.4.3. Establishment of Quality Control Index System

In accordance with the primary selection and screening of the control index, abandoning the noncompliant index, the retaining control index is established according to the designed frame structure of the control system, and the tunnel smooth blasting quality control index system, which includes the seven criteria layers of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, and a total of nine indexes, is established, as shown in Table24.Table 24
Establishment of the quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layer (unit)Quality control index system for tunnel smooth blastingAGeological conditionsB1Rock categoryC11Explosive propertiesB2Blasting speedC21 (m/s)Borehole parametersB3Neighboring eyes spacingC31 (mm)Minimum resistance lineC32 (m)Relative distanceC33Charge parametersB4Linear charge densityC41 (kg/m)Method of initiationB5Sequence of initiationC51Tunnel parametersB6Excavation methodC61Construction factorsB7Measuring and setting outC71


## 2.4.1. Primary Election of Quality Control Index System

On the basis of the factors that influence the quality of tunnel smooth blasting, this paper analyzes the index adoption rate of the control indexes involved in a domestic tunnel and underground project from three aspects, namely, domestic project case statistics, standard statistics, and foreign project case statistics. A total of 210 cases and 43 indicators were counted in domestic project cases, as shown in Figures14–20.Figure 14
Geological conditions.Figure 15
Explosive properties.Figure 16
Borehole parameters.Figure 17
Charge parameters.Figure 18
Method of initiation.Figure 19
Tunnel parameters.Figure 20
Construction factors.To ensure the validity, feasibility, and scientificity of the control index while analyzing the above figures, only the index with the indicatoradoptionrate≥60% is analyzed. Therefore, for geological conditions, the index adoption rate of rock category is 89%; for the borehole blasting design, the index adoption rate of neighboring eyes spacing is 92.4%, the index adoption rate of minimum resistance line is 86.2%, the index adoption rate of relative distance is 66.2%, and the adoption rate of linear charge density is 77.1%. The adoption rates of construction factors, drilling accuracy, measuring and setting out, personnel quality, on-site management system, and other indicators are low.The statistics on the adoption rate of control indicators in various current regulations in China mainly include nine specifications, such as Technical Specifications for Construction of Highway Tunnel (JTG/T 3660-2020), Code for construction and acceptance of metro engineering (2012 version) (GB 50299-1999), and Code for construction on tunnel of railway (TB 10204-2002), as shown in Figure21. The figure shows that, in the current specification, the index adoption rate of charge noncoupling coefficient is 44%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of minimum resistance line is 100%, the index adoption rate of relative distance is 67%, the adoption rate of linear charge density is 100%, the adoption rate of rock category is 100%, and the adoption rate of borehole depth is 11%.Figure 21
Statistics on the adoption rate of quality control index of tunnel blasting in current specification.The quality control index of tunnel smooth blasting used in foreign engineering cases is analyzed statistically [5, 6, 33–48], as shown in Figure 22. The figure shows that the index adoption rate of charge noncoupling coefficient is 10%, the index adoption rate of neighboring eyes spacing is 100%, the index adoption rate of neighboring eyes minimum resistance line is 100%, the index adoption rate of relative distance is 30%, the adoption rate of linear charge density is 100%, the adoption rate of borehole depth is 40%, the adoption rate of rock category is 100%, and the adoption rate of measuring and setting out is 30%.Figure 22
Foreign engineering case statistics.Therefore, combined with the domestic engineering case statistics, standard statistics, foreign engineering case statistics, and tunnel smooth blasting quality control index data collection, from the seven aspects of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, the tunnel smooth blasting quality control index system was primarily established, with a total of 22 indicators, as seen in Table2.Table 2
Primary election of quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layerQuality control index system for tunnel smooth blastingGeological conditionsRock categoryJoint fractureGroundwaterExplosive propertiesExplosive componentsBlasting forceBlasting speedBorehole parametersBorehole depthNeighboring eyes spacingMinimum resistance lineRelative distanceCharge parametersLinear charge densityNoncoupling coefficientPlugging qualityMethod of initiationSequence of initiationTime difference of initiationMethod of initiationTunnel parametersExcavation methodBlasting methodExcavation sectionConstruction factorsDrilling accuracyMeasuring and setting outOn-site management system


## 2.4.2. Selection of Quality Control Index System

In accordance with the principle of constructing the quality control index system of tunnel smooth blasting, the control index needs to be screened and modified, and the modified method mainly adopts gray correlation [30] and principal component analyses [31].(1) Geological conditions. X1–X3 represent the rock category, joint fracture, and groundwater, respectively. The correlation degree of geological condition index calculated by gray correlation analysis is shown in Table 3Table 3
Correlation degree of geological condition index.
Control indexCorrelation degreeRock category0.6493Joint fracture0.6423Groundwater0.5008The above analysis indicates that in each control index, the rock category has the highest correlation degree, followed by the joint fracture and the groundwater.The normalized eigenvectors of geological condition indexes calculated by principal component analysis are shown in Table4, and the eigenvalues are shown in Table 5.Table 4
Normalized eigenvectors of geological condition index.
Control indexControl index 1Control index 2Control index 3X10.64620.25770.7183X20.63350.3438-0.6932X3-0.42560.9030.0589Table 5
Eigenvalues of geological condition index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.14571.5071.5020.749524.9896.4830.10553.51100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 96.48% of the total amount of information, and the first principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of geological conditions is the rock category.(2) Explosive properties. X1–X3 represent the explosive components, blasting force, and blasting speed, respectively. The correlation degree of the explosive property index calculated by gray correlation analysis is shown in Table 6Table 6
Correlation degree of the explosive property index.
Control indexCorrelation degreeExplosive components0.487Blasting force0.544Blasting speed0.544The above analysis shows that the most significant influencing factors of correlation degree are blasting force and blasting speed.The normalized eigenvectors of explosive property indexes calculated by principal component analysis are shown in Table7, and the eigenvalues are shown in Table 8.Table 7
Normalized eigenvectors of explosive property index.
Control indexControl index 1Control index 2Control index 3X1-0.57520.59050.5661X20.53420.7952-0.2868X30.6195-0.13740.7729Table 8
Eigenvalues of explosive property index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.318977.2977.2920.51317.1094.3930.1685.60100The above analysis shows that the amount of information contained in the first main component is 77.29% of the total amount of information, and the first principal component represents X3. Combined with the gray correlation and principal component analyses, findings indicate that the optimal characteristic index of explosive properties is the blasting speed.(3) Borehole parameters. X1–X4 represent the borehole depth, neighboring eyes spacing, minimum resistance line, and relative distance, respectively. The correlation degree of the borehole parameter index calculated by gray correlation analysis is shown in Table 9Table 9
Correlation degree of the borehole parameter index.
Control indexCorrelation degreeBorehole depth0.5787Neighboring eyes spacing0.6063Minimum resistance line0.6655Relative distance0.6473The above analysis shows that the most significant influencing factor of correlation degree is the minimum resistance line.The normalized eigenvectors of borehole parameter indexes calculated by principal component analysis are shown in Table10, and the eigenvalues are shown in Table 11.Table 10
Normalized eigenvectors of borehole parameter index.
Control indexControl index 1Control index 2Control index 3Control index 4X10.4328-0.28730.8544-0.0101X20.65360.1733-0.2809-0.6811X30.5135-0.5147-0.42690.5377X40.3490.78890.09440.4968Table 11
Eigenvalues of borehole parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)12.117652.9452.9421.177629.4382.3730.693217.3399.7140.01160.28100Combined with the above analyses, findings indicate that the amount of information contained in the first two main components is 82.37% of the total amount of information, the first principal component represents X2, and the second principal component represents X4.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic indicators of borehole parameters are the rock category, minimum resistance line, and relative distance.(4) Charge parameters. X1–X3 represent the linear charge density, noncoupling coefficient, and plugging quality, respectively. The correlation degree of charge parameter index calculated by gray correlation analysis is shown in Table 12Table 12
Correlation degree of the charge parameter index.
Control indexCorrelation degreeLinear charge density0.6502Noncoupling coefficient0.6109Plugging quality0.6383The above analysis shows that the first influencing factor of correlation degree is linear charge density, the second influencing factor is plugging quality, and the third is noncoupling coefficient.The normalized eigenvectors of charge parameter indexes calculated by principal component analysis are shown in Table13, and the eigenvalues are shown in Table 14.Table 13
Normalized eigenvectors of charge parameter index.
Control indexControl index 1Control index 2Control index 3X10.20760.90610.3687X20.6577-0.40830.6331X3-0.7241-0.11110.6806Table 14
Eigenvalues of charge parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.26542.1642.1621.035934.5376.6930.699123.30100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 76.69% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of charge parameters is the linear charge density.(5) Method of initiation. X1–X3 represent the sequence of initiation, time difference of initiation, and method of initiation, respectively. The correlation degree of the method of initiation index calculated by gray correlation analysis is shown in Table 15.Table 15
Correlation degree of the method of initiation index.
Control indexCorrelation degreeSequence of initiation0.7904Time difference of initiation0.7885Method of initiation0.6664The above analysis shows that the first influencing factor of correlation degree is the sequence of initiation, the second is the time difference of initiation, and the third is the method of initiation.The normalized eigenvectors of the method of initiation index calculated by principal component analysis are shown in Table16, and the eigenvalues are shown in Table 17.Table 16
Normalized eigenvectors of method of initiation index.
Control indexControl index 1Control index 2Control index 3X10.69890.06080.7126X20.67320.2805-0.6842X3-0.24150.95790.1551Table 17
Eigenvalues of method of initiation index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.355545.1845.1820.986432.8778.0630.658121.93100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 78.06% of the total amount of information, the first principal component represents X1, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of the method of initiation is the sequence of initiation.(6) Tunnel parameters. X1–X3 represent the excavation method, blasting method, and excavation section, respectively. The correlation degree of tunnel parameter index calculated by gray correlation analysis is shown in Table 18.Table 18
Correlation degree of the tunnel parameter index.
Control indexCorrelation degreeExcavation method0.6639Blasting method0.5711Excavation section0.6261The above analysis shows that the first influencing factor of correlation degree is the excavation method, the second is the blasting method, and the third is the excavation section.The normalized eigenvectors of the tunnel parameter indexes calculated by principal component analysis are shown in Table19, and the eigenvalues are shown in Table 20.Table 19
Normalized eigenvectors of tunnel parameter index.
Control indexControl index 1Control index 2Control index 3X10.52010.7564-0.3967X2-0.55590.65240.5151X30.6484-0.04740.7598Table 20
Eigenvalues of tunnel parameter index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.892963.0963.0920.756525.2188.3130.350611.68100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 88.31% of the total amount of information, the first principal component represents X3, and the second principal component represents X1.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of tunnel parameters is the excavation method.(7) Construction factors. X1–X3 represent the drilling accuracy, measuring and setting out, and on-site management system, respectively. The correlation degree of the construction factor index calculated by gray correlation analysis is shown in Table 21.Table 21
Correlation degree of the construction factor index.
Control indexCorrelation degreeDrilling accuracy0.5910Measuring and setting out0.6499On-site management system0.6012The above analysis shows that the first influencing factor of correlation degree is the measuring and setting out, the second is on-site management system, and the third is drilling accuracy.The normalized eigenvectors of construction factor indexes calculated by principal component analysis are shown in Table22, and the eigenvalues are shown in Table 23.Table 22
Normalized eigenvectors of construction factor index.
Control indexControl index 1Control index 2Control index 3X10.5837-0.53050.6147X20.6117-0.2105-0.7625X30.53390.82110.2017Table 23
Eigenvalues of construction factor index.
No.EigenvaluePercentage (%)Cumulative percentage (%)11.654855.1555.1520.747424.9180.0730.597819.92100Combined with the above analysis, findings indicate that the amount of information contained in the first two main components is 80.07% of the total amount of information, the first principal component represents X2, and the second principal component represents X3.Combined with the above gray correlation and principal component analyses, findings indicate that the optimal characteristic index of construction factor is the measuring and setting out.


## 2.4.3. Establishment of Quality Control Index System

In accordance with the primary selection and screening of the control index, abandoning the noncompliant index, the retaining control index is established according to the designed frame structure of the control system, and the tunnel smooth blasting quality control index system, which includes the seven criteria layers of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, and a total of nine indexes, is established, as shown in Table24.Table 24
Establishment of the quality control index system for tunnel smooth blasting.
Control target layerControl criterion layerControl index layer (unit)Quality control index system for tunnel smooth blastingAGeological conditionsB1Rock categoryC11Explosive propertiesB2Blasting speedC21 (m/s)Borehole parametersB3Neighboring eyes spacingC31 (mm)Minimum resistance lineC32 (m)Relative distanceC33Charge parametersB4Linear charge densityC41 (kg/m)Method of initiationB5Sequence of initiationC51Tunnel parametersB6Excavation methodC61Construction factorsB7Measuring and setting outC71


## 3. Results and Discussion

On the basis of the comprehensive optimization control model of BP-ANN, ENN, and ANFIS, the following steps are used to adjust the subsequent blasting parameters to achieve quality control of tunnel smooth blasting.(1)
The measured tunnel smooth blasting data is used as a training sample of the neural network to establish an intelligent optimization model(2)
The uniform design method is used to optimize and adjust the blasting parameters of the tunnel section to be controlled, including the neighboring eyes spacing, the minimum resistance line, and linear charge density, and the parameter is adjusted locally and slightly mainly based on the actual blasting situation in the field, which primarily involves including upward adjustment (represented as “+”), downward adjustment (represented as “-”), and no adjustment (represented as “0”), and the adjustment range is selected from three levels, with a total of seven levels(3)
The optimized and adjusted smooth blasting parameter table data in step (2) are taken as a test sample of the comprehensive optimization model. The prediction results obtained by the comprehensive optimization control model are the tunnel smooth blasting quality index, which corresponds to the relevant level of each parameter(4)
The quality parameters of tunnel smooth blasting quality are evaluated by using the evaluation method established in the quality evaluation system of tunnel smooth blasting(5)
With the comprehensive index of tunnel smooth blasting quality taken as the standard, the obtained sets of parameters are sorted, and the optimal blasting parameter group is selected as the sample for tunnel smooth blasting quality control(6)
On the basis of the ANFIS and the ENN, comprehensive optimization control model is used to repeat steps (3)–(5). The two obtained tunnel smooth blasting quality control suggestions, together with the control suggestions obtained by the BP neural network, will be used as the suggested reference for design and construction personnel involved in the quality control of tunnel smooth blastingTaking the Chengdu–Chongqing high-speed rail Da’an Tunnel as an example [32], three comprehensive optimization control models were validated by using 34 sets of on-site obtained data (see Tables 25 and 26). First, these 34 sets of data were taken as the training samples of the comprehensive optimization control model. Nine control indexes, including the rock category, blasting speed, neighboring eyes spacing, and minimum resistance line in the tunnel smooth blasting quality control index system, were selected as inputs. Five evaluation indexes, including the maximum overbreak, maximum underbreak, and area of overbreak, were selected as outputs. To ensure the accuracy of the comprehensive optimization control model, the neural network structure of a double hidden layer (see Figure 23) was used, and the smooth blasting control parameters to be evaluated were grouped, with each group of a comprehensive optimization control neural network model including 9 inputs and 1 output. Then, the 34th set of data was selected as the test sample, and three constructed comprehensive optimization control models were used for testing to verify the accuracy of the test results and expected results. The prediction results of the three comprehensive optimization control models are compared in Table 27. Then, on the basis of the determined adjustment range of tunnel smooth blasting quality control parameters, the multifactor test was conducted by using a uniform design, which is based on the working condition of test factor level 7. The optimization scheme of tunnel smooth blasting quality control of seven test combinations was constructed (see Table 28). Otherwise, 343 tests must be conducted. Then, three comprehensive optimization control models were used to predict the established blasting optimization adjustment parameters. Finally, the conclusion of the prediction of the three prediction models was evaluated according to the index evaluation model constructed in the tunnel smooth blasting quality evaluation system to ensure the tunnel smooth blasting quality index of each control index, and it was sorted to determine the optimal smooth blasting quality control indexes and provide suggestions for tunnel smooth blasting quality control. The prediction results of BP-ANN, ENN, and ANFIS are shown in Tables 29–31.Table 25
Comprehensive optimization control model input training data.
No.Rock categoryBlasting speed (m/s)Neighboring eyes spacing (mm)Minimum resistance line (m)Relative distanceLinear charge density (kg/m)Sequence of initiationExcavation methodMeasuring and setting out10.3320060700.860.130.90.60.420.3320065700.930.150.90.60.230.3320065700.930.150.90.60.240.3320065700.930.150.90.60.250.3320065700.930.150.90.60.460.3320065700.930.150.90.60.470.3320065700.930.150.90.60.480.53600707010.20.90.60.490.53600707010.20.90.60.4100.53600707010.20.90.60.4110.53600707010.20.90.60.4120.53600707010.20.90.60.4130.3320060650.920.250.90.60.4140.3320060650.920.250.90.60.4150.3320080701.140.150.90.60.4160.54000707010.30.90.60.2170.54000707010.30.90.60.2180.54000707010.30.90.60.2190.54000707010.30.90.60.2200.5320060650.920.150.90.60.2210.5320060650.920.150.90.60.2220.5320060650.920.150.90.60.2230.5320060650.920.150.90.60.2240.5320060650.920.150.90.60.2250.5320060650.920.150.90.60.2260.5320060650.920.150.90.60.2270.53200606010.250.90.60.2280.53200606010.250.90.60.2290.53200606010.250.90.60.2300.3420065700.930.30.90.60.2310.3420065700.930.30.90.60.2320.3420065700.930.450.90.60.2330.3420060700.860.40.90.60.4340.3420060700.860.150.90.60.4Table 26
Comprehensive optimization control model output training data.
No.Maximum overbreak (m)Maximum underbreak (m)Area of overbreak (m2)Volume of overbreak (m3)Blast hole utilization factor (%)10.810.2310.410.47920.70.687.787.789230.730.0410.915.468440.850.049.644.828450.650.027.693.859560.780.416.039.058970.660.247.523.768980.570.087.983.998990.640.1411.785.8995100.80.1412.633.7995110.780.2612.172.4395120.730.1110.165.0895130.560.039.884.9495140.660.139.620.9684150.980.2113.914.1792160.60.18.672.695170.520.077.741.5595180.70.17.483.7495190.740.058.894.4595200.850.0110.635.3295210.580.196.093.0592220.780.0312.433.7392230.750.0712.922.5892240.590.0310.95.4592250.690.284.72.3579260.580.029.462.8479270.880.0494.579280.910.338.584.2984290.860.2610.975.4984300.710.346.853.4387310.610.099.974.9987320.450.145.632.8287330.490.156.613.3187340.730.178.924.4682Figure 23
Neural network structure of synthetically optimized control model.Table 27
Comparison of prediction results of three comprehensive optimization control models.
Evaluation indexActual outputDesired outputError (%)BP-ANNENNANFISBP-ANNENNANFISMaximum overbreak (m)0.7500.7000.7300.732.7304.1100.014Maximum underbreak (m)0.1730.2000.1700.171.58817.6470.059Area of overbreak (m2)7.7349.0008.9208.9213.2910.8970.001Volume of overbreak (m3)5.2564.0004.4604.4617.84110.3140.002Blast hole utilization factor (%)87.51982.00081.99982.006.73100.001Table 28
Optimization scheme of tunnel smooth blasting quality control.
SchemeNeighboring eyes spacingMinimum resistance lineLinear charge density1+10%+20%02+15%-10%+3%3-10%0-3%4+20%+10%-2%5-15%+15%+2%6-20%-15%-1%70-20%+1%Table 29
Prediction and calculation results of BP-ANN.
SchemeMaximum overbreak (m)Maximum underbreak (m)Area of overbreak (m2)Volume of overbreak (m3)Blast hole utilization factor (%)Comprehensive quality indexRankingEvaluation levels10.733210.140687.64262.049391.89555.73057Lower20.52380.205296.29714.762194.5295.03853Intermediate30.590190.165555.38134.271384.71945.04714Intermediate40.665310.170237.49795.213790.21355.38015Intermediate50.606580.134247.77085.134985.20395.68216Intermediate60.683560.132957.45222.196691.99124.96272Intermediate70.669450.08297.10154.640190.97934.78261IntermediateTable 30
Prediction and calculation results of ENN.
SchemeMaximum overbreak (m)Maximum underbreak (m)Area of overbreak (m2)Volume of overbreak (m3)Blast hole utilization factor (%)Comprehensive quality indexRankingEvaluation levels10.600.28.006.0087.006.09945Lower20.700.111.002.0081.005.65253Intermediate30.800.110.005.0082.006.41146Lower40.700.35.007.0092.005.96874Lower50.800.28.005.0076.006.80017Lower60.600.15.004.0078.004.66701Intermediate70.60.111.001.0087.004.67612IntermediateTable 31
Prediction and calculation results of ANFIS.
SchemeMaximum overbreak (m)Maximum underbreak (m)Area of overbreak (m2)Volume of overbreak (m3)Blast hole utilization factor (%)Comprehensive quality indexRankingEvaluation levels10.651790.0423711.26662.370583.80925.05503Intermediate20.75010.190159.12084.661382.19397.00896Lower30.671070.110918.33113.869981.43166.24114Lower40.910530.348410.78486.167685.00238.14797Very poor50.744230.184239.06314.600982.15726.58275Lower60.509910.050686.72082.256179.87764.07841Better70.593490.033137.5563.093180.68374.28722IntermediateAs shown in Table27, the ANFIS has the highest accuracy among the three comprehensive optimization control models; the maximum error is the maximum underbreak of 0.059%, and the minimum error is the area of overbreak and the blast hole utilization factor, which is 0.001%. The ENN has a general accuracy; the maximum error is the maximum underbreak of 17.647%, and the minimum error is the blast hole utilization factor, which is 0. By contrast, the BP-ANN has poor accuracy; the maximum error is the volume of overbreak of 17.841%, and the minimum error is the maximum underbreak, which is 1.588%. The table also shows that when the tunnel smooth blasting quality is controlled and predicted by using the three constructed comprehensive optimization control models, the maximum and minimum errors of their respective predictions are not identical, thereby showing that these methods have their own advantages in the prediction and can complement each other. Thus, providing the control suggestions of the above three methods comprehensively are necessary, scientific, and feasible.Table29 shows that the sequence of the comprehensive quality index of tunnel smooth blasting of the seven designed schemes is as follows: scheme7<scheme6<scheme2<scheme4<scheme3<scheme5<scheme1, and the corresponding comprehensive quality index is as follows: 4.7826<4.9627<5.0385<5.0471<5.3801<5.6821<5.7305. For its evaluation level, the other six scheme levels are intermediate, except the scheme 1 level is lower. Therefore, scheme 7 is the optimal one and can be used as the recommended control parameters, that is, the neighboring eyes spacing is not adjusted, the minimum resistance line is down-adjusted by 20%, and the linear charge density is up-adjusted by 1%. It is followed by scheme 6, which can also be used as the recommended control parameters, that is, the neighboring eyes spacing is down-adjusted by 20%, the minimum resistance line is down-adjusted by 15%, and the linear charge density is down-adjusted by 1%.Table30 shows that the sequence of the comprehensive quality index of tunnel smooth blasting of the seven designed schemes is as follows: scheme6<scheme7<scheme2<scheme4<scheme1<scheme3<scheme5, and the corresponding comprehensive quality index is successively as follows: 4.6670<4.6761<5.6525<5.9687<6.0994<6.4114<6.8001. The evaluation levels of schemes 2, 6, and 7 are intermediate, and the evaluation levels of the other three schemes are lower. Therefore, scheme 6 is the optimal scheme, which can be used as the recommended control parameters, that is, the neighboring eyes spacing is down-adjusted by 20%, the minimum resistance line is down-adjusted by 15%, and the linear charge density is down-adjusted by 1%. It is followed by scheme 7, which can also be used as the recommended control parameters, that is, the neighboring eyes spacing is not adjusted, the minimum resistance line is down-adjusted by 20%, and the linear charge density is up-adjusted by 1%.Table31 shows that the sequence of the comprehensive quality index of tunnel smooth blasting of seven designed schemes is as follows: scheme6<scheme7<scheme1<scheme3<scheme5<scheme2<scheme4, and the corresponding comprehensive quality index is as follows: 4.0784<4.2872<5.0550<6.2411<6.5827<7.0089<8.1479. The evaluation level of scheme 1 is better, the evaluation levels of schemes 6 and 7 are intermediate, and the evaluation levels of schemes 2, 3, and 5 are lower. Therefore, scheme 6 is the optimal scheme and can be used as the recommended control parameters, that is, the neighboring eyes spacing is down-adjusted by 20%, the minimum resistance line is down-adjusted by 15%, and the linear charge density is down-adjusted by 1%. It is followed by scheme 7, which can also be used as the recommended control parameters, that is, the neighboring eyes spacing is not adjusted, the minimum resistance line is down-adjusted by 20%, and the linear charge density is up-adjusted by 1%;To further analyze the advantages of the BP-ANN, the ENN, and the ANFIS in the application of tunnel smooth blasting quality control, the corresponding optimal scheme and the better scheme are compared.Table32 shows that, among the three comprehensive optimization control models, the comprehensive quality index accuracy given by the ANFIS prediction is the highest; the proposed control scheme is more reliable, followed by the ENN, and then the BP-ANN. After comprehensive optimization, the optimal recommendation control scheme given by the ANFIS and ENN is scheme 6, and the optimal control scheme is scheme 7, which proceeds is as follows: the neighboring eyes spacing is down-adjusted by 20%, the minimum resistance line is down-adjusted by 15%, and the linear charge density is down-adjusted by 1%. In the better scheme, the neighboring eyes spacing is not adjusted, the minimum resistance line is down-adjusted by 20%, and the linear charge density is up-adjusted by 1%. In addition, the control scheme obtained by BP-ANN optimization is opposite to the optimal and better control scheme obtained by ANFIS and ENN optimization. Thus, the above three comprehensive optimization models can complement each other in controlling tunnel smooth blasting, and the field tunnel duty engineer can perform appropriate adjustment of the tunnel blasting parameters according to the actual situation of blasting, combined with the obtained blasting control, to ensure that the tunnel blasting molding is regular and meets the requirements of the design contour line, guaranteeing the safe construction of the tunnel.Table 32
Comparison of the optimal scheme and the better scheme of three comprehensive optimization control models.
Comprehensive optimization control modelSchemeComprehensive quality indexScheme sequenceEvaluation levelBP-ANN74.78261Intermediate64.96272IntermediateENN64.6671Intermediate74.67612IntermediateANFIS64.07841Better74.28722Intermediate


## 4. Conclusion

(1)
This paper presents a method of constructing the tunnel smooth blasting quality control index system and establishes a tunnel smooth blasting quality control index system with seven criteria layers of geological conditions, explosive properties, borehole parameters, charge parameters, method of initiation, tunnel parameters, and construction factors, and a total of nine indexes(2)
The comprehensive optimization control models of BP-ANN, ANFIS, and ENN for tunnel smooth blasting quality are established. The established models can provide real-time, accurate, and objective control suggestions and control values of tunnel smooth blasting quality, can quickly optimize and adjust the tunnel smooth blasting parameters according to the evaluation level of tunnel smooth blasting quality, and change the postcontrol of smooth blasting quality to precontrol(3)
Taking the Chengdu–Chongqing high-speed rail Da’an Tunnel as the background, the blasting parameters of the tunnel section that needs to be controlled are optimized and adjusted by using the uniform design method to verify the practicability and correctness of the comprehensive optimization control model of the BP-ANN, ANFIS, and ENN. Results show that the comprehensive optimization control models can change the focus of tunnel smooth blasting quality control from the traditional single index control method to a dynamic, intelligent, pluralistic, and integrated control technology



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