# Predicting Tunnel Squeezing Using Multiclass Support Vector Machines

Authors: Yang Sun; Xianda Feng; Lingqiang Yang
Journal: Advances in Civil Engineering
 (2018)

---

## Abstract

Tunnel squeezing is one of the major geological disasters that often occur during the construction of tunnels in weak rock masses subjected to high in situ stresses. It could cause shield jamming, budget overruns, and construction delays and could even lead to tunnel instability and casualties. Therefore, accurate prediction or identification of tunnel squeezing is extremely important in the design and construction of tunnels. This study presents a modified application of a multiclass support vector machine (SVM) to predict tunnel squeezing based on four parameters, that is, diameter (D), buried depth (H), support stiffness (K), and rock tunneling quality index (Q). We compiled a database from the literature, including 117 case histories obtained from different countries such as India, Nepal, and Bhutan, to train the multiclass SVM model. The proposed model was validated using 8-fold cross validation, and the average error percentage was approximately 11.87%. Compared with existing approaches, the proposed multiclass SVM model yields a better performance in predictive accuracy. More importantly, one could estimate the severity of potential squeezing problems based on the predicted squeezing categories/classes.


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## Body

## 1. Introduction

Redistributed stresses owing to tunnel excavation may exceed rock strength, and this could cause large plastic deformations, a phenomenon often referred to as tunnel squeezing [1]. Tunnel squeezing often occurs in soft/weak rock masses (such as shales and schists) subjected to high in situ stresses and constitutes one of the main geological disasters for rock underground engineering [2]. It could cause shield jamming, budget overruns, and construction delays and could even lead to tunnel instability and casualties. Therefore, accurate prediction or identification of tunnel squeezing is extremely important in the design and construction of tunnels. Many researchers have been studying the prediction or identification of tunnel squeezing since the 1980s. A summary of these studies for predicting tunnel squeezing is listed in Table 1. Overall, these approaches can be divided into three categories: (i) those based on the relationship between rock mass strength and in situ stress, (ii) those based on the correlations between overburden and the rock mass classification (such as Q), and (iii) those based on the prediction of deformation ε. Note that the deformation ε used herein refers to the percentage strain (or is alternatively referred to as “normalized convergence”) and is defined as 100x the ratio of the tunnel closure to tunnel diameter [3]. The commonly accepted threshold for squeezing occurrence is ε = 1% [4–6]; that is, the tunnels with strains larger than 1% will likely encounter construction problems.Table 1
Summary of previously published empirical correlations for predicting tunnel squeezing.
Proposed by
Correlations
Required parameters
Sources
Type
Jethwa et al. [10]
N
c
=
σ
cm
/
γ
H
≤
2.0
;
σ
cm
=
2
c
p
cos
ϕ
p
/
1
−
sin
ϕ
p
σ
cm
,
γ
,
and
H
—
Semiempirical
Singh et al. [11]
H
≥
350
Q
1
/
3
H
and
Q
Thirty-nine case histories
Empirical
Aydan et al. [12]
α
=
σ
c
/
γ
H
≤
2.0
σ
c
,
γ
,
and
H
Cases from Japan tunnels
Semiempirical
Barla [13]
σ
cm
/
γ
H
≤
1.0
σ
cm
,
γ
,
and
H
—
Semiempirical
Bhasin and Grimstad [14]
σ
θ
/
σ
cm
≥
1.0
with
σ
cm
=
0.7
γ
Q
1
/
3
σ
cm
and
σ
θ
Tunnel case histories
Semiempirical
Hoek [15]
ε
%
=
0.15
1
−
p
i
/
p
0
⋅
σ
cm
/
p
0
−
3
p
i
/
p
0
+
1
/
3.8
p
i
/
p
0
+
0.54
≥
1
%
p
i
,
p
0
,
and
σ
cm
Finite element models
Semiempirical
Jimenez and Recio [6]
H
≥
424.4
Q
0.32
H
and
Q
Sixty-two case histories
Empirical
Dwivedi et al. [16]
ε
=
0.0191
σ
v
Q
−
0.2
/
K
+
1
+
0.0025
≥
1
%
with
σ
v
=
0.027
H
σ
v
,
Q
,
and
K
Sixty-three case histories
Empirical
N
c (or α): competency factor (also called “strength stress ratio (SSR)”), σcm: rock mass uniaxial compressive strength (MPa), γ: rock mass specific weight (MN/m3), H: overburden or depth of tunnel (m), cp: rock mass peak cohesion (MPa), ϕp: rock mass peak friction angle (degree), Q: rock tunneling quality index, σc: uniaxial compressive strength of intact rock (MPa), σθ: tangential stress (MPa), ε: percentage strain (ratio of tunnel closure to tunnel diameter), p0: in situ vertical stress at tunnel depth (MPa), pi: internal support pressure (MPa), σv: vertical in situ stress (MPa), and K: support stiffness (MPa).In addition, numerical simulation has also been used as an important tool in squeezing prediction or tunnel support design, by considering, among others, the three-dimensional (3D) stress conditions and the time-dependent response. Numerical studies and solutions to time-dependent (or creep) deformations (e.g., [7–9]) are not reviewed herein because they are beyond the scope of this study.Recently, soft computational methods, such as artificial neural networks (ANNs) and support vector machines (SVMs), have been proposed to predict tunnel squeezing (or convergence) [1, 17–20] because ANN and SVM do not require prior knowledge of a particular model form and possess a flexible nonlinear modeling capability [21]. For instance, Shafiei et al. [1] proposed an SVM classifier, which yields a higher accuracy than the commonly used empirical method to predict tunnel squeezing based on the Q tunneling index and the buried depth of the tunnel (H). However, the proposed SVM classifier is a binary classifier, which means it can only classify each tunnel case as squeezing or nonsqueezing, but cannot estimate the severity of tunnel squeezing. In addition, the input parameters for the proposed SVM classifier are only Q and H, indicating that the influence of the support systems cannot be properly considered.To overcome these problems, we propose a multiclass SVM classifier to predict the severity of tunnel squeezing based on four parameters, that is, diameter (D), buried depth (H), support stiffness (K), and rock tunneling quality index (Q). The main advantages of the proposed multiclass SVM classifier with respect to previous approaches, such as those listed in Table 1, are that (a) multiclass SVM can carry out a multiclassification prediction (in other words, the severity of potential squeezing problems could be estimated based on the predicted squeezing classes), (b) the influences of support systems can be properly accounted for through the input of support stiffness, and (c) the predicted results are expected to be more accurate. To this end, an extensive database, including 117 case histories from different countries, was compiled to train the multiclass SVM classifier with LibSVM, which is a simple, easy-to-use, fast, and effective software package, for the construction of SVM models, developed by Chang and Lin [22]. Finally, the predictions of the proposed multiclass SVM classifier have been validated using 8-fold cross validation.


## 2. Database Description

We compiled a database based on an extensive literature review, including a total of 117 datasets obtained from different countries, such as India, Nepal, Bhutan, Venezuela, China, Austria, and Greece. All the datasets contained the values of diameter (D), buried depth (H), support stiffness (K), rock tunneling quality index (Q), normalized convergence (%), and squeezing classes (1/2/3). Based on the five categories of squeezing problems in rock tunnels proposed by Hoek and Marinos [3], the squeezing problems are divided into three classes associated with different levels of normalized convergence in this study, that is, nonsqueezing problems (with ε < 1%), minor squeezing problems (with 1% ≤ ε < 2.5%), and severe to extreme squeezing problems (with ε ≥ 2.5%), as shown in Figure 1 (Figure 1 is reproduced from Hoek and Marinos [3], under the Creative Commons Attribution License/Public Domain). The squeezing class labels are defined as 1 = nonsqueezing problems, 2 = minor squeezing problems, and 3 = severe to extreme squeezing problems.Figure 1
Multiclass squeezing problems with different levels of normalized convergence (modified from Hoek and Marinos [3]).Figure2 shows the histograms, cumulative distributions, and additional statistics, including the number of data (N), minimum and maximum values (Min and Max), means (Mean), and standard deviations (Std. Dev.) of D, H, Q, K, and ε. According to Figure 2(f), among the total 117 case histories, 33 cases are nonsqueezing tunnels with ε < 1%, 24 cases are minor squeezing tunnels with 1% ≤ ε < 2.5%, and the remaining 60 cases are severe to extreme squeezing tunnels with ε ≥ 2.5%.Figure 2
Histograms, cumulative distributions, and statistical evaluations of the experimental data.
(a)
(b)
(c)
(d)
(e)
(f)Note that only 56 case histories in our database reported specific values ofK and the remaining provided information allowing us to compute the values of K using the methods described below [20]:(a)
Stiffness of concrete or shotcrete liningsAssuming that a closed ring of concrete or shotcrete is installed in a circular tunnel, its elastic stiffness,Kc, can be expressed as [23](1)Kc=EcR2−R−tc21+vc1−2vcR2+R−tc2,where Ec = elastic modulus of concrete or shotcrete, vc = Poisson’s ratio of concrete or shotcrete, R = radius of tunnel, and tc = thickness of concrete or shotcrete ring.(b)
Stiffness of steel setsThe effective stiffness of a steel set with backfill,Ksb, can be estimated as [16](2)Ksb=pRu,where p = monitored radial support pressure and u = measured radial deformation.(c)
Stiffness of ungrouted rock bolts and cablesThe stiffness of an ungrouted rock bolt or cable,Kb, can be computed as [23]:(3)1Ksb=scslR4lπdbEb+Qld,where sc = circumferential spacing of rock bolts or cables, sl = longitudinal spacing of rock blots or cables, l = free length of rock bolts or cables, db = diameter of rock bolts or cables, Eb = elastic modulus of rock bolts or cables, and Qld = a load-displacement constant (in units of displacement/force).(d)
Stiffness of combined support systemsAssuming that several support systems are installed together at the same time, their combined stiffness can be computed as the summation of their individual support stiffness [23].


## 3. Multiclass Support Vector Machine (SVM) Method

### 3.1. Classic SVM Method

The support vector machine (SVM) is a type of the machine learning method developed based on statistical learning theory (SLT) [24, 25] and is extensively used as one of the most robust binary classifiers [1]. SVMs do not require prior knowledge of a particular model form, possess a flexible nonlinear modeling capability, and have high generalization performance. Therefore, they have become popular in various fields, such as mechanical engineering [26], biomedical engineering [27, 28], information and communication engineering [29], and agriculture [30]. They have also been employed in geotechnical engineering [31–35].In fact, the SVM is a classifier dividing the data into two groups by devising a hyperplane as a decision surface. In other words, the dataset is separated by the “optimal” hyperplane, as illustrated by the linearly separable case of Figure3. Additionally, the reference used herein to “optimal” indicates that the distance between the nearest points to the hyperplane is maximized. As described below, the optimal decision plane could be determined by maximizing the margin of separation between the members of the two classes, that is, maximizing the classification margin between the decision boundary lines H1 and H2, which are parallel to the optimal classification line (or hyperplane).Figure 3
Schematic diagram of optimal hyperplane.Assume that the datasetx1,y1,…,xN,yN,y∈−1,1, can be optimally separated by the hyperplane determined by the weight vector w and the bias b, that is, wTx + b = 0. The problem is equivalent to determining the parameters w and b which minimize the cost function [1]:(4)fw=12wTw,subject to the constraints(5)yiwTx+b≥1fori=1,2,…N.For the maximal margin hyperplane, the solution to the above optimization problem is given by Vapnik [25] as follows:(6)w=∑i=1Nαiyixi,(7)b=−12wTxr+xs,where α represents the Lagrange multipliers and xr and xs are the support vectors satisfying the equations(8)αr,αs>0,yr=−1,ys=1.It is easy to prove that the Lagrange multipliers are positive real numbers that maximize(9)∑i=1Nαi−12∑i=1N∑j=1NαiαjyiyjxiTxj,subject to(10)∑i=1Nαiyi=0,αi>0.For nonlinear separable cases, the kernel function is often used to map the training data into a higher dimensional space where the data can be separated in an easier manner. The solutions for the kernel SVM could be similarly obtained by replacing the termxiTxj in (17) with Kxi,xj. In addition, the corresponding hyperplane could be expressed as(11)∑i=1NαiKxi,xj+b=0.The four basic kernel functions are as follows: (1) linear kernel function:Kxi,xj=xiTxj, (2) nth order polynomial kernel function: Kxi,xj=xiTxj+1n, (3) radial basis function (RBF): Kxi,xj=exp−xi−xj/2σ2, and (4) sigmoid-kernel functions with parameters k and θ: Kxi,xj=tanhkxiTxj+θ. In this study, the most commonly used RBF kernel has been adopted because it has been reported that the RBF kernel could result in higher classification accuracy than the other kernels [22].


### 3.2. Multiclass SVM

As previously discussed, the classical SVM classifiers were originally designed for binary classifications. However, there are more than two classes in some practical classification problems. For instance, one has to divide the potential squeezing effect into several classes according to the magnitude of the normalized convergence so that the severity of the squeezing could be adequately assessed or predicted. This constitutes a typical multiclass classification problem.Two commonly used strategies for constructing multiclass SVM are the “one-against-one” and “one-against-all” approaches. In the “one-against-one” approach, we build one SVM for each pair of classes, which means that if there arek classes, then k(k − 1)/2 binary SVM classifiers are constructed to distinguish the samples of one class from the samples of another class. In the classification, we use a voting strategy, that is, each binary classification is considered to be a voting, whereby votes can be cast for all the samples. In the end, a point is designated to be part of a class with the maximum number of votes. However, in the one-against-all approach, we build as many binary classifiers as there are classes, and each trained classifier is used to separate one class from the rest. To predict a new instance, we choose the classifier with the largest decision function value.In this study, we used the directed acyclic graph SVM (DAG-SVM) approach that combines the SVM and the decision tree. The training process is the same as the “one-against-one” method, which also constructsk(k − 1)/2 binary SVM classifiers. However, the method uses a binary acyclic graph in the process of detection.If a binary decision tree is constructed for thek-class data samples, each leaf node of the tree corresponds to a class, and each nonleaf node corresponds to a sub-SVM classifier. Therefore, the decision tree has k(k − 1)/2 nonleaf nodes (i.e., the number of sub-SVM classifiers is k(k − 1)/2) and k leaf nodes (the number of classes is k). There are different schemes for constructing a strict DAG with k leaf nodes. For instance, the structure of a DAG-SVM for three-class classification problems is shown in Figure 4, where k¯ indicates that x does not belong to class k. Starting at the root node (i.e., node “sub-SVM23”) for an input data sample x, we determine whether the left or right sub-SVM classifier (i.e., the nodes “sub-SVM21” or “sub-SVM13”) would be used depending on the output value. Subsequently, the class of the input data sample would be finally determined based on the output value of node “sub-SVM21” or “sub-SVM13”.Figure 4
The structure of DAG-SVM used for three-class classification problems.


## 3.1. Classic SVM Method

The support vector machine (SVM) is a type of the machine learning method developed based on statistical learning theory (SLT) [24, 25] and is extensively used as one of the most robust binary classifiers [1]. SVMs do not require prior knowledge of a particular model form, possess a flexible nonlinear modeling capability, and have high generalization performance. Therefore, they have become popular in various fields, such as mechanical engineering [26], biomedical engineering [27, 28], information and communication engineering [29], and agriculture [30]. They have also been employed in geotechnical engineering [31–35].In fact, the SVM is a classifier dividing the data into two groups by devising a hyperplane as a decision surface. In other words, the dataset is separated by the “optimal” hyperplane, as illustrated by the linearly separable case of Figure3. Additionally, the reference used herein to “optimal” indicates that the distance between the nearest points to the hyperplane is maximized. As described below, the optimal decision plane could be determined by maximizing the margin of separation between the members of the two classes, that is, maximizing the classification margin between the decision boundary lines H1 and H2, which are parallel to the optimal classification line (or hyperplane).Figure 3
Schematic diagram of optimal hyperplane.Assume that the datasetx1,y1,…,xN,yN,y∈−1,1, can be optimally separated by the hyperplane determined by the weight vector w and the bias b, that is, wTx + b = 0. The problem is equivalent to determining the parameters w and b which minimize the cost function [1]:(4)fw=12wTw,subject to the constraints(5)yiwTx+b≥1fori=1,2,…N.For the maximal margin hyperplane, the solution to the above optimization problem is given by Vapnik [25] as follows:(6)w=∑i=1Nαiyixi,(7)b=−12wTxr+xs,where α represents the Lagrange multipliers and xr and xs are the support vectors satisfying the equations(8)αr,αs>0,yr=−1,ys=1.It is easy to prove that the Lagrange multipliers are positive real numbers that maximize(9)∑i=1Nαi−12∑i=1N∑j=1NαiαjyiyjxiTxj,subject to(10)∑i=1Nαiyi=0,αi>0.For nonlinear separable cases, the kernel function is often used to map the training data into a higher dimensional space where the data can be separated in an easier manner. The solutions for the kernel SVM could be similarly obtained by replacing the termxiTxj in (17) with Kxi,xj. In addition, the corresponding hyperplane could be expressed as(11)∑i=1NαiKxi,xj+b=0.The four basic kernel functions are as follows: (1) linear kernel function:Kxi,xj=xiTxj, (2) nth order polynomial kernel function: Kxi,xj=xiTxj+1n, (3) radial basis function (RBF): Kxi,xj=exp−xi−xj/2σ2, and (4) sigmoid-kernel functions with parameters k and θ: Kxi,xj=tanhkxiTxj+θ. In this study, the most commonly used RBF kernel has been adopted because it has been reported that the RBF kernel could result in higher classification accuracy than the other kernels [22].


## 3.2. Multiclass SVM

As previously discussed, the classical SVM classifiers were originally designed for binary classifications. However, there are more than two classes in some practical classification problems. For instance, one has to divide the potential squeezing effect into several classes according to the magnitude of the normalized convergence so that the severity of the squeezing could be adequately assessed or predicted. This constitutes a typical multiclass classification problem.Two commonly used strategies for constructing multiclass SVM are the “one-against-one” and “one-against-all” approaches. In the “one-against-one” approach, we build one SVM for each pair of classes, which means that if there arek classes, then k(k − 1)/2 binary SVM classifiers are constructed to distinguish the samples of one class from the samples of another class. In the classification, we use a voting strategy, that is, each binary classification is considered to be a voting, whereby votes can be cast for all the samples. In the end, a point is designated to be part of a class with the maximum number of votes. However, in the one-against-all approach, we build as many binary classifiers as there are classes, and each trained classifier is used to separate one class from the rest. To predict a new instance, we choose the classifier with the largest decision function value.In this study, we used the directed acyclic graph SVM (DAG-SVM) approach that combines the SVM and the decision tree. The training process is the same as the “one-against-one” method, which also constructsk(k − 1)/2 binary SVM classifiers. However, the method uses a binary acyclic graph in the process of detection.If a binary decision tree is constructed for thek-class data samples, each leaf node of the tree corresponds to a class, and each nonleaf node corresponds to a sub-SVM classifier. Therefore, the decision tree has k(k − 1)/2 nonleaf nodes (i.e., the number of sub-SVM classifiers is k(k − 1)/2) and k leaf nodes (the number of classes is k). There are different schemes for constructing a strict DAG with k leaf nodes. For instance, the structure of a DAG-SVM for three-class classification problems is shown in Figure 4, where k¯ indicates that x does not belong to class k. Starting at the root node (i.e., node “sub-SVM23”) for an input data sample x, we determine whether the left or right sub-SVM classifier (i.e., the nodes “sub-SVM21” or “sub-SVM13”) would be used depending on the output value. Subsequently, the class of the input data sample would be finally determined based on the output value of node “sub-SVM21” or “sub-SVM13”.Figure 4
The structure of DAG-SVM used for three-class classification problems.


## 4. Results and Discussion

### 4.1.K-Fold Cross Validation

The aim of our proposed multiclass SVM classifier is to predict the severity of tunnel squeezing, and 8-fold cross validation is performed to estimate its validity in practice. Firstly, the original 117 datasets are equally divided into eight groups. Secondly, seven out of eight groups are used to train the multiclass SVM classifier with LibSVM [22], and the remaining group is left for validation purposes. Finally, the above process will be repeated eight times so that each case is predicted once in the entire database, and the cross validation accuracy is the percentage of data which are correctly classified. The corresponding classification accuracy and confusion matrices are listed in Table 2, and the average classification accuracy is approximately 88.1%. The confusion matrix could clearly show whether the class is misclassified (i.e., if a class is classified erroneously as another class) and describe the difference between the predicted and the actual classes. Furthermore, the sum of the elements on the principal diagonal represents the number of cases which are correctly classified. In addition, the sum of the elements off the principal diagonal represents the number of cases that are misclassified.Table 2
Resultant accuracy and confusion matrices of 8-fold CV.
Validation groups
Accuracy (%)
Error rates (%)
Confusion matrices
No. 1
93.33
6.67
Actual
1
2
3
Predicted
8
0
0
1
0
1
0
2
0
1
5
3
No. 2
86.67
13.33
Actual
1
2
3
Predicted
12
0
0
1
0
0
0
2
1
1
1
3
No. 3
80.00
20.00
Actual
1
2
3
Predicted
8
1
0
1
0
0
2
2
0
0
4
3
No. 4
93.33
6.67
Actual
1
2
3
Predicted
0
0
0
1
0
3
0
2
1
0
11
3
No. 5
80.00
20.00
Actual
1
2
3
Predicted
0
0
0
1
0
4
2
2
0
1
8
3
No. 6
100.00
0.00
Actual
1
2
3
Predicted
0
0
0
1
0
2
0
2
0
0
13
3
No. 7
80.00
20.00
Actual
1
2
3
Predicted
0
0
0
1
0
9
3
2
0
0
3
3
No. 8
91.67
8.33
Actual
1
2
3
Predicted
3
0
0
1
0
0
0
2
0
1
8
3
Average
88.13
11.87When group No. 1 is used for model validation, the resultant classification results are shown in Figure5. The horizontal axis represents the cases of the validation dataset (group No. 1). There are fifteen cases in total. The vertical axis represents the class of the cases. Only case No. 14 was misclassified as class 3 (i.e., ε > 2.5% with severe to extreme squeezing problems) since the actual class of case No. 14 is class 2 (i.e., 1% ≤ ε < 2.5% with minor squeezing problems), thereby indicating that the predicted result is conservative and safe. The classification accuracy is approximately 93.3%.Figure 5
Actual and predicted classification results of group No. 1.


### 4.2. Comparison with Traditional Methods

In order to compare the performance of the proposed multiclass SVM classifier with that of the traditional methods, we have employed both the proposed multiclass SVM classifier and the empirical formula proposed by Singh [11] (i.e., H > 350Q1/3) to predict the squeezing class using all 117 datasets, and the results are listed in Table 3. Note that the accuracy for squeezing ground can be computed as the number of squeezing cases correctly classified divided by the total number of squeezing tunnels tested, the accuracy for nonsqueezing ground can be computed as the number of nonsqueezing cases correctly classified divided by the total number of nonsqueezing tunnels tested, and the overall accuracy can be computed as the number of tunnels correctly classified divided by total number of tunnels tested.Table 3
Performance of the proposed approach, the empirical formula, and the two-class SVMs used to determine the squeezing.
Method
Number of classes
Accuracy for squeezing ground (%)
Accuracy for nonsqueezing ground (%)
Overall accuracy (%)
Empirical formula
2
82.1
78.8
80.3
Binary SVM
2
79.4
88.1
84.1
Multiclass SVM
3
86.9
93.9
88.1From the total number of datasets, 94 cases were correctly classified using the empirical approach, and the predicted accuracy was approximately 80.3% (i.e., 94/117). One probable reason for this relatively worse performance of the empirical formula proposed by Singh et al. [11] is that we have extended the original database employed in their work and constructed the multiclass SVM model based on the extended database.In addition, Shafiei et al. [1] used a more comprehensive database, including 198 tunnel cases, to construct their binary SVM classifier to predict the tunnel squeezing. Unfortunately, this comprehensive database cannot be directly used because their database contains only two input parameters, that is, H and Q, and does not provide any information about the other two parameters (i.e., K and D) considered in this study. The overall accuracy was reported to be equal to 84.1%, and the accuracy for squeezing ground was reported to be 79.4%. For multiclass SVM model, the overall accuracy and the accuracy for squeezing ground are 88.1% and 86.9% (Table 3), respectively, showing that the multiclass SVM model performs slightly better than the binary SVM classifier. As shown in Table 3, for the multiclass SVM model, the accuracy for nonsqueezing ground is higher than that for the squeezing ground, indicating a relatively “conservative” (and safe) model.Instead of predicting the class, many applications require posterior class probability which can be approximated by a sigmoid function (see Platt [36] for detailed descriptions) and such posterior probabilities can be used to assess the acceptability of the prediction [1]. For instance, let us imagine a new tunnel whose design is considered with K = 20 MPa, H = 200 m, Q = 0.4, and D = 6.0 m. The posterior probability P (y = 1|x) can be estimated as 78.3%, indicating that there is probably nonsqueezing problems for this tunnel, and this prediction is accepted with high confidence. And the posterior probability could be useful in tunnel risk analyses.In general, our approach performs slightly better than the empirical approach and the classical binary SVM in terms of the classification accuracy. Additionally, the empirical approach and the binary SVM classifier can only make a binary classification; that is, it can only predict whether squeezing occurs but cannot predict the severity of squeezing. Finally, it is important to mention that, as discussed by Jimenez and Recio [6, 37], the proposed multiclass SVM model should not be considered as a “final solution” and it should be expected to be further updated and improved as more tunnel squeezing cases are included in the training database.


### 4.3. Influence of Support Stiffness and Tunnel Diameter

Tunnel deformation may be effectively controlled by installing appropriate support systems at a proper time. In other words, the squeezing condition could be influenced by the support stiffness applied to the tunnel. However, few studies have employed support stiffness as one of the input parameters to predict tunnel squeezing [16]. In order to assess the influence of support stiffness on tunnel squeezing, the support stiffness (K) is removed from the four input parameters (i.e., diameter (D), depth (H), support stiffness (K), and rock tunneling quality index (Q)); that is, the tunnel squeezing is predicted based on the remaining three parameters, that is, Q, H, and D. The 8-fold CV method is used again to validate the trained multiclass SVM using only three input parameters. The results are listed in Table 4. If the support stiffness is removed, the average accuracy obtained is reduced from 88.1% to 74.0%, showing that support stiffness has a significant influence on the classification accuracy of tunnel squeezing.Table 4
Accuracy elicited using 8-fold CV with all parameters, without parameterK, and without parameter D.
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
Average
Accuracy with all four parameters (%)
93.33
86.67
80.00
93.33
80.00
100.00
80.00
91.67
88.13
Accuracy withoutK (%)
80.00
60.00
60.00
80.00
73.33
73.33
73.33
91.67
73.96
Accuracy withoutD (%)
93.33
86.67
86.67
73.33
86.67
86.67
66.67
91.67
83.96Similarly, the influence of tunnel diameter can be assessed, and the results are also listed in Table4. The resultant average accuracy is slightly reduced from 88.1% to 84.0%, indicating that tunnel diameter does not seem to have a significant influence on the predictive capabilities of the proposed model. This observation is coincident with the study by Jimenez and Recio [37].In addition, we performed analysis of variance (ANOVA) to demonstrate the significance of these two parameters, namely,K and D, and the significance values for K and D are 0.046 and 0.004, respectively, indicating that the influence of K and D on tunnel squeezing is significant.


## 4.1.K-Fold Cross Validation

The aim of our proposed multiclass SVM classifier is to predict the severity of tunnel squeezing, and 8-fold cross validation is performed to estimate its validity in practice. Firstly, the original 117 datasets are equally divided into eight groups. Secondly, seven out of eight groups are used to train the multiclass SVM classifier with LibSVM [22], and the remaining group is left for validation purposes. Finally, the above process will be repeated eight times so that each case is predicted once in the entire database, and the cross validation accuracy is the percentage of data which are correctly classified. The corresponding classification accuracy and confusion matrices are listed in Table 2, and the average classification accuracy is approximately 88.1%. The confusion matrix could clearly show whether the class is misclassified (i.e., if a class is classified erroneously as another class) and describe the difference between the predicted and the actual classes. Furthermore, the sum of the elements on the principal diagonal represents the number of cases which are correctly classified. In addition, the sum of the elements off the principal diagonal represents the number of cases that are misclassified.Table 2
Resultant accuracy and confusion matrices of 8-fold CV.
Validation groups
Accuracy (%)
Error rates (%)
Confusion matrices
No. 1
93.33
6.67
Actual
1
2
3
Predicted
8
0
0
1
0
1
0
2
0
1
5
3
No. 2
86.67
13.33
Actual
1
2
3
Predicted
12
0
0
1
0
0
0
2
1
1
1
3
No. 3
80.00
20.00
Actual
1
2
3
Predicted
8
1
0
1
0
0
2
2
0
0
4
3
No. 4
93.33
6.67
Actual
1
2
3
Predicted
0
0
0
1
0
3
0
2
1
0
11
3
No. 5
80.00
20.00
Actual
1
2
3
Predicted
0
0
0
1
0
4
2
2
0
1
8
3
No. 6
100.00
0.00
Actual
1
2
3
Predicted
0
0
0
1
0
2
0
2
0
0
13
3
No. 7
80.00
20.00
Actual
1
2
3
Predicted
0
0
0
1
0
9
3
2
0
0
3
3
No. 8
91.67
8.33
Actual
1
2
3
Predicted
3
0
0
1
0
0
0
2
0
1
8
3
Average
88.13
11.87When group No. 1 is used for model validation, the resultant classification results are shown in Figure5. The horizontal axis represents the cases of the validation dataset (group No. 1). There are fifteen cases in total. The vertical axis represents the class of the cases. Only case No. 14 was misclassified as class 3 (i.e., ε > 2.5% with severe to extreme squeezing problems) since the actual class of case No. 14 is class 2 (i.e., 1% ≤ ε < 2.5% with minor squeezing problems), thereby indicating that the predicted result is conservative and safe. The classification accuracy is approximately 93.3%.Figure 5
Actual and predicted classification results of group No. 1.


## 4.2. Comparison with Traditional Methods

In order to compare the performance of the proposed multiclass SVM classifier with that of the traditional methods, we have employed both the proposed multiclass SVM classifier and the empirical formula proposed by Singh [11] (i.e., H > 350Q1/3) to predict the squeezing class using all 117 datasets, and the results are listed in Table 3. Note that the accuracy for squeezing ground can be computed as the number of squeezing cases correctly classified divided by the total number of squeezing tunnels tested, the accuracy for nonsqueezing ground can be computed as the number of nonsqueezing cases correctly classified divided by the total number of nonsqueezing tunnels tested, and the overall accuracy can be computed as the number of tunnels correctly classified divided by total number of tunnels tested.Table 3
Performance of the proposed approach, the empirical formula, and the two-class SVMs used to determine the squeezing.
Method
Number of classes
Accuracy for squeezing ground (%)
Accuracy for nonsqueezing ground (%)
Overall accuracy (%)
Empirical formula
2
82.1
78.8
80.3
Binary SVM
2
79.4
88.1
84.1
Multiclass SVM
3
86.9
93.9
88.1From the total number of datasets, 94 cases were correctly classified using the empirical approach, and the predicted accuracy was approximately 80.3% (i.e., 94/117). One probable reason for this relatively worse performance of the empirical formula proposed by Singh et al. [11] is that we have extended the original database employed in their work and constructed the multiclass SVM model based on the extended database.In addition, Shafiei et al. [1] used a more comprehensive database, including 198 tunnel cases, to construct their binary SVM classifier to predict the tunnel squeezing. Unfortunately, this comprehensive database cannot be directly used because their database contains only two input parameters, that is, H and Q, and does not provide any information about the other two parameters (i.e., K and D) considered in this study. The overall accuracy was reported to be equal to 84.1%, and the accuracy for squeezing ground was reported to be 79.4%. For multiclass SVM model, the overall accuracy and the accuracy for squeezing ground are 88.1% and 86.9% (Table 3), respectively, showing that the multiclass SVM model performs slightly better than the binary SVM classifier. As shown in Table 3, for the multiclass SVM model, the accuracy for nonsqueezing ground is higher than that for the squeezing ground, indicating a relatively “conservative” (and safe) model.Instead of predicting the class, many applications require posterior class probability which can be approximated by a sigmoid function (see Platt [36] for detailed descriptions) and such posterior probabilities can be used to assess the acceptability of the prediction [1]. For instance, let us imagine a new tunnel whose design is considered with K = 20 MPa, H = 200 m, Q = 0.4, and D = 6.0 m. The posterior probability P (y = 1|x) can be estimated as 78.3%, indicating that there is probably nonsqueezing problems for this tunnel, and this prediction is accepted with high confidence. And the posterior probability could be useful in tunnel risk analyses.In general, our approach performs slightly better than the empirical approach and the classical binary SVM in terms of the classification accuracy. Additionally, the empirical approach and the binary SVM classifier can only make a binary classification; that is, it can only predict whether squeezing occurs but cannot predict the severity of squeezing. Finally, it is important to mention that, as discussed by Jimenez and Recio [6, 37], the proposed multiclass SVM model should not be considered as a “final solution” and it should be expected to be further updated and improved as more tunnel squeezing cases are included in the training database.


## 4.3. Influence of Support Stiffness and Tunnel Diameter

Tunnel deformation may be effectively controlled by installing appropriate support systems at a proper time. In other words, the squeezing condition could be influenced by the support stiffness applied to the tunnel. However, few studies have employed support stiffness as one of the input parameters to predict tunnel squeezing [16]. In order to assess the influence of support stiffness on tunnel squeezing, the support stiffness (K) is removed from the four input parameters (i.e., diameter (D), depth (H), support stiffness (K), and rock tunneling quality index (Q)); that is, the tunnel squeezing is predicted based on the remaining three parameters, that is, Q, H, and D. The 8-fold CV method is used again to validate the trained multiclass SVM using only three input parameters. The results are listed in Table 4. If the support stiffness is removed, the average accuracy obtained is reduced from 88.1% to 74.0%, showing that support stiffness has a significant influence on the classification accuracy of tunnel squeezing.Table 4
Accuracy elicited using 8-fold CV with all parameters, without parameterK, and without parameter D.
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
Average
Accuracy with all four parameters (%)
93.33
86.67
80.00
93.33
80.00
100.00
80.00
91.67
88.13
Accuracy withoutK (%)
80.00
60.00
60.00
80.00
73.33
73.33
73.33
91.67
73.96
Accuracy withoutD (%)
93.33
86.67
86.67
73.33
86.67
86.67
66.67
91.67
83.96Similarly, the influence of tunnel diameter can be assessed, and the results are also listed in Table4. The resultant average accuracy is slightly reduced from 88.1% to 84.0%, indicating that tunnel diameter does not seem to have a significant influence on the predictive capabilities of the proposed model. This observation is coincident with the study by Jimenez and Recio [37].In addition, we performed analysis of variance (ANOVA) to demonstrate the significance of these two parameters, namely,K and D, and the significance values for K and D are 0.046 and 0.004, respectively, indicating that the influence of K and D on tunnel squeezing is significant.


## 5. Conclusions

A multiclass SVM classifier was developed to predict the tunnel squeezing based on four input parameters: diameter (D), depth (H), support stiffness (K), and rock tunneling quality index (Q). An “one-against-one” approach was employed to train the classifier from 117 available training datasets obtained from previous studies (Table 5). The 8-fold cross validation method was used to validate the constructed multiclass SVM classifier, and the results showed that the average error percentage was approximately 11.87%, which is considered acceptable for practical engineering applications. The proposed multiclass SVM classifier elicited some improvements compared to the traditional empirical formula proposed by Singh et al. [11] and the binary SVM classifier proposed by Shafiei [1], as it yielded higher accuracy and allowed the prediction of the squeezing severity. The proposed multiclass SVM classifier can be used for the preliminary classification of tunnel squeezing. However, it is not a substitute for more sophisticated methods, such as numerical simulation, wherein many other factors can be considered, such as the time effect of rock masses. The proposed approach can be further updated and improved as additional tunnel squeezing cases become available for training.Table 5
No.
D (m)
H (m)
Q
K (MPa)
ε (%)
Class
Tunnel
Location
Rock type
Reference
1
6.0
150.0
0.400
26.19
0.42
1
Khara hydroproject
India
Clay conglomerate
[38, 39]
2
6.0
200.0
0.400
20.00
0.75
1
Khara hydroproject
India
Clay conglomerate
[38, 39]
3
5.8
350.0
0.500
2.53
7.90
3
Maneri stage I
India
—
[38]
4
4.8
225.0
3.600
1000.00
0.06
1
Maneri-Bhali hydroproject
India
Fractured quartzite
[39, 40]
5
4.8
340.0
1.800
500.00
0.40
1
Maneri-Uttarkashi power
India
Sheared metabasics
[40]
6
4.8
550.0
5.100
1600.00
0.05
1
Maneri-Uttarkashi power
India
Foliated metabasics
[40]
7
12.0
220.0
0.800
32.89
0.38
1
Tehri dam project
India
Argillaceous phyllite
[38, 39]
8
13.0
52.0
15.000
16.67
0.18
1
Upper Krishna project
India
Banded schists
[38, 39]
9
3.0
280.0
0.050
9.80
2.80
3
Chibro-Khodri tunnel
India
Crushed red shales
[15, 38]
10
3.0
280.0
0.022
5.96
4.50
3
Chibro-Khodri tunnel
India
Soft and plastic black clays
[38]
11
9.0
680.0
0.050
9.90
6.00
3
Chibro-Khodri tunnel
India
Seamy crushed red
[38]
12
9.0
280.0
0.022
48.56
2.00
2
Chibro-Khodri tunnel
India
Soft and plastic black clays
[38]
13
4.2
100.0
0.005
88.96
2.62
3
Khimti 1 hydroproject A1 ch515
Nepal
Sheared schists
[41]
14
4.0
112.0
0.006
71.28
1.19
2
Khimti 1 hydroproject A4 ch1013
Nepal
Sericite schists
[41]
15
4.3
111.0
0.008
1936.00
0.75
1
Khimti 1 hydroproject A1 ch580
Nepal
Sheared schists
[41]
16
4.0
112.0
0.008
936.00
0.20
1
Khimti 1 hydroproject A4 ch974
Nepal
Gneiss
[41]
17
4.0
112.0
0.008
651.00
0.10
1
Khimti 1 hydroproject A4 ch1045
Nepal
Clay-filled sheared gneiss
[41]
18
4.0
140.0
0.009
430.00
0.80
1
Khimti 1 hydroproject A3 ch220
Nepal
Schists
[41]
19
4.2
100.0
0.010
31.72
3.81
3
Khimti 1 hydroproject A1 ch500
Nepal
Sheared schists
[41]
20
4.0
138.0
0.013
1934.00
0.19
1
Khimti 1 hydroproject A2 ch601
Nepal
Sericite schists
[41]
21
4.4
212.0
0.040
5324.00
0.02
1
Khimti 1 hydroproject A2 ch1283
Nepal
Gneiss and sericite schists
[41]
22
5.0
300.0
0.050
1430.00
0.18
1
Khimti 1 hydroproject A3 ch345
Nepal
Gneiss and sericite schists
[41]
23
4.0
112.0
0.060
458.00
0.30
1
Khimti 1 hydroproject A1 ch665
Nepal
Gneiss and schists
[41]
24
4.0
95.0
0.065
933.00
0.29
1
Khimti 1 hydroproject A2 ch1730
Nepal
Gneiss
[41]
25
4.0
218.0
0.070
739.00
0.14
1
Khimti 1 hydroproject A4 ch550
Nepal
Chlorite sericite gneiss
[41]
26
4.0
98.0
0.080
933.00
0.77
1
Khimti 1 hydroproject A1 ch475
Nepal
Gneiss and sericite schists
[41]
27
5.0
284.0
0.090
68.55
1.24
2
Khimti 1 hydroproject A3 ch235
Nepal
Gneiss
[41]
28
5.0
300.0
0.090
664.29
0.28
1
Khimti 1 hydroproject A3 ch340
Nepal
Gneiss and sericite schists
[41]
29
4.0
261.0
0.095
931.00
0.15
1
Khimti 1 hydroproject A2 ch1357
Nepal
Banded gneiss and chlorite schists
[41]
30
4.0
198.0
0.140
934.00
0.29
1
Khimti 1 hydroproject A2 ch895
Nepal
Gneiss and chlorite schists
[41]
31
4.0
225.0
0.140
1430.00
0.24
1
Khimti 1 hydroproject A4 ch503
Nepal
Gneiss and sericite schists
[41]
32
5.0
130.0
0.200
936.00
0.34
1
Khimti 1 hydroproject A3 ch15
Nepal
Gneiss and schists
[41]
33
4.1
158.0
0.230
650.00
0.32
1
Khimti 1 hydroproject A3 ch59
Nepal
Gneiss and schists
[41]
34
5.0
276.0
0.250
940.00
0.77
1
Khimti 1 hydroproject A3 ch200
Nepal
Gneiss and schists
[41]
35
5.0
276.0
0.280
652.00
0.56
1
Khimti 1 hydroproject A3 ch210
Nepal
Gneiss and schists
[41]
36
4.0
126.0
0.300
461.00
0.03
1
Khimti 1 hydroproject A2 ch441
Nepal
Gneiss
[41]
37
4.0
114.0
0.470
648.00
0.03
1
Khimti 1 hydroproject A4 ch852
Nepal
Banded gneiss
[41]
38
4.0
114.0
0.600
556.00
0.24
1
Khimti 1 hydroproject A4 ch876
Nepal
Banded gneiss
[41]
39
4.6
300.0
0.023
7.71
7.00
3
Loktak hydro
India
—
[38]
40
4.8
350.0
0.500
25.32
7.90
3
Maneri-Bhali stage I
India
Fractured quartzite
[15, 40]
41
4.8
800.0
2.500
48.99
8.90
3
Maneri-Uttarkashi power
India
Laminated metabasics
[15, 40]
42
7.0
285.0
0.100
9.79
2.87
3
Maneri stage II tunnel
India
Sheared metabasics
[42, 43]
43
7.0
410.0
0.300
9.79
2.80
3
Maneri stage II tunnel
India
Sheared metabasics
[42, 43]
44
7.0
415.0
0.880
9.79
2.19
2
Maneri stage II tunnel
India
Metavolcanic
[42, 43]
45
2.5
480.0
0.800
9.84
2.88
3
Maneri stage II tunnel
India
Metavolcanic
[42, 43]
46
7.0
500.0
1.000
9.79
2.64
3
Maneri stage II tunnel
India
Metavolcanic
[42, 43]
47
2.5
510.0
0.880
9.84
2.42
2
Maneri stage II tunnel
India
Metavolcanic
[42, 43]
48
4.6
240.0
0.120
3.97
4.50
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
49
4.6
440.0
0.050
3.97
10.04
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
50
4.6
450.0
0.060
3.97
10.30
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
51
4.6
400.0
0.030
3.98
10.43
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
52
4.6
400.0
0.050
3.98
7.61
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
53
4.6
200.0
0.020
2.98
6.20
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
54
4.6
325.0
0.030
2.98
8.75
3
Giri-Bata tunnel
India
Crushed phyllites
[42–44]
55
4.6
400.0
0.512
2.98
0.67
1
Giri-Bata tunnel
India
Crushed slates
[42–44]
56
5.8
700.0
0.300
9.81
4.83
3
Maneri stage I tunnel
India
Sheared metabasics
[42, 45]
57
5.8
550.0
1.700
9.81
2.66
3
Maneri stage I tunnel
India
Siliceous phyllites
[42, 45]
58
5.8
635.0
4.000
9.81
2.33
2
Maneri stage I tunnel
India
Foliated metabasics
[42, 45]
59
5.8
650.0
4.120
9.81
2.07
2
Maneri stage I tunnel
India
Siliceous phyllites
[42, 45]
60
5.8
450.0
0.310
5.10
4.83
3
Maneri stage I tunnel
India
Sheared metabasics
[42, 45]
61
5.8
750.0
0.500
8.10
4.14
3
Maneri stage I tunnel
India
Crushed quartzite
[42, 45]
62
7.0
450.0
0.590
9.67
3.00
3
Noonidih colliery
India
Weak coal
[45]
63
6.8
337.0
0.007
44.76
2.10
2
Tala hydro-HRT, tala HRT, Bhutan
Bhutan
AGO (adverse geological occurrences): completely sheared, highly weathered biotite schist associated with banded gneiss, amphibolites, and quartzites in thin bands
[46]
64
6.8
337.0
0.011
16.05
3.80
3
Tala HRT, Bhutan
Bhutan
[46]
65
6.8
337.0
0.006
22.58
3.10
3
Tala HRT, Bhutan
Bhutan
[46]
66
6.8
337.0
0.006
36.36
2.20
2
Tala HRT, Bhutan
Bhutan
[46]
67
6.8
337.0
0.080
14.09
2.20
2
Tala HRT, Bhutan
Bhutan
[46]
68
8.7
550.0
0.029
39.13
2.30
2
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
69
8.7
600.0
0.023
90.71
1.40
2
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
70
8.7
600.0
0.030
34.48
2.90
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
71
8.7
600.0
0.018
26.20
3.90
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
72
8.7
600.0
0.023
28.48
3.20
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
73
8.7
620.0
0.020
26.20
4.90
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
74
8.7
620.0
0.008
14.67
8.50
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
75
8.7
620.0
0.009
14.67
7.70
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
76
8.7
620.0
0.009
14.67
8.20
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
77
8.7
620.0
0.016
26.20
4.40
3
Kaligandaki “A” HRT
Nepal
Siliceous phyllites
[47, 48]
78
8.7
620.0
0.020
26.10
4.10
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
79
8.7
620.0
0.025
50.80
2.50
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
80
8.7
580.0
0.023
26.20
3.70
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
81
8.7
580.0
0.025
74.66
1.70
2
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
82
8.7
550.0
0.025
39.87
2.40
2
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
83
8.7
575.0
0.007
21.17
6.00
3
Kaligandaki “A” HRT
Nepal
Graphitic phyllite
[47, 48]
84
11.0
700.0
0.417
7.43
3.50
3
Nathpa Jhakri-HRT
India
Quartz mica schist, schistose quartzites, and amphibolites
[49]
85
11.0
700.0
0.333
9.14
3.50
3
Nathpa Jhakri-HRT
India
[49]
86
11.0
750.0
0.333
9.14
3.50
3
Nathpa Jhakri-HRT
India
[49]
87
11.0
600.0
0.250
9.14
3.50
3
Nathpa Jhakri-HRT
India
[49]
88
11.0
850.0
0.056
20.40
5.00
3
Nathpa Jhakri-HRT
India
[49]
89
11.0
600.0
0.033
33.33
3.00
3
Nathpa Jhakri-HRT
India
[49]
90
11.0
300.0
0.001
16.50
6.00
3
Nathpa Jhakri-HRT
India
[49]
91
11.0
400.0
0.003
17.00
6.00
3
Nathpa Jhakri-HRT
India
[49]
92
11.0
800.0
0.194
17.14
3.50
3
Nathpa Jhakri-HRT
India
[49]
93
6.5
300.0
0.033
10.00
3.00
3
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
94
6.5
312.0
0.094
34.67
1.50
2
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
95
6.5
280.0
0.083
29.33
1.50
2
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
96
6.5
270.0
0.125
15.91
2.20
2
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
97
6.5
285.0
0.063
12.80
2.50
3
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
98
6.5
280.0
0.031
11.54
2.60
3
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
99
6.5
280.0
0.042
12.50
2.40
2
Udhampur rail tunnel (T1)
India
Claystone, silty claystone
[49]
100
6.0
727.0
2.287
5.88
1.70
2
Chenani–Nashri escape tunnel
India
Siltstone, silty claystone
[49]
101
6.0
736.0
2.426
7.69
1.30
2
Chenani–Nashri escape tunnel
India
Siltstone, silty claystone
[49]
102
6.0
733.0
2.903
6.25
1.60
2
Chenani–Nashri escape tunnel
India
Siltstone, silty claystone
[49]
103
6.0
690.0
1.650
9.38
1.60
2
Chenani–Nashri escape tunnel
India
Siltstone, silty claystone
[49]
104
13.0
577.0
1.517
11.11
1.80
2
Chenani–Nashri escape tunnel
India
Siltstone
[49]
105
5.4
199.7
0.020
1217.16
4.58
3
Chameliya hydroelectric project headrace tunnel 3 + 172
Nepal
Dolomite
[50]
106
5.4
217.5
0.013
1217.16
25.54
3
Chameliya hydroelectric project headrace tunnel 3 + 190
Nepal
Dolomite
[50]
107
5.4
252.2
0.010
1523.07
12.50
3
Chameliya hydroelectric project headrace tunnel 3 + 296
Nepal
Brownish
[50]
108
5.4
246.3
0.010
1523.07
3.80
3
Chameliya hydroelectric project headrace tunnel 3 + 314
Nepal
Foliated phyllite
[50]
109
5.4
283.9
0.008
1645.38
36.73
3
Chameliya hydroelectric project headrace tunnel 3 + 404
Nepal
Talcose phyllite
[50]
110
5.4
284.5
0.008
1828.98
30.19
3
Chameliya hydroelectric project headrace tunnel 3 + 420
Nepal
Talcose phyllite
[50]
111
5.4
210.8
0.010
1575.72
18.30
3
Chameliya hydroelectric project headrace tunnel 3 + 681
Nepal
Talcose phyllite
[50]
112
5.4
237.7
0.010
1575.72
10.96
3
Chameliya hydroelectric project headrace tunnel 3 + 733
Nepal
Talcose phyllite
[50]
113
5.4
230.0
0.015
1217.16
9.80
3
Chameliya hydroelectric project headrace tunnel 3 + 764
Nepal
Foliated phyllite
[50]
114
5.4
222.6
0.015
1217.16
1.20
2
Chameliya hydroelectric project headrace tunnel 3 + 795
Nepal
Foliated phyllite
[50]
115
5.4
80.0
93.500
0.00
0.00
1
Austria (Oetscher unit)
Austria
—
[51]
116
5.4
190.0
7.450
0.00
0.00
1
Austria (Oetscher unit)
Austria
—
[51]
117
5.4
130.0
1.530
0.00
0.00
1
Austria (Oetscher unit)
Austria
—
[51]



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*Source: 4543984-2018-05-16.xml*