# Evaluation of the Adaptability of an EPB TBM to Tunnelling through Highly Variable Composite Strata

Authors: Tao Li; Jinwu Zhan; Chao Li; Zhongsheng Tan
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

The adaptability of an earth pressure balance (EPB) tunnel boring machine (TBM) to complex geological strata needs to be evaluated when a tunnel project is set up. It is helpful for better design and more suitable technical parameters of the machine. Because the factors that influence adaptability are numerous and interrelated, their effects also differ; hence, a quantitative assessment of adaptability is generally difficult. In the present study, a method for quantitatively evaluating the excavation adaptability of an EPB TBM was developed using an analytic hierarchy process (AHP) and fuzzy comprehensive evaluation. The method first involves an initial selection of factors that may influence tunnelling. Based on the expert questionnaire and their influence weights determined by AHP, the 10 evaluation indexes from 25 primary indexes were selected to establish the evaluation index system (EIS) including a target, criteria, and index level. Fuzzy membership functions are then derived one after another based on the effect of each evaluation index on the EBP TBM tunnelling process. A fuzzy mathematical method was finally presented to determine the adaptability of an EPB TBM excavation performance. The proposed method was applied to two special sections of diameter 6.98 m excavated by two EPB TBMs in the Shenzhen Metro Line 11 project. The geological exploration shows that these two tunnel sections pass through typical composite strata in Shenzhen. The determined adaptability grades of the EPB TBMs used for composite strata were confirmed by the actual tunnel excavation. It indicates that the developed method is reasonable and useful to evaluate tunnelling adaptability of EPB TBM.


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## Body

## 1. Introduction

Composite strata are often encountered when using the shield tunnelling method to construct subway tunnels in South China. Strata of this type are characterized by a complex and highly variable composition, with large differences occurring between the strengths of different sections. Researchers in China first encountered such strata during the tunnelling of Line 1 of the Guangzhou Metro. The unique geological conditions created enormous difficulties when using ordinary earth pressure balance (EPB) shield machines for tunnel excavation [1, 2]. Composite EPB shield machines were first introduced to China to address this issue [3, 4]. Such machines combine the advantages of hard-rock tunnel boring machines (TBMs) and soft-ground shield machines, and they are commonly referred to as EPB TBMs. Although these machines are now widely used in the region, composite strata continue to pose difficulties in tunnelling. This includes the need for frequent switching of boring modes, severe wear and tear of the cutterheads, and schedule overruns. In severe cases, the shield tunnelling method may have to be abandoned and replaced by the shallow tunnelling method [5]. There is thus an urgent need for a method for evaluating the tunnelling adaptability of an EPB TBM in composite strata. It could help to decide whether mechanical excavation should be adopted for such tunnel projects. The evaluation results would further determine the technical parameters of EPB TBM and even the tunnelling method.There have been some research findings on the factors that affect EPB TBM excavation and the associated construction risks. For example, Zhao et al. [6] detailed the effects of composite strata on EPB TBM tunnelling based on a case study conducted on an actual engineering project. Tokgoz et al. [7] also analysed the relationship between the geotechnical and tunnelling parameters to evaluate the capability of an EPB TBM for tunnelling through fine-grained soil strata and examine the associated risks. Hu et al. [8] and Hyun et al. [9] used fault tree analysis and the analytic hierarchy process (AHP) to examine the risks of EPB TBM construction and proposed some targeted control measures. Hong et al. [10] used event tree analysis to evaluate the risks of underwater tunnelling using an EPB TBM. More studies have, however, been conducted on the boreability and performance of hard-rock TBMs and the influencing factors. Sapigni et al. [11] used geotechnical grading standards to evaluate the performance of a TBM, while Yan et al. [12] took energy consumption during the tunnelling process as a key indicator and analysed the construction efficiency of shield tunnelling through soft deposit. Mikaeil et al. [13] applied the multifactor fuzzy method to examine the hard-rock boreability of a TBM. Lin et al. [14] proposed a novel fuzzy model for identifying high-risk factors during deep excavations in karst geological ground. Dudt and Delisio [15] used the penalty factor method to predict the performance of a TBM in highly variable strata. Furthermore, owing to the uncertainties of the various impact factors of TBM tunnelling, fuzzy mathematical methods have been widely used to predict the boreability of the machine [16–19]. Rostami [20] presented a comprehensive review and evaluation of existing models for predicting TBM’s performance under difficult strata conditions and reported several new research findings. Bernados and Kaliampakos [21] introduced a vulnerability index for describing the uncertainties of the strata parameters and proposed a methodology for evaluating the probability of a geological disaster occurring during TBM tunnelling. Farrokh and Rostami [22] presented a detailed description of the impact of poor geological conditions on the performance of double-shield TBMs based on the construction of the Ghomroud Tunnel in Iran. In a recent comprehensive report, Gong et al. [23] discussed the main issues encountered during TBM tunnelling under poor geological conditions and the corresponding mitigation measures. Considering the complexity of the relevant issues, mathematical methods applicable to multifactorial analysis are used to select the appropriate TBM and shield and assess the construction risks of a project. Such methods include AHP, decision analysis, and the use of expert systems [24–29]. Recently, artificial intelligence (AI) models and related methods have been applied to some issues in shield tunnelling, for example, predicting disc cutter life and modelling performance of EPB shield tunnelling [30–34].It can thus be seen that many efforts have been devoted to determine the various factors affecting EPB TBM tunnelling and also to evaluate the EPB TBM’s performance and the construction risks in difficult ground conditions. Nevertheless, there remains a lack of a method to quantitatively evaluate the tunnelling adaptability of EPB TBMs under complex geological conditions.The aim of the present study was to develop a viable and quantitative method for evaluating the tunnelling adaptability of EPB TBMs in composite strata. The methodology for evaluation is first presented, which is based on AHP and fuzzy comprehensive evaluation (FCE). Secondly, the factors that affect the adaptability of an EPB TBM were then described according to the study and practice of EPB TBM in Shenzhen Metro construction. AHP was then used to determine the weights of these primary factors. Based on the expert questionnaire and their influence weights determined by AHP, the evaluation indexes were selected to form the evaluation index system (EIS) comprising the target, criteria, and index layers. Fuzzy membership functions were then derived one after another based on the effect of each evaluation index on the EBP TBM tunnelling process. Thirdly, a fuzzy mathematical method was presented to determine the adaptability of an EPB TBM excavation performance. Finally, the proposed method was verified by applying it to two special sections passing through composite strata of the Shenzhen Metro Line 11. These sections were excavated using the EBP TBPs with a diameter of 6.98 m, which were applied for the first time in Shenzhen Metro construction.


## 2. Methodology for Evaluating Adaptability

For an EPB TBM, tunnelling adaptability refers to the ability of the machine to adapt to the various factors that affect tunnel excavation. This ensures that the machine can manifest its design effectiveness to complete the tunnelling task.


### 2.1. Evaluation Indexes and Evaluation Index System

Because the adaptability of an EPB TBM is affected by numerous factors, it was necessary to first select the most important or critical factors in the present study. Each shortlisted factor was then comprehensively described using a type of quantitative index. The evaluation indexes were selected based on considerations such as project implementation, results of scientific research, expert opinion, and mathematical assessment.Based on the selected quantitative indexes, an evaluation index system (EIS) can be established so as to accurately reflect the impact of the various factors on tunnelling adaptability. Because influencing factors are not only often numerous but also interrelated, each evaluation index in an EIS should be highly representative when used to characterize the impact of a particular factor. Moreover, the principles of hierarchy, validity, and conciseness were needed to construct an EIS [35, 36].


### 2.2. Fuzzy Membership Function of the Evaluation Indexes

The evaluation indexes have different units, attributes, and degrees of importance, which causes a lack of commensurability among them. Hence, a fuzzy membership function (FMF) can be used to achieve commensurability among the indexes. The value of the function describes the relationship between an uncertain quantityx and a membership function v (x), which is defined in the interval [0, 1]. The FMF may take different forms such as trigonometric, exponential, and Gaussian. To simplify the implementation of FMF, only a straight line and trapezoid were considered in this study.


### 2.3. Weights of the Evaluation Indexes

The weights of the different evaluation indexes were determined using AHP [35, 36]. The process was as follows.


#### 2.3.1. Hierarchy of Evaluation Indexes

After setting the evaluation targets, their mutual impact and membership relationships between the evaluation indexes were used as the bases for ranking them in descending order, with respect to the target, determined criteria, and index layers. The indexes at higher levels thus predominated over those at lower levels.


#### 2.3.2. The Judgment Matrix

The relative importance of a pair of indexes can be qualitatively determined using the judgment matrix. For the comparison of evaluation indexesUi and Uj (i, j = 1, …, n), Saaty [35] proposed the use of Table 1 for the assignment of values to aij in the judgment matrix A. A comparison of Ui and Uj defines aij, while that of Uj and Ui defines aij = 1/aij.Table 1
Method for assigning values to elementsaij in the judgment matrix A.
Value assignment basisaijUi and Uj are equally important1Ui is slightly more important than Uj3Ui is obviously more important than Uj5Ui is definitely more important than Uj7Ui is extremely more important than Uj9Intermediate judgment for the above pairs2, 4, 6, and 8Although the judgment matrixA established using the above method may objectively reflect the different impacts between a pair of indexes, a certain degree of inconsistency is unavoidable when analysing the results of comparing all indexes. To address this problem, the elements of the matrix A should also satisfy the following equation:(1)aijajk=aik,∀i,j,k=1,2,3,…,n.


#### 2.3.3. Single Hierarchical Arrangement (SHA)

For the matrixA, it was assumed that Ω (ωi) is the eigenvector corresponding to the maximum eigenvalue of λmax. After normalization, Ω would represent the hierarchy of weights and the relative importance between the indexes on one level and a specific index on a higher level. The maximum eigenvalue of A and its corresponding eigenvector could be approximately determined using the root mean square method, as follows:(a)
The product of the elements in each row of the matrixA is obtained:(2)δi=∏j=1naij1/n,i=1,2,…,n.(b)
δi is normalized before the eigenvector Ω is calculated:(3)ωj=δj∑k=1nδk,j=1,2,⋯,n.(c)
The maximum eigenvalueλmax of the matrix A is calculated. Because AΩ = λmaxΩ, then(4)∑j=1naijωj=λmaxωj,j=1,2,…,n.Hence,(5)λmax=1n∑i=1n∑j=1naijωjωi.The consistency testing of the SHA is conducted as follows:(a)
The consistency index CI can be calculated as follows:(6)CI=λmax−nn−1.(b)
To determine the corresponding mean random consistency index RI, the random method is used to construct 500 sample matrices. Random numbers between 1 and 9 were chosen and their respective reciprocals were used to construct a positive reciprocal matrix. The following definition would apply:(7)RI=λ¯max−nn−1,whereλ¯max is the mean of the maximum eigenvalues of these matrices.(c)
Consistency check: the consistency ratio is defined as CR = CI/RI. If CR < 0.10, then the matrixA meets the condition for consistency; otherwise, a revision is required.


#### 2.3.4. Total Hierarchical Arrangement (THA)

Determination of the THA of various indexes is based on the hierarchical weights, especially those at the lowest layer, with respect to the target layer. The weights of the THA could be obtained by summing the weights of the SHA from top to bottom.For the index setU = {U1, U2,..., Um}, its THA weights are denoted by u1, u2, ..., um, respectively. Assuming that the index set one layer below U is V = {V1, V2, ..., Vn}, the SHA weights of the latter set with respect to Uj would be v1j, ..., vnj. Obviously, vij = 0 when Vi and Uj are unrelated. The method illustrated in Table 2 can be used to calculate the weight of the indexes in V with respect to the THA weights v1, v2, ..., vn.Table 2
Method for calculating the THA weights ofV.
U/VU1U2…UmTHA weights for index setVu1u2…umV1v11v12…v1mv1=∑j=1mv1jujV2v21v22…v2mv2=∑j=1mv2juj⋮⋮⋮⋮⋮⋮Vnvn1vn2…vnmvn=∑j=1mvnjujEven when all layers pass the consistency test for SHA, it is still possible for the nonuniformity of the various layers to accumulate during comprehensive analyses. To avoid this nonuniformity in the final judgment, a consistency check of the THA should be conducted as follows.Regarding the paired comparative judgment matrices formed by the indexes in setV that are related to Uj, it is assumed that these have passed the consistency test at the SHA stage and that the corresponding CIj and RIj have been solved. The THA of V would thus be given by(8)CR=∑j=1nCIjuj∑j=1nRIjuj.The THA results are considered consistent if CR < 0.1.


### 2.4. Fuzzy Comprehensive Evaluation Model

Assuming thatU = {U1, U2, ..., Um} is the set of evaluation indexes for the evaluation target set O = {O1, O2, ..., On}, then the basic model for FCE would be(9)D=U¯×R,or(10)D1,D2,…,Dn=u1,u2,…,um×r11r12⋯r1nr21r22⋯r2n⋮rm1⋮rm2⋱⋮⋯rmn,where D is the set of comprehensive judgment values for O and Di is the adaptability degree of the evaluation target Oi. When 0 ≤ Di ≤ 1, “0” indicates complete inadaptability, while “1” indicates complete adaptability. U¯ is the set of THA weights for the evaluation index U, where ui ≥ 0 and ∑i=1mui=1. R is the matrix for the degree of membership between V and O. The adaptability evaluation of Oi can be performed based on the numerical value of Di and in accordance with the classification criteria in Table 3.Table 3
Adaptability classification for the evaluation targets.
GradeDescription of adaptabilityDegree of adaptabilityICompletely adaptable≥0.9IIAdaptable0.6–0.9IIISlightly adaptable0.4–0.6IVInadaptable0.1–0.4VCompletely inadaptable≤0.1


## 2.1. Evaluation Indexes and Evaluation Index System

Because the adaptability of an EPB TBM is affected by numerous factors, it was necessary to first select the most important or critical factors in the present study. Each shortlisted factor was then comprehensively described using a type of quantitative index. The evaluation indexes were selected based on considerations such as project implementation, results of scientific research, expert opinion, and mathematical assessment.Based on the selected quantitative indexes, an evaluation index system (EIS) can be established so as to accurately reflect the impact of the various factors on tunnelling adaptability. Because influencing factors are not only often numerous but also interrelated, each evaluation index in an EIS should be highly representative when used to characterize the impact of a particular factor. Moreover, the principles of hierarchy, validity, and conciseness were needed to construct an EIS [35, 36].


## 2.2. Fuzzy Membership Function of the Evaluation Indexes

The evaluation indexes have different units, attributes, and degrees of importance, which causes a lack of commensurability among them. Hence, a fuzzy membership function (FMF) can be used to achieve commensurability among the indexes. The value of the function describes the relationship between an uncertain quantityx and a membership function v (x), which is defined in the interval [0, 1]. The FMF may take different forms such as trigonometric, exponential, and Gaussian. To simplify the implementation of FMF, only a straight line and trapezoid were considered in this study.


## 2.3. Weights of the Evaluation Indexes

The weights of the different evaluation indexes were determined using AHP [35, 36]. The process was as follows.


### 2.3.1. Hierarchy of Evaluation Indexes

After setting the evaluation targets, their mutual impact and membership relationships between the evaluation indexes were used as the bases for ranking them in descending order, with respect to the target, determined criteria, and index layers. The indexes at higher levels thus predominated over those at lower levels.


### 2.3.2. The Judgment Matrix

The relative importance of a pair of indexes can be qualitatively determined using the judgment matrix. For the comparison of evaluation indexesUi and Uj (i, j = 1, …, n), Saaty [35] proposed the use of Table 1 for the assignment of values to aij in the judgment matrix A. A comparison of Ui and Uj defines aij, while that of Uj and Ui defines aij = 1/aij.Table 1
Method for assigning values to elementsaij in the judgment matrix A.
Value assignment basisaijUi and Uj are equally important1Ui is slightly more important than Uj3Ui is obviously more important than Uj5Ui is definitely more important than Uj7Ui is extremely more important than Uj9Intermediate judgment for the above pairs2, 4, 6, and 8Although the judgment matrixA established using the above method may objectively reflect the different impacts between a pair of indexes, a certain degree of inconsistency is unavoidable when analysing the results of comparing all indexes. To address this problem, the elements of the matrix A should also satisfy the following equation:(1)aijajk=aik,∀i,j,k=1,2,3,…,n.


### 2.3.3. Single Hierarchical Arrangement (SHA)

For the matrixA, it was assumed that Ω (ωi) is the eigenvector corresponding to the maximum eigenvalue of λmax. After normalization, Ω would represent the hierarchy of weights and the relative importance between the indexes on one level and a specific index on a higher level. The maximum eigenvalue of A and its corresponding eigenvector could be approximately determined using the root mean square method, as follows:(a)
The product of the elements in each row of the matrixA is obtained:(2)δi=∏j=1naij1/n,i=1,2,…,n.(b)
δi is normalized before the eigenvector Ω is calculated:(3)ωj=δj∑k=1nδk,j=1,2,⋯,n.(c)
The maximum eigenvalueλmax of the matrix A is calculated. Because AΩ = λmaxΩ, then(4)∑j=1naijωj=λmaxωj,j=1,2,…,n.Hence,(5)λmax=1n∑i=1n∑j=1naijωjωi.The consistency testing of the SHA is conducted as follows:(a)
The consistency index CI can be calculated as follows:(6)CI=λmax−nn−1.(b)
To determine the corresponding mean random consistency index RI, the random method is used to construct 500 sample matrices. Random numbers between 1 and 9 were chosen and their respective reciprocals were used to construct a positive reciprocal matrix. The following definition would apply:(7)RI=λ¯max−nn−1,whereλ¯max is the mean of the maximum eigenvalues of these matrices.(c)
Consistency check: the consistency ratio is defined as CR = CI/RI. If CR < 0.10, then the matrixA meets the condition for consistency; otherwise, a revision is required.


### 2.3.4. Total Hierarchical Arrangement (THA)

Determination of the THA of various indexes is based on the hierarchical weights, especially those at the lowest layer, with respect to the target layer. The weights of the THA could be obtained by summing the weights of the SHA from top to bottom.For the index setU = {U1, U2,..., Um}, its THA weights are denoted by u1, u2, ..., um, respectively. Assuming that the index set one layer below U is V = {V1, V2, ..., Vn}, the SHA weights of the latter set with respect to Uj would be v1j, ..., vnj. Obviously, vij = 0 when Vi and Uj are unrelated. The method illustrated in Table 2 can be used to calculate the weight of the indexes in V with respect to the THA weights v1, v2, ..., vn.Table 2
Method for calculating the THA weights ofV.
U/VU1U2…UmTHA weights for index setVu1u2…umV1v11v12…v1mv1=∑j=1mv1jujV2v21v22…v2mv2=∑j=1mv2juj⋮⋮⋮⋮⋮⋮Vnvn1vn2…vnmvn=∑j=1mvnjujEven when all layers pass the consistency test for SHA, it is still possible for the nonuniformity of the various layers to accumulate during comprehensive analyses. To avoid this nonuniformity in the final judgment, a consistency check of the THA should be conducted as follows.Regarding the paired comparative judgment matrices formed by the indexes in setV that are related to Uj, it is assumed that these have passed the consistency test at the SHA stage and that the corresponding CIj and RIj have been solved. The THA of V would thus be given by(8)CR=∑j=1nCIjuj∑j=1nRIjuj.The THA results are considered consistent if CR < 0.1.


## 2.3.1. Hierarchy of Evaluation Indexes

After setting the evaluation targets, their mutual impact and membership relationships between the evaluation indexes were used as the bases for ranking them in descending order, with respect to the target, determined criteria, and index layers. The indexes at higher levels thus predominated over those at lower levels.


## 2.3.2. The Judgment Matrix

The relative importance of a pair of indexes can be qualitatively determined using the judgment matrix. For the comparison of evaluation indexesUi and Uj (i, j = 1, …, n), Saaty [35] proposed the use of Table 1 for the assignment of values to aij in the judgment matrix A. A comparison of Ui and Uj defines aij, while that of Uj and Ui defines aij = 1/aij.Table 1
Method for assigning values to elementsaij in the judgment matrix A.
Value assignment basisaijUi and Uj are equally important1Ui is slightly more important than Uj3Ui is obviously more important than Uj5Ui is definitely more important than Uj7Ui is extremely more important than Uj9Intermediate judgment for the above pairs2, 4, 6, and 8Although the judgment matrixA established using the above method may objectively reflect the different impacts between a pair of indexes, a certain degree of inconsistency is unavoidable when analysing the results of comparing all indexes. To address this problem, the elements of the matrix A should also satisfy the following equation:(1)aijajk=aik,∀i,j,k=1,2,3,…,n.


## 2.3.3. Single Hierarchical Arrangement (SHA)

For the matrixA, it was assumed that Ω (ωi) is the eigenvector corresponding to the maximum eigenvalue of λmax. After normalization, Ω would represent the hierarchy of weights and the relative importance between the indexes on one level and a specific index on a higher level. The maximum eigenvalue of A and its corresponding eigenvector could be approximately determined using the root mean square method, as follows:(a)
The product of the elements in each row of the matrixA is obtained:(2)δi=∏j=1naij1/n,i=1,2,…,n.(b)
δi is normalized before the eigenvector Ω is calculated:(3)ωj=δj∑k=1nδk,j=1,2,⋯,n.(c)
The maximum eigenvalueλmax of the matrix A is calculated. Because AΩ = λmaxΩ, then(4)∑j=1naijωj=λmaxωj,j=1,2,…,n.Hence,(5)λmax=1n∑i=1n∑j=1naijωjωi.The consistency testing of the SHA is conducted as follows:(a)
The consistency index CI can be calculated as follows:(6)CI=λmax−nn−1.(b)
To determine the corresponding mean random consistency index RI, the random method is used to construct 500 sample matrices. Random numbers between 1 and 9 were chosen and their respective reciprocals were used to construct a positive reciprocal matrix. The following definition would apply:(7)RI=λ¯max−nn−1,whereλ¯max is the mean of the maximum eigenvalues of these matrices.(c)
Consistency check: the consistency ratio is defined as CR = CI/RI. If CR < 0.10, then the matrixA meets the condition for consistency; otherwise, a revision is required.


## 2.3.4. Total Hierarchical Arrangement (THA)

Determination of the THA of various indexes is based on the hierarchical weights, especially those at the lowest layer, with respect to the target layer. The weights of the THA could be obtained by summing the weights of the SHA from top to bottom.For the index setU = {U1, U2,..., Um}, its THA weights are denoted by u1, u2, ..., um, respectively. Assuming that the index set one layer below U is V = {V1, V2, ..., Vn}, the SHA weights of the latter set with respect to Uj would be v1j, ..., vnj. Obviously, vij = 0 when Vi and Uj are unrelated. The method illustrated in Table 2 can be used to calculate the weight of the indexes in V with respect to the THA weights v1, v2, ..., vn.Table 2
Method for calculating the THA weights ofV.
U/VU1U2…UmTHA weights for index setVu1u2…umV1v11v12…v1mv1=∑j=1mv1jujV2v21v22…v2mv2=∑j=1mv2juj⋮⋮⋮⋮⋮⋮Vnvn1vn2…vnmvn=∑j=1mvnjujEven when all layers pass the consistency test for SHA, it is still possible for the nonuniformity of the various layers to accumulate during comprehensive analyses. To avoid this nonuniformity in the final judgment, a consistency check of the THA should be conducted as follows.Regarding the paired comparative judgment matrices formed by the indexes in setV that are related to Uj, it is assumed that these have passed the consistency test at the SHA stage and that the corresponding CIj and RIj have been solved. The THA of V would thus be given by(8)CR=∑j=1nCIjuj∑j=1nRIjuj.The THA results are considered consistent if CR < 0.1.


## 2.4. Fuzzy Comprehensive Evaluation Model

Assuming thatU = {U1, U2, ..., Um} is the set of evaluation indexes for the evaluation target set O = {O1, O2, ..., On}, then the basic model for FCE would be(9)D=U¯×R,or(10)D1,D2,…,Dn=u1,u2,…,um×r11r12⋯r1nr21r22⋯r2n⋮rm1⋮rm2⋱⋮⋯rmn,where D is the set of comprehensive judgment values for O and Di is the adaptability degree of the evaluation target Oi. When 0 ≤ Di ≤ 1, “0” indicates complete inadaptability, while “1” indicates complete adaptability. U¯ is the set of THA weights for the evaluation index U, where ui ≥ 0 and ∑i=1mui=1. R is the matrix for the degree of membership between V and O. The adaptability evaluation of Oi can be performed based on the numerical value of Di and in accordance with the classification criteria in Table 3.Table 3
Adaptability classification for the evaluation targets.
GradeDescription of adaptabilityDegree of adaptabilityICompletely adaptable≥0.9IIAdaptable0.6–0.9IIISlightly adaptable0.4–0.6IVInadaptable0.1–0.4VCompletely inadaptable≤0.1


## 3. Tunnel Construction for the Shenzhen Metro Line 11

The Shenzhen Metro Line 11 starts from Futian Station and ends at Bitou Station, with a total length of 51.681 km and 17 stations. In all the tunnel sections of Line 11, only the Chegongmiao-Hongshuwan section (Section C-H) with a length of 5477.9 m and the Nanshan-Qianhaiwan section (Section N-Q) with a length of 3582.6 m were excavated using EPB TBMs of diameter 6.98 m, while other sections were constructed with common shield machines of diameter 6.30 m. The site location of these two sections is shown in Figure1.Figure 1
Site location map of Section C-H and Section N-Q.


### 3.1. Geotechnical Investigation

To investigate the site geotechnical conditions of these two sections, geophysical method and boreholes were mainly used before tunnel construction. A seismic reflection survey was carried out to explore the thickness of the overburden layers and the subsurface structures along the tunnel alignment. A total number of 1,047 boreholes were drilled to provide the site information. The borehole spacing along the tunnel alignment is arranged as follows: 100–500 m for a simple site, 30–50 m for a moderately complex site, and less than 30 m for a complex site. The physicomechanical parameters of the main stratum have been ascertained by geotechnical tests in laboratory.The geological cross-sections of these two sections are shown in Figures2 and 3, respectively. The profile gives an overall image of the ground condition along the tunnel alignment. The main strata and stratigraphic distribution traversed by this tunnel section are detailed in Figure 4. The different types of strata and complex geological conditions are typical of composite strata. Some basic strength parameters of soil and rock samples are given in Table 4, which were obtained from laboratory tests such as direct and triaxial shear test. It can be seen that a large proportion of the strata comprises weathered granite strata, which is characterized by substantial strength variation.Figure 2
Geological profile of Section C-H of the Shenzhen Metro Line 11.Figure 3
Geological profile of Section N-Q of the Shenzhen Metro Line 11.Figure 4
Distribution of main ground conditions along the tunnel alignment. (a) Section C-H. (b) Section N-Q.
(a)(b)Table 4
Physical and mechanical indexes of cored samples from tunnel site.
Rock and soil typeUnit weight (kN/m3)Cohesion (kPa)Inner friction angle (degree)UCS (MPa)Clay19.2–19.920.0–25.020.0–22.0Gravel-sand20.0–20.432.0–35.0Gravelly clay18.3–18.724.0–25.022.0–25.0Fully weathered granite18.2–18.628.0–30.025.0–28.0Severely weathered granite19.0–21.538.0–40.032.0–35.0Moderately weathered granite25.1–25.545.0–60.0Lightly weathered granite26.0–26.5145.0–170.0The investigation report recognized that varied ground conditions and transitions from high strength granite to low strength weathered materials (and vice versa) would be a major challenge to EPB TBM tunnelling. The poor geological conditions encountered in Section C-H and Section N-Q during the tunnelling caused several difficulties (see Table5).Table 5
Difficulties encountered during tunnel excavation of Section C-H and Section N-Q.
Adverse geological conditionsDifficulties during tunnellingSilt and soft soil layerLoss of stability at excavation surfaces; excessive strata deformation causing surface collapseArtificial accumulation layerComplex soil compositions and properties; uneven hardness; difficult shield tunnellingClay layerLarge stratigraphic disturbances; tendency for formation of mud cakes; augers tending to squirt easilyMix groundDifficulty in controlling TBM attitude; poor adaptability of cutterheads and cutter bits to ground conditions, necessitating frequent changing of construction methodLayer with mildly weathered graniteSevere wear and tear of cutterheads due to very strong rocksLayer with spherical weathered granite bouldersSevere wear and tear of cutterheads and cutter bits due to very strong boulders, affecting the progress of shield tunnellingFractured zone of faultsHigh likelihood of squirting; unstable TBM attitudeFully saturated sand layerHigh likelihood of water inrush and sand boiling; risk of excavation surface collapse


### 3.2. Basic Functions of an EPB TBM

The EBP TBM of diameter 6.98 m used for tunnelling was manufactured by China Railway Engineering Equipment Group Co., Ltd. And first used in Shenzhen subway construction. Targeted designs are incorporated into a composite EPB TBM for overcoming the difficulties encountered during tunnelling through composite strata. The basic functions of the machine and the specifications of its cutterheads are detailed in Tables6 and 7, respectively.Table 6
Technical parameters of the EPB TBM.
ParameterValueUnitExcavation diameter6,980mmDiameter of shield machine6,950/6,940/6,930mmRotation speed of cutterhead0–3.6 (inflection speed = 1.37)rev/minMaximum advancing speed80mm/minMaximum speed49,588kNMain drive power1,120kWRated torque7,806kN·mTorque turnaround9,757kN·mScrew conveyor (diameter/power/torque)900/315/210mm/kW/kN·mTable 7
Specifications of the cutterhead and cutters.
PropertySpecificationStructural formHybrid (spokes + plate)Opening ratio (central opening rate)33% (38%)Cutterhead specifications (diameter × length)6,980 mm × 1,635 mm17-inch center hob (number/height/spacing)6/175 mm/90 mm17-inch single-blade hob (number/height/spacing)38/175 mm/75–85 mmSide scraper (number/height)12/135 mmScraper (number/height/width)49/135 mm/250 mm


## 3.1. Geotechnical Investigation

To investigate the site geotechnical conditions of these two sections, geophysical method and boreholes were mainly used before tunnel construction. A seismic reflection survey was carried out to explore the thickness of the overburden layers and the subsurface structures along the tunnel alignment. A total number of 1,047 boreholes were drilled to provide the site information. The borehole spacing along the tunnel alignment is arranged as follows: 100–500 m for a simple site, 30–50 m for a moderately complex site, and less than 30 m for a complex site. The physicomechanical parameters of the main stratum have been ascertained by geotechnical tests in laboratory.The geological cross-sections of these two sections are shown in Figures2 and 3, respectively. The profile gives an overall image of the ground condition along the tunnel alignment. The main strata and stratigraphic distribution traversed by this tunnel section are detailed in Figure 4. The different types of strata and complex geological conditions are typical of composite strata. Some basic strength parameters of soil and rock samples are given in Table 4, which were obtained from laboratory tests such as direct and triaxial shear test. It can be seen that a large proportion of the strata comprises weathered granite strata, which is characterized by substantial strength variation.Figure 2
Geological profile of Section C-H of the Shenzhen Metro Line 11.Figure 3
Geological profile of Section N-Q of the Shenzhen Metro Line 11.Figure 4
Distribution of main ground conditions along the tunnel alignment. (a) Section C-H. (b) Section N-Q.
(a)(b)Table 4
Physical and mechanical indexes of cored samples from tunnel site.
Rock and soil typeUnit weight (kN/m3)Cohesion (kPa)Inner friction angle (degree)UCS (MPa)Clay19.2–19.920.0–25.020.0–22.0Gravel-sand20.0–20.432.0–35.0Gravelly clay18.3–18.724.0–25.022.0–25.0Fully weathered granite18.2–18.628.0–30.025.0–28.0Severely weathered granite19.0–21.538.0–40.032.0–35.0Moderately weathered granite25.1–25.545.0–60.0Lightly weathered granite26.0–26.5145.0–170.0The investigation report recognized that varied ground conditions and transitions from high strength granite to low strength weathered materials (and vice versa) would be a major challenge to EPB TBM tunnelling. The poor geological conditions encountered in Section C-H and Section N-Q during the tunnelling caused several difficulties (see Table5).Table 5
Difficulties encountered during tunnel excavation of Section C-H and Section N-Q.
Adverse geological conditionsDifficulties during tunnellingSilt and soft soil layerLoss of stability at excavation surfaces; excessive strata deformation causing surface collapseArtificial accumulation layerComplex soil compositions and properties; uneven hardness; difficult shield tunnellingClay layerLarge stratigraphic disturbances; tendency for formation of mud cakes; augers tending to squirt easilyMix groundDifficulty in controlling TBM attitude; poor adaptability of cutterheads and cutter bits to ground conditions, necessitating frequent changing of construction methodLayer with mildly weathered graniteSevere wear and tear of cutterheads due to very strong rocksLayer with spherical weathered granite bouldersSevere wear and tear of cutterheads and cutter bits due to very strong boulders, affecting the progress of shield tunnellingFractured zone of faultsHigh likelihood of squirting; unstable TBM attitudeFully saturated sand layerHigh likelihood of water inrush and sand boiling; risk of excavation surface collapse


## 3.2. Basic Functions of an EPB TBM

The EBP TBM of diameter 6.98 m used for tunnelling was manufactured by China Railway Engineering Equipment Group Co., Ltd. And first used in Shenzhen subway construction. Targeted designs are incorporated into a composite EPB TBM for overcoming the difficulties encountered during tunnelling through composite strata. The basic functions of the machine and the specifications of its cutterheads are detailed in Tables6 and 7, respectively.Table 6
Technical parameters of the EPB TBM.
ParameterValueUnitExcavation diameter6,980mmDiameter of shield machine6,950/6,940/6,930mmRotation speed of cutterhead0–3.6 (inflection speed = 1.37)rev/minMaximum advancing speed80mm/minMaximum speed49,588kNMain drive power1,120kWRated torque7,806kN·mTorque turnaround9,757kN·mScrew conveyor (diameter/power/torque)900/315/210mm/kW/kN·mTable 7
Specifications of the cutterhead and cutters.
PropertySpecificationStructural formHybrid (spokes + plate)Opening ratio (central opening rate)33% (38%)Cutterhead specifications (diameter × length)6,980 mm × 1,635 mm17-inch center hob (number/height/spacing)6/175 mm/90 mm17-inch single-blade hob (number/height/spacing)38/175 mm/75–85 mmSide scraper (number/height)12/135 mmScraper (number/height/width)49/135 mm/250 mm


## 4. Evaluation Indexes and Fuzzy Membership Functions for EPB TBM Tunnelling

### 4.1. Evaluation Indexes and EIS

#### 4.1.1. Preliminary Selection of Evaluation Indexes

The factors that affect EPB TBM tunnelling include the EPB TBM design, tunnelling method, geological conditions, and surrounding environment. A detailed analysis of the various influencing factors was conducted in this study, taking into account the geological and environmental conditions along the two aforementioned sections. Based on the study and practice of constructing Shenzhen Metro using shield tunnelling technology [5], 25 primary evaluation indexes W1 ∼ W25 were selected, as detailed in Table 8.Table 8
Primary evaluation indexes for the adaptability of an EPB TBM during tunnelling.
Target layerAdaptability degree of EPB TBM under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnelling methodU2Geological conditionsU3Environment conditionsU4Index layerTotal thrustW1Cutterhead structure W2Cutterhead torque W3Cutterhead opening ratio W4Muck improvement technique W5Selection and layout of cutters W6Cutter spacing W7Muck amount of screw conveyor W8Advancing speedW9Rotating speed of cutterhead W10Earth pressure in cutterhead chamber W11Shield tail void W12Wall-back grouting pressure W13Artificial fillW14Soft soil stratum W15Liquefied sand layer W16Residual soil layer W17Composite strata W18Microweathered granite protrusions W19Hard-rock layer W20Fault crushed zone W21Spherical weathered boulders W22Underground structuresW23Ground buildings W24Structure of existing tunnel lines W25To determine the mutual impacts of these indexes, 20 experts from universities, design institutes, and construction companies were asked to complete a questionnaire survey. Based on their judgments, values were first assigned to the judgment matrix as shown in Table1. AHP was then used to analyse the weights and hierarchy of the indexes in each layer. Based on the analysis of weights and hierarchy, the 25 primary indexes were evaluated and reduced to 10 indexes that have strong influencing weights.


#### 4.1.2. Evaluation Index System

As shown in Table9, the 10 remaining indexes marked with V1 ∼ V10 were used to form the EIS of EBP TBM according to the principles for establishing an EIS. The fuzzy membership function of these indexes and the way they are evaluated are given in the next section.Table 9
EIS of the EPB TBM.
Target layerAdaptability of EPB TBM to tunnelling under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnel constructionU2Geological conditionsU3Index layerTotal thrustV1 (kN)Cutterhead torque V2 (kN∙m)Cutterhead opening ratio V3 (%)Muck amount of screw conveyor V4 (m3/h)Cutter spacing V5 (mm)Earth pressure in cutterhead chamberV6 (MPa)Wall-back grouting pressure V7 (kPa)Shield tail void V8 (mm)Composite strataV9 (%)Spherical weathered boulders V10 (m)


### 4.2. Fuzzy Membership Function of Indexes in the EIS

#### 4.2.1. Total ThrustV1

The equation commonly used to predict the total thrust of an EPB TBM is(11)F=FsπDe24,where Fs is an empirical coefficient with a value within 700–1,200 kN/m2 and De is the excavation diameter [37]. Based on the known value of De = 6.980 m, the adaptability range of the total thrust was determined to be 26,785–45,918 kN. According to these values, the FMF of the total thrust was established as expressed by equation (12).(12)v1x=0,x−2678545918−26785,1,x<26785,26785≤x<45918,x≥45918.


#### 4.2.2. Cutterhead TorqueV2

The empirical equation for calculating the cutterhead torque is(13)T=αDe3,where α is the torque coefficient, which ranges within 15–23 [37]. For De = 6.980 m, the adaptability range of the cutterhead torque was determined to be 5,101–7,821 kN∙m. The corresponding FMF is as expressed by equation (14).(14)v2x=0,x−51017821−5101,1,x<5101,5101≤x<7821,x≥7821.


#### 4.2.3. Cutterhead Opening RatioV3

The selection of the cutterhead opening ratio is related to the adaptability of the cutterhead to the soil layer. The ratio is defined as(15)ξ=AsAr,where As and Ar are the opening area and the full cutting area of the cutterhead, respectively. The various magnitudes of the correlation value ξ between the EBP TBM tunnelling time and the soil layer [37] are detailed in Table 10.Table 10
Correlation between the cutterhead opening ratio and the soil layer.
Geological stratificationSoil layerξ (%)DiluviumCohesive soil25–30Sandy soil15–20Gravelly soil20–25Interbedding of soft and hard soil30–35AlluviumCohesive soil20–25Sandy soil10–15Gravelly soil15–20Interbedding of soft and hard soil20–25It can be seen from Table11 that there is an optimal adaptability range for the cutterhead opening ratio. The corresponding FMF is expressed by equation (16).(16)v3x=0,x−15%25%−15%,1,45%−x45%−35%,0,x<15%,15%≤x<25%,25%≤x<35%,35%≤x<45%,x≥45%.Table 11
Cutter spacing for different rock types.
Rock typeCutter spacing (mm)Limestone70–85Granite50–85Gneiss60–70Sandstone70–85Shale85–100


#### 4.2.4. Slagging Ability of the Screw ConveyorV4

Theoretically, the maximum amount of soil cut by the cutters of an EPB TBM during continuous excavation is given by(17)Q1=vmaxπDe24,where vmax is the maximum driving speed of the EPB TBM [37]. Based on the data in Table 7, Q1 was determined to be 183.7 m3/h. The slagging ability of the screw conveyor was thus determined to be given by(18)Q2=dFz2.5KdKβ,where d is the diameter of the screw, Kz is the synthetic characteristic coefficient of the muck (0.049 is generally used), Kd is the filling coefficient (0.32 is generally used), and Kβ is the inclination coefficient (0.65 is generally used). For d = 0.9 m, Q2 = 300.7 m3/h.Because the mixing of bentonite slurry with the soil inside the chamber of the EPB TBM expands the muck volume, the maximum amount of muck conveyed by the screw is given by(19)Qmax=KsQ1,where Ks is the expansion coefficient of the muck, with 2.1 being considered as the maximum value, based on which Qmax = 385.8 m3/h.Using the above calculation results, the expression of the FMF of the slagging ability of the screw conveyor was derived as(20)v4x=0,x−300.7385.8−300.7,1,x<300.7,300.7≤x<385.8,x≥385.8.


#### 4.2.5. Cutter SpacingV5

The layout of the cutter spacing is significantly determined by the strength of the rock being cut. The cutter spacing used for common rocks is presented in Table11 [2].Based on a consideration of the rock strata of the two tunnel sections and noting that the adaptability range of the cutter spacing should be 40–100 mm, the corresponding FMF was derived as expressed by equation (21).(21)v5x=0,x−4060−40,1,100−x100−80,0,x<40,40≤x<60,60≤x<80,80≤x<100,x≥100.


#### 4.2.6. Earth Pressure in the Cutterhead ChamberV6

During EPB TBM tunnelling, the maximum and minimum control pressures on the excavation surface are, respectively, given by [38].(22)Pmax=Pw+P0+Pi,Pmin=Pw+Pa+Pi,where Pw is the groundwater pressure, P0 is the static earth pressure, Pa is the active earth pressure (for strata with differentially weathered granite, the loose pressure of the granite could be considered representative), and Pi is the preparatory pressure for compensating for the loss in pressure during tunnelling (0.01–0.02 MPa is generally used).Using the known maximum depth of the tunnelling section of 30.5 m and geotechnical data,Pmax was determined to be 0.320 MPa; using Rankine’s theory, Pa was determined to be 0.170 MPa; and using Protodyakonov’s theory, the loose pressure was determined to be 0.150 MPa. Based on these results, the FMF of the earth pressure in the cutterhead chamber was derived as expressed by equation (23). It should be noted that ground uplift due to excessive pressure was not considered.(23)v6x=0,x−0.150.32−0.15,1,x<0.15,0.15≤x<0.32,x≥0.32.


#### 4.2.7. Grouting PressureV7

The grouting pressure is related to the earth and water pressures, segment strength, TBM type, and characteristics of the slurry material. It was observed during the construction of the Shenzhen Metro that the synchronous grouting pressure generally did not fall below 200 kPa [5]. Hence, the maximum permissible grouting pressure [1] was determined to be given by(24)Pf=p0+0.9lnη+0.73qu,where η = (De + 2H)/De, H is the buried depth, p0 is the overburden pressure, and qu is the unconfined compressive strength of the soil. Using the geotechnical data of the shallowest tunnel profile in the tunnel sections, it was determined that Pf = 600 kPa. Based on this result, the adaptability range of the grouting pressure was determined to be 200–660 kPa. The corresponding FMF is expressed by equation (25).(25)v7x=0,x−200660−200,1,x<200,200≤x<660,x≥660.


#### 4.2.8. Shield Tail VoidV8

The selected amount of shield tail impacts its sealing effect and determines the soil deformation. Statistical data from actual cases of using different tail voids are presented in Table12 [37].Table 12
Case values of the shield tail void [37].
Outer diameter of shield (m)Number of constructed tunnels25 mm30 mm40 mm<393703–5633425–789110>7252550Generally, the shield tail void should not be less than 30 mm. In addition, based on observations from the construction of the Shenzhen Metro, the maximum void is approximately 65 mm [5]. Thus, the adaptability range for the void should be 30–65 mm. The corresponding FMF is (26)v8x=0,x−3065−30,1,x<30,30≤x<65,x≥65.


#### 4.2.9. Composite StrataV9

This refers to the occurrence of two or more strata with significantly different strengths on the excavation surface during tunnelling. Typical examples that were encountered in the two tunnel sections under consideration included strata containing differentially weathered granite, bedrock protrusions, and so on. The average uniaxial compressive strength of the rocks was 80 MPa, although the maximum strength could reach 135 MPa. This implies substantial strength variation over the different parts of the excavation surface. The existence of hard rocks within the composite strata clearly impacted the tunnelling negatively. The strata composition ratio is defined as(27)Rc=HhDe,where Hh is the thickness of the hard-rock layer at the excavation surface.Based on the observations from tunnelling through composite strata during the construction of the Shenzhen Metro, whenRc < 15%, the excavation surface may be treated as a homogeneous soil layer, which does not adversely affect EPB TBM tunnelling. However, when Rc is 40%–60%, the impact on shield tunnelling is the most severe. This includes partial loading of the main bearing, increased wear and tear of the cutter bits, and difficult tunnelling and attitude control [5]. The FMF of the composite strata was determined to be as expressed by equation (28).(28)v9x=1,35%−x35%−30%,0,x−60%65%−60%,1,x<30%,30%≤x<35%,35%≤x<60%,60%≤x<65%,x≥65%.


#### 4.2.10. Spherical Weathered BouldersV10

Spherical weathered boulders occur in various shapes, with their sizes ranging from tens of centimeters to several meters. Their uniaxial compressive strength is 80–200 MPa and they mostly occur in strata comprising fully and severely weathered granite. Their random spatial distributions pose severe challenges to shield tunnelling. However, construction experience has shown that boulders smaller than 0.3 m minimally impact excavation. Conversely, those larger than 2 m easily jam the cutterhead, with a supplementary measure such as manual excavation or directional blasting required to continue the tunnelling. The FMF of spherical weathered boulders is(29)v10x=1,2−x2−0.3,0,x<0.3,0.3≤x<2.0,x≥2.0.


### 4.3. Hierarchy of Evaluation Indexes

The hierarchy of the 10 evaluation indexes in Table10 must be established before evaluating the adaptability of the EPB TBM shield tunnelling.


#### 4.3.1. SHA

The experience gained from tunnelling through composite strata during the construction of the Shenzhen Metro was combined with existing research findings and expert opinion in assigning the judgment matrix values. This was done based on the relative importance of the evaluation indexes in the three layers. The weight of each index was then calculated before testing for consistency. The calculation results are presented in Tables13 and 14.Table 13
Weights of the evaluation indexes in the criteria layer.
DU1U2U3U1132U21/311/2U31/221Single-layer weight0.53960.16340.2970Single hierarchy132λmax = 3.0183, CI = 0.0092, RI = 0.5149, and CR = 0.0179 < 0.1Table 14
Weights of the evaluation indexes in the index layer.
U1V1V2V3V4V5V112567V21/21456V31/51/4123V41/61/51/212λmax = 5.1189V51/71/61/31/21CI = 0.0297Single-layer weight0.46310.31290.10870.06940.0459RI = 1.1185Single hierarchy12345CR = 0.0266 < 0.1U2V6V7V8V6156V71/512λmax = 3.0291V81/61/21CI = 0.0146Single-layer weight0.72580.17210.1020RI = 0.5149Single hierarchy123CR = 0.0282 < 0.1U3V9V10V912λmax = 2.0V101/21CI = 0Single-layer weight0.66670.3333RI = 0Single hierarchy12CR = 0 < 0.1


#### 4.3.2. THA

The single hierarchies of the evaluation indexes in the three layers were used to obtain the THA weights using the method in Table2. The results are presented in Table 15.Table 15
THA of the evaluation indexes.
Evaluation indexSHATHAU1U2U3WeightHierarchyV10.46310.2501V20.31290.1693V30.10870.0596V40.06940.0377V50.04590.0259V60.72580.1194V70.17210.0288V80.10200.01710V90.66670.1982V100.33330.0985CR = 0.056 < 0.1


## 4.1. Evaluation Indexes and EIS

### 4.1.1. Preliminary Selection of Evaluation Indexes

The factors that affect EPB TBM tunnelling include the EPB TBM design, tunnelling method, geological conditions, and surrounding environment. A detailed analysis of the various influencing factors was conducted in this study, taking into account the geological and environmental conditions along the two aforementioned sections. Based on the study and practice of constructing Shenzhen Metro using shield tunnelling technology [5], 25 primary evaluation indexes W1 ∼ W25 were selected, as detailed in Table 8.Table 8
Primary evaluation indexes for the adaptability of an EPB TBM during tunnelling.
Target layerAdaptability degree of EPB TBM under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnelling methodU2Geological conditionsU3Environment conditionsU4Index layerTotal thrustW1Cutterhead structure W2Cutterhead torque W3Cutterhead opening ratio W4Muck improvement technique W5Selection and layout of cutters W6Cutter spacing W7Muck amount of screw conveyor W8Advancing speedW9Rotating speed of cutterhead W10Earth pressure in cutterhead chamber W11Shield tail void W12Wall-back grouting pressure W13Artificial fillW14Soft soil stratum W15Liquefied sand layer W16Residual soil layer W17Composite strata W18Microweathered granite protrusions W19Hard-rock layer W20Fault crushed zone W21Spherical weathered boulders W22Underground structuresW23Ground buildings W24Structure of existing tunnel lines W25To determine the mutual impacts of these indexes, 20 experts from universities, design institutes, and construction companies were asked to complete a questionnaire survey. Based on their judgments, values were first assigned to the judgment matrix as shown in Table1. AHP was then used to analyse the weights and hierarchy of the indexes in each layer. Based on the analysis of weights and hierarchy, the 25 primary indexes were evaluated and reduced to 10 indexes that have strong influencing weights.


### 4.1.2. Evaluation Index System

As shown in Table9, the 10 remaining indexes marked with V1 ∼ V10 were used to form the EIS of EBP TBM according to the principles for establishing an EIS. The fuzzy membership function of these indexes and the way they are evaluated are given in the next section.Table 9
EIS of the EPB TBM.
Target layerAdaptability of EPB TBM to tunnelling under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnel constructionU2Geological conditionsU3Index layerTotal thrustV1 (kN)Cutterhead torque V2 (kN∙m)Cutterhead opening ratio V3 (%)Muck amount of screw conveyor V4 (m3/h)Cutter spacing V5 (mm)Earth pressure in cutterhead chamberV6 (MPa)Wall-back grouting pressure V7 (kPa)Shield tail void V8 (mm)Composite strataV9 (%)Spherical weathered boulders V10 (m)


## 4.1.1. Preliminary Selection of Evaluation Indexes

The factors that affect EPB TBM tunnelling include the EPB TBM design, tunnelling method, geological conditions, and surrounding environment. A detailed analysis of the various influencing factors was conducted in this study, taking into account the geological and environmental conditions along the two aforementioned sections. Based on the study and practice of constructing Shenzhen Metro using shield tunnelling technology [5], 25 primary evaluation indexes W1 ∼ W25 were selected, as detailed in Table 8.Table 8
Primary evaluation indexes for the adaptability of an EPB TBM during tunnelling.
Target layerAdaptability degree of EPB TBM under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnelling methodU2Geological conditionsU3Environment conditionsU4Index layerTotal thrustW1Cutterhead structure W2Cutterhead torque W3Cutterhead opening ratio W4Muck improvement technique W5Selection and layout of cutters W6Cutter spacing W7Muck amount of screw conveyor W8Advancing speedW9Rotating speed of cutterhead W10Earth pressure in cutterhead chamber W11Shield tail void W12Wall-back grouting pressure W13Artificial fillW14Soft soil stratum W15Liquefied sand layer W16Residual soil layer W17Composite strata W18Microweathered granite protrusions W19Hard-rock layer W20Fault crushed zone W21Spherical weathered boulders W22Underground structuresW23Ground buildings W24Structure of existing tunnel lines W25To determine the mutual impacts of these indexes, 20 experts from universities, design institutes, and construction companies were asked to complete a questionnaire survey. Based on their judgments, values were first assigned to the judgment matrix as shown in Table1. AHP was then used to analyse the weights and hierarchy of the indexes in each layer. Based on the analysis of weights and hierarchy, the 25 primary indexes were evaluated and reduced to 10 indexes that have strong influencing weights.


## 4.1.2. Evaluation Index System

As shown in Table9, the 10 remaining indexes marked with V1 ∼ V10 were used to form the EIS of EBP TBM according to the principles for establishing an EIS. The fuzzy membership function of these indexes and the way they are evaluated are given in the next section.Table 9
EIS of the EPB TBM.
Target layerAdaptability of EPB TBM to tunnelling under mixed ground conditionsDCriteria layerEPB TBM designU1Tunnel constructionU2Geological conditionsU3Index layerTotal thrustV1 (kN)Cutterhead torque V2 (kN∙m)Cutterhead opening ratio V3 (%)Muck amount of screw conveyor V4 (m3/h)Cutter spacing V5 (mm)Earth pressure in cutterhead chamberV6 (MPa)Wall-back grouting pressure V7 (kPa)Shield tail void V8 (mm)Composite strataV9 (%)Spherical weathered boulders V10 (m)


## 4.2. Fuzzy Membership Function of Indexes in the EIS

### 4.2.1. Total ThrustV1

The equation commonly used to predict the total thrust of an EPB TBM is(11)F=FsπDe24,where Fs is an empirical coefficient with a value within 700–1,200 kN/m2 and De is the excavation diameter [37]. Based on the known value of De = 6.980 m, the adaptability range of the total thrust was determined to be 26,785–45,918 kN. According to these values, the FMF of the total thrust was established as expressed by equation (12).(12)v1x=0,x−2678545918−26785,1,x<26785,26785≤x<45918,x≥45918.


### 4.2.2. Cutterhead TorqueV2

The empirical equation for calculating the cutterhead torque is(13)T=αDe3,where α is the torque coefficient, which ranges within 15–23 [37]. For De = 6.980 m, the adaptability range of the cutterhead torque was determined to be 5,101–7,821 kN∙m. The corresponding FMF is as expressed by equation (14).(14)v2x=0,x−51017821−5101,1,x<5101,5101≤x<7821,x≥7821.


### 4.2.3. Cutterhead Opening RatioV3

The selection of the cutterhead opening ratio is related to the adaptability of the cutterhead to the soil layer. The ratio is defined as(15)ξ=AsAr,where As and Ar are the opening area and the full cutting area of the cutterhead, respectively. The various magnitudes of the correlation value ξ between the EBP TBM tunnelling time and the soil layer [37] are detailed in Table 10.Table 10
Correlation between the cutterhead opening ratio and the soil layer.
Geological stratificationSoil layerξ (%)DiluviumCohesive soil25–30Sandy soil15–20Gravelly soil20–25Interbedding of soft and hard soil30–35AlluviumCohesive soil20–25Sandy soil10–15Gravelly soil15–20Interbedding of soft and hard soil20–25It can be seen from Table11 that there is an optimal adaptability range for the cutterhead opening ratio. The corresponding FMF is expressed by equation (16).(16)v3x=0,x−15%25%−15%,1,45%−x45%−35%,0,x<15%,15%≤x<25%,25%≤x<35%,35%≤x<45%,x≥45%.Table 11
Cutter spacing for different rock types.
Rock typeCutter spacing (mm)Limestone70–85Granite50–85Gneiss60–70Sandstone70–85Shale85–100


### 4.2.4. Slagging Ability of the Screw ConveyorV4

Theoretically, the maximum amount of soil cut by the cutters of an EPB TBM during continuous excavation is given by(17)Q1=vmaxπDe24,where vmax is the maximum driving speed of the EPB TBM [37]. Based on the data in Table 7, Q1 was determined to be 183.7 m3/h. The slagging ability of the screw conveyor was thus determined to be given by(18)Q2=dFz2.5KdKβ,where d is the diameter of the screw, Kz is the synthetic characteristic coefficient of the muck (0.049 is generally used), Kd is the filling coefficient (0.32 is generally used), and Kβ is the inclination coefficient (0.65 is generally used). For d = 0.9 m, Q2 = 300.7 m3/h.Because the mixing of bentonite slurry with the soil inside the chamber of the EPB TBM expands the muck volume, the maximum amount of muck conveyed by the screw is given by(19)Qmax=KsQ1,where Ks is the expansion coefficient of the muck, with 2.1 being considered as the maximum value, based on which Qmax = 385.8 m3/h.Using the above calculation results, the expression of the FMF of the slagging ability of the screw conveyor was derived as(20)v4x=0,x−300.7385.8−300.7,1,x<300.7,300.7≤x<385.8,x≥385.8.


### 4.2.5. Cutter SpacingV5

The layout of the cutter spacing is significantly determined by the strength of the rock being cut. The cutter spacing used for common rocks is presented in Table11 [2].Based on a consideration of the rock strata of the two tunnel sections and noting that the adaptability range of the cutter spacing should be 40–100 mm, the corresponding FMF was derived as expressed by equation (21).(21)v5x=0,x−4060−40,1,100−x100−80,0,x<40,40≤x<60,60≤x<80,80≤x<100,x≥100.


### 4.2.6. Earth Pressure in the Cutterhead ChamberV6

During EPB TBM tunnelling, the maximum and minimum control pressures on the excavation surface are, respectively, given by [38].(22)Pmax=Pw+P0+Pi,Pmin=Pw+Pa+Pi,where Pw is the groundwater pressure, P0 is the static earth pressure, Pa is the active earth pressure (for strata with differentially weathered granite, the loose pressure of the granite could be considered representative), and Pi is the preparatory pressure for compensating for the loss in pressure during tunnelling (0.01–0.02 MPa is generally used).Using the known maximum depth of the tunnelling section of 30.5 m and geotechnical data,Pmax was determined to be 0.320 MPa; using Rankine’s theory, Pa was determined to be 0.170 MPa; and using Protodyakonov’s theory, the loose pressure was determined to be 0.150 MPa. Based on these results, the FMF of the earth pressure in the cutterhead chamber was derived as expressed by equation (23). It should be noted that ground uplift due to excessive pressure was not considered.(23)v6x=0,x−0.150.32−0.15,1,x<0.15,0.15≤x<0.32,x≥0.32.


### 4.2.7. Grouting PressureV7

The grouting pressure is related to the earth and water pressures, segment strength, TBM type, and characteristics of the slurry material. It was observed during the construction of the Shenzhen Metro that the synchronous grouting pressure generally did not fall below 200 kPa [5]. Hence, the maximum permissible grouting pressure [1] was determined to be given by(24)Pf=p0+0.9lnη+0.73qu,where η = (De + 2H)/De, H is the buried depth, p0 is the overburden pressure, and qu is the unconfined compressive strength of the soil. Using the geotechnical data of the shallowest tunnel profile in the tunnel sections, it was determined that Pf = 600 kPa. Based on this result, the adaptability range of the grouting pressure was determined to be 200–660 kPa. The corresponding FMF is expressed by equation (25).(25)v7x=0,x−200660−200,1,x<200,200≤x<660,x≥660.


### 4.2.8. Shield Tail VoidV8

The selected amount of shield tail impacts its sealing effect and determines the soil deformation. Statistical data from actual cases of using different tail voids are presented in Table12 [37].Table 12
Case values of the shield tail void [37].
Outer diameter of shield (m)Number of constructed tunnels25 mm30 mm40 mm<393703–5633425–789110>7252550Generally, the shield tail void should not be less than 30 mm. In addition, based on observations from the construction of the Shenzhen Metro, the maximum void is approximately 65 mm [5]. Thus, the adaptability range for the void should be 30–65 mm. The corresponding FMF is (26)v8x=0,x−3065−30,1,x<30,30≤x<65,x≥65.


### 4.2.9. Composite StrataV9

This refers to the occurrence of two or more strata with significantly different strengths on the excavation surface during tunnelling. Typical examples that were encountered in the two tunnel sections under consideration included strata containing differentially weathered granite, bedrock protrusions, and so on. The average uniaxial compressive strength of the rocks was 80 MPa, although the maximum strength could reach 135 MPa. This implies substantial strength variation over the different parts of the excavation surface. The existence of hard rocks within the composite strata clearly impacted the tunnelling negatively. The strata composition ratio is defined as(27)Rc=HhDe,where Hh is the thickness of the hard-rock layer at the excavation surface.Based on the observations from tunnelling through composite strata during the construction of the Shenzhen Metro, whenRc < 15%, the excavation surface may be treated as a homogeneous soil layer, which does not adversely affect EPB TBM tunnelling. However, when Rc is 40%–60%, the impact on shield tunnelling is the most severe. This includes partial loading of the main bearing, increased wear and tear of the cutter bits, and difficult tunnelling and attitude control [5]. The FMF of the composite strata was determined to be as expressed by equation (28).(28)v9x=1,35%−x35%−30%,0,x−60%65%−60%,1,x<30%,30%≤x<35%,35%≤x<60%,60%≤x<65%,x≥65%.


### 4.2.10. Spherical Weathered BouldersV10

Spherical weathered boulders occur in various shapes, with their sizes ranging from tens of centimeters to several meters. Their uniaxial compressive strength is 80–200 MPa and they mostly occur in strata comprising fully and severely weathered granite. Their random spatial distributions pose severe challenges to shield tunnelling. However, construction experience has shown that boulders smaller than 0.3 m minimally impact excavation. Conversely, those larger than 2 m easily jam the cutterhead, with a supplementary measure such as manual excavation or directional blasting required to continue the tunnelling. The FMF of spherical weathered boulders is(29)v10x=1,2−x2−0.3,0,x<0.3,0.3≤x<2.0,x≥2.0.


## 4.2.1. Total ThrustV1

The equation commonly used to predict the total thrust of an EPB TBM is(11)F=FsπDe24,where Fs is an empirical coefficient with a value within 700–1,200 kN/m2 and De is the excavation diameter [37]. Based on the known value of De = 6.980 m, the adaptability range of the total thrust was determined to be 26,785–45,918 kN. According to these values, the FMF of the total thrust was established as expressed by equation (12).(12)v1x=0,x−2678545918−26785,1,x<26785,26785≤x<45918,x≥45918.


## 4.2.2. Cutterhead TorqueV2

The empirical equation for calculating the cutterhead torque is(13)T=αDe3,where α is the torque coefficient, which ranges within 15–23 [37]. For De = 6.980 m, the adaptability range of the cutterhead torque was determined to be 5,101–7,821 kN∙m. The corresponding FMF is as expressed by equation (14).(14)v2x=0,x−51017821−5101,1,x<5101,5101≤x<7821,x≥7821.


## 4.2.3. Cutterhead Opening RatioV3

The selection of the cutterhead opening ratio is related to the adaptability of the cutterhead to the soil layer. The ratio is defined as(15)ξ=AsAr,where As and Ar are the opening area and the full cutting area of the cutterhead, respectively. The various magnitudes of the correlation value ξ between the EBP TBM tunnelling time and the soil layer [37] are detailed in Table 10.Table 10
Correlation between the cutterhead opening ratio and the soil layer.
Geological stratificationSoil layerξ (%)DiluviumCohesive soil25–30Sandy soil15–20Gravelly soil20–25Interbedding of soft and hard soil30–35AlluviumCohesive soil20–25Sandy soil10–15Gravelly soil15–20Interbedding of soft and hard soil20–25It can be seen from Table11 that there is an optimal adaptability range for the cutterhead opening ratio. The corresponding FMF is expressed by equation (16).(16)v3x=0,x−15%25%−15%,1,45%−x45%−35%,0,x<15%,15%≤x<25%,25%≤x<35%,35%≤x<45%,x≥45%.Table 11
Cutter spacing for different rock types.
Rock typeCutter spacing (mm)Limestone70–85Granite50–85Gneiss60–70Sandstone70–85Shale85–100


## 4.2.4. Slagging Ability of the Screw ConveyorV4

Theoretically, the maximum amount of soil cut by the cutters of an EPB TBM during continuous excavation is given by(17)Q1=vmaxπDe24,where vmax is the maximum driving speed of the EPB TBM [37]. Based on the data in Table 7, Q1 was determined to be 183.7 m3/h. The slagging ability of the screw conveyor was thus determined to be given by(18)Q2=dFz2.5KdKβ,where d is the diameter of the screw, Kz is the synthetic characteristic coefficient of the muck (0.049 is generally used), Kd is the filling coefficient (0.32 is generally used), and Kβ is the inclination coefficient (0.65 is generally used). For d = 0.9 m, Q2 = 300.7 m3/h.Because the mixing of bentonite slurry with the soil inside the chamber of the EPB TBM expands the muck volume, the maximum amount of muck conveyed by the screw is given by(19)Qmax=KsQ1,where Ks is the expansion coefficient of the muck, with 2.1 being considered as the maximum value, based on which Qmax = 385.8 m3/h.Using the above calculation results, the expression of the FMF of the slagging ability of the screw conveyor was derived as(20)v4x=0,x−300.7385.8−300.7,1,x<300.7,300.7≤x<385.8,x≥385.8.


## 4.2.5. Cutter SpacingV5

The layout of the cutter spacing is significantly determined by the strength of the rock being cut. The cutter spacing used for common rocks is presented in Table11 [2].Based on a consideration of the rock strata of the two tunnel sections and noting that the adaptability range of the cutter spacing should be 40–100 mm, the corresponding FMF was derived as expressed by equation (21).(21)v5x=0,x−4060−40,1,100−x100−80,0,x<40,40≤x<60,60≤x<80,80≤x<100,x≥100.


## 4.2.6. Earth Pressure in the Cutterhead ChamberV6

During EPB TBM tunnelling, the maximum and minimum control pressures on the excavation surface are, respectively, given by [38].(22)Pmax=Pw+P0+Pi,Pmin=Pw+Pa+Pi,where Pw is the groundwater pressure, P0 is the static earth pressure, Pa is the active earth pressure (for strata with differentially weathered granite, the loose pressure of the granite could be considered representative), and Pi is the preparatory pressure for compensating for the loss in pressure during tunnelling (0.01–0.02 MPa is generally used).Using the known maximum depth of the tunnelling section of 30.5 m and geotechnical data,Pmax was determined to be 0.320 MPa; using Rankine’s theory, Pa was determined to be 0.170 MPa; and using Protodyakonov’s theory, the loose pressure was determined to be 0.150 MPa. Based on these results, the FMF of the earth pressure in the cutterhead chamber was derived as expressed by equation (23). It should be noted that ground uplift due to excessive pressure was not considered.(23)v6x=0,x−0.150.32−0.15,1,x<0.15,0.15≤x<0.32,x≥0.32.


## 4.2.7. Grouting PressureV7

The grouting pressure is related to the earth and water pressures, segment strength, TBM type, and characteristics of the slurry material. It was observed during the construction of the Shenzhen Metro that the synchronous grouting pressure generally did not fall below 200 kPa [5]. Hence, the maximum permissible grouting pressure [1] was determined to be given by(24)Pf=p0+0.9lnη+0.73qu,where η = (De + 2H)/De, H is the buried depth, p0 is the overburden pressure, and qu is the unconfined compressive strength of the soil. Using the geotechnical data of the shallowest tunnel profile in the tunnel sections, it was determined that Pf = 600 kPa. Based on this result, the adaptability range of the grouting pressure was determined to be 200–660 kPa. The corresponding FMF is expressed by equation (25).(25)v7x=0,x−200660−200,1,x<200,200≤x<660,x≥660.


## 4.2.8. Shield Tail VoidV8

The selected amount of shield tail impacts its sealing effect and determines the soil deformation. Statistical data from actual cases of using different tail voids are presented in Table12 [37].Table 12
Case values of the shield tail void [37].
Outer diameter of shield (m)Number of constructed tunnels25 mm30 mm40 mm<393703–5633425–789110>7252550Generally, the shield tail void should not be less than 30 mm. In addition, based on observations from the construction of the Shenzhen Metro, the maximum void is approximately 65 mm [5]. Thus, the adaptability range for the void should be 30–65 mm. The corresponding FMF is (26)v8x=0,x−3065−30,1,x<30,30≤x<65,x≥65.


## 4.2.9. Composite StrataV9

This refers to the occurrence of two or more strata with significantly different strengths on the excavation surface during tunnelling. Typical examples that were encountered in the two tunnel sections under consideration included strata containing differentially weathered granite, bedrock protrusions, and so on. The average uniaxial compressive strength of the rocks was 80 MPa, although the maximum strength could reach 135 MPa. This implies substantial strength variation over the different parts of the excavation surface. The existence of hard rocks within the composite strata clearly impacted the tunnelling negatively. The strata composition ratio is defined as(27)Rc=HhDe,where Hh is the thickness of the hard-rock layer at the excavation surface.Based on the observations from tunnelling through composite strata during the construction of the Shenzhen Metro, whenRc < 15%, the excavation surface may be treated as a homogeneous soil layer, which does not adversely affect EPB TBM tunnelling. However, when Rc is 40%–60%, the impact on shield tunnelling is the most severe. This includes partial loading of the main bearing, increased wear and tear of the cutter bits, and difficult tunnelling and attitude control [5]. The FMF of the composite strata was determined to be as expressed by equation (28).(28)v9x=1,35%−x35%−30%,0,x−60%65%−60%,1,x<30%,30%≤x<35%,35%≤x<60%,60%≤x<65%,x≥65%.


## 4.2.10. Spherical Weathered BouldersV10

Spherical weathered boulders occur in various shapes, with their sizes ranging from tens of centimeters to several meters. Their uniaxial compressive strength is 80–200 MPa and they mostly occur in strata comprising fully and severely weathered granite. Their random spatial distributions pose severe challenges to shield tunnelling. However, construction experience has shown that boulders smaller than 0.3 m minimally impact excavation. Conversely, those larger than 2 m easily jam the cutterhead, with a supplementary measure such as manual excavation or directional blasting required to continue the tunnelling. The FMF of spherical weathered boulders is(29)v10x=1,2−x2−0.3,0,x<0.3,0.3≤x<2.0,x≥2.0.


## 4.3. Hierarchy of Evaluation Indexes

The hierarchy of the 10 evaluation indexes in Table10 must be established before evaluating the adaptability of the EPB TBM shield tunnelling.


### 4.3.1. SHA

The experience gained from tunnelling through composite strata during the construction of the Shenzhen Metro was combined with existing research findings and expert opinion in assigning the judgment matrix values. This was done based on the relative importance of the evaluation indexes in the three layers. The weight of each index was then calculated before testing for consistency. The calculation results are presented in Tables13 and 14.Table 13
Weights of the evaluation indexes in the criteria layer.
DU1U2U3U1132U21/311/2U31/221Single-layer weight0.53960.16340.2970Single hierarchy132λmax = 3.0183, CI = 0.0092, RI = 0.5149, and CR = 0.0179 < 0.1Table 14
Weights of the evaluation indexes in the index layer.
U1V1V2V3V4V5V112567V21/21456V31/51/4123V41/61/51/212λmax = 5.1189V51/71/61/31/21CI = 0.0297Single-layer weight0.46310.31290.10870.06940.0459RI = 1.1185Single hierarchy12345CR = 0.0266 < 0.1U2V6V7V8V6156V71/512λmax = 3.0291V81/61/21CI = 0.0146Single-layer weight0.72580.17210.1020RI = 0.5149Single hierarchy123CR = 0.0282 < 0.1U3V9V10V912λmax = 2.0V101/21CI = 0Single-layer weight0.66670.3333RI = 0Single hierarchy12CR = 0 < 0.1


### 4.3.2. THA

The single hierarchies of the evaluation indexes in the three layers were used to obtain the THA weights using the method in Table2. The results are presented in Table 15.Table 15
THA of the evaluation indexes.
Evaluation indexSHATHAU1U2U3WeightHierarchyV10.46310.2501V20.31290.1693V30.10870.0596V40.06940.0377V50.04590.0259V60.72580.1194V70.17210.0288V80.10200.01710V90.66670.1982V100.33330.0985CR = 0.056 < 0.1


## 4.3.1. SHA

The experience gained from tunnelling through composite strata during the construction of the Shenzhen Metro was combined with existing research findings and expert opinion in assigning the judgment matrix values. This was done based on the relative importance of the evaluation indexes in the three layers. The weight of each index was then calculated before testing for consistency. The calculation results are presented in Tables13 and 14.Table 13
Weights of the evaluation indexes in the criteria layer.
DU1U2U3U1132U21/311/2U31/221Single-layer weight0.53960.16340.2970Single hierarchy132λmax = 3.0183, CI = 0.0092, RI = 0.5149, and CR = 0.0179 < 0.1Table 14
Weights of the evaluation indexes in the index layer.
U1V1V2V3V4V5V112567V21/21456V31/51/4123V41/61/51/212λmax = 5.1189V51/71/61/31/21CI = 0.0297Single-layer weight0.46310.31290.10870.06940.0459RI = 1.1185Single hierarchy12345CR = 0.0266 < 0.1U2V6V7V8V6156V71/512λmax = 3.0291V81/61/21CI = 0.0146Single-layer weight0.72580.17210.1020RI = 0.5149Single hierarchy123CR = 0.0282 < 0.1U3V9V10V912λmax = 2.0V101/21CI = 0Single-layer weight0.66670.3333RI = 0Single hierarchy12CR = 0 < 0.1


## 4.3.2. THA

The single hierarchies of the evaluation indexes in the three layers were used to obtain the THA weights using the method in Table2. The results are presented in Table 15.Table 15
THA of the evaluation indexes.
Evaluation indexSHATHAU1U2U3WeightHierarchyV10.46310.2501V20.31290.1693V30.10870.0596V40.06940.0377V50.04590.0259V60.72580.1194V70.17210.0288V80.10200.01710V90.66670.1982V100.33330.0985CR = 0.056 < 0.1


## 5. Evaluation of the Composite Strata Tunnelling Adaptability of an EPB TBM

### 5.1. Assigning Values to the Evaluation Indexes

The values ofV1–V5 are given in Table 7. The values of V6–V8 were obtained using the test sections of length 200 m, as presented in Table 16.Table 16
Evaluation index values obtained from the test sections.
Evaluation indexSection C-HSection N-QLeft lineRight lineLeft lineRight lineV6 (MPa)0.1370.1490.1890.168V7 (kPa)242.2269.9221.2141.0V8 (mm)64.1264.8368.6463.55The distribution, rocks, and thicknesses of the composite strata in the two sections are given in Table17. Because the impact of composite strata on shield tunnelling is related to the strata distribution range, the final value of V9 should be the weighted average.Table 17
Location, length, and composition ratio of the composite strata.
Tunnel sectionLocationLength (m)Rock typeMaximum thickness (m)Rc (%)C–HZCK6 + 600–ZCK6 + 70031.6Medium-weathered coarse-grained granite5.883.1ZCK8 + 550–ZCK8 + 65068.4Medium- to microweathered coarse-grained granite5.274.5YCK7 + 680–YCK7 + 75052.34.970.2N-QZCK16 + 550–ZCK16 + 65089.9Medium- to microweathered coarse-grained granite3.245.8ZCK17 + 850–ZCK17 + 90016.64.665.9YCK15 + 550–YCK15 + 850133.65.883.1YCK16 + 100–YCK16 + 25082.36.288.8The geological exploration data indicated that spherical lightly weathered boulders occurred only in the right line of Section C-H. The sizes of the surveyed boulders range from 0.45 to 4.0 m. As mentioned previously, boulders larger than 2 m are generally removed by other methods. Thus, the value ofV10 would be the highest value less than 2 m.The values assigned to the evaluation indexes using the above-described process are presented in Table18.Table 18
Assigned values of the evaluation indexes for assessing the tunnelling adaptability of an EPB TBM.
Evaluation indexUnitSection C-HSection N-QLeft lineRight lineLeft lineRight lineV1kN49,588V2kN∙m7,806V3%33V4m3/h440V5mm90V6MPa0.1370.1370.1370.137V7kPa242.2269.9221.2141.0V8mm64.1264.8368.6463.55V9%77.270.248.985.3V10m01.200


### 5.2. Adaptability Evaluation

For the evaluation target setO = {O1, O2, O3, O4}, it is assumed that O1 and O2 represent the tunnelling adaptabilities of the EPB TBM in the left and right lines of Section C-H, respectively, and O3 and O4 are the corresponding values for Section N-Q.The set of the THA weights of the evaluation indexesV, denoted by V¯, is presented in Table 19. Substituting the values of the different evaluation indexes in Table 18 into the corresponding FMFs in Section 4.2 would give the matrix R of the degree of membership of V in O as follows:Table 19
Evaluated degrees of tunnelling adaptability of the EPB TBM.
Tunnel sectionSection C-HSection N-QLeft lineRight lineLeft lineRight lineDegree of adaptabilityD0.91350.83320.76210.9556Adaptability gradeIIIIIIR=11111111111111110.50.50.50.50.60240.747010.97590.06710.11110.033700.97490.995110.958611011011.The adaptability degree ofO is obtained by substituting V¯ and R into equation (9):D=V¯×R=0.91350.88320.76210.9556Based on the adaptability classification in Table3, the adaptability grades of EPB TBM tunnelling in Section C-H and Section N-Q are given in Table 19. That means this type of EPB TBM is adaptable to tunnelling through highly variable composite strata. The presence of large spherical weathered boulders along the right line of Section C-H and the left line of Section N-Q leads to a lower adaptability grade, which was confirmed by the actual excavation. Overall, the actual excavation of two sections showed that the proposed method for evaluating tunnelling adaptability of EPB TBM is correct and reasonable.


## 5.1. Assigning Values to the Evaluation Indexes

The values ofV1–V5 are given in Table 7. The values of V6–V8 were obtained using the test sections of length 200 m, as presented in Table 16.Table 16
Evaluation index values obtained from the test sections.
Evaluation indexSection C-HSection N-QLeft lineRight lineLeft lineRight lineV6 (MPa)0.1370.1490.1890.168V7 (kPa)242.2269.9221.2141.0V8 (mm)64.1264.8368.6463.55The distribution, rocks, and thicknesses of the composite strata in the two sections are given in Table17. Because the impact of composite strata on shield tunnelling is related to the strata distribution range, the final value of V9 should be the weighted average.Table 17
Location, length, and composition ratio of the composite strata.
Tunnel sectionLocationLength (m)Rock typeMaximum thickness (m)Rc (%)C–HZCK6 + 600–ZCK6 + 70031.6Medium-weathered coarse-grained granite5.883.1ZCK8 + 550–ZCK8 + 65068.4Medium- to microweathered coarse-grained granite5.274.5YCK7 + 680–YCK7 + 75052.34.970.2N-QZCK16 + 550–ZCK16 + 65089.9Medium- to microweathered coarse-grained granite3.245.8ZCK17 + 850–ZCK17 + 90016.64.665.9YCK15 + 550–YCK15 + 850133.65.883.1YCK16 + 100–YCK16 + 25082.36.288.8The geological exploration data indicated that spherical lightly weathered boulders occurred only in the right line of Section C-H. The sizes of the surveyed boulders range from 0.45 to 4.0 m. As mentioned previously, boulders larger than 2 m are generally removed by other methods. Thus, the value ofV10 would be the highest value less than 2 m.The values assigned to the evaluation indexes using the above-described process are presented in Table18.Table 18
Assigned values of the evaluation indexes for assessing the tunnelling adaptability of an EPB TBM.
Evaluation indexUnitSection C-HSection N-QLeft lineRight lineLeft lineRight lineV1kN49,588V2kN∙m7,806V3%33V4m3/h440V5mm90V6MPa0.1370.1370.1370.137V7kPa242.2269.9221.2141.0V8mm64.1264.8368.6463.55V9%77.270.248.985.3V10m01.200


## 5.2. Adaptability Evaluation

For the evaluation target setO = {O1, O2, O3, O4}, it is assumed that O1 and O2 represent the tunnelling adaptabilities of the EPB TBM in the left and right lines of Section C-H, respectively, and O3 and O4 are the corresponding values for Section N-Q.The set of the THA weights of the evaluation indexesV, denoted by V¯, is presented in Table 19. Substituting the values of the different evaluation indexes in Table 18 into the corresponding FMFs in Section 4.2 would give the matrix R of the degree of membership of V in O as follows:Table 19
Evaluated degrees of tunnelling adaptability of the EPB TBM.
Tunnel sectionSection C-HSection N-QLeft lineRight lineLeft lineRight lineDegree of adaptabilityD0.91350.83320.76210.9556Adaptability gradeIIIIIIR=11111111111111110.50.50.50.50.60240.747010.97590.06710.11110.033700.97490.995110.958611011011.The adaptability degree ofO is obtained by substituting V¯ and R into equation (9):D=V¯×R=0.91350.88320.76210.9556Based on the adaptability classification in Table3, the adaptability grades of EPB TBM tunnelling in Section C-H and Section N-Q are given in Table 19. That means this type of EPB TBM is adaptable to tunnelling through highly variable composite strata. The presence of large spherical weathered boulders along the right line of Section C-H and the left line of Section N-Q leads to a lower adaptability grade, which was confirmed by the actual excavation. Overall, the actual excavation of two sections showed that the proposed method for evaluating tunnelling adaptability of EPB TBM is correct and reasonable.


## 6. Conclusions

The method for evaluating EPB TBM tunnelling adaptability to tunnel excavation is required for choosing the suitable technical parameters of the machine and to minimize the risks of tunnelling under adverse geological conditions. The evaluation is generally difficult because of the differing effects and complex relationships among the various factors involved. In the present study, a quantitative method based on AHP and fuzzy comprehensive evaluation was developed for the evaluation of EPB TBM adaptability under complex geological conditions. The rationality of the proposed method was verified by an actual tunnel construction project. The following is a summary of the proposed method and the conclusions drawn from the study:(1)
The first step in the evaluation of EPB TBM tunnelling adaptability is the enumeration of various potential influencing factors and pairwise comparisons of their impacts. The bases of the comparison include construction experience, findings of scientific research, and expert opinion. This is used as a foundation for the application of AHP to determine the impact weights of various factors. The weights are then used to hierarchically arrange the selected evaluation indexes. An understanding of the effects of the factors would directly impact the quality of the selected evaluation indexes.(2)
For the establishment of the EIS of the tunnelling adaptability of an EPB TBM in this study, (i) the tunnelling adaptability of the EPB TBMs applied to the composite strata encountered during the construction of the Shenzhen Metro Line 11 was used as the target layer; (ii) the EPB TBM design, tunnel construction plan, and geological conditions were used as the criteria layer; and (iii) the total thrust, cutterhead torque, cutterhead opening ratio, muck amount of the screw conveyor, cutter spacing, earth pressure in the cutterhead chamber, wall-back grouting pressure, shield tail void, composite strata, and spherical weathered boulders were used as the index layer. The rational EIS was the foundation on which the evaluation targets were determined.(3)
The corresponding FMFs were established based on the effects of 10 selected evaluation indexes on the tunnelling adaptability of the EPB TBMs. Each FMF prescribed the value range of the related evaluation index. Based on the proposed FMFs, the fuzzy mathematical method was used to ensure the generality of the various evaluation indexes. The validity of the FMFs was dependent on the ability to quantitatively define the effects of the influencing factors.(4)
After the establishment of the EIS, values were assigned to different evaluation indexes using technical and geotechnical data obtained from the Shenzhen Metro Line 11 project. Fuzzy comprehensive evaluation was then used to evaluate the tunnelling adaptability of the EPB TBMs used for the tunnel excavation. The evaluation results were found to be consistent with the observations made from actual shield tunnelling.(5)
The present study was based on the current understanding of the considered influencing factors. It should be noted that there are a few other important factors that were not taken into account owing to the difficulty of quantifying them. Further study is required to consider such factors to improve the accuracy of the proposed EPB TBM tunnelling adaptability evaluation method.



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*Source: 5558833-2021-07-28.xml*