FieldTestsontheAttenuationCharacteristicsoftheBlastAir...

Research ArticleField Tests on the Attenuation Characteristics of the Blast AirWaves in a Long Road Tunnel A Case Study

Yong Fang Yi-Lun Zou Jian Zhou Zhi-gang Yao Shuai Lei and Wenbo Yang

Key Laboratory of Transportation Tunnel Engineering Southwest Jiaotong University Ministry of Education Chengdu China

Correspondence should be addressed to Wenbo Yang yangwenbo1179hotmailcom

Received 30 December 2018 Revised 16 March 2019 Accepted 3 April 2019 Published 24 April 2019

Academic Editor M I Herreros

Copyright copy 2019 Yong Fang et al-is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

After an explosion occurs in a tunnel the blast waves take on diverse forms of attenuation in different regions when it propagatesalong the tunnel However the prediction of the overpressure decay laws proposed in previous studies has not taken into accountthe influence of the different regions in the tunnel-e present paper uses the example of theMicangshan highway tunnel in Chinaand considers many factors that influence the propagation of the blast waves by dividing the tunnel into four zones -e papermodifies the decay equation proposed by Smith and applies it to the Micangshan highway tunnel in China -e decay equationsare different in different zones Field tests in this tunnel show that the modified equation is more suitable to describe theattenuation of the blast waves in the tunnel than the original equation

1 Introduction

-e drilling and blasting method is widely used in theexcavation of mountain tunnels During the advancing of atunnel there are two major problems due to the blastingvibration and shock wave (or air blast wave) Blast-in-duced vibration affects the stability of surrounding rocksand threatens the safety of neighboring buildings orstructures Numerous studies have been published on theresponses and damage to structures subjected to blast-induced vibration [1ndash4] Most of the explosive energy isconsumed in breaking the rocks causing the vibration andthrowing out the fragments A small remaining part of theenergy enters the surrounding air through the gapscompresses the air and creates the air blast waves [5 6]-e air blast waves threaten the safety of personnel andequipment in the tunnel [5 7 8] During the blastingoperation the personnel and properties have to beevacuated far away from the advancing face to avoid thethreat of the air blast waves -is evacuation and sub-sequent recovery takes a lot of time that is unendurableespecially for an extralong tunnel Hence it is very im-portant to determine the safe distance from the explosionfor the properties and personnel

Many studies of the propagation of air blast waves in-duced by the detonation of explosive charges have been donein free fields where the blast waves propagate freely in theatmosphere Baker et al [7] Brode [9] and Henrych [10]proposed general fitting laws to describe the relationshipbetween the maximum overpressure peak and the distance tothe explosive charge Ishikawa and Beppu [11] summarizedsome lessons about the negative air blast waves of explosionsover structures from explosive tests Using the ComputationalFluid Dynamics (CFD) method Chapman et al [12] simu-lated the propagation of an air blast wave in a two-di-mensional free field Wu and Hao [13] built a 3D model tosimulate the effects of an explosion on neighboring structuresconsidering the ground vibration and air blast wave at thesame time Casal and Salla [14] and Genova et al [15] alsodefined the peak intensity of the boiling liquid expandingvapour explosion (BLEVE) blast wave in a free field

-e propagation of blast waves in a free field is differentfrom that in a tunnel which is a confined environmentAlthough the negative effects of the air blast wave onstructures have been studied for many years there are notmany studies set in underground environments Smith et al[16] described a series of scaled model tests of blasting loadingand suggested that scaled models can provide a useful means

HindawiShock and VibrationVolume 2019 Article ID 9693524 11 pageshttpsdoiorg10115520199693524

of obtaining blast loading data for complex structures Smithet al [17] also conducted a scaled model test of the blast wavepropagation along straight tunnels and revealed that theroughness of the tunnel walls has significant effects on theblast wave propagation Li and Zheng [18] conducted scaledmodel tests to investigate the air blast propagation down thetunnel and developed empirical equations to predict the in-tunnel air blast pressure induced by detonations that areexternal internal and at the entrance

Recently the CFD method has been widely used toinvestigate the propagation of air blast waves induced bydense explosives in confined complex geometries [19ndash22]Using a numerical method Liu et al [23] investigated blastwave propagation near the explosion site inside a tunnelBenselama et al [24] and Uystepruyst and Monnoyer [25]revealed that the air blast waves in a tunnel have two pat-terns a free-field overpressure decay pattern near the ex-plosion site and a quasi-one-dimensional pattern far fromthe explosion -ey proposed a correlation law by a nu-merical study to define the transition distance according tothe explosive charge and the geometry of the propagatingdomain Pennetier et al [26] conducted a scaled model testand numerical simulation of blast waves in tunnels andfound that the data of the experimental tests fit well with thenumerical simulation In field tests Rodrıguez et al [6 27]developed a semiempirical model to predict the air wavepressure and sound level outside a tunnel due to the blastinginside A series of explosive detonation experiments wasconducted in NIOSHrsquos Bruceton and Lake Lynn Experi-mental Mines to evaluate the blast wave propagation inunderground mines and a simple scaling relationship of thepeak overpressure with the explosive charge and thepropagation domain was proposed [28 29]

Nevertheless there are little published experimental dataabout blast wave propagation in tunnels -is paper intendsto use field test data to determine a simple law to predict theoverpressure decay in a long tunnel -is has great im-portance to prevent the threat of blast waves in a long tunnelfor personnel and properties

2 Blast Wave Propagation in a Tunnel

Near the explosion charge the blast waves propagate freely inthe atmosphere as shown in Figure 1(a) -e most commonfree-field decay law proposed by Henrych [10] can be used torelate the maximum overpressure peak (in Pa) Δp to thedistance from the explosive charge which is shown as follows

Δp 106 times

14072Z

+0554

Z2 minus00357

Z3 +0000625

Z4 if 005leZle 03

06194Zminus00326

Z2 +02132

Z3 if 03leZle 1

00662Z

+0405

Z2 +03288

Z3 if 1leZle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Z xQ3

radic (2)

where Q is the explosive charge (in kg) and x is the distancefrom the explosion point to the measurement point (in m)However in the tunnel far away from the explosion the blastwaves can be considered to propagate in a quasi-one-di-mensional pattern as shown in Figure 1(b) Benselama et al[24] proposed a fitting law to distinguish the discontinuitylocation ZTrans where the blast wave propagation patterntransforms into

ZTrans 00509

(α100)139 (3)

where the parameter α represents the ratio of the explosivediameter to the tunnelrsquos hydraulic diameter If the parameterZ in equation (1) is bigger than ZTrans the blast waves in thetunnel can be considered to propagate in a quasi-one-di-mensional pattern as shown in Figure 1(c)

-e following empirical law can also be used to predictthe overpressure decay in the tunnel

Δp a middotm middot Q

S middot x+ b middot

m middot Q

S middot x

1113970

1113888 1113889 middot eminusn(xd)

(4)

where Δp is the maximum overpressure (in Pa) at a mea-surement point Q is the explosive charge per delay (in kg) S

is the area of cross section of the tunnel (in m2) x is thedistance from the explosion point to the measurement point(in m) and d is the equivalent diameter of the cross sectionof the tunnel (in m)-e parameters a b m and n have to beestimated by experience Kuzyk [30] suggested the param-eters a and b to be 2900000 and 730000 respectively whilethe Chinese governmentrsquos Enforceable Handbook of SafetyRegulations for Blasting [5] suggested the parameters a and bto be 3270000 and 780000 respectively -e parameter mrepresents the amount of explosive energy converted to theair blast waves and the parameter n represents the atten-uation of the maximum overpressure with the distance xRodrıguez et al [6 27] regarded m as a constant value 04and n as a variate less than 015 and changing with thedistance x However in the Enforceable Handbook of SafetyRegulations for Blasting [5] the parameterm is suggested tobe 005sim01 for drilling and blasting to advance the tunneland the parameter n represents the surface roughness co-efficient of the wall

Smith and Sapko [29] investigated the blast wavepropagation in underground mine entries by experimentand put forward the simple decay relationship between themaximum peak overpressure Δp and the pentolite explosivecharge Q and the volume of the propagation domain V

Δp A middotQ

V1113874 1113875

β (5)

By fitting the experimental data to the equation the pa-rameter A and the exponential β were suggested to be 702800and 0514 respectively [29]-is simple correlation for a singleentry fits the data quite well for experimental overpressuresfrom 5 to 50 kPa Silvestrini et al [31] adopted the energyconcentration factor (ECF) to extend the decay laws foropen-space detonation of a TNT charge to one-dimensional

2 Shock and Vibration

propagation in a tunnel with one closed end and suggested theparameter A and the exponential β to be 743538 and 051

However equation (5) has to be modified because theexplosive energy cannot be all converted to the air blastwaves and the difference of the kind of explosive Referringto equation (4) proposed by Kuzyk [30] the parameter m isadded to the numerator -e parameter λ is the TNTequivalent coefficient -e modified equation is as follows

Δp A middotm middot λ middot Q

V1113888 1113889

β

(6)

where the parameter m represents the amount of explosiveenergy converted to the air blast wave and the exponential βrepresents the attenuation of the maximum overpressure-e parameter λ has been found in previous studies to be 06for the emulsion explosive commonly used in tunneling[32] -e parameter m was regarded by Rodrıguez et al as aconstant value 04 [6 27] However the exponential β ismore difficult to determine because the heading face blastingand blast wave propagation are more complicated in a realtunnel -is paper intends to determine the exponential βwhen equation (6) is used to predict the overpressure in-duced by blasting in a road tunnel

3 The Attenuation of Overpressure in aRoad Tunnel

-e investigation of the overpressure attenuation was car-ried out in the Micangshan highway tunnel in WesternChina -e tunnel is 138 km in length and was constructedby the New Austrian tunneling method (NATM) Figure 2

shows the profiles of the Micangshan highway tunnel closeto the explosion site According to the change of the crosssection roughness of the wall and the obstacles in thetunnel the propagation area of the blast waves in a roadtunnel can be divided into four zones In Zone I the sec-ondary lining has not been casted -e tunnel has rough anduneven walls and the area of the cross section is about7798m2 In Zone II the secondary lining is being casted-e cross-sectional area and wall roughness change sud-denly -ere are much equipment placed in Zone II such asthe framework of the secondary lining casting loaders anddrilling jumbo evacuated from the heading face -eseequipment also affect the blast wave propagation and causeadditional attenuation of the overpressure In Zone III thesecondary lining has been casted and the area of the crosssection is about 625m2 Generally the overpressure has alight attenuation in this area as the secondary lining has asmooth flat surface [17] Zone IV has an enlarged crosssection which is generally used in a long road tunnel as anemergency parking strip In this area the cross-sectionalarea increases from 625m2 to 841m2 then decreases backto 625m2 Some equipment like air compressors andventilators are placed in Zone IV In the middle of Zone IVthere is a cross aisle leading to another twin tunnel Not onlythe change of the cross-sectional area but also the branch ofthe tunnel causes great attenuation of the overpressure inthis zone [29] Behind the Zone IV the form of cross sectionis the repetition of Zone III and Zone IV

-e attenuation of overpressure in the tunnel comes fromresistance during the propagation -e exponential β whichrepresents the attenuation of the overpressure in equations (5)and (6) is related to many factors such as the change of cross-

Explosivecharge

(a)

(b)

ZTrans

Z (mkg13)ΔP

P0

0 2 8 106410ndash1

100

101

102

103

Free-field decay One-dimensional decay

Free-field propagationOne-dimensional propagation

(c)

Figure 1 Blast wave propagation in a tunnel (a) propagation near the face (b) propagation far away from the face and (c) the decay ofoverpressure along the tunnel [24 30]

Shock and Vibration 3

sectional area roughness of the wall and the obstacles in thetunnel Consequently a constant value of the exponential βcannot represent all the conditions along the road tunnelConsidering these influence factors the attenuation of over-pressure along the road tunnel can be classified as four types

β1 attenuation in the tunnel with primary support ieZone I where the tunnel has larger profiles and roughwallsβ2 attenuation in Zone II where the cross sectionshrinks suddenly as the secondary lining is casted Itcan also reflect the influence of the equipment placed inthis area on the blast wave propagationβ3 attenuation in the tunnel with secondary liningsuch as Zone III where the tunnel has smaller profilesand flat wallsβ4 attenuation in Zone IV where the tunnel has anenlarged cross section It can also reflect the influenceof the equipment and the cross aisle on the blast wavepropagation

-e overpressure along the tunnel can be predicted usingthese attenuation parameters -e overpressure in Zone Ican be predicted by equation (6) after the parameters aredetermined At the end of Zone I or the beginning of Zone IIthe overpressure can be expressed as

ΔpI A middotm middot λ middot Q

VI1113888 1113889

β1 (7)

where VI is the whole volume of Zone I Similarly theoverpressure at the end of Zone II or the beginning of ZoneIII can be expressed as

ΔpII ΔpI middotVI

VI + VII1113888 1113889

β2 (8)

where VII is the whole volume of Zone II -en the over-pressure in Zone III can be expressed by the attenuation ofthe overpressure at the beginning of Zone III as

Δp ΔpII middotVI + VII

V1113874 1113875

β3 (9)

where V is the whole volume of the propagation domainEquation (9) can be rewritten as

Δp A middot (m middot λ middot Q)β1 middot

1VI

1113888 1113889

β1middot

VI

VI + VII1113888 1113889

β2middot

VI + VII

V1113874 1113875

β3

(10)-e overpressure in Zone IV can be expressed as


1VI

1113888 1113889

β1 VI

VI + VII1113888 1113889

β2

middotVI + VII

VI + VII + VIII1113888 1113889

β3 VI + VII + VIII

V1113874 1113875

β4

(11)

If β1 β2 β3 and β4 are the same equation (11) de-generates to equation (6)

4 Blasting Scheme Used in the MicangshanHighway Tunnel

-e field tests on the overpressure in a tunnel induced by theblasting were carried out in the Micangshan highway tunnelIf the surrounding rocks of the tunnel were stable full-faceexcavation which has a cross-sectional area of 84m2 (ie1256m in width and 87m in height) was applied Figure 3shows one of the blasting schemes for the full-face excavationof the tunnel Four kinds of holes are drilled for the blastingcut holes stope holes bottom holes and contour holes -ecut was used to break out the confinement of the face Twotypes of cut are commonly used in tunneling cuts with angledholes (ie conical cut wedge cut and fan cut) and withparallel holes (parallel cuts) In this case the blasting schemefor full-face excavation adopted the parallel cut After theinitial cut creates a second free surface the stope holes can beblasted at burden into the cut -e bottom holes and the

2m

15m

Testpoint

Primary support

750

1176

Cross-sectional areaS 7798m2

Cross-sectional areaL 3435m

2m

15m

Test point

Primary support

715

1106



Secondary liner

Heading face

Explosion

Zone I Zone II Zone III Zone IV

Framework oflining casting Secondary lining

Cross aisle

1-1 2-2

1

1

2

2

3

3

4 4

4-43-3

Primary supportSecondary liner

Cross-sectional areaS 8414msup2


783

1381 550

600

Cross-sectionalarea

S 2912m2

Cross-sectionalarea

L 1522m


The repetition of Zone III and Zone IV80m~90m 40~50m Cannot determined 40m

Figure 2 Profiles of the Micangshan highway tunnel near the explosion site


contour holes have the task of producing the most exactprofile possible by smooth blasting -e diameters of all theholes are 50mm and the depths of the holes range from 12mto 35m depending on the surrounding rock conditionsHence the hole depth and its corresponding explosive chargechanges frequently in the tunneling

-e emulsion explosive and delay detonators are used inthe blasting -e emulsion explosive has a good water-re-sistant performance and is widely used in tunneling Mil-lisecond detonators are also widely used in tunnel blastingbecause they normally give enough time for the throwing ofthe fragments and also favorably influence the individualblasts through the overlapping of the ground vibrations andthe effect of the gas pressure on the subsequent chargesTable 1 shows the delays of all the detonator series Howeverin some cases of small charges not all the stope holes aredrilled or charged and some detonator series are empty

A safe distance of blasting operation is necessary inpractical tunneling During the blasting operation the spacein a tunnel can be divided into three parts for the consid-eration of safety forbidden area injury area and noise area-e forbidden area is close to the explosive charge where theoverpressure and rock fragments induced by the blastingmight cause personal injury and property damage All peopleand equipment are forbidden to enter this area -e spacefrom the site of the blasting operation to the site where theoverpressure is 2 kPa is classified as the injury area Non-blasting operation personnel must be evacuated out of thisarea -e noise area is far away from the explosive site wherethe overpressure cannot cause personal injury Hence per-sonnel can stay in this area and need not move out of thetunnel It is necessary to determine the border of the injuryarea accurately for a long tunnel in order to ensure personnelsafety and save time in the construction process

5 Testing Program

-e following field tests were carried out mainly in the injuryarea to determine the attenuation parameters β1 β2 β3and β4 For each blasting operation the volume of thepropagation domain V (in m3) and the overpressure Δp (inKPa) were recorded Generally two sensors and two ac-quisition instruments were used at the same time for onetest as shown in Figure 4 V1 and V2 are the volume of thepropagation domain at the sites of sensor 1 and sensor 2-eacquisition instrument (type Blast-PRO manufacturerTytest Co LTD Chengdu China) has two channels with asampling rate 10 ksim4M -e overpressure sensor (modelno PCB 113B28 SN manufacturer PCB Piezotronics IncUS) has a measurement range of 3447 kPa for plusmn5V outputand 6894 kPa for plusmn10V output a sensitivity of 145mVkPa and a resolution of 0007 kPa -e testing scheme isshown in Figure 4

-e overpressure sensors and acquisition instrumentsare placed near the side wall of the tunnel and no obstaclesare nearby Figure 5 shows the field tests in the Micangshantunnel

-e distance between the two sensors has to be largeenough to acquire the whole attenuation And then the

attenuation of the overpressure from the location of sensor 1to the location of sensor 2 can be calculated As is shown inFigure 4 the distance between the two sensors should belonger than 50m to avoid the interference For a certainblasting operation the overpressures Δp1 and Δp2 at the sitesof sensor 1 and sensor 2 can be predicted by equation (6)and the attenuation of the overpressure can be drawn

Δp2

Δp1

V1

V21113888 1113889

β

(12)

where V1 and V2 can be calculated by the product of the areaof the cross section and the distance from the face to theacquisition instrument

6 Testing Results

Figure 6 shows the waveforms acquired by the sensors after ablast -e blast waveforms have its own characteristics It isdifferent from the waves produced by other causes such astunnel vehicle load and metro train [33] Each peak reflectsthe explosion of a detonator series Generally cut holes havethe maximum charge-e cut holes blasted first and inducedthe strongest overpressure -e stope holes are followed bythe cut holes -e bottom holes and the contour holes hadthe minimum charge and blasted last Hence the maximumpeak of the overpressure is decided by the charge of the cutholes In order to control the variables we take the maxi-mum peak of the overpressure as Δp in the test results

-e test results are shown in Table 2 Tests were done fivetimes in each zone and two sensors are placed at a distance ofparameter l in each test -e length of Zone I is about80sim90m-e parameter l in Zone I is 50m-e approximatelength of Zone II is 40sim50m In the test to measure the wholeattenuation in Zone II the sensor 1 was placed 25meters infront of Zone II And the sensor 2 was placed 25metersbehind Zone II So the parameter l in Zone II is 100m -elength of Zone III is extremely long and the two sensors canboth be placed in Zone III -e parameter l in Zone III is200m As for Zone IV the length of Zone IV is about 40mBecause the effect of attenuation in Zone III is not obvious thesensors could be placed in Zone III to acquire the wholeattenuation in Zone IV During the field testing the sensor 1was placed 55m in front of Zone IV -e sensor 2 was placed55m behind Zone IV So the parameter l in Zone IV is 150m-e parameter L1 represents the distance from the work faceto the front sensor at that test moment -e parameter L2represents the distance from the work face to the latter sensorat that test moment In terms of equation (12) every testlocation could provide a parameter β

After averaging the results from the five tests in eachzone the results are as follows parameter β1 is 0515 forZone I parameter β2 is 266 for Zone II parameter β3 is 029for Zone III and parameter β4 is 445 for Zone IV-e orderof attenuation of overpressure in the four zones is ZoneIVgtZone IIgtZone IgtZone III

-e parameter β is related to the change of cross-sec-tional area roughness of the wall and the obstacles in thetunnel -e tunnel has rough and uneven wall in Zone I and


has smooth surface in Zone III By comparing with Zone Iand Zone III it can be seen that the rougher the wall is thegreater the attenuation parameter β is In Zone II there aremany working machines placed such as the framework of thesecondary lining casting loaders By comparing with Zone Iand Zone II it can be seen that the attenuation parameter β isgreater when there are obstacles in the tunnel In Zone IV the

tunnel has an enlarged cross section and cross aisle Bycomparing with Zone III and Zone IV it can be seen that theattenuation parameter β is greater when there is change of thecross-sectional area and the branch of the tunnel

Figure 7 shows the correlation of the overpressure inZone I and Zone III between the tested values and thecalculated values In Zone I the modified equation is the

1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm

Figure 3 Typical blasting scheme for full-face excavation

Table 1 Delays with different detonator seriesDetonator series 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Delay (ms) 0 25 50 75 110 150 200 250 310 380 460 550 650 760 880

Heading face

Explosion

Shock wave

vSensor 1 Sensor 2Acquisition

instrument 1Acquisition

instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)

Figure 4 Testing scheme


(a) (b)

Figure 5 Photos of the testing

Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued


same as the original equation According to the test resultsthe exponential β1 is 0515 in the modified equation and theexponential β is 0514 in the original equation So the fit linesare basically coincident the R2 coefficients for the modifiedequation and the original equation are 06698 and 06699respectively In Zone III the R2 coefficients for the modifiedequation and the original equation are 05474 and 04766respectively -e modified equation takes resistance factorsinto account and uses different exponentials to indicate thesefactors -erefore the R2 coefficient of the modified equationis larger than that of the original equation

Comparing the two R2 coefficients of the originalequation and the modified equation indicates the necessityof dividing the tunnel into different zones to research theattenuation of the overpressure in the tunnel

After taking the logarithm of equations (7) and (10) theoverpressure ln Δp can be calculated by the two variablesexplosive charge Q and volume V Figure 8 shows the re-lationship of the planes that pass the overpressure ln Δp InZone I the two planes that pass ln Δp as calculated by the

modified equation and original equation are coincident InZone III due to the impact of β2 and β3 it can be seen thatthe slope of the plane which passes ln Δp calculated by themodified equation has changed

7 Conclusion and Discussion

Using the equation Δp A middot (QV)β put forward by Smithand Sapko [29] this paper considers many factors such asthe change of cross-sectional area roughness of the wall andobstacles in the tunnel and modifies the equation accord-ingly When blast waves propagate in the tunnel the tunnelcan be divided into several zones -e degree of attenuationof overpressure in each zone is distinct and a constant valueof the exponential β cannot represent all the conditionsalong the tunnel -erefore there are different attenuationequations and exponential β in each zone

-is theory is applied in the Micangshan highway tunnelin China-e tunnel is divided into four zones In Zone I theoverpressure can be expressed as Δp A middot (m middot λ middot QV)β1

Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)

Figure 6 Shock waves test waveform (a) Zone I (b) Zone II (c) Zone III (d) Zone IV

Table 2 Overpressure in the tunnel induced by blasting

Zone no Test no Δp1 (kPa) Δp2 (kPa) V1 (m3) V2 (m3) l (m) L1 (m) L2 (m) Exponential β Mean of β

Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335


where V is the whole volume of the propagation domain andβ1 is the attenuation exponential in Zone I In Zone IIthe overpressure can be expressed as Δp A middot (m middot λmiddot

QVI)β1 middot (VIV)β2 where VI is the whole volume of Zone I

In Zone III the overpressure can be expressed as Δp Amiddot

(m middot λ middot QVI)β1 middot (VI(VI + VII))

β2 middot ((VI + VII)V)β3 whereVII is the whole volume of Zone II In Zone IV the over-pressure can be expressed as Δp A middot (m middot λ middot Q)β1 middot (1VI)

β1 middot

(VI(VI + VII))β2 middot ((VI + VII)(VI + VII + VIII))

β3((VI + VII +

VIII)V)β4 where VIII is the whole volume of Zone III

y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)

Original equationModified equation

(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)

Figure 7 Correlation of overpressure between calculated values and tested values (a) Zone I (b) Zone III

ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28

Modified zone IIIOriginal zoneModified zone I

Figure 8 ln Δp calculated by the modified equation and original equation in Zone I and Zone III


From the field tests about overpressure in the Micang-shan highway tunnel and the calculation of volume theexponential β can be determined as follows β1 0515β2 266 β3 029 and β4 445 In Zone I the R2 co-efficients are almost the same between the modified equationand the original equation for the tested values and calcu-lation values while in Zone III the R2 coefficient of themodified equation is better than that of the originalequation

However when the modified equation is applied fromZone I to Zone III it reflects the change of slope in the planesthat pass the overpressure -e equation could be modifiedfurther at a later time to reflect the change of the slope in astraight line from Zone I to Zone III

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 they have no conflicts of interest

Acknowledgments

-is research was funded by the National Key Research andDevelopment Program of China (no 2016YFC0802205) andthe National Natural Science Foundation of China (nos51578460 and 51678499)

References

[1] R P Dhakal and T-C Pan ldquoResponse characteristics ofstructures subjected to blasting-induced ground motionrdquoInternational Journal of Impact Engineering vol 28 no 8pp 813ndash828 2003

[2] L Tian and Z-X Li ldquoDynamic response analysis of a buildingstructure subjected to ground shock from a tunnel explosionrdquoInternational Journal of Impact Engineering vol 35 no 10pp 1164ndash1178 2008

[3] J H Yang W B Lu Q H Jiang C Yao and C B ZhouldquoFrequency comparison of blast-induced vibration per delayfor the full-face millisecond delay blasting in undergroundopening excavationrdquo Tunnelling and Underground SpaceTechnology vol 51 pp 189ndash201 2016

[4] L B Jayasinghe H Y Zhou A T C Goh Z Y Zhao andY L Gui ldquoPile response subjected to rock blasting inducedground vibration near soil-rock interfacerdquo Computers andGeotechnics vol 82 pp 1ndash15 2017

[5] X G Wang Y L Yu and D Z Liu Enforceable Handbook ofSafety Regulations for Blasting China Communication PressBeijing China 2004

[6] R Rodrıguez J Torantildeo and M Menendez ldquoPrediction of theairblast wave effects near a tunnel advanced by drilling andblastingrdquo Tunnelling and Underground Space Technologyvol 22 no 3 pp 241ndash251 2007

[7] W E Baker P A Cox P S Westine J J Kulesz andR A Strehlow ldquoExplosion hazards and evaluationrdquo inFundamental Studies in Engineering Elsevier New York NYUSA 1983

[8] Y Fang J Fan B Kenneally and M Mooney ldquoAir flowbehavior and gas dispersion in the recirculation ventilationsystem of a twin-tunnel constructionrdquo Tunnelling and Un-derground Space Technology vol 58 pp 30ndash39 2016

[9] H L Brode ldquoBlast wave from a spherical chargerdquo Physics ofFluids vol 2 no 2 pp 217ndash229 1959

[10] J Henrych 0e Dynamics of Explosion and Its Use ElsevierPress Amsterdam Netherlands 1979

[11] N Ishikawa and M Beppu ldquoLessons from past explosive testson protective structures in Japanrdquo International Journal ofImpact Engineering vol 34 no 9 pp 1535ndash1545 2007

[12] T C Chapman T A Rose and P D Smith ldquoBlast wavesimulation using AUTODYN2D a parametric studyrdquo In-ternational Journal of Impact Engineering vol 16 no 5-6pp 777ndash787 1995

[13] C Wu and H Hao ldquoNumerical simulation of structuralresponse and damage to simultaneous ground shock andairblast loadsrdquo International Journal of Impact Engineeringvol 34 no 3 pp 556ndash572 2007

[14] J Casal and J M Salla ldquoUsing liquid superheating energy for aquick estimation of overpressure in BLEVEs and similarexplosionsrdquo Journal of Hazardous Materials vol 137 no 3pp 1321ndash1327 2006

[15] B Genova M Silvestrini and F J Leon Trujillo ldquoEvaluationof the blast-wave overpressure and fragments initial velocityfor a BLEVE event via empirical correlations derived by asimplified model of released energyrdquo Journal of Loss Pre-vention in the Process Industries vol 21 no 1 pp 110ndash1172008

[16] P D Smith G C Mays T A Rose K G Teo andB J Roberts ldquoSmall scale models of complex geometry forblast overpressure assessmentrdquo International Journal of Im-pact Engineering vol 12 no 3 pp 345ndash360 1992

[17] P D Smith P Vismeg L C Teo and L Tingey ldquoBlast wavetransmission along rough-walled tunnelsrdquo InternationalJournal of Impact Engineering vol 21 no 6 pp 419ndash4321998

[18] X Li and Y Zheng ldquoIn-tunnel blast pressure empiricalequations for detonations external internal and at the tunnelentrancerdquo Transactions of Tianjin University vol 12pp 177ndash181 2006

[19] J M Powers and H Krier ldquoAttenuation of blast waves whendetonating explosives inside barriersrdquo Journal of HazardousMaterials vol 13 no 2 pp 121ndash133 1986

[20] T Huld G Peter and H Stadtke ldquoNumerical simulation ofexplosion phenomena in industrial environmentsrdquo Journal ofHazardous Materials vol 46 no 2-3 pp 185ndash195 1996

[21] F Rigas and S Sklavounos ldquoExperimentally validated 3-Dsimulation of shock waves generated by dense explosives inconfined complex geometriesrdquo Journal of Hazardous Mate-rials vol 121 no 1ndash3 pp 23ndash30 2005

[22] A M Benselama M J-P William-Louis and F MonnoyerldquoA 1Dndash3D mixed method for the numerical simulation ofblast waves in confined geometriesrdquo Journal of ComputationalPhysics vol 228 no 18 pp 6796ndash6810 2009

[23] J Liu Q Yan and J Wu ldquoAnalysis of blast wave propagationinside tunnelrdquo Transactions of Tianjin University vol 14no 5 pp 358ndash362 2008

[24] A M Benselama M J-P William-Louis F Monnoyer andC Proust ldquoA numerical study of the evolution of the blastwave shape in tunnelsrdquo Journal of Hazardous Materialsvol 181 no 1ndash3 pp 609ndash616 2010

[25] D Uystepruyst and F Monnoyer ldquoA numerical study of theevolution of the blast wave shape in rectangular tunnelsrdquo


Journal of Loss Prevention in the Process Industries vol 34pp 225ndash231 2015

[26] O Pennetier M William-Louis and A Langlet ldquoNumericaland reduced-scale experimental investigation of blast waveshape in underground transportation infrastructurerdquo ProcessSafety and Environmental Protection vol 94 pp 96ndash1042015

[27] R Rodrıguez C Lombardıa and S Torno ldquoPrediction of theair wave due to blasting inside tunnels approximation to alsquophonometric curversquordquo Tunnelling and Underground SpaceTechnology vol 25 no 4 pp 483ndash489 2010

[28] R J Mainiero and E S Weiss ldquoBlast wave propagation inunderground minesrdquo in Proceedings of the 11th AnnualSymposium on Explosives and Blasting Research NashvilleTN USA February 1995

[29] A C Smith andM J Sapko ldquoDetonation wave propagation inunderground mine entriesrdquo Journal of the Mine VentilationSociety of South Africa vol 58 pp 20ndash25 2005

[30] G W Kuzyk ldquoOverpressure generation and control in tunnelblastsrdquo in Proceedings of the Innovative Mine Design for the21st Century W F Bawen J F Archibald A A BalkemaEds p 527 Rotterdam Netherlands August 1993

[31] M Silvestrini B Genova and F J Leon Trujillo ldquoEnergyconcentration factor A simple concept for the prediction ofblast propagation in partially confined geometriesrdquo Journal ofLoss Prevention in the Process Industries vol 22 no 4pp 449ndash454 2009

[32] J Fan Q Fang Y Zhang and L Chen ldquoExperimental in-vestigation on the TNT equivalence coefficient of a rockemulsion explosiverdquo Acta Armamentarii vol 32 no 10pp 1243ndash1249 2011

[33] J Lai K Wang J Qiu F Niu J Wang and J Chen ldquoVi-bration response characteristics of the cross tunnel structurerdquoShock and Vibration vol 2016 Article ID 9524206 16 pages2016


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation


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wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

of obtaining blast loading data for complex structures Smithet al [17] also conducted a scaled model test of the blast wavepropagation along straight tunnels and revealed that theroughness of the tunnel walls has significant effects on theblast wave propagation Li and Zheng [18] conducted scaledmodel tests to investigate the air blast propagation down thetunnel and developed empirical equations to predict the in-tunnel air blast pressure induced by detonations that areexternal internal and at the entrance

Recently the CFD method has been widely used toinvestigate the propagation of air blast waves induced bydense explosives in confined complex geometries [19ndash22]Using a numerical method Liu et al [23] investigated blastwave propagation near the explosion site inside a tunnelBenselama et al [24] and Uystepruyst and Monnoyer [25]revealed that the air blast waves in a tunnel have two pat-terns a free-field overpressure decay pattern near the ex-plosion site and a quasi-one-dimensional pattern far fromthe explosion -ey proposed a correlation law by a nu-merical study to define the transition distance according tothe explosive charge and the geometry of the propagatingdomain Pennetier et al [26] conducted a scaled model testand numerical simulation of blast waves in tunnels andfound that the data of the experimental tests fit well with thenumerical simulation In field tests Rodrıguez et al [6 27]developed a semiempirical model to predict the air wavepressure and sound level outside a tunnel due to the blastinginside A series of explosive detonation experiments wasconducted in NIOSHrsquos Bruceton and Lake Lynn Experi-mental Mines to evaluate the blast wave propagation inunderground mines and a simple scaling relationship of thepeak overpressure with the explosive charge and thepropagation domain was proposed [28 29]

Nevertheless there are little published experimental dataabout blast wave propagation in tunnels -is paper intendsto use field test data to determine a simple law to predict theoverpressure decay in a long tunnel -is has great im-portance to prevent the threat of blast waves in a long tunnelfor personnel and properties

2 Blast Wave Propagation in a Tunnel

Near the explosion charge the blast waves propagate freely inthe atmosphere as shown in Figure 1(a) -e most commonfree-field decay law proposed by Henrych [10] can be used torelate the maximum overpressure peak (in Pa) Δp to thedistance from the explosive charge which is shown as follows

Δp 106 times

14072Z

+0554

Z2 minus00357

Z3 +0000625

Z4 if 005leZle 03

06194Zminus00326

Z2 +02132

Z3 if 03leZle 1

00662Z

+0405

Z2 +03288

Z3 if 1leZle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Z xQ3

radic (2)

where Q is the explosive charge (in kg) and x is the distancefrom the explosion point to the measurement point (in m)However in the tunnel far away from the explosion the blastwaves can be considered to propagate in a quasi-one-di-mensional pattern as shown in Figure 1(b) Benselama et al[24] proposed a fitting law to distinguish the discontinuitylocation ZTrans where the blast wave propagation patterntransforms into

ZTrans 00509

(α100)139 (3)

where the parameter α represents the ratio of the explosivediameter to the tunnelrsquos hydraulic diameter If the parameterZ in equation (1) is bigger than ZTrans the blast waves in thetunnel can be considered to propagate in a quasi-one-di-mensional pattern as shown in Figure 1(c)

-e following empirical law can also be used to predictthe overpressure decay in the tunnel

Δp a middotm middot Q

S middot x+ b middot

m middot Q

S middot x

1113970

1113888 1113889 middot eminusn(xd)

(4)

where Δp is the maximum overpressure (in Pa) at a mea-surement point Q is the explosive charge per delay (in kg) S

is the area of cross section of the tunnel (in m2) x is thedistance from the explosion point to the measurement point(in m) and d is the equivalent diameter of the cross sectionof the tunnel (in m)-e parameters a b m and n have to beestimated by experience Kuzyk [30] suggested the param-eters a and b to be 2900000 and 730000 respectively whilethe Chinese governmentrsquos Enforceable Handbook of SafetyRegulations for Blasting [5] suggested the parameters a and bto be 3270000 and 780000 respectively -e parameter mrepresents the amount of explosive energy converted to theair blast waves and the parameter n represents the atten-uation of the maximum overpressure with the distance xRodrıguez et al [6 27] regarded m as a constant value 04and n as a variate less than 015 and changing with thedistance x However in the Enforceable Handbook of SafetyRegulations for Blasting [5] the parameterm is suggested tobe 005sim01 for drilling and blasting to advance the tunneland the parameter n represents the surface roughness co-efficient of the wall

Smith and Sapko [29] investigated the blast wavepropagation in underground mine entries by experimentand put forward the simple decay relationship between themaximum peak overpressure Δp and the pentolite explosivecharge Q and the volume of the propagation domain V

Δp A middotQ

V1113874 1113875

β (5)

By fitting the experimental data to the equation the pa-rameter A and the exponential β were suggested to be 702800and 0514 respectively [29]-is simple correlation for a singleentry fits the data quite well for experimental overpressuresfrom 5 to 50 kPa Silvestrini et al [31] adopted the energyconcentration factor (ECF) to extend the decay laws foropen-space detonation of a TNT charge to one-dimensional





V1113888 1113889

β

(6)






Explosivecharge

(a)

(b)

ZTrans

Z (mkg13)ΔP

P0

0 2 8 106410ndash1

100

101

102

103



(c)







VI1113888 1113889

β1 (7)


ΔpII ΔpI middotVI

VI + VII1113888 1113889

β2 (8)



V1113874 1113875

β3 (9)



1VI

1113888 1113889

β1middot

VI

VI + VII1113888 1113889

β2middot

VI + VII

V1113874 1113875

β3



1VI

1113888 1113889

β1 VI

VI + VII1113888 1113889

β2

middotVI + VII

VI + VII + VIII1113888 1113889

β3 VI + VII + VIII

V1113874 1113875

β4

(11)




2m

15m

Testpoint

Primary support

750

1176



2m

15m

Test point

Primary support

715

1106



Secondary liner

Heading face

Explosion



Cross aisle

1-1 2-2

1

1

2

2

3

3

4 4

4-43-3




783

1381 550

600

Cross-sectionalarea

S 2912m2

Cross-sectionalarea

L 1522m








5 Testing Program





Δp2

Δp1

V1

V21113888 1113889

β

(12)


6 Testing Results









1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm



Heading face

Explosion

Shock wave



instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)



(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





V1113888 1113889

β

(6)






Explosivecharge

(a)

(b)

ZTrans

Z (mkg13)ΔP

P0

0 2 8 106410ndash1

100

101

102

103



(c)







VI1113888 1113889

β1 (7)


ΔpII ΔpI middotVI

VI + VII1113888 1113889

β2 (8)



V1113874 1113875

β3 (9)



1VI

1113888 1113889

β1middot

VI

VI + VII1113888 1113889

β2middot

VI + VII

V1113874 1113875

β3



1VI

1113888 1113889

β1 VI

VI + VII1113888 1113889

β2

middotVI + VII

VI + VII + VIII1113888 1113889

β3 VI + VII + VIII

V1113874 1113875

β4

(11)




2m

15m

Testpoint

Primary support

750

1176



2m

15m

Test point

Primary support

715

1106



Secondary liner

Heading face

Explosion



Cross aisle

1-1 2-2

1

1

2

2

3

3

4 4

4-43-3




783

1381 550

600

Cross-sectionalarea

S 2912m2

Cross-sectionalarea

L 1522m








5 Testing Program





Δp2

Δp1

V1

V21113888 1113889

β

(12)


6 Testing Results









1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm



Heading face

Explosion

Shock wave



instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)



(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






VI1113888 1113889

β1 (7)


ΔpII ΔpI middotVI

VI + VII1113888 1113889

β2 (8)



V1113874 1113875

β3 (9)



1VI

1113888 1113889

β1middot

VI

VI + VII1113888 1113889

β2middot

VI + VII

V1113874 1113875

β3



1VI

1113888 1113889

β1 VI

VI + VII1113888 1113889

β2

middotVI + VII

VI + VII + VIII1113888 1113889

β3 VI + VII + VIII

V1113874 1113875

β4

(11)




2m

15m

Testpoint

Primary support

750

1176



2m

15m

Test point

Primary support

715

1106



Secondary liner

Heading face

Explosion



Cross aisle

1-1 2-2

1

1

2

2

3

3

4 4

4-43-3




783

1381 550

600

Cross-sectionalarea

S 2912m2

Cross-sectionalarea

L 1522m








5 Testing Program





Δp2

Δp1

V1

V21113888 1113889

β

(12)


6 Testing Results









1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm



Heading face

Explosion

Shock wave



instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)



(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





5 Testing Program





Δp2

Δp1

V1

V21113888 1113889

β

(12)


6 Testing Results









1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm



Heading face

Explosion

Shock wave



instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)



(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1357911 1 3 5 7 9 11

9

9

11

13

15

11 50

50

8585

90

220

460

1256

870

50

Contour holes

Cut holes

60

Stope holes

40

Bottom holes

Unit cm



Heading face

Explosion

Shock wave



instrument 2

V1

l gt 50m

V2

(a)

2m

15m

Test point

Hei

ght

Width

(b)



(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


(a) (b)


Ove

rpre

ssur

e (kP

a)

Cut holes

0 200 400 600 800 1000Time (ms)

0

5

10

15

20

25

30

(a)

Cut holes

0 200 400 600 800Time (ms)

1210

86420O

verp

ress

ure (

kPa)

(b)

Time (ms)0 200 400 600 800

8

6

4

2

0

Cut holes

Ove

rpre

ssur

e (kP

a)

(c)

Figure 6 Continued









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Time (ms)

Cut holes

0 500 1000 1500 2000 2500

Ove

rpre

ssur

e (kP

a)

6543210

(d)




Zone I

1-1 26803 23762 14972 18871 50 192 242 0520

β1 05151-2 22388 19503 12555 16454 50 161 211 05091-3 36814 32094 12945 16844 50 166 216 05211-4 29190 25250 11697 15596 50 150 200 05041-5 25837 22587 13256 17156 50 170 220 0521

Zone II

2-1 19080 9849 20665 27381 100 265 365 2350

β2 2662-2 20105 10026 20899 27615 100 268 368 24972-3 16359 7720 21289 28005 100 273 373 27392-4 15908 6815 20275 26991 100 251 351 29632-5 18670 7921 18403 25120 100 236 336 2756

Zone III

3-1 8583 7881 25254 37760 200 350 550 0212

β3 0293-2 10494 9109 23373 35879 200 314 514 03303-3 8259 7350 24310 36816 200 327 527 02813-4 7595 6608 25126 37632 200 335 535 03453-5 9859 8828 26437 38943 200 363 563 0285

Zone IV

4-1 6456 1561 36614 49235 150 525 675 4793

β4 4454-2 5625 1655 36614 49235 150 525 675 41314-3 7259 1989 36880 49521 150 530 680 43934-4 5936 1289 31877 44498 150 550 700 45834-5 7853 2205 37067 49688 150 533 683 4335







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







β1 middot


β3((VI + VII +


y = 04095x + 77249

R2 = 06698

y = 04074x + 76509R2 = 06699

0

5000

10000

15000

20000

25000

12000 17000 22000 27000 32000 37000 42000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(a)

y = 10498x + 25025R2 = 04766

y = 0611x + 10995R2 = 05474

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000

Calc

ulat

ed v

alue

s (Pa

)

Tested values (Pa)


(b)


ln vln mλ

Q

ln ∆P

105

10

95

9

85

11 108 106 104 102 10 98 96 94 92 2 222426

28






Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


FieldTestsontheAttenuationCharacteristicsoftheBlastAir...

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