# Study on Identification of Construction Method for Ultra-Large-Span Tunnel

Authors: Xu Chongbang; Qin Youlin
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

Although the determination of tunnel construction methods is extremely critical for the construction of ultra-large-span tunnels, the determination of construction methods is still at a qualitative level, which relies on the engineering experience of on-site technicians and lacks rigorous and systematic theoretical basis and technical standards. By means of orthogonal test method, the proper construction method was established for the deep-buried ultra-large-span tunnel where the tunnel excavation span, tunnel surrounding rock strength, and rock integrity coefficient were set as the main control factors. The stability of tunnel surrounding rock under various test conditions was quantified according to the plastic zone properties calculated by the three-factor and five-level orthogonal test model. Meanwhile, the macro form and quantitative method of test combinations under different levels of various factors were proposed to obtain the influence of each factor on the stability of tunnel surrounding rock, and thus the functional relations between various factors and tunnel stability were obtained. On this basis, the identification and the criterion of the ultra-large-span tunnel construction method were established, which can quantitatively reflect the contribution of excavation span of the tunnel, the number of lateral drifts in cross section, surrounding rock strength, and rock integrity coefficient to surrounding rock stability of the tunnel. The construction method calculation results of the Malin tunnel, a practical underground project, are obtained according to the orthogonal test model calculation. Based on the method, Malin tunnel can be constructed safely and efficiently. The research results could provide the theoretical basis for the identification and selection of construction method for ultra-large-span tunnel.


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## Body

## 1. Introduction

The determination of tunnel construction methods is extremely critical for the construction of ultra-large-span tunnels, which directly affects the construction safety, progress, costs, and the configuration of humans, machines, and materials during construction. Various methods for ultra-large-span tunnel construction have been developed under the influences of many factors including the size of the tunnel section and topographical, engineering geological, and hydrogeological conditions. The commonly used methods include the center diaphragm method (CD method) [1], center cross diagram method (CRD) [2–6], the double-side drift method [7–9] and the three-stage and seven-step method [10, 11], and other methods derived from these basic methods. In the construction of ultra-large-span tunnels, the determination of construction methods is still at a qualitative level, which relies on the engineering experience of on-site technicians and lacks rigorous and systematic theoretical basis and related technical standards [12].In common practices, factors considered during selecting construction methods often include (1) project factors, such as overall excavation span of the tunnel, the maximum single excavation span, and auxiliary engineering measures [13], and (2) geological and environmental factors, such as the properties of surrounding rock (the strength of the surrounding rock and the integrity coefficient of the rock mass) [14–19], groundwater [20], and the in situ stress [21]. In order to ensure the stability of the tunnel after blasting and before the initial support construction, the maximum one-step excavation span of the tunnel, the strength of the surrounding rock, and rock integrity are placed at the top priority. Other factors are generally considered as supplementary grounds for final decision. In this paper, we established the orthogonal test model to determine the proper construction method for the deep-buried ultra-large-span tunnel where the tunnel excavation span, tunnel surrounding rock strength, and rock integrity coefficient were set as the main control factors. Our work aims to establish the evaluation system for selection of construction method and provide theoretical calculation basis for determining the number of lateral drifts in cross section of ultra-large-span tunnels through the quantification of control factors on the stability of surrounding rock during tunnel excavation.


## 2. Orthogonal Test Design

### 2.1. The Level of Orthogonal Factors

In order to elucidate the influence of tunnel span, surrounding rock strength, and rock integrity coefficient on the stability of tunnel surrounding rock, a five-level orthogonal test scheme is designed in this paper. The tunnel span, surrounding rock strength, and rock integrity coefficient are represented by A, B, and C, respectively. The five levels of the three factors are set as follows:(1)
Factor A: with reference to the drift span, common tunnel span, and ultra-large-span tunnel span in highway tunnels, the five levels of factor A are designed as 6 m, 9 m, 12 m, 15 m, and 18 m, and the tunnel cross section is shown in Figure1.(2)
Factor B: factor B is the rock strength, which is divided according to the degree of soft and hard rock. The five levels of factor B are designed as 2 MPa, 10 MPa, 20 MPa, 40 MPa, and 65 MPa. According to the Mohr–Coulomb criterion, the internal friction angleφ and cohesive force C corresponding to the five levels are listed in Table 1.(3)
Factor C: the five levels of factor C, which represents the coefficient of surrounding rock integrity, are 0.1, 0.2, 0.4, 0.6, and 0.75. The five levels of factor C in the test are shown in Table2. The test parameters of the joint plane are selected in accordance with the recommended values of the peak shear strength of the rock discontinuity structural plane in the “Road Tunnel Design Rules” [22], as listed in Table 3.Figure 1
Five types of tunnel cross section. (a) With span of 6 m. (b) With span of 9 m. (c) With span of 12 m. (d) With span of 15 m. (e) With span of 18 m.
(a)(b)(c)(d)(e)Table 1
Parameter values of each level of factor A.
LevelCompressive strength (MPa)Internal friction angleφ (°)Cohesive forceC (MPa)Volumetric weightγ (kN·m−3)Elasticity modulusE (GPa)Poisson’s ratioμ1227.51.6221.00.3210372.5221.00.332046.44221.00.344056.66221.00.3565637.8221.00.3Note. The influences of volumetric weight, elasticity modulus, and Poisson's ratio were not considered.Table 2
Parameter values of each level of factor C.
LevelNumber of joint planesSpace of joint planeJoint inclination angle (°)Coefficient of surrounding rock integrity140.20/90/45/1350.1230.30/90/450.2320.40/900.4420.80/900.6521.50/900.75Table 3
Joint plane parameters.
Internal friction angleφ (°)Cohesive forceC (MPa)Compressive strength (MPa)150.060.13


### 2.2. Orthogonal Test Combinations

According to the orthogonal test design [23], the three-factor and five-level orthogonal test requires a total of 25 tests. The combinations of orthogonal tests are shown in Table 4:Table 4
Orthogonal test analysis.
No.Excavation spanSurrounding rock strengthCoefficient of surrounding rock integrityCodeABC11 (6 m)1 (2 MPa)1 (0.1)A1B1C121 (6 m)2 (10 MPa)2 (0.2)A1B2C231 (6 m)3 (20 MPa)3 (0.4)A1B3C341 (6 m)4 (40 MPa)4 (0.6)A1B4C451 (6 m)5 (65 MPa)5 (0.75)A1B5C562 (9 m)1 (2 MPa)2 (0.2)A2B1C272 (9 m)2 (10 MPa)3 (0.4)A2B2C382 (9 m)3 (20 MPa)4 (0.6)A2B3C492 (9 m)4 (40 MPa)5 (0.75)A2B4C5102 (9 m)5 (65 MPa)1 (0.1)A2B5C1113 (12 m)1 (2 MPa)3 (0.4)A3B1C3123 (12 m)2 (10 MPa)4 (0.6)A3B2C4133 (12 m)3 (20 MPa)5 (0.75)A3B3C5143 (12 m)4 (40 MPa)1 (0.1)A3B4C1153 (12 m)5 (65 MPa)2 (0.2)A3B5C2164 (15 m)1 (2 MPa)4 (0.6)A4B1C4174 (15 m)2 (10 MPa)5 (0.75)A4B2C5184 (15 m)3 (20 MPa)1 (0.1)A4B3C1194 (15 m)4 (40 MPa)2 (0.2)A4B4C2204 (15 m)5 (65 MPa)3 (0.4)A4B5C3215 (18 m)1 (2 MPa)5 (0.75)A5B1C5225 (18 m)2 (10 MPa)1 (0.1)A5B2C1235 (18 m)3 (20 MPa)2 (0.2)A5B3C2245 (18 m)4 (40 MPa)3 (0.4)A5B4C3255 (18 m)5 (65 MPa)4 (0.6)A5B5C4


## 2.1. The Level of Orthogonal Factors

In order to elucidate the influence of tunnel span, surrounding rock strength, and rock integrity coefficient on the stability of tunnel surrounding rock, a five-level orthogonal test scheme is designed in this paper. The tunnel span, surrounding rock strength, and rock integrity coefficient are represented by A, B, and C, respectively. The five levels of the three factors are set as follows:(1)
Factor A: with reference to the drift span, common tunnel span, and ultra-large-span tunnel span in highway tunnels, the five levels of factor A are designed as 6 m, 9 m, 12 m, 15 m, and 18 m, and the tunnel cross section is shown in Figure1.(2)
Factor B: factor B is the rock strength, which is divided according to the degree of soft and hard rock. The five levels of factor B are designed as 2 MPa, 10 MPa, 20 MPa, 40 MPa, and 65 MPa. According to the Mohr–Coulomb criterion, the internal friction angleφ and cohesive force C corresponding to the five levels are listed in Table 1.(3)
Factor C: the five levels of factor C, which represents the coefficient of surrounding rock integrity, are 0.1, 0.2, 0.4, 0.6, and 0.75. The five levels of factor C in the test are shown in Table2. The test parameters of the joint plane are selected in accordance with the recommended values of the peak shear strength of the rock discontinuity structural plane in the “Road Tunnel Design Rules” [22], as listed in Table 3.Figure 1
Five types of tunnel cross section. (a) With span of 6 m. (b) With span of 9 m. (c) With span of 12 m. (d) With span of 15 m. (e) With span of 18 m.
(a)(b)(c)(d)(e)Table 1
Parameter values of each level of factor A.
LevelCompressive strength (MPa)Internal friction angleφ (°)Cohesive forceC (MPa)Volumetric weightγ (kN·m−3)Elasticity modulusE (GPa)Poisson’s ratioμ1227.51.6221.00.3210372.5221.00.332046.44221.00.344056.66221.00.3565637.8221.00.3Note. The influences of volumetric weight, elasticity modulus, and Poisson's ratio were not considered.Table 2
Parameter values of each level of factor C.
LevelNumber of joint planesSpace of joint planeJoint inclination angle (°)Coefficient of surrounding rock integrity140.20/90/45/1350.1230.30/90/450.2320.40/900.4420.80/900.6521.50/900.75Table 3
Joint plane parameters.
Internal friction angleφ (°)Cohesive forceC (MPa)Compressive strength (MPa)150.060.13


## 2.2. Orthogonal Test Combinations

According to the orthogonal test design [23], the three-factor and five-level orthogonal test requires a total of 25 tests. The combinations of orthogonal tests are shown in Table 4:Table 4
Orthogonal test analysis.
No.Excavation spanSurrounding rock strengthCoefficient of surrounding rock integrityCodeABC11 (6 m)1 (2 MPa)1 (0.1)A1B1C121 (6 m)2 (10 MPa)2 (0.2)A1B2C231 (6 m)3 (20 MPa)3 (0.4)A1B3C341 (6 m)4 (40 MPa)4 (0.6)A1B4C451 (6 m)5 (65 MPa)5 (0.75)A1B5C562 (9 m)1 (2 MPa)2 (0.2)A2B1C272 (9 m)2 (10 MPa)3 (0.4)A2B2C382 (9 m)3 (20 MPa)4 (0.6)A2B3C492 (9 m)4 (40 MPa)5 (0.75)A2B4C5102 (9 m)5 (65 MPa)1 (0.1)A2B5C1113 (12 m)1 (2 MPa)3 (0.4)A3B1C3123 (12 m)2 (10 MPa)4 (0.6)A3B2C4133 (12 m)3 (20 MPa)5 (0.75)A3B3C5143 (12 m)4 (40 MPa)1 (0.1)A3B4C1153 (12 m)5 (65 MPa)2 (0.2)A3B5C2164 (15 m)1 (2 MPa)4 (0.6)A4B1C4174 (15 m)2 (10 MPa)5 (0.75)A4B2C5184 (15 m)3 (20 MPa)1 (0.1)A4B3C1194 (15 m)4 (40 MPa)2 (0.2)A4B4C2204 (15 m)5 (65 MPa)3 (0.4)A4B5C3215 (18 m)1 (2 MPa)5 (0.75)A5B1C5225 (18 m)2 (10 MPa)1 (0.1)A5B2C1235 (18 m)3 (20 MPa)2 (0.2)A5B3C2245 (18 m)4 (40 MPa)3 (0.4)A5B4C3255 (18 m)5 (65 MPa)4 (0.6)A5B5C4


## 3. Calculations and Results

### 3.1. Model Size

In order to eliminate the boundary effect of the tunnel calculation model, the size of the model was determined as 200 m (width) × 110 m (height). The buried depth of the tunnel was set as 50 m, as the typical depth of deep-buried tunnel. The tunnel structure was placed in the center of the model (Figure2). The simulated tunnel construction employed a one-step excavation method without considering the role of lining support structure. The stress release rate of the tunnel surrounding rock was defined as 30%.Figure 2
Calculation model of no. 1 test.


### 3.2. Criterion of Surrounding Rock Instability

In the experimental calculation model, the surrounding rock was assumed as ideal elastoplastic material, and thus the Mohr–Coulomb constitutive model was used to develop the criterion of surrounding rock instability [22] based on “Road Tunnel Design Rules.” It is assumed that the surrounding rock becomes unstable when plastic zones appear in the surrounding rock at the tunnel arch and the side walls and these zones communicate with each other. Meanwhile, in order to quantify the stability of the tunnel under each simulated condition, the properties of the plastic zone were quantified according to Table 5.Table 5
Criterion and quantitative standard of surrounding rock stability state.
No.Conditions of the plastic zoneStability of surrounding rockQuantitative score1Communicated plastic zones occur in both joint planes and rock blocksUnstable12Plastic zones occur in both joint planes and rock blocks, but only communicate in joint planesUnstable23Communicated plastic zones only occur in joint planesUnstable34Noncommunicated plastic zones occur in both joint planes and rock blocksStable45Noncommunicated plastic zones occur in joint planesStable56No plastic zones occur in both joint planes and rock blocksStable6


### 3.3. Calculation Results

#### 3.3.1. Example of Surrounding Rock Stability Analysis

Here no. 1 A1B1C1 is taken as an example to illustrate the analysis process of surrounding rock stability. In the no. 1 test, there are multiple tensile stress distribution areas in the tunnel vault and arch wall (Figure3). Plastic zones are found at the joint planes and rock blocks of the tunnel arch and the side walls, which connect each other (Figure 4). Therefore, it can be concluded that the full-face excavation under this three-factor combination is unstable. The quantitative score of the no. 1 test is 1 point.Figure 3
Principal stress distribution of surrounding rock.Figure 4
Distribution of plastic zone of surrounding rock.


#### 3.3.2. Test Results

According to the conditions of the plastic zone calculated from the 25 sets of experiments, the results of the experimental calculations were quantified according to the quantitative rules. The quantitative statistical results and the tunnel stability are listed in Table6.Table 6
Quantification of test data and stability index.
Test no.Test codeStabilityQuantitative score1A1B1C1Unstable12A1B2C2Unstable23A1B3C3Stable54A1B4C4Stable65A1B5C5Stable66A2B1C2Unstable17A2B2C3Unstable38A2B3C4Stable59A2B4C5Stable510A2B5C1Unstable311A3B1C3Unstable112A3B2C4Unstable313A3B3C5Stable514A3B4C1Unstable315A3B5C2Stable416A4B1C4Unstable117A4B2C5Unstable318A4B3C1Unstable119A4B4C2Unstable320A4B5C3Stable521A5B1C5Unstable222A5B2C1Unstable123A5B3C2Unstable224A5B4C3Unstable325A5B5C4Stable5


## 3.1. Model Size

In order to eliminate the boundary effect of the tunnel calculation model, the size of the model was determined as 200 m (width) × 110 m (height). The buried depth of the tunnel was set as 50 m, as the typical depth of deep-buried tunnel. The tunnel structure was placed in the center of the model (Figure2). The simulated tunnel construction employed a one-step excavation method without considering the role of lining support structure. The stress release rate of the tunnel surrounding rock was defined as 30%.Figure 2
Calculation model of no. 1 test.


## 3.2. Criterion of Surrounding Rock Instability

In the experimental calculation model, the surrounding rock was assumed as ideal elastoplastic material, and thus the Mohr–Coulomb constitutive model was used to develop the criterion of surrounding rock instability [22] based on “Road Tunnel Design Rules.” It is assumed that the surrounding rock becomes unstable when plastic zones appear in the surrounding rock at the tunnel arch and the side walls and these zones communicate with each other. Meanwhile, in order to quantify the stability of the tunnel under each simulated condition, the properties of the plastic zone were quantified according to Table 5.Table 5
Criterion and quantitative standard of surrounding rock stability state.
No.Conditions of the plastic zoneStability of surrounding rockQuantitative score1Communicated plastic zones occur in both joint planes and rock blocksUnstable12Plastic zones occur in both joint planes and rock blocks, but only communicate in joint planesUnstable23Communicated plastic zones only occur in joint planesUnstable34Noncommunicated plastic zones occur in both joint planes and rock blocksStable45Noncommunicated plastic zones occur in joint planesStable56No plastic zones occur in both joint planes and rock blocksStable6


## 3.3. Calculation Results

### 3.3.1. Example of Surrounding Rock Stability Analysis

Here no. 1 A1B1C1 is taken as an example to illustrate the analysis process of surrounding rock stability. In the no. 1 test, there are multiple tensile stress distribution areas in the tunnel vault and arch wall (Figure3). Plastic zones are found at the joint planes and rock blocks of the tunnel arch and the side walls, which connect each other (Figure 4). Therefore, it can be concluded that the full-face excavation under this three-factor combination is unstable. The quantitative score of the no. 1 test is 1 point.Figure 3
Principal stress distribution of surrounding rock.Figure 4
Distribution of plastic zone of surrounding rock.


### 3.3.2. Test Results

According to the conditions of the plastic zone calculated from the 25 sets of experiments, the results of the experimental calculations were quantified according to the quantitative rules. The quantitative statistical results and the tunnel stability are listed in Table6.Table 6
Quantification of test data and stability index.
Test no.Test codeStabilityQuantitative score1A1B1C1Unstable12A1B2C2Unstable23A1B3C3Stable54A1B4C4Stable65A1B5C5Stable66A2B1C2Unstable17A2B2C3Unstable38A2B3C4Stable59A2B4C5Stable510A2B5C1Unstable311A3B1C3Unstable112A3B2C4Unstable313A3B3C5Stable514A3B4C1Unstable315A3B5C2Stable416A4B1C4Unstable117A4B2C5Unstable318A4B3C1Unstable119A4B4C2Unstable320A4B5C3Stable521A5B1C5Unstable222A5B2C1Unstable123A5B3C2Unstable224A5B4C3Unstable325A5B5C4Stable5


## 3.3.1. Example of Surrounding Rock Stability Analysis

Here no. 1 A1B1C1 is taken as an example to illustrate the analysis process of surrounding rock stability. In the no. 1 test, there are multiple tensile stress distribution areas in the tunnel vault and arch wall (Figure3). Plastic zones are found at the joint planes and rock blocks of the tunnel arch and the side walls, which connect each other (Figure 4). Therefore, it can be concluded that the full-face excavation under this three-factor combination is unstable. The quantitative score of the no. 1 test is 1 point.Figure 3
Principal stress distribution of surrounding rock.Figure 4
Distribution of plastic zone of surrounding rock.


## 3.3.2. Test Results

According to the conditions of the plastic zone calculated from the 25 sets of experiments, the results of the experimental calculations were quantified according to the quantitative rules. The quantitative statistical results and the tunnel stability are listed in Table6.Table 6
Quantification of test data and stability index.
Test no.Test codeStabilityQuantitative score1A1B1C1Unstable12A1B2C2Unstable23A1B3C3Stable54A1B4C4Stable65A1B5C5Stable66A2B1C2Unstable17A2B2C3Unstable38A2B3C4Stable59A2B4C5Stable510A2B5C1Unstable311A3B1C3Unstable112A3B2C4Unstable313A3B3C5Stable514A3B4C1Unstable315A3B5C2Stable416A4B1C4Unstable117A4B2C5Unstable318A4B3C1Unstable119A4B4C2Unstable320A4B5C3Stable521A5B1C5Unstable222A5B2C1Unstable123A5B3C2Unstable224A5B4C3Unstable325A5B5C4Stable5


## 4. Identification of Construction Method for Ultra-Large-Span Tunnel

### 4.1. Data Processing

In order to quantitatively analyze the influence of a single factor on the stability of the tunnel, the test data of each group were processed in combinations from a macro perspective to eliminate the impact of other factors based on the same frequency and probability of each level of every factor in the orthogonal test. Factor A is used as an example to explain the detailed process.


#### 4.1.1. Combination of Test Conditions

The levels of factor A are the main study targets. Combining the levels of factor A with the five levels of factor B and factor C obtains the macro form of the test combinations (Table7). The obtained combinations have the same macro combination of factor B and factor C for each level of factor A. Therefore, on this basis, comparative analysis of the influence of various levels of factor A on tunnel stability can be performed.Table 7
Macro form of test combination at each level of factor A.
No.Excavation span (A)Code of test combinationsMacro form of the test combinations11A1B1C1、A1B2C2、A1B3C3、A1B4C4、A1B5C5A1B(5)C(5)22A2B1C2、A2B2C3、A2B3C4、A2B4C5、A2B5C1A2B(5)C(5)33A3B1C3、A3B2C4、A3B3C5、A3B4C1、A3B5C2A3B(5)C(5)44A4B1C4、A4B2C5、A4B3C1、A4B4C2、A4B5C3A4B(5)C(5)55A5B1C5、A5B2C1、A5B3C2、A5B4C3、A5B5C4A5B(5)C(5)Note. B(5) represents the combinations of five levels of factor B and C(5) represents the combinations of five levels of factor C.


#### 4.1.2. Quantification of the Macro Form of the Test Combinations

In order to quantify the influence of various factors on the tunnel stability, it is necessary to quantify the macro form of the test combinations. Given that the conditions under the combination are all independent, the linear superposition method is used to define the quantitative scores of factor A under each level to obtain the quantitative index F of tunnel stability under different combinations. The detailed calculation process is as follows:(a)
The first level of factor A (6 m span): IA = A1B(5)C(5) = 1 + 2 + 5 + 6 + 6 = 20.(b)
The second level of factor A (9 m span): IIA = A2B(5)C(5) = 1 + 3 + 5 + 5 +3 = 17.(c)
The third level of factor A (12 m span): IIIA = A3B(5)C(5) = 1 + 3 + 5 + 3+ 4 = 16.(d)
The fourth level of factor A (15 m span): IVA = A4B(5)C(5) = 1 + 3 + 1 + 3 +5 = 13.(e)
The fifth level of factor A (18 m span): VA = A5B(5)C(5) = 2 + 1 + 2 + 3 + 5 = 13.


#### 4.1.3. Processing Results

The data processing of factors B and C is carried out in the same way, and their quantitative index F under various levels is calculated, as listed in Table8.Table 8
Quantitative index value of tunnel stability under different factor levels.
Level of factorQuantitative index value of tunnel stability FTunnel spanARock strengthBCoefficient of rock integrityCI2069II171212III161817IV132020V132321Range71712As indicated by the range of the stability quantitative index of three factors in Table8 [24], the strength of the surrounding rock has the most significant impact on tunnel stability, followed by the surrounding rock integrity and the span of the tunnel in decreasing order.


### 4.2. The Influence of Main Control Factors on Tunnel Stability

Based on the stability quantitative index of three factors listed in Table8, the influence rule of these factors on tunnel stability can be drawn, as shown in Figures 5–7, respectively.Figure 5
Fitting curve between stability index of surrounding rock and span of tunnel.Figure 6
Fitting curve between stability index and strength of surrounding rock.Figure 7
Fitting curve between stability index of surrounding rock and rock mass integrity coefficient.


#### 4.2.1. Tunnel Span

According to Figure5, the tunnel excavation span has a negative correlation with the stability of the surrounding rock. The stability of the tunnel deteriorates with the increase of tunnel span. The relationship between them is expressed as a power function:(1)fA=42.39A−0.41.


#### 4.2.2. Compressive Strength of Surrounding Rock

Figure6 shows a strong positive correlation between surrounding rock strength and tunnel stability. A higher compressive strength of surrounding rock is beneficial for better tunnel stability. Their relation can be expressed as(2)fB=4.80B0.393.


#### 4.2.3. Coefficient of Surrounding Rock Integrity

The tunnel stability is positively related with the coefficient of surrounding rock integrity, indicating that higher coefficient of surrounding rock integrity contributes to tunnel stability. The relation can be expressed as(3)fC=6.208lnC+22.78,where fC>0; therefore, the coefficient of surrounding rock C should be greater than 0.03.


### 4.3. The Expression of Quantitative Index of Surrounding Rock Stability

The stability of the surrounding rock of the tunnel is the result of the combined action of the three main control factors. The influences of the main control factors on the stability are interrelated and coupled. This correlation can be expressed by their product and a coefficientk. Therefore, the tunnel stability after excavation can be quantified as(4)F=kfAfBfC.Substituting equations (1)–(3) into equation (4), F can be derived:(5)F=A−0.41B0.3936.208lnC+22.78,where k is a constant value (k = 0.004907).


### 4.4. Criterion of Quantification of Surrounding Rock Stability

Substituting the test calculation parameters (Table4) into equation (5), the value of the tunnel stability quantitative index F for each test can be obtained (Table 9).Table 9
Index calculation value of tunnel stability.
Test no.Test codeStabilityF1A1B1C1Unstable5.322A5B2C1Unstable6.46A2B1C2Unstable6.811A3B1C3Unstable8.121A5B1C5Unstable8.416A4B1C4Unstable8.518A4B3C1Unstable9.123A5B3C2Unstable12.714A3B4C1Unstable13.12A1B2C2Unstable15.217A4B2C5Unstable17.17A2B2C3Unstable17.212A3B2C4Unstable17.510A2B5C1Unstable17.819A4B4C2Unstable1824A5B4C3Unstable22.315A3B5C2Stable23.813A3B3C5Stable24.68A2B3C4Stable25.93A1B3C3Stable26.620A4B5C3Stable2925A5B5C4Stable30.99A2B4C5Stable36.34A1B4C4Stable40.15A1B5C5Stable51.9It can be seen from Table9 that in 25 sets of orthogonal tests, the minimum index is 5.3 and the maximum is 22.3 when the surrounding rock is unstable after tunnel excavation. And the minimum index is 23.8 and the maximum is 51.9 when the surrounding rock of the tunnel remains stable. Therefore, the criteria for stability of surrounding rock can be given as follows:(1)
IfF ≥ 23, the surrounding rock is in stable sate.(2)
IfF < 23, the surrounding rock becomes unstable.According to this criterion and the quantification rules, the stability index F can be classified as six levels specifically, as listed in Table10.Table 10
Index value and qualitative description of tunnel stability.
FUnstable stateStable state<13[13, 17)[17, 23)[23, 26)[26, 40)≥40Description of stabilityExtremely unstableVery unstableUnstableBasically stableVery stableHighly stable


### 4.5. Criterion for Tunnel Construction Method Selection

#### 4.5.1. One-Step Maximum Excavation Span

According to equation (5), for a given tunnel surrounding rock, a proper one-step excavation span should be selected to satisfy the index F ≥ 23 to ensure the stability of the surrounding rock during excavation. Thus, maximum span Amax of the next-step excavation can be calculated under given surrounding rock properties (strength and integrity coefficient) when assuming that F = 23, as shown in the following equation:(6)Amax=B0.3936.208lnC+22.78232.44.


#### 4.5.2. Determination of the Number of Drifts

Assuming that the maximum span of tunnel excavation isL and the number of lateral drifts in the cross section is N, it can be seen from equation (6) that the number of lateral drifts in the tunnel section should be(7)N≥LAmax=LB0.3936.208lnC+22.78/232.44.Thus,(8)Nmin=LB0.3936.208lnC+22.78/232.44,where Nmin should be integer.


#### 4.5.3. Bench Division of Tunnel Drift

After determining the number of lateral drifts, the stability state of the tunnel drift is used as a reference for the necessity of bench cut. It is recommended to perform bench cut construction in the lateral drifts as instructed by Table11.Table 11
Stability index value and bench division of tunnel drift.
Description of tunnel stabilityBasically stableVery stableHighly stableBench divisionBench division is necessary and temporary invert should be adoptedBench division is necessary and temporary invert is not compulsiveBench division is unnecessary


### 4.6. Influencing Analysis of Other Factors

In the construction phase of tunnel engineering, the identification of construction method should consider not only the three crucial factors including tunnel span, rock mass integrity coefficient, and strength of surrounding rock but also the secondary factors such as in situ stress, groundwater, and construction capacity of the subcontractors. The secondary influence factors are restricted by the geological conditions of the tunnel site, which is not universal. Therefore, in the actual tunnel projects, the influence of secondary factors can be revised according to the specific situation of projects, and the influence of secondary factors is reflected by means of revision.


## 4.1. Data Processing

In order to quantitatively analyze the influence of a single factor on the stability of the tunnel, the test data of each group were processed in combinations from a macro perspective to eliminate the impact of other factors based on the same frequency and probability of each level of every factor in the orthogonal test. Factor A is used as an example to explain the detailed process.


### 4.1.1. Combination of Test Conditions

The levels of factor A are the main study targets. Combining the levels of factor A with the five levels of factor B and factor C obtains the macro form of the test combinations (Table7). The obtained combinations have the same macro combination of factor B and factor C for each level of factor A. Therefore, on this basis, comparative analysis of the influence of various levels of factor A on tunnel stability can be performed.Table 7
Macro form of test combination at each level of factor A.
No.Excavation span (A)Code of test combinationsMacro form of the test combinations11A1B1C1、A1B2C2、A1B3C3、A1B4C4、A1B5C5A1B(5)C(5)22A2B1C2、A2B2C3、A2B3C4、A2B4C5、A2B5C1A2B(5)C(5)33A3B1C3、A3B2C4、A3B3C5、A3B4C1、A3B5C2A3B(5)C(5)44A4B1C4、A4B2C5、A4B3C1、A4B4C2、A4B5C3A4B(5)C(5)55A5B1C5、A5B2C1、A5B3C2、A5B4C3、A5B5C4A5B(5)C(5)Note. B(5) represents the combinations of five levels of factor B and C(5) represents the combinations of five levels of factor C.


### 4.1.2. Quantification of the Macro Form of the Test Combinations

In order to quantify the influence of various factors on the tunnel stability, it is necessary to quantify the macro form of the test combinations. Given that the conditions under the combination are all independent, the linear superposition method is used to define the quantitative scores of factor A under each level to obtain the quantitative index F of tunnel stability under different combinations. The detailed calculation process is as follows:(a)
The first level of factor A (6 m span): IA = A1B(5)C(5) = 1 + 2 + 5 + 6 + 6 = 20.(b)
The second level of factor A (9 m span): IIA = A2B(5)C(5) = 1 + 3 + 5 + 5 +3 = 17.(c)
The third level of factor A (12 m span): IIIA = A3B(5)C(5) = 1 + 3 + 5 + 3+ 4 = 16.(d)
The fourth level of factor A (15 m span): IVA = A4B(5)C(5) = 1 + 3 + 1 + 3 +5 = 13.(e)
The fifth level of factor A (18 m span): VA = A5B(5)C(5) = 2 + 1 + 2 + 3 + 5 = 13.


### 4.1.3. Processing Results

The data processing of factors B and C is carried out in the same way, and their quantitative index F under various levels is calculated, as listed in Table8.Table 8
Quantitative index value of tunnel stability under different factor levels.
Level of factorQuantitative index value of tunnel stability FTunnel spanARock strengthBCoefficient of rock integrityCI2069II171212III161817IV132020V132321Range71712As indicated by the range of the stability quantitative index of three factors in Table8 [24], the strength of the surrounding rock has the most significant impact on tunnel stability, followed by the surrounding rock integrity and the span of the tunnel in decreasing order.


## 4.1.1. Combination of Test Conditions

The levels of factor A are the main study targets. Combining the levels of factor A with the five levels of factor B and factor C obtains the macro form of the test combinations (Table7). The obtained combinations have the same macro combination of factor B and factor C for each level of factor A. Therefore, on this basis, comparative analysis of the influence of various levels of factor A on tunnel stability can be performed.Table 7
Macro form of test combination at each level of factor A.
No.Excavation span (A)Code of test combinationsMacro form of the test combinations11A1B1C1、A1B2C2、A1B3C3、A1B4C4、A1B5C5A1B(5)C(5)22A2B1C2、A2B2C3、A2B3C4、A2B4C5、A2B5C1A2B(5)C(5)33A3B1C3、A3B2C4、A3B3C5、A3B4C1、A3B5C2A3B(5)C(5)44A4B1C4、A4B2C5、A4B3C1、A4B4C2、A4B5C3A4B(5)C(5)55A5B1C5、A5B2C1、A5B3C2、A5B4C3、A5B5C4A5B(5)C(5)Note. B(5) represents the combinations of five levels of factor B and C(5) represents the combinations of five levels of factor C.


## 4.1.2. Quantification of the Macro Form of the Test Combinations

In order to quantify the influence of various factors on the tunnel stability, it is necessary to quantify the macro form of the test combinations. Given that the conditions under the combination are all independent, the linear superposition method is used to define the quantitative scores of factor A under each level to obtain the quantitative index F of tunnel stability under different combinations. The detailed calculation process is as follows:(a)
The first level of factor A (6 m span): IA = A1B(5)C(5) = 1 + 2 + 5 + 6 + 6 = 20.(b)
The second level of factor A (9 m span): IIA = A2B(5)C(5) = 1 + 3 + 5 + 5 +3 = 17.(c)
The third level of factor A (12 m span): IIIA = A3B(5)C(5) = 1 + 3 + 5 + 3+ 4 = 16.(d)
The fourth level of factor A (15 m span): IVA = A4B(5)C(5) = 1 + 3 + 1 + 3 +5 = 13.(e)
The fifth level of factor A (18 m span): VA = A5B(5)C(5) = 2 + 1 + 2 + 3 + 5 = 13.


## 4.1.3. Processing Results

The data processing of factors B and C is carried out in the same way, and their quantitative index F under various levels is calculated, as listed in Table8.Table 8
Quantitative index value of tunnel stability under different factor levels.
Level of factorQuantitative index value of tunnel stability FTunnel spanARock strengthBCoefficient of rock integrityCI2069II171212III161817IV132020V132321Range71712As indicated by the range of the stability quantitative index of three factors in Table8 [24], the strength of the surrounding rock has the most significant impact on tunnel stability, followed by the surrounding rock integrity and the span of the tunnel in decreasing order.


## 4.2. The Influence of Main Control Factors on Tunnel Stability

Based on the stability quantitative index of three factors listed in Table8, the influence rule of these factors on tunnel stability can be drawn, as shown in Figures 5–7, respectively.Figure 5
Fitting curve between stability index of surrounding rock and span of tunnel.Figure 6
Fitting curve between stability index and strength of surrounding rock.Figure 7
Fitting curve between stability index of surrounding rock and rock mass integrity coefficient.


### 4.2.1. Tunnel Span

According to Figure5, the tunnel excavation span has a negative correlation with the stability of the surrounding rock. The stability of the tunnel deteriorates with the increase of tunnel span. The relationship between them is expressed as a power function:(1)fA=42.39A−0.41.


### 4.2.2. Compressive Strength of Surrounding Rock

Figure6 shows a strong positive correlation between surrounding rock strength and tunnel stability. A higher compressive strength of surrounding rock is beneficial for better tunnel stability. Their relation can be expressed as(2)fB=4.80B0.393.


### 4.2.3. Coefficient of Surrounding Rock Integrity

The tunnel stability is positively related with the coefficient of surrounding rock integrity, indicating that higher coefficient of surrounding rock integrity contributes to tunnel stability. The relation can be expressed as(3)fC=6.208lnC+22.78,where fC>0; therefore, the coefficient of surrounding rock C should be greater than 0.03.


## 4.2.1. Tunnel Span

According to Figure5, the tunnel excavation span has a negative correlation with the stability of the surrounding rock. The stability of the tunnel deteriorates with the increase of tunnel span. The relationship between them is expressed as a power function:(1)fA=42.39A−0.41.


## 4.2.2. Compressive Strength of Surrounding Rock

Figure6 shows a strong positive correlation between surrounding rock strength and tunnel stability. A higher compressive strength of surrounding rock is beneficial for better tunnel stability. Their relation can be expressed as(2)fB=4.80B0.393.


## 4.2.3. Coefficient of Surrounding Rock Integrity

The tunnel stability is positively related with the coefficient of surrounding rock integrity, indicating that higher coefficient of surrounding rock integrity contributes to tunnel stability. The relation can be expressed as(3)fC=6.208lnC+22.78,where fC>0; therefore, the coefficient of surrounding rock C should be greater than 0.03.


## 4.3. The Expression of Quantitative Index of Surrounding Rock Stability

The stability of the surrounding rock of the tunnel is the result of the combined action of the three main control factors. The influences of the main control factors on the stability are interrelated and coupled. This correlation can be expressed by their product and a coefficientk. Therefore, the tunnel stability after excavation can be quantified as(4)F=kfAfBfC.Substituting equations (1)–(3) into equation (4), F can be derived:(5)F=A−0.41B0.3936.208lnC+22.78,where k is a constant value (k = 0.004907).


## 4.4. Criterion of Quantification of Surrounding Rock Stability

Substituting the test calculation parameters (Table4) into equation (5), the value of the tunnel stability quantitative index F for each test can be obtained (Table 9).Table 9
Index calculation value of tunnel stability.
Test no.Test codeStabilityF1A1B1C1Unstable5.322A5B2C1Unstable6.46A2B1C2Unstable6.811A3B1C3Unstable8.121A5B1C5Unstable8.416A4B1C4Unstable8.518A4B3C1Unstable9.123A5B3C2Unstable12.714A3B4C1Unstable13.12A1B2C2Unstable15.217A4B2C5Unstable17.17A2B2C3Unstable17.212A3B2C4Unstable17.510A2B5C1Unstable17.819A4B4C2Unstable1824A5B4C3Unstable22.315A3B5C2Stable23.813A3B3C5Stable24.68A2B3C4Stable25.93A1B3C3Stable26.620A4B5C3Stable2925A5B5C4Stable30.99A2B4C5Stable36.34A1B4C4Stable40.15A1B5C5Stable51.9It can be seen from Table9 that in 25 sets of orthogonal tests, the minimum index is 5.3 and the maximum is 22.3 when the surrounding rock is unstable after tunnel excavation. And the minimum index is 23.8 and the maximum is 51.9 when the surrounding rock of the tunnel remains stable. Therefore, the criteria for stability of surrounding rock can be given as follows:(1)
IfF ≥ 23, the surrounding rock is in stable sate.(2)
IfF < 23, the surrounding rock becomes unstable.According to this criterion and the quantification rules, the stability index F can be classified as six levels specifically, as listed in Table10.Table 10
Index value and qualitative description of tunnel stability.
FUnstable stateStable state<13[13, 17)[17, 23)[23, 26)[26, 40)≥40Description of stabilityExtremely unstableVery unstableUnstableBasically stableVery stableHighly stable


## 4.5. Criterion for Tunnel Construction Method Selection

### 4.5.1. One-Step Maximum Excavation Span

According to equation (5), for a given tunnel surrounding rock, a proper one-step excavation span should be selected to satisfy the index F ≥ 23 to ensure the stability of the surrounding rock during excavation. Thus, maximum span Amax of the next-step excavation can be calculated under given surrounding rock properties (strength and integrity coefficient) when assuming that F = 23, as shown in the following equation:(6)Amax=B0.3936.208lnC+22.78232.44.


### 4.5.2. Determination of the Number of Drifts

Assuming that the maximum span of tunnel excavation isL and the number of lateral drifts in the cross section is N, it can be seen from equation (6) that the number of lateral drifts in the tunnel section should be(7)N≥LAmax=LB0.3936.208lnC+22.78/232.44.Thus,(8)Nmin=LB0.3936.208lnC+22.78/232.44,where Nmin should be integer.


### 4.5.3. Bench Division of Tunnel Drift

After determining the number of lateral drifts, the stability state of the tunnel drift is used as a reference for the necessity of bench cut. It is recommended to perform bench cut construction in the lateral drifts as instructed by Table11.Table 11
Stability index value and bench division of tunnel drift.
Description of tunnel stabilityBasically stableVery stableHighly stableBench divisionBench division is necessary and temporary invert should be adoptedBench division is necessary and temporary invert is not compulsiveBench division is unnecessary


## 4.5.1. One-Step Maximum Excavation Span

According to equation (5), for a given tunnel surrounding rock, a proper one-step excavation span should be selected to satisfy the index F ≥ 23 to ensure the stability of the surrounding rock during excavation. Thus, maximum span Amax of the next-step excavation can be calculated under given surrounding rock properties (strength and integrity coefficient) when assuming that F = 23, as shown in the following equation:(6)Amax=B0.3936.208lnC+22.78232.44.


## 4.5.2. Determination of the Number of Drifts

Assuming that the maximum span of tunnel excavation isL and the number of lateral drifts in the cross section is N, it can be seen from equation (6) that the number of lateral drifts in the tunnel section should be(7)N≥LAmax=LB0.3936.208lnC+22.78/232.44.Thus,(8)Nmin=LB0.3936.208lnC+22.78/232.44,where Nmin should be integer.


## 4.5.3. Bench Division of Tunnel Drift

After determining the number of lateral drifts, the stability state of the tunnel drift is used as a reference for the necessity of bench cut. It is recommended to perform bench cut construction in the lateral drifts as instructed by Table11.Table 11
Stability index value and bench division of tunnel drift.
Description of tunnel stabilityBasically stableVery stableHighly stableBench divisionBench division is necessary and temporary invert should be adoptedBench division is necessary and temporary invert is not compulsiveBench division is unnecessary


## 4.6. Influencing Analysis of Other Factors

In the construction phase of tunnel engineering, the identification of construction method should consider not only the three crucial factors including tunnel span, rock mass integrity coefficient, and strength of surrounding rock but also the secondary factors such as in situ stress, groundwater, and construction capacity of the subcontractors. The secondary influence factors are restricted by the geological conditions of the tunnel site, which is not universal. Therefore, in the actual tunnel projects, the influence of secondary factors can be revised according to the specific situation of projects, and the influence of secondary factors is reflected by means of revision.


## 5. Case Study

The Malin tunnel is located in Wudang District, Guiyang City. It is a separated two-way six-lane tunnel. The inner outline is a three-center round curved side wall structure. The net area is 123.68 m2, the net span is 17.61 m, the net height is 5.0 m, and the flatness ratio is 0.618 (as shown in Figure 8). The designed speed of 100 km/h is tailored, as that of expressway. The total length of the left tunnel is 745 m, the total length of the right tunnel is 760 m, and the maximum buried depth of the tunnel is about 98.7 m.Figure 8
Inside outline of Malin tunnel.The surrounding rock is mainly composed of full-moderately weathered dolomite and dolomitic limestone. The rock grades mainly fall into grade IV and grade V. The grade V surrounding rock is mainly gravel, highly weathered dolomitic limestone, and cataclasite. The self-stability of surrounding rock is poor, so it is not controversial to use the double-side drift method for the grade V rock. Our method is applied to determine the construction method for the grade IV surrounding rock.According to the survey and design of the Malin tunnel, the excavation span, rock strength, and rock integrity coefficient of grade IV rock are 19.54 m, 25.4 MPa, and 0.69, respectively. The calculation results based on our evaluation system are listed in Table12.Table 12
Calculation results of Malin tunnel construction method.
ItemQuantitative indexOne-step span15.9Overall span19.9Number of calculated lateral drift1.2Number of determined lateral drift2.0Determined one-step excavation span9.94Index of surrounding rock stability F27.81Stability of surrounding rockVery stableRecommended methodCD methodTherefore, the grade IV surrounding rock section of the Malin tunnel should be constructed using the CD method with two lateral drifts in the cross section. The left and right drifts are divided into upper and lower drifts, and the tunnel construction is implemented with the CD method (Figure9). The safety and efficiency of the construction process have been verified in the whole construction process.Figure 9
Photo of CD method construction in Malin tunnel.


## 6. Conclusions

In this paper, the orthogonal test method was used to establish a three-factor five-level test model, and the quantitative relationship functions between the three factors and the stability of the surrounding rock of the tunnel were given. The following conclusions can be drawn from this paper:(1)
The tunnel excavation span is negatively related to the stability of the surrounding rock of the tunnel, which can be described by a power function. The strength of the surrounding rock of the tunnel is positively related to the stability of the surrounding rock of the tunnel and can be described by a power function; the rock integrity coefficient is positively related to the stability of the surrounding rock of the tunnel, and their relationship can be described by a logarithmic function.(2)
An equation for determining the construction method of ultra-large-span tunnel is constructed, which can quantitatively reflect the contribution of excavation span of tunnel, the number of lateral drifts in cross section, surrounding rock strength, and rock integrity coefficient to surrounding rock stability of tunnel. The research results provide the theoretical basis for the identification and selection of construction method for ultra-large-span tunnel and provide theoretical calculation basis for determining the number of drifts in the cross section.



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