Research Article Experimental and Theoretical Study on ...(A) Time-history curve of vibration velocity (B) e power spectrum (c) Water-decoupling charging structure r = 12.747 F : Schedule

Research ArticleExperimental and Theoretical Study on Influence of DifferentCharging Structures on Blasting Vibration Energy

Wenbin Gu Zhenxiong Wang Jianghai Chen Jianqing Liu and Ming Lu

College of Field Engineering PLA University of Science and Technology Nanjing Jiangsu 210007 China

Correspondence should be addressed to Zhenxiong Wang wangzhenxiong70310126com

Received 20 April 2015 Revised 1 July 2015 Accepted 2 July 2015

Academic Editor Mario Terzo

Copyright copy 2015 Wenbin Gu et al This 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

As an important parameter in blasting design charging structure directly influences blasting effect Due to complex conditionsof this blasting and excavating engineering in Jiangsu China the authors carried out comparative researches with couplingstructure air-decoupling structure and water-decoupling structure After collecting comparing and analyzing produced signalson blasting vibration the authors summarized that when proportional distances are the same water-decoupling structure canreduce instantaneous energy of blasting vibration more effectively with more average rock fragmentation and less harm of dustFrom the perspective of impedance matching the present paper analyzed influence of charging structure on blasting vibrationenergy demonstrating that impedance matching relationship between explosive and rock changes because of different chargingstructures Through deducing relationship equation that meets the impedance matching of explosive and rock under differentcharging structures the research concludes that when blasting rocks with high impedance explosive with high impedance canbetter transmits blasting energy Besides when employing decoupling charging there exists a reasonable decoupling coefficienthelping realize impedance matching of explosive and rock

1 Introduction

In rock blasting of engineering energy that can be effectivelyused through explosion approximately accounts for 60sim70percent of the total explosive energy The rest may be used inexploding surrounding medium or produce harmful effectssuch as blasting vibration blasting shockwave blasting flyingblasting blasting soot blasting noise and blasting harmfulgas [1 2] thus it is of great significance to improve effectiveuse of blasting vibration energy According to damage char-acteristics of rock blasting with explosion as the center thereare crushed zone fracture zone and vibration zone [3] fromthe center to distant area and how to apply more explosiveenergy to fracture zone is key to engineering on rock blastingand excavating Parameters affecting geotechnical blastingresults are mainly on characteristics of rock and characteris-tics of explosive and blasting parameters and specific param-eters are over 20 categories When blasting environmentand explosive are determined charging structure plays apivotal role in influencing blasting energy transmissionWithdecoupling charging decoupling way between blasting hole

and blasting charging decoupling coefficient compressibledegree of decoupling medium (air or water) and initiatingposition of charging will largely affect transmitting process ofblasting energy Aimed at investigating charging structurersquosinfluence on blasting energy and effect scholars both at homeand abroad have carried out numerous researches on exper-iment and numerical simulation Day examined distributionof explosiversquos pressure on rock hole wall of air-decouplingwater-decoupling and coupling charging structures with thesame distance explosive conditions [4] Zong and Meng ana-lyzed effects of different charging structures of blasting holeon blasting energy and concluded that decoupling chargingstructure is beneficial under certain conditions [5] Chenet al conducted experiments on charging structurersquos influ-ence on blasting seismic effects and concluded attenuationlaw of particle vibration velocity and vibration frequency [6]Wang and Li carried out comparative numerical calculationon different radial coupling coefficient of water-decouplingcharging structure in infinite concrete medium and thencomprehensively analyzed relationships between damagezone distribution and pore wall pressure and acceleration as

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 248739 11 pageshttpdxdoiorg1011552015248739

2 Shock and Vibration

Measuring point 1

Measuring point 2

Measuring point 3

Blasting area

Blasting holeBlasting hole

middot middot middot


Figure 1 Schematic diagram and site layout of measuring points and blasting region

well as velocity and radial decoupling coefficient [7] Papeet al carried out finite-element analysis methods studied theexplosion phenomena and effects of explosions on structuressystematically and predicted the harmful effects of blastingwith different criterions [8 9] By evaluating charging struc-turersquos influence on blasting effect and blasting vibration ofnear area a large number of engineering practices tests andnumerical simulations on charging structure indicate thatdecoupling charging structure can enhance utilization rateof explosive energy and improve blasting effect Howeverin practical engineering different construction environmentrequires different charging structures yet there are notenough studies about analysis of energy transmission andblasting effects of different charging structures as well ascarried energy of blasting vibration of far region of blastingHence the present paper intends to explore relevant factorsto provide an insightful reference for further investigations

During rock excavation of engineering scene in Jiangsuprovince researchers adopted rock drilling blasting methodwhich is widely applied in geotechnical engineering Becauseof complexity of test scene and condition the test accord-ingly selected different blasting charging structuresThroughcollecting blasting vibration signals vibration speed wasobtained and so was instantaneous explosion vibrationenergy and it was concluded that different charging struc-turesrsquo attenuation law of blasting vibration is different [10]After explosion observation on rock fragmentation of blast-ing area revealed that distribution of rock fragmentationproduced by different blasting charging structures is obvi-ously different Based on the test this research theoreticallyanalyzed energy transmission of different charging structuresfrom the perspective of impedance matching The presentstudy was designed to deduce the law of different charging

structuresrsquo influence on blasting vibration energy of far regionof blasting and provide reference for controlling side-effectsof blasting vibration and designing parameters of chargingstructure

2 Experimental Research

21 Set of Tests To determine the influence of different charg-ing structures on blasting vibration energy the present papertook a blasting engineering in Jiangsu China as the examplecarrying out experimental researches on the transmission ofseismic wave of coupling charging water-decoupling charg-ing and air-decoupling charging structuresThrough test andanalysis on vibration velocity of three charging structures infar region of blasting blasting vibration energy was calcu-lated

Blasting network employed in experiment was multiplerow hole blasting with differential time of 25ms and twoholes were blasted together consequently dosage of the twoholes should be counted together to get the single detonationquantity in fitting calculating formulaThe hole diameter was009m and in experiments of decoupling charging chargingdiameter was 007m hole depth was 10m and charginglength was 7m Schematic diagram as well as site layout ofblasting region andmeasuring points are clarified in Figure 1

Tests monitored vibration velocity with blasting vibrationtester TC-4850 produced by Zhongke Measurement andControl Company The tester has three parallel channels formonitoring vibration velocity in three directions samplingrate is 1sim50KHz with frequency response range 0sim10 KHzTC-4850 is widely used in engineering and its stability as wellas accuracy can meet test requirements In order to bettergather blasting vibration signals the test fixed collecting part

Shock and Vibration 3

Table 1 Peak vibration velocity of different charging structures at measuring points (cms)

Charging structure Proportional distance 119903 V119909max V119910max V119911max Vsum Vformula

Coupling charging4281 14361 11769 19666 20180 6614sim259868561 4136 0003 7652 7936 2339sim1055412842 3143 3244 3430 4748 1273sim6230

Air-decoupling charging

13922 1305 2155 1814 2561 0962sim488814228 1753 1003 1108 2481 0932sim475418573 0667 0003 1924 1991 0625sim336321341 1360 0757 0888 1792 0507sim280623208 1210 1242 0962 1671 0447sim251630826 1096 0677 0767 1237 0292sim1740

Water-decoupling charging12747 1103 1952 2483 2654 1099sim548416995 0574 1320 0943 1618 0714sim377325493 0534 0003 1119 1170 0388sim2227

Figure 2 Site layout of blasting vibration tester

of TC-4850 on the ground with gypsum and the site set isapparent in Figure 2

22 Test Results Prediction of blasting vibration is usuallyjudged by peak vibration velocity of the particle and themostcommonly used one is Steve Sadove formula where rela-tionship between peak vibration velocity and proportionaldistance is [11]

V = 119896119903minus120572 (1)

Here 119903 is for proportional distance and its calculatingformula is 119903 = 119877

3radic119876 where 119877 is the distance from blasting

hole with m as the unit 119896 and 120572 are coefficients associatedwith explosive conditions and rock properties 119876 is for thetotal dosage of one time with kg as the unit Rock in testarea is limestone that belongs tomiddle-hard rock accordingto whose characteristics 119896rsquos value range in the formula is50sim150 and 120572rsquos value range is 13sim15 [12]

Figure 3 is time-history curve of vibration velocity andpower spectrum of different charging structures The mainfrequency of blasting vibration is about 0sim200Hz andto reduce high frequencyrsquos influence on blasting vibrationsignals those high frequency components are processed bysoftware in data analysis to get the table of peak vibrationvelocity as is demonstrated in Table 1 The superscript standsfor direction In Table 1 Vsumrsquos are in the data range deducedand calculated from experience formula (1) so the test data

are reliable From those data it can be seen that particle veloc-ity ofmeasuring points in three directions varies numericallyand peak value of the single component will also vary underdifferent blasting environments time and frequency So it isreasonable to choose square root from the square sumof threeportionsrsquo peak speed as the particlersquos peak vibration velocityThe value of peak vibration velocity of the particle is [13]

1003816

1003816

1003816

1003816

Vsum1003816

1003816

1003816

1003816

=

radic

(V119909)

2

+ (V119910)

2

+ (V119911)

2

(2)

Therefore to better predict blasting vibration it maybe most reasonable to evaluate it with module of the totalvibration velocity vector (like formula (2)) [14]With analysisof test data through least square method [15] it is indicatedthat for different charging structures values of 119896 and 120572

in vibration velocity formula are demonstrated in Table 2And Figure 4 displays data fitting curve of different chargingstructures

Table 2 clearly indicates that there exist huge distinctionsamong coefficients in vibration predicting formula fitted fordifferent charging structures To better compare and analyzethree charging structuresrsquo influence on blasting vibration 120572can be supposed as 13 then the analysis can be realizedwith comparison of 119896rsquos values Through calculating and datafitting when 120572 = 13 and proportional distance 119903 are


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus01

minus0050

00501

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

Z-v

eloc

ity (m

s)

minus01minus005

0005

01

minus01minus005

0005

01

Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 20 40 60 80 100 120 140 160 180 2000

001002003004

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0001002003004

Y-p

ower

spec

trum

(dB)

0001002003004

X-p

ower

spec

trum

(dB)

(A) Time-history curve of vibration velocity (B) The power spectrum

Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Z-v

eloc

ity (m

s)

minus004minus002

0002004

minus004minus002

0002004

minus004minus002

0002004

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 2000

0005

001

0015

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

0

0005

001

0015

Y-p

ower

spec

trum

(dB)

X-p

ower

spec

trum

(dB)


X-v

eloc

ity (m

s)

minus005

0

005

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0

0005

001

0015

X-p

ower

spec

trum

(dB)

(a) Coupling charging structure r = 12842

(b) Air-decoupling charging structure r = 13922

Figure 3 Continued

Shock and Vibration 5Z

-vel

ocity

(ms

)Y

-vel

ocity

(ms

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus005

0

005

minus005

0

005

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0

0005

001

0015

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

Y-p

ower

spec

trum

(dB)


(c) Water-decoupling charging structure r = 12747

Figure 3 Schedule chart of different charging structuresrsquo vibration velocity and power spectrum in three directions

34

32

30

28

26

24

22

20

18

16

14

12

103028262422201816141210

ln

ln r

(a) Coupling charging structure

3432302826

12

11

10

09

08

07

06

05

04

03

ln

ln r

(b) Air-decoupling charging structure

20

18

16

14

12

10

08

06

04

02

00

ln

32302826

ln r

(c) Water-decoupling charging structure

Figure 4 Fitting curve of three charging structures


Table 2 Value of 119896 and 120572 in fitting vibration formula of different charging structures

Charging structure 119896 120572 Correlation coefficient 119896rsquos value with 120572 = 13Coupling 136866 1320 minus099986 131368Air-decoupling 28479 0872 minus099231 101646Water-decoupling 47500 1157 minus097652 71586

X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)

minus100 0 100 200 300 400 500 600 700 800 900 1000minus01minus005

0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

(b) Water-decoupling charging structure

Figure 5 Schedule chart of different charging structuresrsquo vibration acceleration in three directions

determined vibration velocity formula of three chargingstructures can be compared as follows

Vcoupling = 131368119903minus13

gt Vair-decoupling = 101646119903minus13

gt Vwater-decoupling = 71586119903minus13

(3)

In blasting rocks instantaneous energy 119864 of blastingvibration at a moment is proportional to V2 that is instanta-neous energy of blasting vibration is proportional to vibrationvelocityrsquos quadratic [16] hence instantaneous energy of blast-ing vibration carried by seismic wave of measuring pointscan be reflected by vibration velocity With formula (3) rela-tionship between instantaneous energy of blasting vibrationof three charging structures is

119864coupling gt 119864air-decoupling gt 119864water-decoupling (4)

At measuring points with close rational distance that is119903 = 12842 in coupling charging and 119903 = 12747 in water-decoupling charging when charging structures are differenttime-history curves of acceleration in three directions areshown in Figure 5 and peak value of vibration accelerationat that rational distance is about 01 g If there exist struc-tural buildings near the blasting area a series of protectiveactions should be taken [17 18] Comparative relationshipof vibration acceleration intensity of blasting with differentcharging structures is in accordance with conclusions in (3)on comparative relationship of vibration velocity intensity aswell as (4) on comparative relationship of energy intensity

3 Theoretical Research

Explosion produces detonation wave in the hole and whentransmitting between different media there may be refrac-tion and reflection at the interface due to different waveimpedance thus energy transmitted in wave may changeTest data suggest that with different charging structuresdetonation products have different effects on hole wall distri-bution pressure produced on hole wall is different and so isvibration energy at themeasuring points of far region of blast-ing According to speed fitting formula (3) vibration energytransmitted in coupling charging structure is the largest andthat of water-decoupling charging is the smallest From theperspective of impedance matching when detonation prod-ucts equal rock impedance detonation products of couplingcharging directly affect hole wall explosive of air-decouplingcharging structure explodes in the air and detonation prod-ucts inflate and fill the blasting hole and then affect hole wallexplosive of water-decoupling charging structure explodes inthe water and detonation products compress the mediumwater and then transmit blasting energy to rock To sum upwhen rock impedance is determined detonation products ofdifferent charging structures have different impedance on thehole wall so impedance matching relationships are differentsuggesting that charging structure will have influence onblasting vibration energy

No matter which kind of charging structure is adopteddetonation products will keep touching rock at the interface


And according to continuous conditions and Newtonrsquos thirdlaw after reflection and transmission velocity and stress ofthe particle on interfacersquos both sides are equal therefore thefollowing equation group can be deduced [3 19]

V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)

Here V stands for particlersquos velocity 120590 is particlersquos stressand subscripts 119868 119877 and 119879 respectively refer to relevantelements disturbed by incident reflection and transmissionAs momentum of wave-front conserves

120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)

combine (5)sim(6) as follows

120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862

119910 respectively stand for denotation

products of the explosive and rockrsquos impedance with 119899 asimpedance ratio Combine the equations and then transmis-sion coefficient 119879 = 2(1 + 119899) and reflection coefficient 119865 =

(1minus119899)(1+119899) can be calculatedTherefore119879 and119865 depend onimpedance ratio of denotation products and the rock When119899 = 1 120588

119887119862

119887= 120588

119910119862

119910 119879 = 1 and 119865 = 0 the largest amount

of energy can be transmitted from denotation products tothe rock

31 Coupling Charging Coupling chargingmeans that explo-sive fills hole in direct contact with the holewallWhen explo-sive blows up explosion products of denotation directly affectthe holewall transmitting blasting energy to the rock tomakeit broken with cracks then some energy can be transmittedin the form of seismic wave to far region of blasting Thetransmission of blasting energy is relatively easy and accord-ing to the denotation theory of denotation explosive [13 17]due to high denotation pressure explosiversquos initial pressurecan be negligible and then denotation productsrsquo acousticvelocity and density can be

119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)

Here 120588 and119863 respectively are density and velocity sub-scripts 119911 and 119887 stand for explosive and detonation productsand 120574 stands for adiabatic index When detonation productsrsquo

wave impedance equals that of the explosive (ie impedanceratio 119899 = 1) the largest amount of energy from explosion canget transmitted into the rockThough it is generally difficult torealize impedance matching according to relevant theoriesexplosives with high impedance can better help transmitexplosive energy to rocks with high impedance

32 Air-DecouplingCharging When air-decoupling chargingstructure was adopted charging diameter 119889

119911is different from

that of blasting hole 1198890and decoupling coefficient of charging

is 119896119889

119896

119889=

119889

0

119889

119911

(10)

After explosive blasting detonation products firstly trans-mitted in air cushion forming air shock wave and actingon the hole wall Detonation products expand adiabaticallyin the hole Ignore quality of the air and then relationshipbetween decoupling coefficient and density of the denotationproducts 120588

119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)

Subscript 119896 stands for correlative of detonation productsin the air after explosion (same as below) Combine (9)sim(11)

120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)

Regardless of other factorsrsquo influence detonation prod-ucts in the hole follow adiabatic expansion then

119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)

Here 119875119896refers to detonation productsrsquo pressure that fills

the hole and 119875119887is detonation productsrsquo initial pressure upon

explosiversquos blasting Combine (13)

119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)

Relationship between detonation productsrsquo acousticvelocity119863

119896and pressure in the hole 119875

119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)

Combine (12) and (15) it can be seen that in air-decou-pling charging structure impedance of detonation productsoperating on the wall of borehole after explosion is

120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)


Supposing adiabatic exponent 120574 is determined in air-decoupling charging structure relationship between deto-nation productsrsquo impedance and explosiversquos impedance isrelevant to decoupling coefficient According to impedancematching theory when impedance of detonation productsequals that of the rock energy produced by explosion can betransmitted to the rock more effectively that is

120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)

As decoupling coefficient 119896119889

is larger than 1 120588119896119863

119896

decreases with the increase of 119896119889 From the perspective of

impedance matching to better transmit blasting energy it isnecessary to synthetically analyze relationship between therockrsquos impedance of blasting area explosiversquos categories anddecoupling coefficient of the chargingWhen rock and explo-sive are determined if air-decoupling charging structure isselected decoupling coefficient in (17) should be adopted toadvance the transmission of blasting energy

33 Water-Decoupling Charging When adopting water-decoupling charging structure to blast detonation productsexpand and compress the water resulting in changes ofwaterrsquos density and wave velocity Based on adiabatic expan-sion rule and the theory of fluidmechanics [20] the followingequations can be concluded

120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)

Here 120588119904is waterrsquos density under the influence of the deto-

nation 1205881199040is waterrsquos original density 120596 refers to waterrsquos radial

compression in the expanding and compressing process 119863119904

stands for waterrsquos acoustic velocity after compression and 119896119908

stands for waterrsquos bulk modulus 119875 and 119881 respectively referto pressure and waterrsquos volume in the compressing process

Combine (18) and reorganize it to get

120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)

Combine (18)sim(19) and then waterrsquos impedance afterdetonation productsrsquo compression is

120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)

Equation (20) shows that impedance matching rela-tionship of water charging is different from that of cou-pling structure or air-decoupling charging structure Withwater-decoupling charging structure relationship betweenimpedance detonation products acting on the hole wall andexplosiversquos impedance turns into exponential relationship

To realize impedance matching between detonation prod-ucts and the rock not only charging radius but also bulkmodulus of the water should be taken into considerationConsequently impedance matching can be achieved throughadjusting the decoupling coefficient And when rock andexplosive are determined explosiversquos utilization can be fur-ther improved with adjustment on decoupling coefficient

With analysis of explosion energyrsquos transmission ofthree charging structures from the perspective of impedancematching [21 22] it can be summarized that impedanceof explosive and rock directly influences explosive energyrsquostransmission No matter which charging structure to takethe rock with high impedance requires explosive with highimpedance to better utilize explosion energy When bothexplosive and rock are determined different decouplingmedia result in different influences of decoupling coefficientsnevertheless formulas can be employed to calculate and get adecoupling coefficient realizing impedance matching of det-onation products and the rock

4 Discussions

Intensity of shock wave of explosion inside the rock quicklydecreases with the increase of transmitting distance Accord-ing to damage characteristics of rock blasting with explosionas the center there are crushed zone fracture zone and vibra-tion zone [15] from the blasting center to distant area Anal-ysis on test data suggests that charging structure has a signifi-cant influence on blasting vibration energyUnder the geolog-ical condition of present test comparison of three chargingstructures confirms that when proportional distance of themeasuring point is determined coupling charging generatesblasting larger vibration energy blasting vibration energy ofdecoupling charging is relatively small and blasting vibrationenergy of water-decoupling charging is smaller than that ofair-decoupling charging The present paper identified influ-ence of different charging structures on explosion energyrsquostransmission from the perspective of impedance matchingsuggesting that advanced charging structure can better trans-mit explosion energy Combining test and theory chargingstructure apparently plays a significant role in transmissionand distribution of blasting energy thus adjusting chargingstructure in blasting excavation engineering can help enlargerockrsquos fracture zone and reduce explosion energyrsquos distribu-tion in crushed zone and vibration zone

Explosive of coupling charging structure directly operateson the hole wall hence the instant the explosive blasts(regarding the explosive as completely detonating) detona-tion products operate on hole wall and directly transmitexplosion energy to rock On the basis of theoretical analysisin Section 3 when impedance of explosive matches that ofrock explosion energy can be completely transmitted to rockand a large amount of explosion energy is consumed aroundthe explosive for rock smashing Energy consumption occursbefore shock wave as well as behind wave-front part of theenergy is transformed into left elastic deformation energy andanother part of the energy is sent out in the form of elasticwave (seismic wave) [23] According to (4) when analyzed


(a) Coupling charging structure (b) Air-decoupling charging structure


Figure 6 The effect diagram of blasting of different charge structures

energy is carried by seismic wave coupling charging gener-ates the largest amount of blasting vibration energy in otherwords energy is transformed into elastic wave to the largestextent but the energy is unavailable and increases damagingeffects of blasting vibration Thus the less ratio energyaccounts for the more effective utilization of explosive canbe achieved In addition when coupling charging explodesexplosion energy acts on hole wall and then the intensityshock wave generated is far more than rockrsquos dynamic com-pressive strength As produced explosion energy will enlargerockrsquos crushed area more explosion energy can be applied torock smashing Besides blasting rocks requires appropriaterock size for convenient transportation and reuse thereforeto reduce explosion energy on smashing rocks and enlargerockrsquos fracture zone better charging structure is essential forthe engineering

When decoupling charging structure is adopted deto-nation products firstly operate on decoupling medium andthen transmit explosive energy to the hole wall When airis selected as decoupling medium explosive explodes in theair and detonation products act on hole wall after fillingthe hole According to impedance matching theory whenexplosive and rock are determined decoupling coefficientdecides impedance relationship between detonation productsoperating on hole wall and the rock Impedance of explosiveadopted in the test is smaller than that of the rock so basedon (17) with the increase of decoupling coefficient ratio ofdetonation energy transmitted to rock decreases And it canalso get demonstrated for the test suggests that at measuringpoints with the same proportional distance explosion vibra-tion energy generated by air-decoupling charging is smallerthan that of coupling charging

Water and air have different physical properties thuswater has more apparent incompressibility while water iscompressible for rockWhen explosionrsquos detonation productsare transmitted in water energy of detonation shock wavemay decrease however detonation energy acting on hole wallcan be more evenly distributed

Test data confirm that at measuring points with the sameproportional distance explosion vibration velocity generatedby water-decoupling charging structure is the smallest inthree charging structures Equation (20) is based on theoret-ical derivation stating that impedance relationship betweendetonation products produced by water-decoupling chargingand rock is relatively complex and it is not only related todecoupling coefficient but also influenced by waterrsquos radialcompression in the hole At the test scene when water-decoupling charging structure is adopted rock dust is obvi-ously produced rarely in blasting area which reveals blastingdust can be effectively reduced by water-decoupling chargingstructure

Through observation on rock fragmentation after blastingand analysis of pictures (like Figure 6) whether from the per-spective of impedance matching theory or actual situationsin tests it turns out that charging structures have influenceon blasting effects especially water-decoupling charging for itcan enhance the utilization of explosive energy and distribu-tion of explosion rock fragmentation According to tests andtheoretical analysis when explosive and rock are fixed thecloser their impedance matching is the more the explosionenergy can be transmitted to the rock And for couplingcharging structures without transmission through decou-pling media explosion energy cannot be evenly operated onrocks thus crushing zonersquos scope will be larger than that


of decoupling charging structure With different decouplingmedia impedance matching relationships between explo-sives and rocks may change And in tests when used asdecouplingmedium water can help operate explosion energyon rocks and can generate the least crushing zone in blasting

Hence decoupling charging is beneficial to utilizationof explosive crushing [24 25] When coupling chargingstructure is adopted operating time of explosiversquos blasting isshort and its instantaneous energy carried when transmittingto the rock is larger than that of decoupling charging somoreenergy is consumed on rock smashing Consequently decou-pling charging can effectively reduce the initial shock pressureacting on hole wall and prolong operating time tomake deto-nation energy slowly act on the rock therefore instantaneousenergy can be reduced and it can be ensured to use moredetonation energy on enlarging fracture zone and reduce det-onation energy in crushed zone and vibration zone In sum-mary vibration velocity of coupling charging structure in farregion of blasting is larger than that of decoupling charging

5 Conclusions

With test and theoretical analysis this research presented theinfluence of charging structure on blasting vibrating energyand the following conclusions can be obtained

(1) Charging structure greatly influences instantaneousenergy of blasting vibration and blasting effectsdecoupling charging structure can prolong detona-tion productsrsquo operating time distribute explosionenergy more evenly reduce instantaneous energy ofblasting vibration and apply more explosions to frac-ture zone Furthermore water-decoupling chargingstructure has the best effects on reducing vibrationand generating the most even rock fragmentation

(2) Analyzed from the perspective of impedance match-ing impedance of explosive and rock has a pivotalimpact on transmission of explosion energy explo-sive with high impedance can help better transmitenergy of high-impedance rock blasting No matterwhich charging structure to choose matching rela-tionship determines energy projection therefore dif-ferent engineering requirements need comprehensiveanalysis and selection of appropriate charging struc-tures

(3) Decoupling charging structurersquos medium and coef-ficient can influence blasting vibration energy andeffects to some extent For different engineeringrequirements different charging structures shouldbe adopted and appropriate decoupling coefficientshould be selected to help improve explosion utiliza-tion and achieve better blasting effects

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by a grant from Department ofInfrastructure Barracks Grant no KYGYZXJK0914 Theircontribution to bringing this project to fruition is muchappreciated In addition the authors would like to expresstheir gratitude to Blasting Technology Service Department ofCollege of Field Engineering for their invaluable support andconsiderable helpMeanwhile sincere thanks go to graduatedstudentsWang Zheng Qin Ruping and Chen Xueping of thelaboratory who have offered selfless devotion and profoundconcern in completion of the research And high tribute willbe paid to Liang Ting who has provided insightful commenton editing and translating for this thesis The authors wouldlike to express their appreciation to the referees for makingvaluable advice in contributing to this paper

References

[1] J R Brickman ldquoCrushing mechanism separation shock waveand gas expansion effectsrdquo in Proceedings of the 2nd Inter-national Symposium on Rock Blasting pp 1ndash8 Yangtze RiverScientific Research Wuhan China 1990

[2] X Xie Precision Blasting Huazhong University of Science andTechnology Press Wuhan China 2010

[3] J Ning C Wang and T Ma Explosion and Shock DynamicsNational Defense Industry Press Beijing China 2010

[4] P R Day ldquoControlled blasting to minimize over break with bigboreholes undergroundrdquo in Proceedings of the 8th Conference onExplosives and Blasting Techniques pp 262ndash274 Louisiana StateUniversity New Orleans La USA January-February 1982

[5] Q Zong and D Meng ldquoInfluence of different kinds of holecharging structure on explosive energy transmissionrdquo ChineseJournal of Rock Mechanics and Engineering vol 22 no 4 pp641ndash645 2003

[6] J Chen C Bai Y Zeng ZWang and J Li ldquoExperiment study ofcharging constriction influence on explosion seismic effectrdquo inProceedings of the National Security Emergency and HazardousSubstances Technical Symposium pp 1098ndash1103 2013

[7] Z-L Wang and Y-C Li ldquoNumerical simulation on effects ofradial water-decoupling coefficient in engineering blastrdquo Rockand Soil Mechanics vol 26 no 12 pp 1926ndash1930 2005

[8] R Pape K R Mniszewski and A Longinow ldquoExplosion phe-nomena and effects of explosionson structures IndashIIIrdquo PracticePeriodical on Structural Design and Construction vol 15 no 2pp 135ndash169 2010

[9] A Longinow and K R Mniszewski ldquoProtecting buildingsagainst vehicle bomb attacksrdquo Practice Periodical on StructuralDesign and Construction vol 1 no 1 pp 51ndash54 1996

[10] W M Yan and K-V Yuen ldquoOn the proper estimation of theconfidence interval for the design formula of blast-inducedvibrationswith site recordsrdquoRockMechanics andRock Engineer-ing vol 48 no 1 pp 361ndash374 2015

[11] P Segarra J A Sanchidrian R Castedo L M Lopez and Idel Castillo ldquoPerformance of some coupling methods for blastvibration monitoringrdquo Journal of Applied Geophysics vol 112pp 129ndash135 2015

[12] Y NianhuaTheroy of Blasting Vibration and Testing TechnologyChina Railway Publishing House Beijing China 2014

[13] C H Dowing Blast Vibration Monitoring and Control vol 3Prentice Hall Englewood Cliffs NJ USA 1985


[14] L P Orlenko Explosion Physics Science Press Beijing China2011

[15] D ZhangMATLAB Numerical Analysis China Machine PressBeijing China 2012

[16] H Li W Lu D Shu X Yang and C Yi ldquoStudy of energy atten-uation law of blast-induced seismic waverdquo Chinese Journal ofRock Mechanics and Engineering vol 29 supplement 1 pp3364ndash3369 2010

[17] A Longinow ldquoBlast protection of buildingsrdquo Practice Periodicalon StructuralDesign andConstruction vol 18 no 4 pp 194ndash1952013

[18] G F Revey ldquoManaging rock blasting work in urban environ-mentsrdquo Practice Periodical on Structural Design and Construc-tion vol 11 no 2 pp 86ndash92 2006

[19] LWang Foundation of StressWaves National Defense IndustryPress Beijing China 2005

[20] J Ye Z Liu and S Xu FluidMechanics FudanUniversity PressShanghai China 1989

[21] Q Zhang ldquoExplosion and impedance matching between explo-sive and rockrdquo Coal Science and Technology vol 18 no 7 1990

[22] X Li ldquoThe energy study of impedance matching between rockand explosiverdquo Journal of Mid-South Mining Industry Academyvol 23 no 1 1992

[23] Q Qian andMWang Impact and Explosion Effects in Rock andSoil National Defense Industry Press Beijing China 2010

[24] W Liang H Liu and F Zhou ldquoInfluence of air-decouplingcharge on rock blastingrdquo Transactions of Beijing Institute ofTechnology vol 32 no 12 pp 1215ndash1218 2012

[25] W Wang X-C Li L Shi and Z-M Fang ldquoDiscussion ondecoupled charge loosening blasting in deep rock massrdquo Rockand Soil Mechanics vol 29 no 10 pp 2837ndash2842 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Measuring point 1

Measuring point 2

Measuring point 3

Blasting area

Blasting holeBlasting hole



Figure 1 Schematic diagram and site layout of measuring points and blasting region

well as velocity and radial decoupling coefficient [7] Papeet al carried out finite-element analysis methods studied theexplosion phenomena and effects of explosions on structuressystematically and predicted the harmful effects of blastingwith different criterions [8 9] By evaluating charging struc-turersquos influence on blasting effect and blasting vibration ofnear area a large number of engineering practices tests andnumerical simulations on charging structure indicate thatdecoupling charging structure can enhance utilization rateof explosive energy and improve blasting effect Howeverin practical engineering different construction environmentrequires different charging structures yet there are notenough studies about analysis of energy transmission andblasting effects of different charging structures as well ascarried energy of blasting vibration of far region of blastingHence the present paper intends to explore relevant factorsto provide an insightful reference for further investigations

During rock excavation of engineering scene in Jiangsuprovince researchers adopted rock drilling blasting methodwhich is widely applied in geotechnical engineering Becauseof complexity of test scene and condition the test accord-ingly selected different blasting charging structuresThroughcollecting blasting vibration signals vibration speed wasobtained and so was instantaneous explosion vibrationenergy and it was concluded that different charging struc-turesrsquo attenuation law of blasting vibration is different [10]After explosion observation on rock fragmentation of blast-ing area revealed that distribution of rock fragmentationproduced by different blasting charging structures is obvi-ously different Based on the test this research theoreticallyanalyzed energy transmission of different charging structuresfrom the perspective of impedance matching The presentstudy was designed to deduce the law of different charging

structuresrsquo influence on blasting vibration energy of far regionof blasting and provide reference for controlling side-effectsof blasting vibration and designing parameters of chargingstructure

2 Experimental Research

21 Set of Tests To determine the influence of different charg-ing structures on blasting vibration energy the present papertook a blasting engineering in Jiangsu China as the examplecarrying out experimental researches on the transmission ofseismic wave of coupling charging water-decoupling charg-ing and air-decoupling charging structuresThrough test andanalysis on vibration velocity of three charging structures infar region of blasting blasting vibration energy was calcu-lated

Blasting network employed in experiment was multiplerow hole blasting with differential time of 25ms and twoholes were blasted together consequently dosage of the twoholes should be counted together to get the single detonationquantity in fitting calculating formulaThe hole diameter was009m and in experiments of decoupling charging chargingdiameter was 007m hole depth was 10m and charginglength was 7m Schematic diagram as well as site layout ofblasting region andmeasuring points are clarified in Figure 1

Tests monitored vibration velocity with blasting vibrationtester TC-4850 produced by Zhongke Measurement andControl Company The tester has three parallel channels formonitoring vibration velocity in three directions samplingrate is 1sim50KHz with frequency response range 0sim10 KHzTC-4850 is widely used in engineering and its stability as wellas accuracy can meet test requirements In order to bettergather blasting vibration signals the test fixed collecting part











V = 119896119903minus120572 (1)






1003816

1003816

1003816

1003816

Vsum1003816

1003816

1003816

1003816

=

radic

(V119909)

2

+ (V119910)

2

+ (V119911)

2

(2)





0 200 400 600 800 1000 1200 1400 1600 1800 2000minus01

minus0050

00501

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

Z-v

eloc

ity (m

s)

minus01minus005

0005

01

minus01minus005

0005

01

Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 20 40 60 80 100 120 140 160 180 2000

001002003004

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0001002003004

Y-p

ower

spec

trum

(dB)

0001002003004

X-p

ower

spec

trum

(dB)


Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Z-v

eloc

ity (m

s)

minus004minus002

0002004

minus004minus002

0002004

minus004minus002

0002004

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 2000

0005

001

0015

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

0

0005

001

0015

Y-p

ower

spec

trum

(dB)

X-p

ower

spec

trum

(dB)


X-v

eloc

ity (m

s)

minus005

0

005

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0

0005

001

0015

X-p

ower

spec

trum

(dB)



Figure 3 Continued


-vel

ocity

(ms

)Y

-vel

ocity

(ms

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus005

0

005

minus005

0

005

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0

0005

001

0015

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

Y-p

ower

spec

trum

(dB)




34

32

30

28

26

24

22

20

18

16

14

12

103028262422201816141210

ln

ln r


3432302826

12

11

10

09

08

07

06

05

04

03

ln

ln r


20

18

16

14

12

10

08

06

04

02

00

ln

32302826

ln r






X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)







(3)









V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















V = 119896119903minus120572 (1)






1003816

1003816

1003816

1003816

Vsum1003816

1003816

1003816

1003816

=

radic

(V119909)

2

+ (V119910)

2

+ (V119911)

2

(2)





0 200 400 600 800 1000 1200 1400 1600 1800 2000minus01

minus0050

00501

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

Z-v

eloc

ity (m

s)

minus01minus005

0005

01

minus01minus005

0005

01

Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 20 40 60 80 100 120 140 160 180 2000

001002003004

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0001002003004

Y-p

ower

spec

trum

(dB)

0001002003004

X-p

ower

spec

trum

(dB)


Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Z-v

eloc

ity (m

s)

minus004minus002

0002004

minus004minus002

0002004

minus004minus002

0002004

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 2000

0005

001

0015

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

0

0005

001

0015

Y-p

ower

spec

trum

(dB)

X-p

ower

spec

trum

(dB)


X-v

eloc

ity (m

s)

minus005

0

005

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0

0005

001

0015

X-p

ower

spec

trum

(dB)



Figure 3 Continued


-vel

ocity

(ms

)Y

-vel

ocity

(ms

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus005

0

005

minus005

0

005

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0

0005

001

0015

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

Y-p

ower

spec

trum

(dB)




34

32

30

28

26

24

22

20

18

16

14

12

103028262422201816141210

ln

ln r


3432302826

12

11

10

09

08

07

06

05

04

03

ln

ln r


20

18

16

14

12

10

08

06

04

02

00

ln

32302826

ln r






X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)







(3)









V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 200 400 600 800 1000 1200 1400 1600 1800 2000minus01

minus0050

00501

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

Z-v

eloc

ity (m

s)

minus01minus005

0005

01

minus01minus005

0005

01

Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 20 40 60 80 100 120 140 160 180 2000

001002003004

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0001002003004

Y-p

ower

spec

trum

(dB)

0001002003004

X-p

ower

spec

trum

(dB)


Y-v

eloc

ity (m

s)

X-v

eloc

ity (m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Z-v

eloc

ity (m

s)

minus004minus002

0002004

minus004minus002

0002004

minus004minus002

0002004

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 2000

0005

001

0015

Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

0

0005

001

0015

Y-p

ower

spec

trum

(dB)

X-p

ower

spec

trum

(dB)


X-v

eloc

ity (m

s)

minus005

0

005

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0

0005

001

0015

X-p

ower

spec

trum

(dB)



Figure 3 Continued


-vel

ocity

(ms

)Y

-vel

ocity

(ms

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus005

0

005

minus005

0

005

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0

0005

001

0015

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

Y-p

ower

spec

trum

(dB)




34

32

30

28

26

24

22

20

18

16

14

12

103028262422201816141210

ln

ln r


3432302826

12

11

10

09

08

07

06

05

04

03

ln

ln r


20

18

16

14

12

10

08

06

04

02

00

ln

32302826

ln r






X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)







(3)









V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










-vel

ocity

(ms

)Y

-vel

ocity

(ms

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus005

0

005

minus005

0

005

Time (ms)

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ms)

0

0005

001

0015

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

Z-p

ower

spec

trum

(dB)

0

0005

001

0015

Y-p

ower

spec

trum

(dB)




34

32

30

28

26

24

22

20

18

16

14

12

103028262422201816141210

ln

ln r


3432302826

12

11

10

09

08

07

06

05

04

03

ln

ln r


20

18

16

14

12

10

08

06

04

02

00

ln

32302826

ln r






X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)







(3)









V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












X-a

ccel

erat

ion

(g)

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)

minus01minus005

0005

01

minus01minus005

0005

01


minus02minus01

00102

X-a

ccel

erat

ion

(g)

minus01minus005

0005

01

Y-a

ccel

erat

ion

(g)


0005

01

Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

minus100 0 100 200 300 400 500 600 700 800 900 1000Time (ms)

Z-a

ccel

erat

ion

(g)







(3)









V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











V119868+ V119877= V119879

120590

119868+120590

119877= 120590

119879

(5)


120590

119868

120588

119887119862

119887

minus

120590

119877

120588

119887119862

119887

=

120590

119879

120588

119910119862

119910

(6)


120590

119877= 119865120590

119868

V119877= minus119865V

119868

120590

119879= 119879120590

119868

V119879= 119899119879V

119868

119899 =

(120588

119887119862

119887)

(120588

119910119862

119910)

(7)

Here 120588119887119862

119887and 120588

119910119862




119887119862

119887= 120588

119910119862




119863

119887=

120574

120574 + 1

119863

119911 (8)

120588

119887=

120574 + 1

120574

120588

119911 (9)






is 119896119889

119896

119889=

119889

0

119889

119911

(10)


119896is

120588

119887

120588

119896

=

119889

2

0

119889

2

119911

= 119896

2

119889 (11)


120588

119896=

120574 + 1

120574

119896

minus2

119889120588

119911 (12)


119875

119896

119875

119887

= (

120588

119896

120588

119887

)

120574

119875

119887=

1

8

120588

119911119863

2

119911

(13)




119875

119896=

1

8

119896

minus2120574

119889120588

119911119863

2

119911 (14)



119896is

119863

119896= (

120574119875

119896

120588

119896

)

12

=

radic2 (120574 + 1)

4 (120574 + 1)

120574119896

1minus120574

119889119863

119911

(15)


120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911

(16)



120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120588

119896119863

119896=

radic2 (120574 + 1)

4

119896

minus120574minus1

119889120588

119911119863

119911= 120588

119910119863

119910

(17)


is larger than 1 120588119896119863

119896




120588

119904

120588

1199040

=

119889

2

0minus 119889

2

119911

119889

2

0minus (119889

119911+ 120596)

2

119863

119904= (

119896

119908

120588

119904

)

12

119889119875 =

119896

119908

119881

119889119881

(18)







120588

119904= 120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

(19)


120588

119904119863

119904= [119896

119908120588

1199040119890

(1205881199111198632

8119896119908)(119889119911(119889119911+120596))6

]

12

(20)




4 Discussions















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












5 Conclusions







Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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Research Article Experimental and Theoretical Study on ...(A) Time-history curve of vibration velocity (B) e power spectrum (c) Water-decoupling charging structure r = 12.747 F : Schedule