EvaluationoftheTotalQualityofTunnelContourUsing ...rock mass Blasting stone per round Detonator consumption First-line rate 0.6 0.8 1.0 1.2 1.4 Evaluation indicator 0 2 4 6 Indicator

Research ArticleEvaluation of the Total Quality of Tunnel Contour UsingProjection Pursuit Dynamic Cluster Method

Baoping Zou 123 ZhipengXu 4 JianxiuWang 2 ZhanyouLuo 1 and LishengHu 5

1School of Civil Engineering and Architecture Zhejiang University of Science and Technology Hangzhou 310023 China2Department of Geotechnical Engineering Tongji University Shanghai 200092 China3State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyBeijing 100083 China4College of Water Resource and Hydropower Sichuan University Chengdu 610065 China5China Railway No 2 Engineering Group Co Ltd Chengdu 610031 China

Correspondence should be addressed to Zhipeng Xu zpxu2018126com

Received 10 November 2020 Revised 20 February 2021 Accepted 1 March 2021 Published 11 March 2021

Academic Editor Mingfeng Lei

Copyright copy 2021 Baoping Zou et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Full understanding of the total quality of tunnel contour after smooth blasting is quite a valuable task for accurately assessing thecost and construction ratee traditional evaluation of tunnel contour quality which is always based on a single index such as theoverunderbreakmight not be rational enough because the contour quality at specific positions cannot completely stand for that ofthe total contour Unreasonable evaluation of contour quality might cause construction delay or overbudget as well as safety- andstability-related issues or even catastrophic accidents under some specific conditions In this case evaluating the total quality oftunnel contour considering all influential factors is of significance to smooth tunnelling e aim of this paper is to develop amultiple indices systemwhich can represent the total quality of the contour from different aspects and then the projection pursuitdynamic cluster (PPDC) method is utilized to quantitatively evaluate the total quality of tunnel contour e multiple indices arescreened using the principal component analysis (PCA) and gray correlation analysis (GCA) e selected 9 indices to form themultiple indices system include the maximum overbreak average overbreak maximum underbreak maximum size of stepbetween two guns area of overbreak measured area rate of overbreak volume of overbreak and blast hole utilization factor etotal quality of tunnel contour is quantitatively defined with 5 levels by using the dynamic cluster (DC) analysis With the obtainedvalues of the 9 indices the total quality of the tunnel contour could be determined quantitatively according to the calculatedprojection eigenvalues e result of the total quality of tunnel contour obtained using the proposed method is much moreaccordant with the site than that based on a single evaluation indexe proposedmethod will offer a promising alternative to fullyunderstand the total quality of tunnel contour

1 Introduction

It is well known that the quality of tunnel contour aftersmooth blasting always correlates with the tunnelling safetyand construction cost as well as the penetration rate [1ndash5]Consequently appropriate evaluation of the total quality oftunnel contour is of vital importance to the advancing ofdrilling-blasting tunnelling In general the contour qualitydepends on the complexity of geological conditions and thedrilling-blasting (DampB) operations which might cause ad-verse effects on the integrity and stability of the surrounding

rock mass [2 6 7] In view of applicability the quality oftunnel contour is now mainly determined by the overbreakin quality rating [8 9]

Many attempts have been made to predict the scale ofoverunderbreak and the range of blast-induced damage foroptimizing the blast designoperation and improvement ofthe contour quality in DampB tunnelling [10ndash15] Because ofthe uncertainty of site geology and the diversity of influentialfactors of DampB operation however most of the investiga-tions on evaluation of contour quality mainly focused on theoverbreaks at specific locations of the contour As of now

HindawiAdvances in Civil EngineeringVolume 2021 Article ID 6660719 17 pageshttpsdoiorg10115520216660719

very few efforts were devoted to quantify the contourcondition of the entire tunnel after a round of DampB oper-ation Yangkyun Kim [16] proposed an index named TunnelContour Quality Index (TCI) to quantify the general geo-metric features of the tunnel contour after smooth blastingconsidering the average overbreak depth and average ratio ofactual contour length to the planned contour length (RCL)in two cross-sections of a round and the average of absolutevalue of difference in overbreak depth between twoneighboring sections in longitudinal direction Elisa Cos-tamagna et al [2] conducted an assessment of over-excavation and TCI and then compared it with the Q-systemvaluesey suggested that the TCI index can be selected as aquantitative and applicable tool to evaluate the tunnelcontour quality to some extent Following their previouswork Yangkyun Kim and Amund Bruland [8] also estab-lished another index named Tunnel Contour Quality Indexfor Construction Cost (TCIC) to evaluate the contourquality and the expenditure Although the indices of TCIand TCIC offered a way to quantify the tunnel contourquality after smooth blasting only the overbreaks in somespecific linear directions in selected crosslongitudinalsections were taken into account In fact the total quality oftunnel contour not only depends on the depth of overunderbreaks at some specific positions but also is deter-mined by the total scale features in terms of area and volumeof overunderexcavations Koopialipoor et al [17] analyzedthe overbreak using both the artificial neural network(ANN) and hybrid genetic algorithm (GA)-ANN and foundthat the GA-ANN was more reliable to predict the over-break Considering the multiplicity of causing factors ofoverbreak and the complexity of interactions among thesefactors Koopialipoor et al [18] attempted to develop a newoverbreak prediction method by using artificial neuralnetwork Navarro et al [19] reported an engineering tool topredict high risk of overbreak zones based on the MWDdata Day [20] indicated that the brittle overbreak in theheterogeneous rock mass containing hydrothermal veinsand breccia can behave quite differently than the homo-geneous rock mass resulting in the traditional predictiontolls of depth of brittle overbreak which will be ineffectiveJang et al [21] defined an overbreak resistance factor todevelop an empirical method for overbreak estimationFodera et al [22] proposed an operative methodology toestimate overbreak volumes and to distinguish the technicaloverbreak based on the tunnel laser scanning surveys andhigh-resolution images of the excavated surfaces and theinfluence of influential parameters is assessed by the mul-tiple regression analysis Delonca and Vallejos [23] pre-sented a generalized failure criterion which includes the scaleeffect for prediction of the stress-induced overbreak for allexcavation diameters It could be found that great attentionhas been paid to the estimation of overbreak depth anddamage zone prediction However the contour quality doesnot only depend on the depth of overbreak at some specificlocations

In engineering applications the majority of qualityrating methods of tunnel contour after smooth blasting arebased on empirical or semiempirical formulas engineering

analogies and field tests [2 24 25] Recently some datamining approaches have been tried to estimate the overbreakand damage zone of surrounding rocks including adaptivefinite element method fractal theory image-processingtechnique wavelet analysis model testing artificial neuralnetwork and multiple regression analysis But most of thesemethods are generally qualitative and based on singleevaluation index which might be only applicable undersome specific conditions [7 26ndash29] A comprehensive indexsystem including multiple indices which can be used toquantitatively characterize the total quality of contour is stillunavailable In the reality of tunnel construction using DampBmethod different departments might use various indices tojudge the quality of tunnel contour according to theirconcerns For example the overunderbreak depth is oftenselected as the index to estimate the contour quality in theChinese code for construction on tunnel of railway [30] andthe code for construction technical specifications forhighway tunnels [31] Other factors including the area andvolume of overunderbreaks are neglected in practical ap-plications However effects of these factors on the qualityestimation of tunnel contour cannot be ignored in manycases For rational understanding and assessing the con-struction safety and time therefore development of acomprehensive evaluation method for the quantitative as-sessment of the total quality of a tunnel contour after smoothblasting is very promising in DampB tunnelling

is paper targets developing a quantitative evaluationapproach with multiple indices to fully understand the totalquality of tunnel contour based on the projection pursuitdynamic cluster (PPDC) method Both of the engineeringpractical experiences site measurements technical stan-dards expertsrsquo knowledge and relevant literatures are in-cluded in the proposed evaluation approach e influencesof overunderexcavations in 3 dimensions including thedepth area and volume are all counted into the assessmentto fully understand the total quality of tunnel contour aftersmooth blasting

2 Principles of the Quality Evaluation

21 Selection of Evaluation Indices e indices representingthe quality of tunnel contour might differ from each otheraccording to the primary purpose of the evaluation As isknown it is often impossible to involve all factors into theanalysis of complicated problem Appropriate determina-tion of the evaluation indices virtually plays a very importantrole in the reliability of the assessment Identification of theproper indices is the first but also themost important step Inthis work determining the indices follows the followingprinciples high correlation to the contour quality beingapplicable to be obtained considering both qualitative andquantitative factors and being easy to use

22 Structure of theMultiple Indices System In order to fullyunderstand the total quality of the contour the multipleindices system should be established Following the conceptof the analytic hierarchy process (AHP) method for

2 Advances in Civil Engineering

complicated issues [32] a hierarchical structure model of theproposed multiple indices system for evaluating the tunnelcontour quality is utilized as shown in Figure 1 It can clearlyshow the influential factors involved in this investigation andcorrelations among various factors

3 Data Collection

e data means the values of potential factors that may affectthe total quality of tunnel contour Identification of thesedata is performed by using site investigation expert con-sultation and experimental study According to their uti-lization frequencies in existing cases these potential indicesrepresenting the contour quality can be grouped into twotypes the qualitative indices and quantitative indices For aqualitative index grading its effect on the contour qualityand accordingly giving a score as its values are employed toquantify the influence of this index On the other hand thequantitative index should be converted into dimensionlessform to reduce the influences of variations of absolutevalues of these factors

31 Identification of Potential Indices e potential indicescan be obtained from literatures engineering experiencesexpert knowledge and technical codes in railway highwaycoal mine hydropower industries and other undergroundconstructions In this work 83 cases of rock tunnelling usingDampB method in China 20 overseas cases and 16 technicalcodes are examined and investigated In this work we definethe utilization rate to represent the frequency of the indexused in quality rating Following the definition in literature[33] the utilization rate is defined as the ratio of the utili-zation times of the index to the total number of existingmethods e adoption rate of the index utilized in tradi-tional quality rating is statistically analyzed as shown inFigures 2ndash4

It could be found that the cast factor blast hole utili-zation factor advance per round and overbreak can beconsidered as the main indicators representing the contourquality of tunnel smooth blasting in China from differentaspects However the overbreak is often selected as themajor index to indicate the contour quality in othercountries Statistically 32 potential indices can be identifiedto represent the tunnel contour quality after smoothblasting which should be taken into account in the proposedcomprehensive quality rating

32 Screening of Qualitative Indices In this work whether anindex should be counted into the evaluation depends on itsutilization rate in existing methods that is the adoption rateshould be no less than 50 Qualified qualitative indices can beidentified via on-site investigation and expert consultationAccording to the importance degree in the evaluation ofcontour quality the influence level of qualitative index isgrouped into five levels Specifically level 1 means very im-portant factor which will be given a score of 5 points Similarlylevel 2 represents relatively important factor (4 points) level 3indicates that its importance degree is fair (3 points) level 4 is

less important factor (2 points) and level 5 is unimportant (1point) In this work the qualitative indices include the eco-nomic benefits stability of the surrounding rock mass in-fluence of fly-rock rock supporting factors vibration effectcracking of retaining wall of surrounding rock and difficulty inoperation of construction method According to the result ofgrading and score the very important indices are the economicbenefits stability of the surrounding rock mass rock sup-porting factors and difficulty in operation of constructionmethod as shown in Figure 5 Only one index shows relativeimportance to the contour quality that is the fly-rock

33 Collection of Quantitative Indices e quantitative in-dices can be identified via on-site investigation expertconsultation and experimental study Similarly a quanti-tative index is qualified if its utilization rate is no less than50 Based on site investigation and expert consultation 25quantitative indices are collected as shown in Table 1

According to the utilization rate the indices which arevery important (5 points) to the contour quality includeoverbreak underbreak overbreak rate average overbreakmaximum size of step between two guns explosive dosageand the drilling footage per unit area as shown in Figure 6Accordingly the indices with relative importance includeaverage block size disturbance depth of the surroundingrock explosive charge ratio irregularity degree blastingvibration velocity advance per round drilling footage perunit area and retaining the thickness of surrounding rockdamage zone (4 points) as shown in Figure 7

e experimental studies including field testing andnumerical modelling also can provide some valuable in-formation on quantitative indices e indices investigatedat the site include measured cross-sectional area overbreakarea underbreak area maximum overbreak maximumunderbreak and average overbreak by using a tunnelprofilometer e first five indices also can be identifiedbased on numerical simulations

4 Determinationof theMultiple Indices System

41 General Method e multiple indices system is con-siderably critical to the reliability of the quality evaluation oftunnel contour after smooth blasting Appropriate indicessystem can provide convincing result of contour qualityevaluatione determination of the multiple indices systemis based on the following considerations

(1) Selecting a serial of indices that can generally indi-cate the contour quality e index used in mostevaluation methods can be considered as a qualifiedone which will represent the characteristics of thecontour quality to some extent Indices which areadopted frequently in most existing evaluationsshould be involved in this work

(2) Ranking the selected indices based on their utiliza-tion rateemore frequently the index is employedthe more important it is Meanwhile the contribu-tion of each index to the entire contour quality isquantitatively evaluated by the principal component

Advances in Civil Engineering 3

helliphellip helliphellip

Decision objective A

Criterial B1 Criterial B2 Criterial Bk

Objective level

Criterial level

Index levelhelliphellipEvaluation

index C11

Evaluation index C1n

Evaluation index

C21


Evaluation index

Ck1

Evaluation index Ckn

helliphelliphellip

Figure 1 e hierarchical structure for the multiple indices system

Maximum overbreakAdvance per roundHalf cast factor

OverbreakMaximum size of stepbetween two gunsBlast hole utilization factor

05

1015202530354045505560657075

Indi

cato

r ado

ptio

n ra

te (

)

08 10 12 1406Evaluation indicator

(a)

Hole consumption perunit volumeIrregularity degreeStability of surroundingrock mass

Blasting stone per roundDetonator consumptionFirst-line rate


0

2

4

6In

dica

tor a

dopt

ion

rate

()

(b)

Figure 2 Continued


analysis (PCA) method and the gray correlationanalysis (GCA) In this case the importance degreeof an index can be indicated by the weight eframework of determining the multiple indicessystem is shown in Figure 8

42 Primary Screening of the Indices Up to date there is stillno universal index system for the evaluation of the contourquality e indices utilized in one method might differ fromthose of another method Admittedly each index has its valuebut the limitations cannot be ignored For example the av-erage overbreak and maximum overbreak which are widely

utilized in many evaluations can only represent the contourquality at one specific point while the overunderbreaks in 2or 3 dimensions cannot be assessed In order to fully un-derstand the contour quality in 3 dimensions other indicesrepresenting the total area and volume of overunderbreaksshould be counted in erefore 21 indices with at least 50of utilization rate are primarily selected as parts of themultiple indices system As shown in Table 2 these indices aregrouped into 4 levels point indices linear indices surfaceindices and volumetric indices e point indices representthe depth of overunderbreak at some specific points thelinear indices reveal the linear distribution of overunder-break depth at different points the surface indices show the

Time of ventilation forsmoke extractionTotal depth of boreholesDosage of detonator

Explosive dosageDrilling footage per unit areaDifficulty in operation ofconstruction method

00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(c)

Vibration effectRetaining the thickness ofsurrounding rock damage zoneCracking of retaining wallof surrounding rock

Influence of flyrockUnderbreakTransmission distance

00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(d)

Disturbance depthof surrounding rockBlasting vibration velocityBoulder yield

Number of holes ratioExplosive charge ratioAverage block sizeEconomic benefits


0

2

4

6

8

10

Indi

cato

r ado

ptio

n ra

te (

)

(e)

Figure 2 Statistical indices for quality rating of tunnel contour after smooth blasting in China


area of overunderbreak on a certain inner surface of thetunnel and the volumetric indices indicate the total volume ofoverunderbreak in 3 dimensions

43Optimizationof the Indices In general a large number ofindices are often not applicable to perform the evaluation

work due to both the computing efficiency and applicabilityIn this case the selected 21 indices should be further op-timized according to their importance degree e couplingmethod of principal component analysis (PCA) method andgray correlation analysis (GCA) is employed to determinethe importance degree

431 Optimization of Point Indices In this section X1 X2X3 and X4 denote the maximum overbreak maximumunderbreak average overbreak and average underbreakrespectively eir weights are determined by coupling

Indi

cato

r ado

ptio

nrat

e (

)

Evaluation indicator

Average overbreakMaximum overbreakHalf cast factorSurrounding rock spallingMaximum size of stepbetween two gunsExcavation contourFlatness of excavation face

Advance per roundAverage block sizeOverbreakunderbreakDisturbance depth ofsurrounding rockBlasting vibration velocityBlast hole utilization factorIrregularity degree

0

10

20

30

40

50

60

70

80

90

Figure 3 Statistical indices for tunnel contour quality in technical codes

Indi

cato

r ado

ptio

nrat

e (

)


OverbreakAdvance per roundAverage overbreakBlasting vibration velocityHalf cast factorStability of surroundingrock mass

Overbreak areaUnderbreakExplosive dosageEconomic benefitsDisturbance depthof surrounding rockBlast hole utilizationfactor

0

20

40

60

80

100

Figure 4 Indices for quality of tunnel contour after smoothblasting in overseas countries


Economic benefitsStability of surroundingrock mass

Supporting factorsDifficulty in operation ofconstruction method

0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)

Figure 5 Very important qualitative indices (5 points)


method of the GCA and PCAe GCA is often utilized todetermine the correlation degree among different factorsin the system on the basis of the similarity or dissimilarityof the development trend [34] e correlations of factorscan be defined by the similarity of the geometric shapes ofthe sequence curves e correlation degree is significantif the geometric shapes of the curves are approximate Toperform the GCA the reference sequence can be defined

as x0 [x0(1) x0(2) x0(n) ] while the comparativesequence can be xi [xi(1) xi(2) xi(n)] and i 1 2 m To reduce the effect of deviation of factor unit thesequence should be nondimensionalized by the meanvalue processing method e reference sequence denotedas x0prime can be expressed as Equation (1) while the com-parative sequence indicated as x0prime can be described asEquation (2)

x0prime x0prime(1) x0prime(2) x0prime(n)1113858 1113859

x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)

x0prime xiprime(1) xiprime(2) xi

prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)

e correlation coefficient is defined as

η0i(k) Δmin + wΔmax

xo(k) minus xi(k) + wΔmax1113868111386811138681113868

1113868111386811138681113868 (3)

in which w is the resolution coefficient Δmin is the minimumdifference between the two sequences and Δmax is themaximum difference between the two sequences ereforethe correlation degree can be determined by

c0i 1113936

ni1 η0i(k)

n (4)

In this work the relational order of the point indices isshown in Table 3e correlation degree for each point indexis shown in Table 4

It could be found that the maximum overbreak X1 hasthe strongest correlation with the tunnel contour qualitywhile the average underbreak X4 shows the lowest corre-lation with the contour quality

On the other hand the contribution of each index to thetotal contour quality also can be determined using the PCAmethod As is known the PCA is probably the oldest andbest known of the techniques for multivariate analysis [35]

Table 1 Quantitative indices obtained via site investigation and expert consultation

No Index Utilization rate() No Index Utilization rate

()1 Overbreak 7143 14 Maximum size of step between two guns 502 Half cast factor 4286 15 Explosive charge ratio 57153 Blasting stone per round 3571 16 Irregularity degree 504 Underbreak 5714 17 Blasting vibration velocity 57155 Average block size 5714 18 Number of holes ratio 3571

6 Detonator consumptiondosage ofdetonator 35714285 19 Blast hole utilization factor 4286

7 Overbreak rate 6429 20 Advance per round 50018 Boulder yield 4286 21 Total depth of boreholes 35719 First-line rate 4286 22 Explosive dosage 642910 Average overbreak 5715 23 Transmission distance 3572

11 Disturbance depth of the surroundingrock 7144 24 Drilling footage per unit area 50

12 Time of ventilation for smokeextraction 4286 25 Retaining the thickness of surrounding rock

damage zone 50

13 Maximum overbreak 4286 mdash mdash mdash


It was first introduced by Pearson in 1901 and then de-veloped independently by Hottelling in 1933 e philoso-phy of the PCA is to reduce the dimensionality of a data setwhere there are a large number of interrelated variants whileretaining as much as possible of the variation present in thedata set [35 36] Following Eriksson et al [37] the PCAmodel is

X TPT

+ E (5)

in which X is the input matrix (n times p) which representsoriginal parameters T is the score matrix (n times k) whichrepresents the relationship between original parameters P isthe loading matrix (p times k) which represents the contributionof original parameters and E is the residual matrix (n times p)

which represents the uncaptured variance n is the number oftime steps p is the number of original parameters and k is thenumber of principal components

On the basis of the maximum variance criterion eachprincipal component obtained from the PCA model is ir-relevant to another one e first principal component hasthe highest variance which also reveals that it contains themost information while the second principal componentwill capture the next highest variance which has alreadyremoved the information of the first principal component[36] And the rest can be deduced in the same manner Forthe kth principal component for the point index it can bedenoted as follows

PCk a1kPintakepointindice + a2kPdischargepointindice

+ a3kPintakepointindice + a4kPdischargepointindice++apkPvibration

(6)

e first three principal components have the highestvariance It means that most of the information in theoriginal parameter is visualized by the first three principal

components e normalized eigenvectors of the point in-dices are shown in Table 5 and the corresponding eigen-values are given in Table 6 It can be seen that the firstprinciple component involves the average overbreak X3 andthe maximum overbreak X1 the second principle compo-nent is the maximum underbreak X2 and the third principlecomponent is the average underbreak X4

Combining both the results of PCA and GCA the op-timized point indices are shown in Table 7 In point level themaximum overbreak X1 average overbreak X3 and themaximum underbreak X2 are selected as the optimum pointindices in sequence

432 Optimization of Linear Indices Y1ndashY5 represent thedisturbance depth of the surrounding rock maximum sizeof step between two guns irregularity degree averageblock size and advance per round respectivelyAccording to the results of PCA and GCA the optimizedlinear indices are shown in Table 8 e maximum size ofstep between two guns Y2 is determined as the optimumlinear index

433 Optimization of Surface Indices W1ndashW6 denote themeasured cross-sectional area area of overbreak area ofunderbreak rate of overbreak rate of underbreak and halfcast factor respectively e results of optimized surfaceindices are given in Table 9 Area of overbreakW2 measuredarea W1 and rate of overbreak W4 are selected as the op-timum surface indices

434 Optimization of Volumetric Indices Z1-Z6 indicate thevolume of overbreak volume of underbreak blast holeutilization factor explosive dosage economic benefits andstability of the surrounding rock mass respectively eoptimized volumetric indices are shown in Table 10 basedon the analysis of PCA and GCA It could be found that thevolume of overbreak Z1 and blast hole utilization factor Z3can be determined as the optimum volumetric indices

44 Development of theMultiple Indices System On the basisof the two rounds of screening the optimal indices that willbe used to establish the multiple indices system can befigured out clearly According to the hierarchical structurethe proposed multiple indices system is given in Table 11 Itincludes four levels under the criterion layer and in total 9indices representing the contour quality for the index layer

5 Contour Quality Evaluation Using thePPDC Method

e proposed multiple indices system has 9 indices torepresent the contour quality from different aspects As isknown it is hard to quantitatively analyze the multiple-dimensional data us the projection pursuit (PP) methodis used to reduce the dimensions of the data in this work andthe dynamic clustering (DC) is employed to establish therating of the contour quality As a result the total contour


OverbreakUnderbreakOverbreak rateAverage overbreak

Maximum size of stepbetween two gunsExplosive dosageDrilling footage perunit area

0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)

Figure 6 Very important quantitative indices (5 points)



Average block sizeDisturbance depthof surrounding rockExplosive charge ratioIrregularity degree

Blasting vibration velocityAdvance per roundDrilling footage per unit areaRetaining the thickness ofsurrounding rock damage zone

0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)

Figure 7 Relatively important quantitative indices (4 points)

Analysis of factors for quality evaluation of smooth blasting in tunnel

Point indices Linear indices Surface indices Volumetric indices

Engineering cases and specifications in China Expert Surveys Foreign engineering cases

Design of frame structure of smooth blasting quality evaluation system in tunnel

Evaluation index data acquisition

Qualitative index collection Quantitative index collection

Primary selection of quality evaluation index system for smooth blasting of tunnel

Indicator adoption

rate method

The evaluation indices system of tunnel smooth blasting quality is established

Construction principle

Figure 8 Framework of the multiple indices system


quality can be determined appropriately if the values of the 9indices are available

51 Projection Pursuit (PP) Method For multiple factorsevaluation problems mapping of multivariate data ontolow-dimensional manifolds for visual inspection has beenconsidered as a common technique in data analysis eprojection pursuit (PP) algorithm is such a tool to solve the

multiple factors evaluation problems [38] It can converthigh-dimensional data into low-dimensional space bymapping in a projection direction [39] In low-dimensionalspace the salient features of the original data can be analyzedconveniently by the human gift for pattern recognitionSpecifically the PP algorithm provides a linear mappingmethod that uses interpoint distance as well as the varianceof the point swarm to pursue optimum projections [38] emajor task of PP analysis is particularly a dimension-

Table 2 Primary determination of the index system in four levels

Objective level Criteria level Index (unit)

Index system

Point indices

Maximum overbreak X1 (m)Maximum underbreak X2 (m)Average overbreak X3 (m)Average underbreak X4 (m)

Linear indices

Disturbance depth of the surrounding rock Y1 (m)Maximum size of step between two guns Y2 (cm)

Irregularity degree Y3 (cm)Average block size Y4 (cm)Advance per round Y5 (m)

Surface indices

Measured area W1 (m2)Area of overbreak W2 (m2)Area of underbreak W3 (m2)

Overbreak rate W4 ()Underbreak rate W5 ()Half cast factor W6 ()

Volumetric indices

Volume of overbreak Z1 (m3)Volume of underbreak Z2 (m3)

Blast hole utilization factor Z3 ()Explosive dosage Z4 (kg)Economic benefits Z5

Stability of the surrounding rock mass Z6

Table 3 Relational order of point indices

Relational order between X1and others




Index Correlation coefficient Index Correlation coefficient Index Correlation coefficient Index Correlation coefficientX3 09562 X4 08209 X1 09563 X2 08259X2 08022 X1 07962 X2 07928 X1 07583X4 07577 X3 07861 X4 07511 X3 07511

Table 4 Correlation degree of point indices

Index Correlation degree Index Correlation degreeMaximum overbreak X1 05860 Average overbreak X3 05834Maximum underbreak X2 05672 Average underbreak X4 05559

Table 5 Eigenvectors of point indices

Index Factor 1 Factor 2 Factor 3 Factor 4X1 05145 0571 minus00208 minus06394X2 minus03774 06946 minus05138 03333X3 0605 02372 03228 06881X4 minus04763 03677 07946 minus00808

Table 6 Eigenvalues of point indices

No Eigenvalue Percentage () Accumulated percentage ()1 19791 4947 49472 10652 2662 76103 06413 1603 92134 03145 786 100


reducingmapping issue to determine the optimal projectiondirection which can provide more valuable informationfrom the original high-dimensional data e procedure ofPP mapping is given as follows

(1) Normalization of the original data In order toreduce the effect of different magnitudes of variousfactors the original data should be first normalizedSuppose xlowast(i j)| i 1 n j 1 p1113864 1113865where xlowast(i j) is the value of jth factor after nor-malization n is the number of samples and p is thenumber of factors For factors that are better withbigger values the normalization formula is given inEquation 7 For others the original data could benormalized by Equation 8

x(i j) xlowast(i j) minus xmin(j)

xmax(j) minus xmin(j) (7)

x(i j) xmax(j) minus x

lowast(i j)


(2) Establishing the function of linear projection Sup-pose a a(1) a(2) a(p)1113864 1113865 is a p-dimensionalunit vector and z (i) is the projection characteristicvalue of xlowast(i j) e linear projection value can beobtained from

z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)

(3) Optimization of the projection index function eoptimal projection direction can be determined bythe maximum value of the projection index in whichthe genetic algorithm (GA) could be employed toperform the optimizatione projection index Q(a)

is a function of the projection axis ararr which can be

defined as follows

Q(a) Sz times Dz (10)

st 1113944

p

j1a2(j) 1 (11)

where Sz denotes the spread of the data which can becalculated by Equation (12) and Dz is the localdensity of the projection values on the projectiondirection a which can be defined as Equation (13)

Sz

1113936

mj1 (z(i) minus z(i))

2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n

k1[R minus r(i j)] times u[R minus r(i j)]1113864 1113865

r(i j) |z(i) minus z(j)|

(13)

in which z(i) is the mean value of z (i) along theprojection axis a

rarr and R Sz times 10 which meansthe cutoff radius

(4) Calculation of the projection value After the de-termination of the optimal projection direction a

rarrthe projection value of samples can be calculated byEquation (9) As a result a characteristic projectionvalue which represents the total quality of contourcan be obtained

52 Dynamic Clustering (DC)

521 General Method In order to qualify the quality gradeof the tunnel contour using the projection value of themultiple indices the rating of contour quality should bedeveloped in advance In this study dynamic clustering(DC) algorithm is used to quantitatively determine thequality grade with 5 levels e concept of classification is topartition a set of data described by frequency distributions

Table 7 Optimized point indices

No Optimization methodVariables

Optimized point indicesFirst selected Second selected ird selected

1 GCA X1 X3 X2 X1 X3 X22 PCA X3 X1 X2 X4

Table 8 Optimized linear indices


Optimized surface indicesFirst selected Second selected ird selected Fourth selection

1 GCA Y2 Y4 Y5 Y1 Y22 PCA Y2 Y3 Y5 Y1


[40] It is a general partitioning algorithm of a set of objectsinK clusters which is based on the definition of a criterion ofthe best fitting between the partition of a set of individualsand the representation of the clusters of the partition [41]e partitioning operation is described as follows

(1) Initial partitioning M selected samples αi(i 1 2

m) are randomly divided into f initial groupsthat is Fz(z 1 2 f)

(2) Calculating the distance the mean vector zz of eachinitial group Fz could be calculated by

zz Hz

nz

(14)

where Hz and nz are the sum of vectors and numberof vectors respectively Consequently the distancebetween the value of ith sample αi and mean vectorzz can be calculated by

σ2iz αi minus zz1113872 1113873 αi minus zz1113872 1113873 (15)

(3) Establishing the first group the sample value αi ismodified by Equation (16) and thus the first groupcan be obtained

min σ2iz αi minus zz1113872 11138732

1113876 1113877 (16)

(4) Repeating the calculation steps of (2) and (3) withmodified sample values to get the ranges of othergroups

522 Rating of Each Index e rating of each evaluationindex in the proposed multiple indices system is performedby DC algorithm and the confidence interval estimatione importance degree of each index is grouped into 5levels e original data of each index and related effects oncontour quality are collected from the huge number ofexisting projects Taking the average overbreak as an ex-ample the calculated result is shown in Table 12 e updown limits of each level could be determined by thesignificance level

Accordingly the rating of average overbreak can beobtained as shown in Table 13

Similarly the rating of other 8 indices involved in theproposed multiple indices system could be obtained asshown in Table 14

53 Contour Quality Rating Based on Projection Valuee comprehensive contour quality can be determined bythe eigenvalues of the data set of the multiple indices Basedon Table 14 the optimal projection direction of the multipleindices can be obtained by using the MATLAB code ecomputer configuration for performing the calculation isshown in Table 15

Calculated optimal projection direction ararr is

alowast (03154 03663 01952 02508 05209 02346 0374702091 03934) and the computed eigenvalues using the PPmethod for each level are given in Table 16 As shown inTable 16 the total quality of tunnel contour can be classifiedinto 5 levels according to the eigenvalues

Table 9 Optimized surface indices


Optimized surface indicesFirst selected Second selected

1 GCA W2 W4 W1 W2 W1 W42 PCA W1 W2 W4 W6

Table 10 Optimized volumetric indices

No Optimization methodVariable

Optimum volumetric indicesFirst selected Second selected ird selected Fourth selected

1 GCA Z4 Z3 Z6 Z1 Z1 Z32 PCA Z1 Z3 Z2 Z6

Table 11 Developed multiple indices system

Target layer Criterion layer Index layer (unit)

e index system for contour quality rating A

Point indices B1Maximum overbreak C11 (m)Average overbreak C12 (m)

Maximum underbreak C13 (m)Linear indices B2 Maximum size of step between two guns C21 (cm)

Surface indices B3Area of overbreak C31 (m2)Measured area C32 (m2)Rate of overbreak C33 ()

Volumetric indices B4Volume of overbreak C41 (m3)

Blast hole utilization factor C42 ()


6 Application

61 Project Background A high-speed railway tunnel fromChengdu to Chongqing excavated by the drill-blast methodis selected as the site of field study e tunnel is located atthe mountainous area in west of Chongqing During tun-nelling the smooth blasting was conducted to excavate therock formations e designed length of the tunnel is up to5054m and the height of the test cross section is 1108mwhile for width it is 1490m According to the Chinesetechnical standard TB10003 [42] the grade of the sur-rounding rock is classified to level IV meaning the inte-gration and stability of the surrounding rock are poor emain lithology exposed during excavation is argillaceoussandstone with age of Jurassic (J2s) e properties of thesurrounding rocks are shown in Table 17

62 Measured Data e values of the multiple indices in-cluding the maximum overbreak average overbreak maxi-mum underbreak maximum size of step between two guns

area of overbreak measured area overbreak rate volume ofoverbreak and blast hole utilization factor are measuredcollected at 3 cross-sections that is at DK247+0335mDK247+0475m and DK247+0495m as shown in Table 18

63 Calculated Eigenvalues Based on the measured data theoptimal projection of the 9 indices representing the tunnelcontour quality can be obtained by using MATLAB pro-gramming that is alowast (01841 04406 00007 00034 0504504941 05099 01154 00001) Substituting the obtained optimalprojection direction into the linear projection function that isEquation (9) the calculated projection values of comprehen-sive quality of the 3 measure contours are Zlowast (057 081 217)

64 Rating of Contour Quality Consequently the rating ofcontour quality can be obtained by comparing the calculatedeigenvalues with the developed rating (Table 16) e resultof quality rating of the 3 measured tunnel contours is shownin Table 19e actual profiles of the 3 contours are shown inFigures 9ndash11

From the site pictures of the contours it could be foundthat the rating of total contour quality defined by the proposedmultiple indices-based evaluation method is much differentfrom that obtained using single index If the single index isselected to describe the contour quality for example themagnitude of the maximum overbreak or underbreak of

Table 13 e rating of average overbreak

Level Range (m)I ＜015II 015ndash021III 021ndash026IV 026ndash031V ＞031

Table 14 Rating of each evaluation index for tunnel contour quality (for medium-hard rocks)

Rating Maximumoverbreak

Averageoverbreak

Maximumunderbreak

Maximum size of stepbetween two guns

Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

Blast holeutilization factor

I 1 lt042 lt015 lt002 lt10 lt35 lt3 lt15 lt15 gt95II 3 042ndash062 015ndash021 002ndash006 10ndash15 35ndash55 3ndash6 15ndash35 15ndash35 95ndash90III 5 062ndash072 021ndash026 006ndash010 15ndash20 55ndash75 6ndash9 35ndash55 35ndash55 90ndash85IV 7 072ndash082 026ndash031 010ndash021 20ndash25 75ndash95 9ndash12 55ndash75 55ndash75 85ndash80V 9 gt082 gt031 gt021 gt25 gt95 gt12 gt75 gt75 lt80

Note e area deviation is the difference between the measured cross-sectional area and the designed area

Table 15 Computer configuration for the calculation

CPU AMD Ryzen 5 pro 3500U wRadeon VegaMobile Gfx 210GHz

RAM At least 800GOS Windows 7 64 bit

Table 12 Calculated result of the rating of the average overbreak

Rating Significance level α Average overbreak Rating Significance level α Average overbreak

Very good (I) 005 01588ndash01812 Poor (IV) 005 03145ndash03248001 01539ndash01861 001 03127ndash03266

Good (II) 005 02130ndash02248 Very poor (V) 005 03550ndash03825001 02108ndash02270 001 03484ndash03891

Fair (III) 005 02671ndash02762 mdash mdash mdash001 02655ndash02777 mdash mdash mdash


contour at DK247+0495m is relatively higher than the other2 contours which will lead to a poor contour quality Howeverthe total volume of overunderbreaks in contour atDK247+0495m is much lower than that of others and theobserved maximum overunderbreak only occurs in very fewpositions e relative low value of overunderbreaks of thecontour at DK247+0495m also can be examined by the

measured area and volume of overbreak In fact the contour atDK247+0495m shows much better quality than that of othercontours because of low volume of overbreak which will re-duce the expenditure on backfill and rock support Obviouslythe result from the proposed contour quality evaluationmethod is more accordant with the fact of the site which willbenefit the cost-effective decision-making by the site engineers

Table 16 Rating of tunnel contour quality

Eigenvalue Range Rating286 194ndash286 Very good (I)194 128ndash194 Good (II)128 067ndash128 Fair (III)067 0ndash067 Poor (IV)000 0 Very poor (V)

Table 17 Properties of the surrounding rocks

No Rocksoil Age Consistency or weatheringdegree Density (gcm3) Cohesive (kPa) Internal friction

angle (deg)lt6ndash2gt Soft soil (soft silty clay) Q4 Flow plastic 172 85 54lt6ndash3gt Soft soil (soft plastic silty clay) Q4 Soft plastic 188 121 76lt6ndash4gt Silty clay Q4 Hard plastic 194 277 12lt7ndash1gt Silty clay Q4 Hard plastic 189 251 109

lt27ndash2gt Sandstone J2sW4 200 20 20W3 220 - 40W2 250 - 50

lt27ndash3gt Mudstone mixed with sandstone J2sW4 196 20 18W3 210 - 35W2 252 - 45

lt27ndash5gt Argillaceous sandstone J2sW4 196 20 18W3 210 - 35W2 252 - 45

Table 18 Collected indices representing the contour quality after smooth blasting

Layer IndexMeasured value

DK247+ 0335 DK247 + 0475 DK247+ 0495

Point indices B1Maximum overbreak C11 (m) 064 059 069Average overbreak C12 (m) 032 030 021

Maximum underbreak C13 (m) 014 003 028Linear indices B2 Maximum size of step between two guns C21 (cm) 15 8 23

Surface indices B3Area of overbreak C31 (m2) 1178 1090 470Measured area C32 (m2) 15110 15031 14219Overbreak rate C33 () 845 782 337

Volumetric indices B4Volume of overbreak C41 (m3) 589 545 235

Blast hole utilization factor C42 () 95 92 79

Table 19 Rating of total quality of measured tunnel contours

Contour DK247 + 0335 DK247 + 0475 DK247+ 0495Eigenvalue 057 081 217Quality rating Poor (IV) Fair (III) Very good (I)


7 Conclusions

e tunnel contour quality after smooth blasting is con-siderably critical to the estimation of construction cost andtime as well as the safety of tunnelling and the stability of the

surrounding rock Comprehensive understanding of thecontour quality in 3 dimensions is of vital importance toreasonably evaluate the construction time and cost Com-pared with single index the proposed multiple indices canbetter represent the total quality of tunnel contour ispaper developed a multiple indices-based evaluation ap-proach and thus the projection pursuit dynamic cluster(PPDC) method is utilized to qualify the quality grade of thetunnel contour Some conclusions can be drawn as follows

(1) Based on statistical analysis of engineering cases siteinvestigation literatures expert knowledge and thetechnical codes 7 qualitative indices and 25 quan-titative indices representing the contour quality areeffectively figured out According to the utilizationrate 21 indices are preliminarily selected to fullydescribe the contour quality in 3 dimensions

(2) To identify the most influential factors affecting thetotal contour quality the coupling method of theGCA and PCA is utilized to determine the multipleindices system e selected 9 indices include themaximum overbreak average overbreak maximumunderbreak maximum size of step between twoguns area of overbreak measured area rate ofoverbreak volume of overbreak and blast holeutilization factor

(3) To rationally determine the quality grade of contourthe projection pursuit (PP) method is used to processthe high-dimensional data of the multiple indicesand the dynamic cluster (DC) analysis is utilized toestablish the rating of total contour quality e totalquality of tunnel contour in 3 dimensions is groupedinto 5 levels according to the eigenvalues

(4) If the measured values of the 9 indices are availablethe optimal projection direction and eigenvalues canbe obtained by using the PP algorithm In this casethe rating of contour quality can be determinedaccordingly Compared with the traditional methodbased on overbreak the result of contour qualityusing the proposed method is more accordant withthe fact of the site It is believed that the developedPPDC-based evaluation method will offer a pro-moting alternative to reasonably describe the totalquality of tunnel contour after smooth blasting

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e financial supports for this research project by the Na-tional Natural Science Foundation of China (nos 41602308

Figure 9 e actual contour at DK247 + 0335




and 41572299) the Zhejiang Provincial Natural ScienceFoundation of China (no LY20E080005) the graduateteaching reform research project of Zhejiang University ofScience and Technology (Grant no 2019yjsjg01) the Zhe-jiang Science and Technology Project (no 2016C33033) andthe Foundation of China Railway No 2 Engineering GroupCo Ltd (no 201218) are all gratefully acknowledged

References

[1] Y Hu W Lu M Chen P Yan and J Yang ldquoComparison ofblast-induced damage between presplit and smooth blastingof high rock sloperdquo Rock Mechanics and Rock Engineeringvol 47 no 4 pp 1307ndash1320 2013

[2] E Costamagna C Oggeri P Segarra R Castedo andJ Navarro ldquoAssessment of contour profile quality in DampBtunnellingrdquo Tunnelling and Underground Space Technologyvol 75 pp 67ndash80 2018

[3] N H Maerz J A Ibarra and J A Franklin ldquoOverbreak andunderbreak in underground openings Part 1 measurementusing the light sectioning method and digital image pro-cessingrdquo Geotechnical and Geological Engineering vol 14no 4 pp 307ndash323 1996

[4] J A Ibarra N H Maerz and J A Franklin ldquoOverbreak andunderbreak in underground openings Part 2 causes andimplicationsrdquo Geotechnical and Geological Engineeringvol 14 no 4 pp 325ndash340 1996

[5] A F McKown ldquoPerimeter control blasting for undergroundexcavations in fractured and weathered rockrdquo Environmentalamp Engineering Geoscience vol xxiii no 4 pp 461ndash478 1986

[6] C Oggeri and G Ova ldquoQuality in tunnelling ITA-AITESworking group 16 final reportrdquo Tunnelling and UndergroundSpace Technology vol 19 no 3 pp 239ndash272 2004

[7] S P Singh and P Xavier ldquoCauses impact and control ofoverbreak in underground excavationsrdquo Tunnelling andUnderground Space Technology vol 20 no 1 pp 63ndash71 2005

[8] Y Kim and A Bruland ldquoA study on the establishment ofTunnel Contour Quality Index considering constructioncostrdquo Tunnelling and Underground Space Technology vol 50pp 218ndash225 2015

[9] K Liu and B Liu ldquoOptimization of smooth blasting pa-rameters for mountain tunnel construction with specifiedcontrol indices based on a GA and ISVR coupling algorithmrdquoTunnelling and Underground Space Technology vol 70pp 363ndash374 2017

[10] Z-D Cui ldquoEffect of water-silt composite blasting on thestability of rocks surrounding a tunnelrdquo Bulletin of Engi-neering Geology and the Environment vol 70 no 4pp 657ndash664 2010

[11] J C Li H B Li G W Ma and Y X Zhou ldquoAssessment ofunderground tunnel stability to adjacent tunnel explosionrdquoTunnelling and Underground Space Technology vol 35pp 227ndash234 2013

[12] M Ramulu A K Chakraborty and T G Sitharam ldquoDamageassessment of basaltic rock mass due to repeated blasting in arailway tunnelling project-a case studyrdquo Tunnelling and Un-derground Space Technology vol 24 no 2 pp 208ndash221 2009

[13] H K Verma N K Samadhiya M Singh R K Goel andP K Singh ldquoBlast induced rock mass damage around tun-nelsrdquo Tunnelling and Underground Space Technology vol 71pp 149ndash158 2018

[14] L X Xie W B Lu Q B Zhang Q H Jiang G H Wang andJ Zhao ldquoDamage evolution mechanisms of rock in deep

tunnels induced by cut blastingrdquo Tunnelling and UndergroundSpace Technology vol 58 pp 257ndash270 2016

[15] S K Mandal and M M Singh ldquoEvaluating extent and causesof overbreak in tunnelsrdquo Tunnelling and Underground SpaceTechnology vol 24 no 1 pp 22ndash36 2009

[16] Y Kim Tunnel Contour Quality Index in a Drill and BlastTunnel Definition Analysis and Effects Norwegian Universityof Science and Technology Trondheim Norway 2009

[17] M Koopialipoor D Jahed Armaghani M Haghighi andE N Ghaleini ldquoA neuro-genetic predictive model to ap-proximate overbreak induced by drilling and blasting oper-ation in tunnelsrdquo Bulletin of Engineering Geology and theEnvironment vol 78 no 2 pp 981ndash990 2017

[18] M Koopialipoor E N Ghaleini M HaghighiS Kanagarajan P Maarefvand and E T MohamadldquoOverbreak prediction and optimization in tunnel usingneural network and bee colony techniquesrdquo Engineering withComputers vol 35 no 4 pp 1191ndash1202 2018

[19] J Navarro J A Sanchidrian P Segarra R CastedoE Costamagna and L M Lopez ldquoDetection of potentialoverbreak zones in tunnel blasting from MWD datardquo Tun-nelling and Underground Space Technology vol 82 pp 504ndash516 2018

[20] J J Day ldquoBrittle overbreak prediction in deep excavations forhydrothermally altered and heterogeneous rockmassesrdquoBulletin of Engineering Geology and the Environment vol 79no 2 pp 1041ndash1060 2019

[21] H Jang Y Kawamura and U Shinji ldquoAn empirical approachof overbreak resistance factor for tunnel blastingrdquo Tunnellingand Underground Space Technology vol 92 2019

[22] G M Fodera A Voza G Barovero F Tinti and D BoldinildquoFactors influencing overbreak volumes in drill-and-blasttunnel excavation A statistical analysis applied to the casestudy of the Brenner Base Tunnelndashbbtrdquo Tunnelling and Un-derground Space Technology vol 105 2020

[23] A Delonca and J A Vallejos ldquoIncorporating scale effect into afailure criterion for predicting stress-induced overbreakaround excavationsrdquo International Journal of Rock Mechanicsand Mining Sciences vol 127 2020

[24] G Yilei L Xiaohong D Yungui and X Wang ldquoReasonablesmooth blasting factor used in tunnelrdquo Journal Of ChongqingUniversity(Natural Science Edition) vol 28 no 3 pp 95ndash972005

[25] S Shiwei X Junchen D Shulin and X Yan ldquoExtenicsevaluation of joint rock tunnel blasting quality based onentropy weighting methodrdquo China Civil Engineering Journalvol 46 no 12 pp 118ndash126 2013

[26] A K Chakraborty J L Jethwa and A G PaithankarldquoAssessing the effects of joint orientation and rock massquality on fragmentation and overbreak in tunnel blastingrdquoTunnelling and Underground Space Technology vol 9 no 4pp 471ndash482 1994

[27] A K Chakraborty J L Jethwa and A G Paithankar ldquoEffectsof joint orientation and rock mass quality on tunnel blastingrdquoEngineering Geology vol 37 no 3-4 pp 247ndash262 1994

[28] M Rezaei M Monjezi S Ghorbani Moghaddam andF Farzaneh ldquoBurden prediction in blasting operation usingrock geomechanical propertiesrdquo Arabian Journal of Geo-sciences vol 5 no 5 pp 1031ndash1037 2011

[29] H Jang and E Topal ldquoOptimizing overbreak predictionbased on geological parameters comparing multiple re-gression analysis and artificial neural networkrdquo Tunnellingand Underground Space Technology vol 38 pp 161ndash1692013


[30] China Railway Publishing House Co Ltd TB10204 Code forConstruction on Tunnel of Railway China Railway PublishingHouse Co Ltd Beijing China 2002

[31] China Communications Press JTGF60 Technical Specifica-tions for Construction of Highway Tunnel China Commu-nications Press Beijing China 2009

[32] S G Meshram E Alvandi V P Singh and C MeshramldquoComparison of AHP and fuzzy AHP models for prioriti-zation of watershedsrdquo Soft Computing vol 23 no 24pp 13615ndash13625 2019

[33] K Skrzypkowski ldquoe influence of room and pillar methodgeometry on the deposit utilization rate and rock bolt loadrdquoEnergies vol 12 no 24 2019

[34] C Zheng R Li M Hu and L Zou ldquoDetermination of low-temperature crack control parameter of binding asphaltmaterials based on gray correlation analysisrdquo Constructionand Building Materials vol 217 pp 226ndash233 2019

[35] I T Jolliffe Principal Component Analysis Springer-VerlagNew York NY USA Second edition 2002

[36] L Peng G Han A Landjobo Pagou and J Shu ldquoElectricsubmersible pump broken shaft fault diagnosis based onprincipal component analysisrdquo Journal of Petroleum Scienceand Engineering vol 191 2020

[37] L Eriksson T Byrne E Johansson J Trygg and C VikstromMulti- and Megavariate Data Analysis Basic Principles andApplications Umetrics Academy 2013 Stockholm Swedan2013

[38] J H Friedman and J W Tukey ldquoA projection pursuit al-gorithm for exploratory data analysisrdquo IEEE Transactions onComputers vol 23 no 9 pp 881ndash890 1974

[39] H Li J Li and F Kang ldquoApplication of the artificial beecolony algorithm-based projection pursuit method in statis-tical rock mass stability estimationrdquo Environmental EarthSciences vol 68 no 8 pp 2337ndash2345 2012

[40] E Diday and J C Simon ldquoClustering analysisrdquo in DigitalPattern Recognition K S Fu Ed pp 47ndash94 Springer BerlinHeidelberg 1980

[41] A Irpino R Verde and F d A T De Carvalho ldquoDynamicclustering of histogram data based on adaptive squaredWasserstein distancesrdquo Expert Systems with Applicationsvol 41 no 7 pp 3351ndash3366 2014

[42] China Railway Publishing house Co Ltd TB10003 Code forDesign of Railway Tunnel China Railway Publishing houseCo Ltd Beijing China 2016


very few efforts were devoted to quantify the contourcondition of the entire tunnel after a round of DampB oper-ation Yangkyun Kim [16] proposed an index named TunnelContour Quality Index (TCI) to quantify the general geo-metric features of the tunnel contour after smooth blastingconsidering the average overbreak depth and average ratio ofactual contour length to the planned contour length (RCL)in two cross-sections of a round and the average of absolutevalue of difference in overbreak depth between twoneighboring sections in longitudinal direction Elisa Cos-tamagna et al [2] conducted an assessment of over-excavation and TCI and then compared it with the Q-systemvaluesey suggested that the TCI index can be selected as aquantitative and applicable tool to evaluate the tunnelcontour quality to some extent Following their previouswork Yangkyun Kim and Amund Bruland [8] also estab-lished another index named Tunnel Contour Quality Indexfor Construction Cost (TCIC) to evaluate the contourquality and the expenditure Although the indices of TCIand TCIC offered a way to quantify the tunnel contourquality after smooth blasting only the overbreaks in somespecific linear directions in selected crosslongitudinalsections were taken into account In fact the total quality oftunnel contour not only depends on the depth of overunderbreaks at some specific positions but also is deter-mined by the total scale features in terms of area and volumeof overunderexcavations Koopialipoor et al [17] analyzedthe overbreak using both the artificial neural network(ANN) and hybrid genetic algorithm (GA)-ANN and foundthat the GA-ANN was more reliable to predict the over-break Considering the multiplicity of causing factors ofoverbreak and the complexity of interactions among thesefactors Koopialipoor et al [18] attempted to develop a newoverbreak prediction method by using artificial neuralnetwork Navarro et al [19] reported an engineering tool topredict high risk of overbreak zones based on the MWDdata Day [20] indicated that the brittle overbreak in theheterogeneous rock mass containing hydrothermal veinsand breccia can behave quite differently than the homo-geneous rock mass resulting in the traditional predictiontolls of depth of brittle overbreak which will be ineffectiveJang et al [21] defined an overbreak resistance factor todevelop an empirical method for overbreak estimationFodera et al [22] proposed an operative methodology toestimate overbreak volumes and to distinguish the technicaloverbreak based on the tunnel laser scanning surveys andhigh-resolution images of the excavated surfaces and theinfluence of influential parameters is assessed by the mul-tiple regression analysis Delonca and Vallejos [23] pre-sented a generalized failure criterion which includes the scaleeffect for prediction of the stress-induced overbreak for allexcavation diameters It could be found that great attentionhas been paid to the estimation of overbreak depth anddamage zone prediction However the contour quality doesnot only depend on the depth of overbreak at some specificlocations

In engineering applications the majority of qualityrating methods of tunnel contour after smooth blasting arebased on empirical or semiempirical formulas engineering

analogies and field tests [2 24 25] Recently some datamining approaches have been tried to estimate the overbreakand damage zone of surrounding rocks including adaptivefinite element method fractal theory image-processingtechnique wavelet analysis model testing artificial neuralnetwork and multiple regression analysis But most of thesemethods are generally qualitative and based on singleevaluation index which might be only applicable undersome specific conditions [7 26ndash29] A comprehensive indexsystem including multiple indices which can be used toquantitatively characterize the total quality of contour is stillunavailable In the reality of tunnel construction using DampBmethod different departments might use various indices tojudge the quality of tunnel contour according to theirconcerns For example the overunderbreak depth is oftenselected as the index to estimate the contour quality in theChinese code for construction on tunnel of railway [30] andthe code for construction technical specifications forhighway tunnels [31] Other factors including the area andvolume of overunderbreaks are neglected in practical ap-plications However effects of these factors on the qualityestimation of tunnel contour cannot be ignored in manycases For rational understanding and assessing the con-struction safety and time therefore development of acomprehensive evaluation method for the quantitative as-sessment of the total quality of a tunnel contour after smoothblasting is very promising in DampB tunnelling

is paper targets developing a quantitative evaluationapproach with multiple indices to fully understand the totalquality of tunnel contour based on the projection pursuitdynamic cluster (PPDC) method Both of the engineeringpractical experiences site measurements technical stan-dards expertsrsquo knowledge and relevant literatures are in-cluded in the proposed evaluation approach e influencesof overunderexcavations in 3 dimensions including thedepth area and volume are all counted into the assessmentto fully understand the total quality of tunnel contour aftersmooth blasting

2 Principles of the Quality Evaluation

21 Selection of Evaluation Indices e indices representingthe quality of tunnel contour might differ from each otheraccording to the primary purpose of the evaluation As isknown it is often impossible to involve all factors into theanalysis of complicated problem Appropriate determina-tion of the evaluation indices virtually plays a very importantrole in the reliability of the assessment Identification of theproper indices is the first but also themost important step Inthis work determining the indices follows the followingprinciples high correlation to the contour quality beingapplicable to be obtained considering both qualitative andquantitative factors and being easy to use

22 Structure of theMultiple Indices System In order to fullyunderstand the total quality of the contour the multipleindices system should be established Following the conceptof the analytic hierarchy process (AHP) method for



3 Data Collection

















Objective level

Criterial level


index C11


Evaluation index

C21


Evaluation index

Ck1


helliphelliphellip




05

1015202530354045505560657075

Indi

cato

r ado

ptio

n ra

te (

)


(a)




0

2

4

6In

dica

tor a

dopt

ion

rate

()

(b)

Figure 2 Continued







00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(c)



00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(d)




0

2

4

6

8

10

Indi

cato

r ado

ptio

n ra

te (

)

(e)







Indi

cato

r ado

ptio

nrat

e (

)




0

10

20

30

40

50

60

70

80

90


Indi

cato

r ado

ptio

nrat

e (

)




0

20

40

60

80

100





0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)






x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References















































3 Data Collection

















Objective level

Criterial level


index C11


Evaluation index

C21


Evaluation index

Ck1


helliphelliphellip




05

1015202530354045505560657075

Indi

cato

r ado

ptio

n ra

te (

)


(a)




0

2

4

6In

dica

tor a

dopt

ion

rate

()

(b)

Figure 2 Continued







00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(c)



00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(d)




0

2

4

6

8

10

Indi

cato

r ado

ptio

n ra

te (

)

(e)







Indi

cato

r ado

ptio

nrat

e (

)




0

10

20

30

40

50

60

70

80

90


Indi

cato

r ado

ptio

nrat

e (

)




0

20

40

60

80

100





0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)






x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References

















































Objective level

Criterial level


index C11


Evaluation index

C21


Evaluation index

Ck1


helliphelliphellip




05

1015202530354045505560657075

Indi

cato

r ado

ptio

n ra

te (

)


(a)




0

2

4

6In

dica

tor a

dopt

ion

rate

()

(b)

Figure 2 Continued







00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(c)



00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(d)




0

2

4

6

8

10

Indi

cato

r ado

ptio

n ra

te (

)

(e)







Indi

cato

r ado

ptio

nrat

e (

)




0

10

20

30

40

50

60

70

80

90


Indi

cato

r ado

ptio

nrat

e (

)




0

20

40

60

80

100





0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)






x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References



















































00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(c)



00

05

10

15

20

25

30

Indi

cato

r ado

ptio

n ra

te (

)


(d)




0

2

4

6

8

10

Indi

cato

r ado

ptio

n ra

te (

)

(e)







Indi

cato

r ado

ptio

nrat

e (

)




0

10

20

30

40

50

60

70

80

90


Indi

cato

r ado

ptio

nrat

e (

)




0

20

40

60

80

100





0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)






x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References


















































Indi

cato

r ado

ptio

nrat

e (

)




0

10

20

30

40

50

60

70

80

90


Indi

cato

r ado

ptio

nrat

e (

)




0

20

40

60

80

100





0

10

20

30

40

50

60

70

Indi

cato

r ado

ptio

n ra

te (

)






x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References

















































x0(1)

1113936nk1 x0(k)n( 1113857

x0(2)

1113936nk1 x0(k)n( 1113857

x0(n)

1113936nk1 x0(k)n( 1113857

1113890 1113891

(1)


prime(n)1113858 1113859

xi(1)

1113936nk1 xi(k)n( 1113857

xi(2)

1113936nk1 xi(k)n( 1113857

xi(n)

1113936nk1 xi(k)n( 1113857

1113890 1113891(2)




1113868111386811138681113868 (3)


c0i 1113936

ni1 η0i(k)

n (4)











damage zone 50




X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References















































X TPT

+ E (5)






(6)













0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)






0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References

















































0

10

20

30

40

50

60

70

80

Indi

cato

r ado

ptio

n ra

te (

)









Indicator adoption

rate method










Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References



















































Index system

Point indices


Linear indices



Surface indices



Volumetric indices






















lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References



















































lowast(i j)



z(i) 1113944m

j1a(j)x(i j) i 1 2 n (9)



defined as follows


st 1113944

p

j1a2(j) 1 (11)


Sz

1113936


2

(n minus 1)

1113971

(12)

Dz 1113944n

i11113944

n



(13)




















zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References


















































zz Hz

nz

(14)





1113876 1113877 (16)

























6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References














































6 Application











Averageoverbreak

Maximumunderbreak


Area ofoverbreak

Areadeviationlowast

Overbreakrate

Volume ofoverbreak

























DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References


























































DK247+ 0335 DK247 + 0475 DK247+ 0495









7 Conclusions







Data Availability




Acknowledgments







References














































7 Conclusions







Data Availability




Acknowledgments







References















































References




























































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