Research ArticleInvestigation of Ground Vibration of Full-StoneFoundation under Dynamic Compaction

Jiawen Wu1 Linjian Ma 1 Jun Shi2 Yangyang Sun 3 Jiewei Ke4 and Dan Wang3

1State Key Laboratory of Disaster Prevention amp Mitigation of Explosion amp Impact Army Engineering University of PLANanjing 210007 China2Engineering Agent Management Office of Logistics Department of PLA Navy Beijing 100036 China3College of National Defense Engineering Army Engineering University of PLA Nanjing 210007 China4Unit 31619 of PLA Nanjing 211131 China

Correspondence should be addressed to Linjian Ma patton4400163com

Received 17 June 2019 Revised 18 July 2019 Accepted 3 September 2019 Published 24 October 2019

Academic Editor Laurent Mevel

Copyright copy 2019 Jiawen Wu et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-is study focuses on the ground vibration of a full-stone foundation treatment project-e single-point dynamic compaction testwas performed using a tamping machine at an energy level of 3200 kNmiddotm Time-history curves of ground vibration velocity wererecorded under 10 times tamping within 120m distance -e effects of tamping times on the waveform of velocity and frequencyspectra were assessed as well as of peak ground velocity (PGV) peak ground acceleration (PGA) and average frequencyFurthermore the attenuations of PGV PGA and average frequency were also analyzed in detail It has been founded thatincreasing tamping times of dynamic compaction can effectively improve PGV and PGA For the frequency spectra the increasingtamping times contribute to a higher frequency range more primary frequencies and a larger frequency domain However thethree parameters namely PGV PGA and average frequency remain stable roughly when they reach a threshold of test tampingtimes -e attenuations of PGV and PGA with the proportional distance follow the power law with negative exponentsFurthermore the fitted equivalent factor increases while the damped exponential decreases persistently with the increase oftamping times -e average frequency is negatively linearly correlated with the proportional tamping distances

1 Introduction

Dynamic compaction is a widely used foundation treatmenttechnique which takes full advantage of huge kinetic energyfrom dropping a heavy hammer to densify the foundationand satisfy the settlement requirements in engineering It iswell established that dynamic compaction can not onlyeffectively reduce the compressibility of foundation andenhance its strength but also can improve the antivibrationliquefaction ability and eliminate the collapsibility -emechanism lies in generating a wave field in the foundationunder impact compaction which consists of the body wave(longitudinal wave and transverse wave) and surface wave(Rayleigh wave and Love wave) [1] Rock-soil skeleton isdisintegrated by the tension and compression of the lon-gitudinal wave Furthermore the loose grains are

interlocked and compacted by the shear action of thetransverse wave that arrives later [2] Normally the drop-ping of a hammer with a weight of 15sim20times103 kg from aheight of 18sim23m can remarkably improve the mechanicalproperties of soil foundation within a range of 9sim12m [3]However the surface wave induced by the dynamic com-paction may damage the surrounding buildings preciseequipment as well as affect the lives of residents -ereforeit is necessary to monitor the ground vibration in dynamiccompaction activity to evaluate the safety of the constructionscheme reasonably

It is widely accepted that the ground vibration param-eters such as the peak ground velocity (PGV) peak groundacceleration (PGA) and Fourier spectra are severely affectedby geological and topographic factors [4] while vibrationintensity is closely related to the energy of the vibration

HindawiShock and VibrationVolume 2019 Article ID 2631797 11 pageshttpsdoiorg10115520192631797

source and the distance from it [5] According to statisticaldata [6] the damages on ground structures are mainlycorrelated with the vibration velocity followed by acceler-ation As the tamping time increases the ground vibrationvelocity increases significantly [3] as well as the inertial forceon the ground structure induced by vibration acceleration[7] Hence the vibration safe distance is generally de-termined by controlling PGV and PGA Vibration intensitygradually attenuates with the increase of the distanceGutowski and Dym [8] found that ground vibration am-plitude induced by Rayleigh wave and the tamping distancefollows a negative power function which was validated by agreat number of engineering tests Auersch and Said [9]further investigated the attenuation of ground vibrationsdue to different technical sources Besides the relevantcharacteristics like frequency of the ground vibration are ofvital importance for response level and damage probabilitywhich may serve as an effective supplement in the evaluationof vibration hazards induced by dynamic compaction [5]-e waves induced by dynamic compaction construction arefeatured by low frequency and transiency the principle ofwhich is basically identical to that of earthquake vibration[10] Soil field test results demonstrate that peak frequency ofparticle velocity under dynamic compaction is around2sim20Hz [11ndash13] For gray silty sand and silty clay foun-dation Hwang et al [14] stated that radial vibration durationis longer than vertical vibration duration primary frequencyof vertical vibration ranges from 10 to 20Hz while radialvibration contains two primary frequency range of 3sim4Hzand 13sim14Hz -erefore the effects of vibration on thenearby structures can be estimated by analyzing peak in-tensity Fourier frequency spectra and vibration attenuationcomparing with the corresponding specified limits

Generally ground vibration induced by dynamic com-paction exhibits different propagation rules under differentgeological conditions [15] In particular the investigationshave been rarely devoted to the vibration rules of full-stonefoundation Based on a foundation treatment project thisstudy conducted single-point dynamic compaction tests on afull-stone foundation (mainly composed of andesites) at anenergy level of 3200 kNmiddotm-e vibration velocity waveformsin radial and vertical directions and the Fourier frequencyspectra were analyzed under 10-time repeated tamping indynamic compaction tests Moreover the effects of tampingtime on PGV PGA and average frequency as well as theamplitude attenuation with distance were examined -eresults may provide insightful reference for ensuring safetyin dynamic compaction construction

2 Description of Project andGround Conditions

-e foundation reinforcement projects are located in amountainous area of China including blasting peak cuttingdepression backfilling and dynamic compaction -ecomplex geological and topographic conditions raise achallenge for rock-soil and full-stone foundationsrsquo com-paction in this mountain area After dynamic compactionthe bearing capacity and deformation modulus of all

foundations should be higher than 200 kPa and 16MParespectively In this test area the engineering purposemainly aims at full-stone foundation reinforcement -eproject site was filled with the 5m-thick moderate weath-ering andesite originating from the blasting mountain -edry uniaxial compressive strength of the andesite is7307sim15554MPa the saturated uniaxial compressivestrength is 3308sim12056MPa and the elastic modulus is2794sim5450GPa -e diameters of filled stone are smallerthan 081m and most are in the range of 014msim042m andthe uniform coefficient exceeds 10 -e bedrock is un-disturbed andesite In the tested region a cast steel rammerwith a bottom diameter of 25m was used for dynamiccompaction Figure 1 presents the layout in the tested regionand the surrounding construction -e distance between thesimple road and tamping point is 122m

-ere are many important facilities and precise deviceslocated in the range 80sim130m from the dynamic compac-tion region the ground vibration during dynamic com-paction should be monitored to predict the damagepotential

3 Vibration Monitoring

31 Instrument and Equipment -e equipment for mea-suring ground vibration consists of three-component geo-phones (CDJ-S2C) piezoelectric accelerometers (CA-YD-159) recording and storing devices and connectable electriccables -e three-component geophone developed byChongqing Geological Instrument Plant China was usedfor monitoring ground vibration velocity with a frequencyrange of 2sim500Hz a sensitivity of 200plusmn 10Vms and aharmonic distortion smaller than 02 -e measurementrange of acceleration is plusmn1 g-e sensitivity and resolution ofthe acceleration sensor is 10Vg and 2times10minus 5 g respectively-e resolution of the AD interface is 16-bit and the re-cording precision can reach up to 001 cms with a samplingfrequency of 8000Hz-e acquisition device can display lotsof information including waveform maximum value andfrequency immediately after sampling-e vibration sensorswere fixed by land plaster and an appropriate amount ofwater in the monitoring test

32 Arrangement ofMeasuring Points In order to assess theeffects of single tamping of the dynamic compaction on thesurrounding facilities six measuring points were arrangedon the ground for recording the vibration signal in thedistance within 120m with a spacing of 20m as shown inFigure 2 -e measuring path was led out from the tampingcenter and perpendicular to the road line -e dump-fillingthickness of stones is 4sim5m in the test site -e foundationground of nearby facilities including E-1 E-2 and E-3 inFigure 1 is generally consistent to that of the sensor ar-rangement region However the region from the dynamiccompaction area to the facility F-1 was filled with 5sim85mmoderate weathering andesite mixed with silty sand Itsoriginal foundation has complex topography with numerousgullies as well as different geotechnical conditions Besides

2 Shock and Vibration

considering the strong seismic performance of the facility F-1 and long distance to the dynamic compaction area theimpact of dynamic compaction on facility F-1 is muchsmaller than that of other equipment which can beneglected

4 Results and Discussion

41 Vibration Velocity Waveform Figure 3 presents thewaveforms of three directionsrsquo vibration velocity at V4monitoring point (80m distance) subjected to 9th tampingwith a standard energy of 3200 kNmiddotm As seen in Figure 3 theinitial oscillation time of radial velocity is similar to that ofvertical velocity while the peak velocity in the vertical di-rection appears first -e significant attenuations of radialand vertical velocities take on at the time of 023 and 019 sie the peak velocity of minus 041 and minus 031 cms respectivelyHowever the tangential vibration velocity is in the range ofminus 007sim008 cms and that waveform is complex In thisregard this study only examined ground vibrations in theradial and vertical directions

Figures 4 and 5 show radial and vertical vibration ve-locity histories at 80m distance under different tampingtimes It can be seen from Figure 4 that the radial vibrationvelocity gradually reaches its maximum value at 027 s after 9

tampings -e amplitude began to attenuate significantly at047 s and the time of radial vibration lasts approximately075 s -e radial vibration velocity keeps similar waveforms

E-1

E-2

E-3F-1

Dynamiccompaction area

N

FacilitiesEquipment

Sensor arrangement

37mTamping

points85m

130m

80m

90m

Figure 1 Layout of the plant and the arrangement of velocity sensors in the tested area

20m20m20m20m

V2V1 V6V5V4V3

3200kNmiddotm

Moderate weathering andesite

The bedrock

3~4m

20m20m

Figure 2 Arrangement of dynamic compaction velocity sensors (unit m)

Vel

ocity

(cm

s)

Radial velocityTangential velocityVertical velocity

ndash05

ndash04

ndash03

ndash02

ndash01

00

01

02

03

04

05

01 02 03 04 05 06 07 08 09 1000Time (s)

Figure 3 Waveforms of vibration velocity at 80m distance

Shock and Vibration 3

under different tamping times but only at slightly differentamplitudes As shown in Figure 5 the vertical vibrationvelocity reaches its maximum value at 02 s followed by theperiodic attenuation since 05 s and vibration lasts ap-proximately 1 s Similarly vertical vibration velocity wave-forms are generally not affected by tamping times except forslightly different amplitudes

Table 1 lists the occurrence time of radial and verticalPGV at an 80m distance Overall the radial and verticalPGV appear earlier with the increase of tamping timesHowever after 7 tampings the occurrence time of PGVtends to be stable After 9 tampings the presence momentsof radial and vertical PGV are eventually shortened by0038 s and 0020 s respectively -e tamping energy ismainly consumed by the compressive deformation of rockfoundation at the beginning of impact compaction therebyleading to smaller vibration velocity As the tamping time

increases full-stone foundation is gradually compacted Sothe PGV increases continuously and the correspondingoccurrence time is shortened until the full-stone foundationremains stable roughly

42 PGV Monitoring

421 Effect of Tamping Time on PGV Figure 6 depicts therelationships between PGV and tamping time at differentdirections and distances As shown in Figure 6 both radialand vertical PGV increase with the increasing of tampingtimes but negatively correlated with the measured distance-e radial PGV increases by 1227 after 3 tampings at 20mdistance while the increasing amplitude of the vertical PGVis as high as 6780 after 4 tampings Afterwards both radialand vertical PGV approximately remain stable despite small

9th tamping

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

Time (s)

Time (s)

Time (s)

Time (s)

ndash04ndash02

000204

7th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

5th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

3rd tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)

Figure 4 Radial vibration velocity histories at 80m distance under different times of tamping

4 Shock and Vibration

fluctuations It is noted that the vibration velocity increasesslightly after 9 tampings -is lies in the fact that the stonefoundation is crushed and re-interlocked in the impulsewave field after multiple tampings Overall the increasingtamping time plays a positive role in enhancing the foun-dation characteristics After 4 tampings the mechanicalproperties of the rock foundation were significantly en-hanced After 9 tampings the vibration velocity of thefoundation basically remains stable It is obvious that the

vibration induced by 9 continuous tampings may impose thegreatest damage to nearby structures

422 Effect of Measured Distance on PGV Vibration in-tensity generally undergoes attenuation with distance whichis mainly attributed to geometrical damping and materialdamping [5] -e geometrical damping means that while thewave propagates far from the vibration source the wavefront

9th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

7th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

5th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

3rd tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Time (s)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)

Figure 5 Vertical vibration velocity histories at 80m distance under different times of tamping

Table 1 Occurrence time of PGV at 80m distance

Direction 1st tamping 3rd tamping 5th tamping 7th tamping 9th tampingRadial direction 0268 s 0260 s 0231 s 0230 s 0230 sVertical direction 0214 s 0203 s 0200 s 0194 s 0194 s

Shock and Vibration 5

expands and its energy density decreases with distanceresulting in the decline of vibration amplitude Geometricaldamping is affected by the vibration waveform and wave-front shape -e material damping refers to the energydissipation as the wave travels through the rock-soil layerwhich depends on the soil type moisture content andtemperature and so on [16]

Figure 7 illustrates the attenuation of radial and verticalPGV with the proportional distance subjected to odd timetamping -e proportional tamping distance is defined asR R

Q3

radic where R denotes the distance from the tamping

point andQ 32 times 106 J When the proportional distance issmaller than 040 the PGV decreases rapidly with distanceSpecifically the radial PGV decreases by 6075sim6923while the attenuation of PGV in the vertical direction is ashigh as 7932sim8367 As the proportional distance ex-ceeds 040 both radial and vertical PGV values becomerelatively smaller -e attenuation law of the vibration in-tensity with distance can be fitted by the following powerfunction with a negative exponent [17]

PGV1 k1Rminus α1

PGV2 k2Rminus α2

⎧⎨

⎩ (1)

where k denotes the equivalent factor and α denotes thedamped exponential Subscripts 1 and 2 denote radial di-rection and vertical direction respectively Table 2 lists thefitted values of k and α in equation (1)

As shown in Table 2 the attenuation of PGV with theincrease of proportional distance is reasonably fitted by thepower function with negative exponents As the tampingtime increases the equivalent factor increases and dampedexponential decreases which is on account of the energydissipation decreasing as the rock layer becomes denserBesides the damped exponential of radial PGV is smallerthan that of the vertical direction implying that more energy

is consumed during ground vibration in vertical vibrationthan that in radial direction For gray silty sand foundation[14] the 9-time-tamping average of PGV in radial andvertical directions decreases 9391 and 8826 at a distanceof 20m to 80m respectively -e attenuation ratio of full-stone foundationrsquos radial PGV 6710 is obviously lowerthan the gray silty sand foundation However the verticalattenuation ratio of the two-type foundation is basicallywithin 8826sim9169 It indicates that the radial energytransmission capacity of the full-stone foundation is higherthan that of the gray silty sand foundation which poses apotential threat to buildings and peoplersquos lives

43 PGA Monitoring

431 Effect of Tamping Time on PGA Figure 8 presents therelations between PGA and tamping times at differentmeasured distances -e effect of tamping time on PGA issimilar to that on PGV -e relationship curves can bedivided into three phases After 4 tampings the PGA at atamping distance of within 40m increased significantly Forexample the PGA of ground vibration increased by 4223at a tamping distance of 20m -e PGA at a tamping dis-tance below 100m increased slowly during the next 4-5tampings After 9 tampings the foundation was compactedand the radial PGA was nearly doubled at 20m from thetamping point It is needed to point out that the PGA at120m from the tamping point remained approximately001 g during the whole tamping process which seemedunaffected by the increase of tamping times -is suggeststhat the point at the distance of 120m has already exceededthe effective tamping range

Vertical PGA exhibits a similar variation rule with theincrease of tamping times except for far greater variationamplitude Additionally the vertical PGA was more

00

02

04

06

08

10

12

14

16

20m40m60m

80m100m120m

PGV

(cm

s)

1 2 3 4 5 6 7 8 9 10 110Tamping time

(a)

20m40m60m

80m100m120m

51 3 6 82 40 97 10 11Tamping time

00

05

10

15

20

25

30

35

40

PGV

(cm

s)

(b)

Figure 6 Relations between PGV and tamping times at different measured distances (a) In radial direction (b) In vertical direction

6 Shock and Vibration

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

considering the strong seismic performance of the facility F-1 and long distance to the dynamic compaction area theimpact of dynamic compaction on facility F-1 is muchsmaller than that of other equipment which can beneglected

4 Results and Discussion

41 Vibration Velocity Waveform Figure 3 presents thewaveforms of three directionsrsquo vibration velocity at V4monitoring point (80m distance) subjected to 9th tampingwith a standard energy of 3200 kNmiddotm As seen in Figure 3 theinitial oscillation time of radial velocity is similar to that ofvertical velocity while the peak velocity in the vertical di-rection appears first -e significant attenuations of radialand vertical velocities take on at the time of 023 and 019 sie the peak velocity of minus 041 and minus 031 cms respectivelyHowever the tangential vibration velocity is in the range ofminus 007sim008 cms and that waveform is complex In thisregard this study only examined ground vibrations in theradial and vertical directions

Figures 4 and 5 show radial and vertical vibration ve-locity histories at 80m distance under different tampingtimes It can be seen from Figure 4 that the radial vibrationvelocity gradually reaches its maximum value at 027 s after 9

tampings -e amplitude began to attenuate significantly at047 s and the time of radial vibration lasts approximately075 s -e radial vibration velocity keeps similar waveforms

E-1

E-2

E-3F-1

Dynamiccompaction area

N

FacilitiesEquipment

Sensor arrangement

37mTamping

points85m

130m

80m

90m

Figure 1 Layout of the plant and the arrangement of velocity sensors in the tested area

20m20m20m20m

V2V1 V6V5V4V3

3200kNmiddotm

Moderate weathering andesite

The bedrock

3~4m

20m20m

Figure 2 Arrangement of dynamic compaction velocity sensors (unit m)

Vel

ocity

(cm

s)

Radial velocityTangential velocityVertical velocity

ndash05

ndash04

ndash03

ndash02

ndash01

00

01

02

03

04

05

01 02 03 04 05 06 07 08 09 1000Time (s)

Figure 3 Waveforms of vibration velocity at 80m distance

Shock and Vibration 3

under different tamping times but only at slightly differentamplitudes As shown in Figure 5 the vertical vibrationvelocity reaches its maximum value at 02 s followed by theperiodic attenuation since 05 s and vibration lasts ap-proximately 1 s Similarly vertical vibration velocity wave-forms are generally not affected by tamping times except forslightly different amplitudes

Table 1 lists the occurrence time of radial and verticalPGV at an 80m distance Overall the radial and verticalPGV appear earlier with the increase of tamping timesHowever after 7 tampings the occurrence time of PGVtends to be stable After 9 tampings the presence momentsof radial and vertical PGV are eventually shortened by0038 s and 0020 s respectively -e tamping energy ismainly consumed by the compressive deformation of rockfoundation at the beginning of impact compaction therebyleading to smaller vibration velocity As the tamping time

increases full-stone foundation is gradually compacted Sothe PGV increases continuously and the correspondingoccurrence time is shortened until the full-stone foundationremains stable roughly

42 PGV Monitoring

421 Effect of Tamping Time on PGV Figure 6 depicts therelationships between PGV and tamping time at differentdirections and distances As shown in Figure 6 both radialand vertical PGV increase with the increasing of tampingtimes but negatively correlated with the measured distance-e radial PGV increases by 1227 after 3 tampings at 20mdistance while the increasing amplitude of the vertical PGVis as high as 6780 after 4 tampings Afterwards both radialand vertical PGV approximately remain stable despite small

9th tamping

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

Time (s)

Time (s)

Time (s)

Time (s)

ndash04ndash02

000204

7th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

5th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

3rd tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)

Figure 4 Radial vibration velocity histories at 80m distance under different times of tamping

4 Shock and Vibration

fluctuations It is noted that the vibration velocity increasesslightly after 9 tampings -is lies in the fact that the stonefoundation is crushed and re-interlocked in the impulsewave field after multiple tampings Overall the increasingtamping time plays a positive role in enhancing the foun-dation characteristics After 4 tampings the mechanicalproperties of the rock foundation were significantly en-hanced After 9 tampings the vibration velocity of thefoundation basically remains stable It is obvious that the

vibration induced by 9 continuous tampings may impose thegreatest damage to nearby structures

422 Effect of Measured Distance on PGV Vibration in-tensity generally undergoes attenuation with distance whichis mainly attributed to geometrical damping and materialdamping [5] -e geometrical damping means that while thewave propagates far from the vibration source the wavefront

9th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

7th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

5th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

3rd tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Time (s)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)

Figure 5 Vertical vibration velocity histories at 80m distance under different times of tamping

Table 1 Occurrence time of PGV at 80m distance

Direction 1st tamping 3rd tamping 5th tamping 7th tamping 9th tampingRadial direction 0268 s 0260 s 0231 s 0230 s 0230 sVertical direction 0214 s 0203 s 0200 s 0194 s 0194 s

Shock and Vibration 5

expands and its energy density decreases with distanceresulting in the decline of vibration amplitude Geometricaldamping is affected by the vibration waveform and wave-front shape -e material damping refers to the energydissipation as the wave travels through the rock-soil layerwhich depends on the soil type moisture content andtemperature and so on [16]

Figure 7 illustrates the attenuation of radial and verticalPGV with the proportional distance subjected to odd timetamping -e proportional tamping distance is defined asR R

Q3

radic where R denotes the distance from the tamping

point andQ 32 times 106 J When the proportional distance issmaller than 040 the PGV decreases rapidly with distanceSpecifically the radial PGV decreases by 6075sim6923while the attenuation of PGV in the vertical direction is ashigh as 7932sim8367 As the proportional distance ex-ceeds 040 both radial and vertical PGV values becomerelatively smaller -e attenuation law of the vibration in-tensity with distance can be fitted by the following powerfunction with a negative exponent [17]

PGV1 k1Rminus α1

PGV2 k2Rminus α2

⎧⎨

⎩ (1)

where k denotes the equivalent factor and α denotes thedamped exponential Subscripts 1 and 2 denote radial di-rection and vertical direction respectively Table 2 lists thefitted values of k and α in equation (1)

As shown in Table 2 the attenuation of PGV with theincrease of proportional distance is reasonably fitted by thepower function with negative exponents As the tampingtime increases the equivalent factor increases and dampedexponential decreases which is on account of the energydissipation decreasing as the rock layer becomes denserBesides the damped exponential of radial PGV is smallerthan that of the vertical direction implying that more energy

is consumed during ground vibration in vertical vibrationthan that in radial direction For gray silty sand foundation[14] the 9-time-tamping average of PGV in radial andvertical directions decreases 9391 and 8826 at a distanceof 20m to 80m respectively -e attenuation ratio of full-stone foundationrsquos radial PGV 6710 is obviously lowerthan the gray silty sand foundation However the verticalattenuation ratio of the two-type foundation is basicallywithin 8826sim9169 It indicates that the radial energytransmission capacity of the full-stone foundation is higherthan that of the gray silty sand foundation which poses apotential threat to buildings and peoplersquos lives

43 PGA Monitoring

431 Effect of Tamping Time on PGA Figure 8 presents therelations between PGA and tamping times at differentmeasured distances -e effect of tamping time on PGA issimilar to that on PGV -e relationship curves can bedivided into three phases After 4 tampings the PGA at atamping distance of within 40m increased significantly Forexample the PGA of ground vibration increased by 4223at a tamping distance of 20m -e PGA at a tamping dis-tance below 100m increased slowly during the next 4-5tampings After 9 tampings the foundation was compactedand the radial PGA was nearly doubled at 20m from thetamping point It is needed to point out that the PGA at120m from the tamping point remained approximately001 g during the whole tamping process which seemedunaffected by the increase of tamping times -is suggeststhat the point at the distance of 120m has already exceededthe effective tamping range

Vertical PGA exhibits a similar variation rule with theincrease of tamping times except for far greater variationamplitude Additionally the vertical PGA was more

00

02

04

06

08

10

12

14

16

20m40m60m

80m100m120m

PGV

(cm

s)

1 2 3 4 5 6 7 8 9 10 110Tamping time

(a)

20m40m60m

80m100m120m

51 3 6 82 40 97 10 11Tamping time

00

05

10

15

20

25

30

35

40

PGV

(cm

s)

(b)

Figure 6 Relations between PGV and tamping times at different measured distances (a) In radial direction (b) In vertical direction

6 Shock and Vibration

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

under different tamping times but only at slightly differentamplitudes As shown in Figure 5 the vertical vibrationvelocity reaches its maximum value at 02 s followed by theperiodic attenuation since 05 s and vibration lasts ap-proximately 1 s Similarly vertical vibration velocity wave-forms are generally not affected by tamping times except forslightly different amplitudes

Table 1 lists the occurrence time of radial and verticalPGV at an 80m distance Overall the radial and verticalPGV appear earlier with the increase of tamping timesHowever after 7 tampings the occurrence time of PGVtends to be stable After 9 tampings the presence momentsof radial and vertical PGV are eventually shortened by0038 s and 0020 s respectively -e tamping energy ismainly consumed by the compressive deformation of rockfoundation at the beginning of impact compaction therebyleading to smaller vibration velocity As the tamping time

increases full-stone foundation is gradually compacted Sothe PGV increases continuously and the correspondingoccurrence time is shortened until the full-stone foundationremains stable roughly

42 PGV Monitoring

421 Effect of Tamping Time on PGV Figure 6 depicts therelationships between PGV and tamping time at differentdirections and distances As shown in Figure 6 both radialand vertical PGV increase with the increasing of tampingtimes but negatively correlated with the measured distance-e radial PGV increases by 1227 after 3 tampings at 20mdistance while the increasing amplitude of the vertical PGVis as high as 6780 after 4 tampings Afterwards both radialand vertical PGV approximately remain stable despite small

9th tamping

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

Time (s)

Time (s)

Time (s)

Time (s)

ndash04ndash02

000204

7th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

5th tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

3rd tamping

ndash04ndash02

000204

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)Ra

dial

velo

city

(cm

s)

Radi

alve

loci

ty (c

ms

)

Figure 4 Radial vibration velocity histories at 80m distance under different times of tamping

4 Shock and Vibration

fluctuations It is noted that the vibration velocity increasesslightly after 9 tampings -is lies in the fact that the stonefoundation is crushed and re-interlocked in the impulsewave field after multiple tampings Overall the increasingtamping time plays a positive role in enhancing the foun-dation characteristics After 4 tampings the mechanicalproperties of the rock foundation were significantly en-hanced After 9 tampings the vibration velocity of thefoundation basically remains stable It is obvious that the

vibration induced by 9 continuous tampings may impose thegreatest damage to nearby structures

422 Effect of Measured Distance on PGV Vibration in-tensity generally undergoes attenuation with distance whichis mainly attributed to geometrical damping and materialdamping [5] -e geometrical damping means that while thewave propagates far from the vibration source the wavefront

9th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

7th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

5th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

3rd tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Time (s)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)

Figure 5 Vertical vibration velocity histories at 80m distance under different times of tamping

Table 1 Occurrence time of PGV at 80m distance

Direction 1st tamping 3rd tamping 5th tamping 7th tamping 9th tampingRadial direction 0268 s 0260 s 0231 s 0230 s 0230 sVertical direction 0214 s 0203 s 0200 s 0194 s 0194 s

Shock and Vibration 5

expands and its energy density decreases with distanceresulting in the decline of vibration amplitude Geometricaldamping is affected by the vibration waveform and wave-front shape -e material damping refers to the energydissipation as the wave travels through the rock-soil layerwhich depends on the soil type moisture content andtemperature and so on [16]

Figure 7 illustrates the attenuation of radial and verticalPGV with the proportional distance subjected to odd timetamping -e proportional tamping distance is defined asR R

Q3

radic where R denotes the distance from the tamping

point andQ 32 times 106 J When the proportional distance issmaller than 040 the PGV decreases rapidly with distanceSpecifically the radial PGV decreases by 6075sim6923while the attenuation of PGV in the vertical direction is ashigh as 7932sim8367 As the proportional distance ex-ceeds 040 both radial and vertical PGV values becomerelatively smaller -e attenuation law of the vibration in-tensity with distance can be fitted by the following powerfunction with a negative exponent [17]

PGV1 k1Rminus α1

PGV2 k2Rminus α2

⎧⎨

⎩ (1)

where k denotes the equivalent factor and α denotes thedamped exponential Subscripts 1 and 2 denote radial di-rection and vertical direction respectively Table 2 lists thefitted values of k and α in equation (1)

As shown in Table 2 the attenuation of PGV with theincrease of proportional distance is reasonably fitted by thepower function with negative exponents As the tampingtime increases the equivalent factor increases and dampedexponential decreases which is on account of the energydissipation decreasing as the rock layer becomes denserBesides the damped exponential of radial PGV is smallerthan that of the vertical direction implying that more energy

is consumed during ground vibration in vertical vibrationthan that in radial direction For gray silty sand foundation[14] the 9-time-tamping average of PGV in radial andvertical directions decreases 9391 and 8826 at a distanceof 20m to 80m respectively -e attenuation ratio of full-stone foundationrsquos radial PGV 6710 is obviously lowerthan the gray silty sand foundation However the verticalattenuation ratio of the two-type foundation is basicallywithin 8826sim9169 It indicates that the radial energytransmission capacity of the full-stone foundation is higherthan that of the gray silty sand foundation which poses apotential threat to buildings and peoplersquos lives

43 PGA Monitoring

431 Effect of Tamping Time on PGA Figure 8 presents therelations between PGA and tamping times at differentmeasured distances -e effect of tamping time on PGA issimilar to that on PGV -e relationship curves can bedivided into three phases After 4 tampings the PGA at atamping distance of within 40m increased significantly Forexample the PGA of ground vibration increased by 4223at a tamping distance of 20m -e PGA at a tamping dis-tance below 100m increased slowly during the next 4-5tampings After 9 tampings the foundation was compactedand the radial PGA was nearly doubled at 20m from thetamping point It is needed to point out that the PGA at120m from the tamping point remained approximately001 g during the whole tamping process which seemedunaffected by the increase of tamping times -is suggeststhat the point at the distance of 120m has already exceededthe effective tamping range

Vertical PGA exhibits a similar variation rule with theincrease of tamping times except for far greater variationamplitude Additionally the vertical PGA was more

00

02

04

06

08

10

12

14

16

20m40m60m

80m100m120m

PGV

(cm

s)

1 2 3 4 5 6 7 8 9 10 110Tamping time

(a)

20m40m60m

80m100m120m

51 3 6 82 40 97 10 11Tamping time

00

05

10

15

20

25

30

35

40

PGV

(cm

s)

(b)

Figure 6 Relations between PGV and tamping times at different measured distances (a) In radial direction (b) In vertical direction

6 Shock and Vibration

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

fluctuations It is noted that the vibration velocity increasesslightly after 9 tampings -is lies in the fact that the stonefoundation is crushed and re-interlocked in the impulsewave field after multiple tampings Overall the increasingtamping time plays a positive role in enhancing the foun-dation characteristics After 4 tampings the mechanicalproperties of the rock foundation were significantly en-hanced After 9 tampings the vibration velocity of thefoundation basically remains stable It is obvious that the

vibration induced by 9 continuous tampings may impose thegreatest damage to nearby structures

422 Effect of Measured Distance on PGV Vibration in-tensity generally undergoes attenuation with distance whichis mainly attributed to geometrical damping and materialdamping [5] -e geometrical damping means that while thewave propagates far from the vibration source the wavefront

9th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

7th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

5th tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

3rd tamping

ndash04ndash02

000204

ndash025 000 025 050 075 100 125 150 175 200ndash050

ndash025 000 025 050 075 100 125 150 175 200ndash050

Time (s)

ndash050 ndash025 000 025 050 075 100 125 150 175 200

ndash050 ndash025 000 025 050 075 100 125 150 175 200

1st tamping

ndash04ndash02

000204

Time (s)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)V

ertic

alve

loci

ty (c

ms

)

Figure 5 Vertical vibration velocity histories at 80m distance under different times of tamping

Table 1 Occurrence time of PGV at 80m distance

Direction 1st tamping 3rd tamping 5th tamping 7th tamping 9th tampingRadial direction 0268 s 0260 s 0231 s 0230 s 0230 sVertical direction 0214 s 0203 s 0200 s 0194 s 0194 s

Shock and Vibration 5

expands and its energy density decreases with distanceresulting in the decline of vibration amplitude Geometricaldamping is affected by the vibration waveform and wave-front shape -e material damping refers to the energydissipation as the wave travels through the rock-soil layerwhich depends on the soil type moisture content andtemperature and so on [16]

Figure 7 illustrates the attenuation of radial and verticalPGV with the proportional distance subjected to odd timetamping -e proportional tamping distance is defined asR R

Q3

radic where R denotes the distance from the tamping

point andQ 32 times 106 J When the proportional distance issmaller than 040 the PGV decreases rapidly with distanceSpecifically the radial PGV decreases by 6075sim6923while the attenuation of PGV in the vertical direction is ashigh as 7932sim8367 As the proportional distance ex-ceeds 040 both radial and vertical PGV values becomerelatively smaller -e attenuation law of the vibration in-tensity with distance can be fitted by the following powerfunction with a negative exponent [17]

PGV1 k1Rminus α1

PGV2 k2Rminus α2

⎧⎨

⎩ (1)

where k denotes the equivalent factor and α denotes thedamped exponential Subscripts 1 and 2 denote radial di-rection and vertical direction respectively Table 2 lists thefitted values of k and α in equation (1)

As shown in Table 2 the attenuation of PGV with theincrease of proportional distance is reasonably fitted by thepower function with negative exponents As the tampingtime increases the equivalent factor increases and dampedexponential decreases which is on account of the energydissipation decreasing as the rock layer becomes denserBesides the damped exponential of radial PGV is smallerthan that of the vertical direction implying that more energy

is consumed during ground vibration in vertical vibrationthan that in radial direction For gray silty sand foundation[14] the 9-time-tamping average of PGV in radial andvertical directions decreases 9391 and 8826 at a distanceof 20m to 80m respectively -e attenuation ratio of full-stone foundationrsquos radial PGV 6710 is obviously lowerthan the gray silty sand foundation However the verticalattenuation ratio of the two-type foundation is basicallywithin 8826sim9169 It indicates that the radial energytransmission capacity of the full-stone foundation is higherthan that of the gray silty sand foundation which poses apotential threat to buildings and peoplersquos lives

43 PGA Monitoring

431 Effect of Tamping Time on PGA Figure 8 presents therelations between PGA and tamping times at differentmeasured distances -e effect of tamping time on PGA issimilar to that on PGV -e relationship curves can bedivided into three phases After 4 tampings the PGA at atamping distance of within 40m increased significantly Forexample the PGA of ground vibration increased by 4223at a tamping distance of 20m -e PGA at a tamping dis-tance below 100m increased slowly during the next 4-5tampings After 9 tampings the foundation was compactedand the radial PGA was nearly doubled at 20m from thetamping point It is needed to point out that the PGA at120m from the tamping point remained approximately001 g during the whole tamping process which seemedunaffected by the increase of tamping times -is suggeststhat the point at the distance of 120m has already exceededthe effective tamping range

Vertical PGA exhibits a similar variation rule with theincrease of tamping times except for far greater variationamplitude Additionally the vertical PGA was more

00

02

04

06

08

10

12

14

16

20m40m60m

80m100m120m

PGV

(cm

s)

1 2 3 4 5 6 7 8 9 10 110Tamping time

(a)

20m40m60m

80m100m120m

51 3 6 82 40 97 10 11Tamping time

00

05

10

15

20

25

30

35

40

PGV

(cm

s)

(b)

Figure 6 Relations between PGV and tamping times at different measured distances (a) In radial direction (b) In vertical direction

6 Shock and Vibration

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

expands and its energy density decreases with distanceresulting in the decline of vibration amplitude Geometricaldamping is affected by the vibration waveform and wave-front shape -e material damping refers to the energydissipation as the wave travels through the rock-soil layerwhich depends on the soil type moisture content andtemperature and so on [16]

Figure 7 illustrates the attenuation of radial and verticalPGV with the proportional distance subjected to odd timetamping -e proportional tamping distance is defined asR R

Q3

radic where R denotes the distance from the tamping

point andQ 32 times 106 J When the proportional distance issmaller than 040 the PGV decreases rapidly with distanceSpecifically the radial PGV decreases by 6075sim6923while the attenuation of PGV in the vertical direction is ashigh as 7932sim8367 As the proportional distance ex-ceeds 040 both radial and vertical PGV values becomerelatively smaller -e attenuation law of the vibration in-tensity with distance can be fitted by the following powerfunction with a negative exponent [17]

PGV1 k1Rminus α1

PGV2 k2Rminus α2

⎧⎨

⎩ (1)

where k denotes the equivalent factor and α denotes thedamped exponential Subscripts 1 and 2 denote radial di-rection and vertical direction respectively Table 2 lists thefitted values of k and α in equation (1)

As shown in Table 2 the attenuation of PGV with theincrease of proportional distance is reasonably fitted by thepower function with negative exponents As the tampingtime increases the equivalent factor increases and dampedexponential decreases which is on account of the energydissipation decreasing as the rock layer becomes denserBesides the damped exponential of radial PGV is smallerthan that of the vertical direction implying that more energy

is consumed during ground vibration in vertical vibrationthan that in radial direction For gray silty sand foundation[14] the 9-time-tamping average of PGV in radial andvertical directions decreases 9391 and 8826 at a distanceof 20m to 80m respectively -e attenuation ratio of full-stone foundationrsquos radial PGV 6710 is obviously lowerthan the gray silty sand foundation However the verticalattenuation ratio of the two-type foundation is basicallywithin 8826sim9169 It indicates that the radial energytransmission capacity of the full-stone foundation is higherthan that of the gray silty sand foundation which poses apotential threat to buildings and peoplersquos lives

43 PGA Monitoring

431 Effect of Tamping Time on PGA Figure 8 presents therelations between PGA and tamping times at differentmeasured distances -e effect of tamping time on PGA issimilar to that on PGV -e relationship curves can bedivided into three phases After 4 tampings the PGA at atamping distance of within 40m increased significantly Forexample the PGA of ground vibration increased by 4223at a tamping distance of 20m -e PGA at a tamping dis-tance below 100m increased slowly during the next 4-5tampings After 9 tampings the foundation was compactedand the radial PGA was nearly doubled at 20m from thetamping point It is needed to point out that the PGA at120m from the tamping point remained approximately001 g during the whole tamping process which seemedunaffected by the increase of tamping times -is suggeststhat the point at the distance of 120m has already exceededthe effective tamping range

Vertical PGA exhibits a similar variation rule with theincrease of tamping times except for far greater variationamplitude Additionally the vertical PGA was more

00

02

04

06

08

10

12

14

16

20m40m60m

80m100m120m

PGV

(cm

s)

1 2 3 4 5 6 7 8 9 10 110Tamping time

(a)

20m40m60m

80m100m120m

51 3 6 82 40 97 10 11Tamping time

00

05

10

15

20

25

30

35

40

PGV

(cm

s)

(b)

Figure 6 Relations between PGV and tamping times at different measured distances (a) In radial direction (b) In vertical direction

6 Shock and Vibration

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

dependent on the distance from the tamping point After 10tampings continually the PGA at the tamping distance of20m was up to 0618 g while the PGA at the tampingdistance range of 100sim120m was consistently lower than002 g -erefore it can be concluded that the dynamiccompaction almost has no effects at the distance over 100mfrom the tamping point

432 Effect of Measured Distance on PGA In order to in-vestigate the attenuation law of PGA with distance subjectedto different tamping times the tested data under odd times oftamping were selected for plotting the relations of radial andvertical PGA with distance as shown in Figure 9 It can beobserved that both radial and vertical PGA declined rapidly ata proportional tamping distance below 04 Specifically theattenuation amplitudes of radial and vertical PGA were6213sim7537 and 8232sim8675 respectively -e at-tenuations of both radial and vertical PGA may be fitted bythe following power function with negative exponents

PGA3 k3Rminus α3

PGA4 k4Rminus α4

⎧⎨

⎩ (2)

where k denotes the equivalent factor and α denotes thedamped exponential -e subscripts 3 and 4 denote radial

and vertical directions respectively Table 3 summarizes thefitted values of k and α according to equation (2)

It can be seen from Table 3 that the fitted equivalentfactors increase with the increase of the tamping times whilethe damped exponents are negatively correlated with thetamping times Moreover the damped exponential of ver-tical PGA is greater than that of radial PGA that is thevertical vibration decays more rapidly than radial vibration-is is similar to the attenuation of PGV as described inSection 422 -e ground vibration along the vertical di-rection consumes more energy than that along the radialdirection

44 Fourier Spectra -e vibration frequency componentsand frequency domain range may serve as importantbases for evaluating the safety of the equipment andbuildings By performing Fourier transform (FFT) on therecords of ground variation in radial and vertical di-rections at a typical tamping distance of 80 m under 10tampings the Fourier amplitude spectrum of vibrationvelocities was calculated along radial and vertical di-rections Figure 10 presents the Fourier amplitudespectrum at 80 m from the tamping point subjected toodd time tamping

It can be seen in Figure 10 that the radial and verticalFourier amplitude spectrums exhibit similar shapes Withan increase of tamping times the Fourier amplitude spectracontain more wider frequency bands and higher ampli-tudes -is is attributed to the decline in tamping energydissipation after multiple reflections and diffractions of thestress wave among rock layers [16] As shown inFigure 10(a) the radial vibration frequency mainly rangesfrom 3Hz to 42Hz and the two primary frequencies are inthe ranges of 6sim10Hz and 13sim22Hz Amplitudes at13sim22Hz are strongly influenced by the increase of

01 02 03 04 05 06 07 08 0900

02

04

06

08

10

12

14

PGV

(cm

s)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 09

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGV

(cm

s)

R

00

05

10

15

20

25

30

35

40

(b)

Figure 7 Attenuation of PGV with distance under different tamping times (a) In radial direction (b) In vertical direction

Table 2 Attenuation parameters of PGV under odd time tamping

TimeParameters

k1 α1 R2 k2 α2 R2

1 013 102 098 009 153 0973 017 096 097 011 149 0995 020 090 094 019 142 0977 021 090 093 021 140 0969 023 090 092 021 140 095

Shock and Vibration 7

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

tamping times Particularly the amplitudes at 17sim22Hzand 33sim34Hz increase greatly when tamping times isbeyond 7 However these increasing amplitudes are lower

than the amplitudes at 6sim10Hz in other words the highestFourier amplitude is in the range of 6sim10Hz which in-dicates the low frequency vibration in dynamic compactionconstruction of full-stone foundation

As seen in Figure 10(b) the spectrum range of verticalvibration is in the range of 5sim50Hz and the vibrationspectrum also possess two primary frequencies of 6sim8Hzand 16sim18Hz the amplitude of which increases with theincrease of tamping times It is noted that the amplitudecorresponding to the frequency of 16sim18Hz is lower thanthat of the frequency of 6sim8Hz within 7 tampings but thissituation is reversed subjected to 9th tamping Simulta-neously two higher vibration frequency bands (23sim24Hz

0 1 2 3 4 5 6 7 8 9 10 11000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

Tamping time

20m40m60m

80m100m120m

(a)

0 1 2 3 4 5 6 7 8 9 10 1100

01

02

03

04

05

06

07

20m40m60m

80m100m120m

PGA

(g)

Tamping time

(b)

Figure 8 Relations between PGA and tamping time at different measured distances (a) In radial direction (b) In vertical direction

01 02 03 04 05 06 07 08 09000

002

004

006

008

010

012

014

016

018

020

PGA

(g)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R

(a)

01 02 03 04 05 06 07 08 0900

01

02

03

04

05

06

07

1st tamping3rd tamping5th tamping

7th tamping9th tamping

PGA

(g)

R

(b)

Figure 9 Attenuation of PGA with distance under different times of tamping (a) In radial direction (b) In vertical direction

Table 3 Attenuation parameters of PGA under odd time tamping

TimeParameters

k3 α3 R2 k4 α4 R2

1 001 123 097 001 163 0973 001 121 099 001 160 0995 002 114 094 002 151 0977 002 110 093 003 149 0979 003 105 093 003 149 096

8 Shock and Vibration

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

and 33sim34Hz) appear in the vertical Fourier spectra asincreasing tamping times are beyond 7 Based on theaforementioned data analysis increasing tamping times caneffectively expand the Fourier spectrum frequency range andincrease the number of primary frequencies especiallyvertical vibration

It is reported by Hwang and Tu [14] that the primaryfrequency of vertical vibration is in the range of10sim20 Hz while the radial vibration has two primaryfrequencies of 3sim4 Hz and 12sim13 Hz in a gray silty sandand silty clay foundation For this full-stone foundationunder dynamic compaction the spectra may have 2sim4higher primary frequencies due to lower materialdamping Consequently the Fourier amplitude spectra ofground vibration velocity of the full-stone foundation arefeatured by multiple primary frequencies and widerfrequency band compared to the gray silty sand and siltyclay foundation

441 Effect of Tamping Time on Vibration Frequency Tocomprehensively analyze the law of blasting vibrationfrequency and to consider the continuity of the propaga-tion process the average frequency was introduced fordescribing the spectrum of vibration velocity by Trivintildeoet al [18] Average frequency denoted as fc can be cal-culated as

fc 1113936

ni1Aifi

1113936ni1Ai

(3)

where fi represents the individual frequencies in thespectrum (Hz) and Ai is the amplitude associated with eachfrequency fi

-e relations between primary frequency as well asaverage frequency and the tamping time are displayed inFigure 11 It can be observed that primary frequencies are

maintained in the range of 6sim9Hz except for the verticalprimary frequency under the 9 tampings However theaverage frequencies present better positive correlationwith tamping times which matches with the characteristicof Fourier amplitude spectrum influenced by tampingtimes in Figure 10 -erefore the average frequency maybe used to preferably describe the effect of tamping timesand distance on the bulk characteristic of Fourieramplitude

Figure 12 presents the relations between averagefrequencies and tamping times at various tamping dis-tances During the first 4 tampings the average frequencyincreases significantly with tamping with an increasedamplitude of 2sim5 Hz Average frequency at a closer

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

00090A

mpl

itude

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(a)

0 5 10 15 20 25 30 35 40 45 5000000

00015

00030

00045

00060

00075

Am

plitu

de

Frequency (Hz)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

(b)

Figure 10 Fourier amplitude spectrum in radial and vertical directions at 80m distance (a) In radial direction (b) In vertical direction

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Radial primary frequencyRadial average frequency

Vertical primary frequencyVertical average frequency

Freq

uenc

y (H

z)

Tamping time

Figure 11 Relations between primary and average frequencies andtamping times

Shock and Vibration 9

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

distance from the tamping point increases more rapidlyAt a tamping distance of 20 m both radial and verticalaverage frequencies tend to be stable after 4 tampingsMore tamping times are needed if the average amplitudeis to remain constant at a further location At a tampingdistance of 100 m the average frequency is stabilizedunder 4sim8 tampings -is threshold of tamping times isgenerally positively correlated with the tamping distanceIn other words the closer the distance the easier it is forthe foundation to stabilize when the foundation issubjected to dynamic compaction

442 Effect of Measured Distance on Vibration FrequencyFigure 13 presents the attenuation of both radial and verticalaverage frequencies with distance under different tampingtimes Overall the average frequency in the vertical directionis greater than that in the radial direction Apparently theattenuations of the average frequencies under differenttamping times are roughly similar which decrease linearlywith the proportional tamping distance -e attenuationcurves of the average frequency are close to each other exceptfor the 1st tamping which is due to the insufficient dynamiccompactness of the full-stone foundation

0 1 2 3 4 5 6 7 8 9 10 11

20m40m60m

80m100m120m

Ave

rage

freq

uenc

y (H

z)

Tamping time

5

10

15

20

25

(a)

20m40m60m

80m100m120m

0 1 2 3 4 5 6 7 8 9 10 115

10

15

20

25

30

Ave

rage

freq

uenc

y (H

z)

Tamping time

(b)

Figure 12 Relations between average frequency and tamping times at different tamping distances (a) In radial direction (b) In verticaldirection

01 02 03 04 05 06 07 08 090

5

10

15

20

25

30

1st tamping3rd tamping5th tamping

7th tamping9th tamping

Ave

rage

freq

uenc

y (H

z)

R

(a)

1st tamping3rd tamping5th tamping

7th tamping9th tamping

R01 02 03 04 05 06 07 08 09

0

5

10

15

20

25

30

Cent

roid

freq

uenc

yH

z

(b)

Figure 13 Attenuation of average frequency with distance under different tamping times (a) In radial direction (b) In vertical direction

10 Shock and Vibration

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

5 Conclusions

(1) -e ground vibration of the full-stone foundationunder a standard tamping energy of 3200 kNmiddotm lastsapproximately 075sim1 s longer than the gray siltysand and silty clay foundation-e duration of radialvibration turns out to be the longest -e radial andvertical waveforms are roughly similar under dif-ferent times of tamping in each direction

(2) At 80m distance the Fourier amplitude spectraexhibit a similar shape under different tampingtimes -e frequency domain of radial vibrationmainly ranges from 3 to 42Hz which contains twoprimary frequencies of 6sim10Hz and 13sim22Hz -efrequency domain of vertical vibration ranges from 5to 50Hz which has two primary frequencies of6sim8Hz and 16sim18Hz Meanwhile the amplitudescorresponding to frequencies of 6sim8 Hz turn to behigher than that of 16sim18 Hz -e frequency spectraexhibit more primary frequencies higher frequen-cies and wider domains with the increase of tampingtimes -e frequency spectra exhibit more primaryfrequencies higher frequencies and wider domainswith the increase of tamping times

(3) -e PGV PGA and average frequency of groundvibration first increase significantly with an increaseof tamping time and then remain roughly un-changed due to the compactness of rock foundationBoth PGV and PGA decay with the distance from thetamping point in a negative exponential relationWith the increase of tamping time the attenuationdegree increases correspondingly Generally thevibration frequency of the full-stone foundationunder dynamic compaction is higher than that ofgray silty sand and silty clay foundations and theaverage frequency exhibits negative linear correla-tion with the proportional tamping distance

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

-is research has been supported by the National NaturalSciences Foundation of China (grant nos 51774295 and51808551) and the Natural Sciences Foundation of JiangsuProvince (BK20170754)

References

[1] M Y H Bangash Impact and Explosion Analysis and DesignBlackwell Hoboken NJ USA 1993

[2] J Qiao and L Li ldquoModel Test Study on vibration transferringof dynamic compaction of hydraulic filling foundation re-inforcementrdquo Systems Engineering Procedia vol 1 pp 61ndash682011

[3] P W Mayne ldquoGround vibrations during dynamic compac-tionrdquo in Proceedings of the Vibration Problems in GeotechnicalEngineering ASCE Detroit MI USA October 1985

[4] R G LukasGeotechnical Engineering Circular No 1 DynamicCompaction Federal Highway Administration WashingtonDC USA 1995

[5] M Srbulov Ground Vibration Engineering Simplified Ana-lyses with Case Studies and Examples Vol 12 Springer Scienceamp Business Media Berlin Germany 2010

[6] W I Duvall and D E Fogelson Review of Criteria for Es-timating Damage to Residences from Blasting Vibrations USDepartment of the Interior Bureau of Mines WashingtonDC USA 1962

[7] P Leger and R Tremblay ldquoEarthquake ground motions forseismic damage assessment and re-evaluation of existingbuildings and critical facilitiesrdquo in Damage Assessment andReconstruction after War or Natural Disaster pp 193ndash219Springer Dordrecht Netherlands 2009

[8] T G Gutowski and C L Dym ldquoPropagation of ground vi-bration a reviewrdquo Journal of Sound and Vibration vol 49no 2 pp 179ndash193 1976

[9] L Auersch and S Said ldquoAttenuation of ground vibrations dueto different technical sourcesrdquo Earthquake Engineering andEngineering Vibration vol 9 no 3 pp 337ndash344 2010

[10] B B Xu R Q Zhang and L Y Guo ldquoResearch of dynamiccompaction a review of recent academic literaturerdquoAdvancedMaterials Research vol 1079-1080 pp 406ndash409 2014

[11] J K Mitchell ldquoSoil improvement-state of the art reportrdquo inProceedings of the Eleventh International Conference on SoilMechanics and Foundation Engineering vol 4 pp 509ndash565San Francisco CA USA August 1985

[12] W F Van Impe Soil Improvement Techniques and eirEvolution Balkema Rotterdam Netherlands 1989

[13] B Hamidi N Hamid and S Varaksin ldquoA case study of vi-bration monitoring in a dynamic compaction projectrdquo inProceedings of the 14th Asian Regional Conference on SoilMechanics and Geotechnical Engineering -e Hong KongGeotechnical Society and -e Hong Kong Polytechnic Uni-versity Hong Kong China May 2011

[14] J H Hwang and T Y Tu ldquoGround vibration due to dynamiccompactionrdquo Soil Dynamics and Earthquake Engineeringvol 26 no 5 pp 337ndash346 2006

[15] M Lauzon and J-F Morel ldquoGround vibrations induced bydynamic compaction and rapid impact compactionrdquo in 2011Pan-Am CGS Geotechnical Conference 64th Canadian Geo-technical Conference and 14th Pan-American Conference onSoil Mechanics and Geotechnical Engineering Toronto Can-ada October 2011

[16] D Adam C Adam F-J Falkner and I Paulmichl ldquoVibrationemission induced by rapid impact compactionrdquo in Proceedingsof the 8th International Conference on Structural DynamicsG De Roeck G Degrande G Lombaert and G Muller Edspp 914ndash921 Leuven Belgium July 2011

[17] J F Wiss ldquoConstruction vibrations state-of-the-art discus-sion and closurerdquo Journal of Geotechnical and Geo-environmental Engineering vol 108 no GT3 1982

[18] L F Trivintildeo B Mohanty and B Milkereit ldquoSeismic wave-forms from explosive sources located in boreholes and ini-tiated in different directionsrdquo Journal of Applied Geophysicsvol 87 pp 81ndash93 2012

Shock and Vibration 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom