Research ArticleExperimental Study on the Dynamic Mechanical Properties ofLarge-Diameter Mortar and Concrete Subjected to Cyclic Impact

Bi Sun 12 Yang Ping2 Zhende Zhu3 Zhijian Jiang2 and Nan Wu 4

1Shenzhen Key Laboratory of Urban and Civil Engineering for Disaster Prevention and Mitigation Shenzhen Graduate SchoolHarbin Institute of Technology Shenzhen 518055 China2Shenzhen Water Planning and Design Institute Co Ltd Shenzhen 518001 China3Key Laboratory of Ministry of Education of Geomechanics and Embankment Engineering Hohai UniversityNanjing 210098 China4Guangzhou University-Tamkang University Joint Research Centre for Engineering Structure Disaster Prevention and ControlGuangzhou University Guangzhou 510006 China

Correspondence should be addressed to Bi Sun sunbi58126com

Received 24 August 2020 Revised 16 November 2020 Accepted 14 December 2020 Published 24 December 2020

Academic Editor Qing Ma

Copyright copy 2020 Bi Sun et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Rock bursts are typically accompanied by multiple shocks In order to explore the dynamic characteristics of filling materials inrock burst roadways we employ the split Hopkinson pressure bar (SHPB) test to analyze the dynamic mechanical response ofmortar and concrete under cyclical impact e SHPB test results of the large-size specimen indicate the improvement in thewaveform shape and the reduction in the wave dispersion via the application of the rubber sheet as the pulse shaper Under cyclicimpact the peak stress and energy utilization ratio of mortar and concrete specimens were reduced demonstrating obviousfatigue characteristics e mortar peak stress and energy utilization ratio were observed to be sensitive to the impact times whilethose of concrete were sensitive to impact pressure e damage evolution of mortar and concrete exhibited very similar trendsunder the cyclic impact load whereby the impact pressure had minimal effect on the damage evolution

1 Introduction

e development of deep coal mining has increased thecomplexity of deep coal resource geological conditions[1ndash5] In many mining areas in China controlling rock burstroadway with traditional roadway support methods is dif-ficult particularly as the rock burst is often accompanied bymultiple shocks erefore it is of great significance forengineering practice to study the dynamic characteristicsand differences of backfill materials (mortar and concrete)under cyclic impact

Due to the complexity of underground engineering theoccurrence of rock burst is affected by multiple factors [6]Du et al [7] employed three-dimensional in situ stressmeasurements in order to investigate rock burst Zhu et al[8] Heasley and Tulu [9] and Li et al [10] each proposeddistinct analysis methods for the evaluation of rock burst

Previous research has effectively determined in situ stress vianumerical simulations [11 12]

e split Hopkinson pressure bar (SHPB) test device wasfirst used by Hopkinson to investigate the variations inpressure (bar) with time is pioneering method hassubsequently received much attention due to its ability tostudy the dynamic mechanical properties of materials[13ndash15] Frew et al [16] determined stress-strain data of rockmaterials via SHPB technology e SHPB test device isbased on the application of a thin copper sheet on the impactsurface of the incident bar to improve the SHPB waveformthus producing an almost constant strain rate in the spec-imen Li et al [17] carried out repeated impact tests ongranite with the SHPB device and revealed the damagecaused by each impact to be very low for peak stress valuesbetween 60 and 70 of the rock static strength Li et al [5]examined the degradation process of green sandstone

HindawiShock and VibrationVolume 2020 Article ID 8861197 9 pageshttpsdoiorg10115520208861197

subjected to repetitive impact loading by a SHPB apparatusdriven with a pendulum hammer eir test results canimprove the understanding of stability evaluations of rockstructures subjected to repetitive impact loading Wang et al[18] discussed the microproperties of fracture morphologyin granite at different temperatures and repeated impactsFollowing years of accumulation and development thecomplete theory and wide application SHPB technology iscurrently in place [19ndash22]

Concrete is a typical heterogeneous material with a largeaggregate size and many microdefects In order to ensureuniformity the concrete specimen should be of a consid-erable size thus large SHPB devices are required for testing[23] A key bottleneck of large-diameter SHPB experimentaltechnology is the geometric dispersion caused by the lateralinertia effect when the stress pulse propagates in the com-pression bar [24 25] Wang and Wang [26] indicated thatthe pulse shaper can eliminate the high frequency oscillationof the incident wave In particular the pulse shaper extendsthe rise time to reduce the lateral inertia effect and is alsoconducive to constant strain rate loading while also reducingthe specimen strain rate Lee et al [27] investigated theshaping effect of a brass sheet at varying sizes in a 100mmdiameter SHPB experiment Results demonstrated that thesmaller the thickness and diameter of the shaper the longerthe rising edge of the incident wave and the smoother thewaveform enhancing the stress uniformity in the specimenZhu et al [28] used the characteristic method to evaluate thestress uniformity of viscoelastic materials in a high strainrate SHPB experiment revealing the stress uniformity ofbrittle viscoelastic materials to be affected by the increasedincident wave with negative effects for excessive rise times

In this paper cyclic impact compression tests are per-formed using a SHPB device with mortar and concrete as theresearch objects We compare the dynamic mechanics anddamage evolution between mortar and concrete under cyclicimpact Our results provide a theoretical reference for researchon the stability of roadway filling material under rock bursts

2 SHPB Testing Process

21 Specimen Preparation Ordinary Portland cement andpotable laboratory tap water were used for the experimentsConventional crushed stones with particle sizes between 08and 12 cm and natural river sand were employed as the coarseand fine aggregate respectively e concrete was mixed at theproportion of 052 1 167 247 (water cement sand aggre-gate) and subsequently set standing for 24 hours e mold ofthe specimen was then removed and placed in a constanttemperature (20degC) and humidity (95) curing box for 28 daysFollowing curing the specimens were drilled and polished tosmooth the end face e mortar specimen was composed ofconcrete slurry with preparation and curing methods fol-lowing those of concrete e size of both the mortar andconcrete specimens was 71mmtimes 71mm (Figure 1)

22 Experimental Principle e split Hopkinson pressurebar (SHPB) is considered as the most reliable experimental

method when investigating the mechanical properties ofmaterials at medium and high strain rates e SHPB systemused in this paper is located at the structural laboratory ofHohai University and operates at the strain rate range102ndash104 sminus1 e basic working principle of the SHPB testingdevice is described as follows e bullet is pushed by airpressure to impact the incident pressure bar such that anincident wave εI is formed in the bar Once the incident wavereaches the end of the incident bar part of it is reflected toform reflected wave εR e remaining wave energy passesthrough the specimen and enters the transmission bar toform transmission wave εT (Figure 2)

e strain εS(t) strain rate _εS(t) and stress σS(t) of thespecimens during the test were calculated as follows

εS(t) minus2C0

l01113946

t

0εI(t) + εR(t) minus εT(t)1113858 1113859dt

_εS(t) minus2C0

l0εI(t) + εR(t) minus εT(t)1113858 1113859

σS(t) AE0

2AS

εI(t) + εR(t) + εT(t)1113858 1113859

(1)

where C0 is the propagation velocity of the impact wave inthe bar l0 is the specimen thickness A andAS are the cross-sectional area of the bar and the specimen respectively E0 isthe elastic modulus of the bar and εI(t) εR(t) and εT(t) arethe strain signals of the incident transmission and reflectedwaves respectively

23 Experimental Scheme Large diameter specimens willresult in wave dispersion In order to improve the initialincident waveform a pulse shaper is attached to the incidentbar [26]e shaper can ldquotransformrdquo a rectangular pulse intoa triangular pulse to lengthen its rising edge [27] e straingauge on the transmission bar should be close to thespecimen as far as possible which can also reduce the wavedispersion Vaseline was applied to the contact surfacebetween the specimen and bar to reduce the end frictionaleffect e accuracy of the test data can be improved byapplying a filter using the data processing software providedby the SHPB manufacturer Prior to the experiment emptybar tests of two brass and butyl rubber sheet pulse shaperswere performed with a shaper diameter and thickness of20mm and 2mm respectively

Figure 3 demonstrates that the dispersion of thewaveform is effectively reduced following the filtering ewaveform obtained using the brass shaper is rectangularwhile that of the rubber gasket shaper is a half sine wave witha longer rising edge A half-sine incident waveform canbetter meet the constant strain rate condition compared toits rectangular counterpart and thus we selected the rubbersheet pulse shaper for the proceeding experiments

Multiple impact tests must be performed on the samespecimen and hence the critical impact stress should bedetermined to ensure that the specimen can withstandmultiple impacts e impact stress at different amplitudeswas obtained by controlling the air pressure for cyclic

2 Shock and Vibration

impact According to the characteristics of rock burst andprevious experiments the critical impact pressure value ofthe mortar and concrete is 026ndash028MPa erefore themortar and concrete were tested with an air pressure of026MPa and 028MPa respectively

3 Experimental Results and Analysis

31 Stress-Strain Curve Prior to testing the cyclic impactuniaxial compression tests were performed e uniaxialcompressive strength strain and elastic modulus of themortar were determined as 5307MPa 546times10-3 and1310GPa respectively (Figure 4) e corresponding valuesfor concrete were 3123MPa 473times10-3 and 997GPa re-spectively (Figure 5)

Figure 4 shows that the strength brittleness and elasticmodulus of the two mortar specimen groups were signifi-cantly reduced following the multiple impacts e straincorresponding to the peak strength of the two groups wasnot obviously related to the impact times No obviousdifferences were observed in the strength reduction betweenthe two air pressure groups

(a) (b)

Figure 1 Specimens used for the SHPB testing (a) Mortar (b) Concrete

Air gun Striker bar Electronic counterPulse shaper

Incident bar Strain gauge Specimen Transmissionbar

Strain gaugeDamp

Firing chamber

600 3200 1800

37 74

Unit mm

Figure 2 Diagram of the split Hopkinson pressure bar test

ndash01

0

01

02

03

04

05

06

07

0 100 200 300 400 500 600Time (μs)

Volta

ge si

gnal

(V)

Brass sheetRubber sheet

Figure 3 Incident waveform of two pulse shapers

Shock and Vibration 3

Figure 5 shows that at an air pressure of 026MPa nosignificant increases were observed in the strength of thefirst four impact times of the concrete specimen Howeverthe fifth impact time is associated with an obvious decreaseand the specimen has no bearing capacity e elasticmodulus decreased with the increase in impact time At anair pressure of 028MPa the strength associated with thesecond impact was reduced significantly e elasticmodulus exhibited an obvious reduction with increasingimpact time

32 Relation between Peak Stress and Number of CyclicImpacts Figure 6 presents the relation between the mortarand concrete peak stress and the number of cyclic impacts

e mortar and concrete peak stress continuouslydecreased with the increasing impact time indicating thecontinuous deterioration of the bearing capacity e peakstress of mortar specimens varies with the impact pressure(Figure 6(a)) while the slopes of the two curves are almostequal As the number of cyclic impacts increased the peakstress reduction rate of mortar stabilized Following thefourth impact time the peak stress of specimen CC-1decreased from 12026MPa to 2237MPa (8140) whilethe peak stress of specimen CC-2 decreased from14240MPa to 5815MPa (5916) Despite its low impactpressure specimen CC-1 exhibited a marked decrease inpeak stress

Specimens HC-1 and HC-2 had air pressures of026MPa and 028MPa respectively (Figure 6(b)) withthe slope of HC-2 curve double that of HC-1 Morespecifically a rise in the impact number increased theimpact pressure which consequently resulted in a steeperreduction of the concrete peak stress After repeatedimpacts the peak stress of specimen HC-1 decreased from7492MPa to 4093MPa (4537) while that of specimenHC-2 decreased from 8761MPa to 4654MPa (4688)e two specimens exhibit an almost equal reduction inpeak stress

e fitting degree of the mortar specimen is higher thanthat of concrete Although the homogeneity of the concretespecimens could be ensured by the use of large-sizespecimens the dispersion of test data was still relativelylarge Under the same impact pressure the initial peakstress of the mortar was greater than that of concrete eabsolute value of the mortar slope was also larger than thatof concrete indicating the sensitivity of the mortar peakstress to the impact time Moreover the two mortar curvesare parallel while those of concrete intersect e resultsdemonstrate the greater sensitivity of the peak stress to theimpact pressure

33RelationbetweentheEnergyUtilizationRatioandNumberof Cyclic Impacts e energy carried by the incident andtransmission waves and energy utilization rate betweenloading and unloading were determined as follows

WI E0AC0 1113946t

0ε2Idt

WT E0AC0 1113946t

0ε2Tdt

η WT

WI

middot 100

(2)

where WI WT and η are the incident energy transmissionenergy and energy utilization ratio respectively Figure 7depicts the relation between the energy utilization ratio ofmortar and concrete and number of cyclic impacts

e curves in Figures 6 and 7 exhibit similar trends eenergy utilization ratio of both the mortar and concretespecimens decreased as the number of impact cycles in-creased e energy utilization ratio of the mortar specimenvaries with impact pressure (Figure 7(a)) while the slopes ofthe two curves are almost equal In particular under the twoimpact pressures the rate of reduction of the mortar peakstress is almost equal to the increase in cyclic impact timesFollowing the fourth impact time the energy utilization ratioof specimen CC-1 decreased from 789 to 024 (9696)while that of specimen CC-2 decreased from 1050 to164 (8438) e energy utilization ratio of specimensCC-1 and CC-2 decreased greatly following the repeatedimpacts is indicates close to complete breakage of thespecimen

e slope of the specimen HC-2 curve is 264 times thatof HC-1 (Figure 7(b)) revealing that the higher the impactnumber the greater the impact pressure and the steeper thereduction in the energy utilization ratio of the concretesamples After repeated impacts the energy utilization ratioof specimen HC-1 decreased from 471 to 074 (8429)while that of specimen HC-2 decreased from 750 to 097(8707) e reduction ranges are almost equal Moreoverthe fitting degree of the mortar sample is greater than that ofconcrete

Under the same impact pressure the initial energyutilization ratio of mortar was higher than that of concretee absolute value of the mortar slope is larger than that ofconcrete indicating that the energy utilization ratio ofmortar is more sensitive to the impact times Furthermorethe two mortar curves are parallel while those of concreteintersect is demonstrates that the energy utilization ratioof concrete is more sensitive to the impact pressure

34 Relation between Damage Degree and Number of CyclicImpacts e load-unload response ratio (LURR) was ini-tially proposed by Yin Xiangchu [29] who extracted thedamage degree of the target medium based on the concept ofldquothe change of physical quantityrdquo e LURR is used toquantify the damage of the medium e common axialstress is employed as the LURR load variable and thecorresponding strain is used as the response variable eLURR (Y) is defined as follows

4 Shock and Vibration

Y X+

Xminus

(3)

where X+ and Xminus are the response rate under loading andunloading conditions respectively and are defined asfollows

X limΔP⟶0

ΔRΔP

(4)

where ΔP and ΔR denote the increments of load P andresponse R respectively

For the elastic phase the response rate X+ Xminus andthus Y 1 However X+ gtXminus occurs when the load exceedsthe elastic limit and thus Ygt 1emore severe the damageof the material the larger the Y value When the systemapproaches instability Y⟶infin

Based on the assumption that the damage at the fracturelimit obeys the Weibull distribution on the mesoscale

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

0

20

40

60

80

100

120St

ress

(MPa

)

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(a)

0

20

40

60

80

100

140

160

120

Stre

ss (M

Pa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(b)

Figure 4 Cyclic impact stress-strain curves of mortar under different air pressures (a) CC-1 (air pressure of 026MPa) (b) CC-2 (airpressure of 028MPa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

006

0

005

5

3rd

1st2nd

0

20

40

60

80

10

30

50

70

Stre

ss (M

Pa)

4th5th

(a)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

3rd4th

1st2nd

0

20

40

60

80

100

Stre

ss (M

Pa)

(b)

Figure 5 Cyclic impact stress-strain curves of concrete under different air pressures (a) HC-1 (air pressure of 026MPa) (b) HC-2 (airpressure of 028MPa)

Shock and Vibration 5

[30ndash32] Zhang et al [33 34] established a relationshipbetween Y and the damage variable D as follows

D 1 minus exp1 minus Y

mY1113874 1113875 (5)

where m is the Weibull index

e loading and unloading section secant slopes of thestress-strain curve were used to calculate the LURR allowingfor the damage degree of the specimen following eachimpact to be determined (Figure 8)

e first impact was the most damaging for both themortar and concrete samples In particular damage to themortar specimens CC-1 and CC-2 was 073 and 070

0

20

40

60

80

100

120

140

160

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

Stre

ss (M

Pa)

(R2 = 09940)σS = minus28003n + 167875

(R2 = 09893)σS = minus31956n + 154164

(a)

HC-1HC-2Fitting curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Number of cycles

Stre

ss (M

Pa)

(R2 = 07639)σS = minus70337n + 835026

(R2 = 09016)σS = minus14372n + 107798

(b)

Figure 6 Relation between peak stress and the number of cyclic impacts (a) Mortar (b) Concrete

00

20

40

60

80

100

120

Ener

gy u

sage

ratio

()

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

(R2 = 09953)σS = minus2607n + 10549

(R2 = 09937)σS = minus2968n + 13230

(a)

00

10

20

30

40

50

60

70

80

Ener

gy u

sage

ratio

()

0 1 2 3 54

HC-1HC-2Fitting curve

Number of cycles

(R2 = 08920)σS = minus0849n + 5199

(R2 = 09712)σS = minus2239n + 10208

(b)

Figure 7 Relation between the energy utilization ratio and number of cyclic impacts (a) Mortar (b) Concrete

6 Shock and Vibration

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

impact According to the characteristics of rock burst andprevious experiments the critical impact pressure value ofthe mortar and concrete is 026ndash028MPa erefore themortar and concrete were tested with an air pressure of026MPa and 028MPa respectively

3 Experimental Results and Analysis

31 Stress-Strain Curve Prior to testing the cyclic impactuniaxial compression tests were performed e uniaxialcompressive strength strain and elastic modulus of themortar were determined as 5307MPa 546times10-3 and1310GPa respectively (Figure 4) e corresponding valuesfor concrete were 3123MPa 473times10-3 and 997GPa re-spectively (Figure 5)

Figure 4 shows that the strength brittleness and elasticmodulus of the two mortar specimen groups were signifi-cantly reduced following the multiple impacts e straincorresponding to the peak strength of the two groups wasnot obviously related to the impact times No obviousdifferences were observed in the strength reduction betweenthe two air pressure groups

(a) (b)

Figure 1 Specimens used for the SHPB testing (a) Mortar (b) Concrete

Air gun Striker bar Electronic counterPulse shaper

Incident bar Strain gauge Specimen Transmissionbar

Strain gaugeDamp

Firing chamber

600 3200 1800

37 74

Unit mm

Figure 2 Diagram of the split Hopkinson pressure bar test

ndash01

0

01

02

03

04

05

06

07

0 100 200 300 400 500 600Time (μs)

Volta

ge si

gnal

(V)

Brass sheetRubber sheet

Figure 3 Incident waveform of two pulse shapers

Shock and Vibration 3

Figure 5 shows that at an air pressure of 026MPa nosignificant increases were observed in the strength of thefirst four impact times of the concrete specimen Howeverthe fifth impact time is associated with an obvious decreaseand the specimen has no bearing capacity e elasticmodulus decreased with the increase in impact time At anair pressure of 028MPa the strength associated with thesecond impact was reduced significantly e elasticmodulus exhibited an obvious reduction with increasingimpact time

32 Relation between Peak Stress and Number of CyclicImpacts Figure 6 presents the relation between the mortarand concrete peak stress and the number of cyclic impacts

e mortar and concrete peak stress continuouslydecreased with the increasing impact time indicating thecontinuous deterioration of the bearing capacity e peakstress of mortar specimens varies with the impact pressure(Figure 6(a)) while the slopes of the two curves are almostequal As the number of cyclic impacts increased the peakstress reduction rate of mortar stabilized Following thefourth impact time the peak stress of specimen CC-1decreased from 12026MPa to 2237MPa (8140) whilethe peak stress of specimen CC-2 decreased from14240MPa to 5815MPa (5916) Despite its low impactpressure specimen CC-1 exhibited a marked decrease inpeak stress

Specimens HC-1 and HC-2 had air pressures of026MPa and 028MPa respectively (Figure 6(b)) withthe slope of HC-2 curve double that of HC-1 Morespecifically a rise in the impact number increased theimpact pressure which consequently resulted in a steeperreduction of the concrete peak stress After repeatedimpacts the peak stress of specimen HC-1 decreased from7492MPa to 4093MPa (4537) while that of specimenHC-2 decreased from 8761MPa to 4654MPa (4688)e two specimens exhibit an almost equal reduction inpeak stress

e fitting degree of the mortar specimen is higher thanthat of concrete Although the homogeneity of the concretespecimens could be ensured by the use of large-sizespecimens the dispersion of test data was still relativelylarge Under the same impact pressure the initial peakstress of the mortar was greater than that of concrete eabsolute value of the mortar slope was also larger than thatof concrete indicating the sensitivity of the mortar peakstress to the impact time Moreover the two mortar curvesare parallel while those of concrete intersect e resultsdemonstrate the greater sensitivity of the peak stress to theimpact pressure

33RelationbetweentheEnergyUtilizationRatioandNumberof Cyclic Impacts e energy carried by the incident andtransmission waves and energy utilization rate betweenloading and unloading were determined as follows

WI E0AC0 1113946t

0ε2Idt

WT E0AC0 1113946t

0ε2Tdt

η WT

WI

middot 100

(2)

where WI WT and η are the incident energy transmissionenergy and energy utilization ratio respectively Figure 7depicts the relation between the energy utilization ratio ofmortar and concrete and number of cyclic impacts

e curves in Figures 6 and 7 exhibit similar trends eenergy utilization ratio of both the mortar and concretespecimens decreased as the number of impact cycles in-creased e energy utilization ratio of the mortar specimenvaries with impact pressure (Figure 7(a)) while the slopes ofthe two curves are almost equal In particular under the twoimpact pressures the rate of reduction of the mortar peakstress is almost equal to the increase in cyclic impact timesFollowing the fourth impact time the energy utilization ratioof specimen CC-1 decreased from 789 to 024 (9696)while that of specimen CC-2 decreased from 1050 to164 (8438) e energy utilization ratio of specimensCC-1 and CC-2 decreased greatly following the repeatedimpacts is indicates close to complete breakage of thespecimen

e slope of the specimen HC-2 curve is 264 times thatof HC-1 (Figure 7(b)) revealing that the higher the impactnumber the greater the impact pressure and the steeper thereduction in the energy utilization ratio of the concretesamples After repeated impacts the energy utilization ratioof specimen HC-1 decreased from 471 to 074 (8429)while that of specimen HC-2 decreased from 750 to 097(8707) e reduction ranges are almost equal Moreoverthe fitting degree of the mortar sample is greater than that ofconcrete

Under the same impact pressure the initial energyutilization ratio of mortar was higher than that of concretee absolute value of the mortar slope is larger than that ofconcrete indicating that the energy utilization ratio ofmortar is more sensitive to the impact times Furthermorethe two mortar curves are parallel while those of concreteintersect is demonstrates that the energy utilization ratioof concrete is more sensitive to the impact pressure

34 Relation between Damage Degree and Number of CyclicImpacts e load-unload response ratio (LURR) was ini-tially proposed by Yin Xiangchu [29] who extracted thedamage degree of the target medium based on the concept ofldquothe change of physical quantityrdquo e LURR is used toquantify the damage of the medium e common axialstress is employed as the LURR load variable and thecorresponding strain is used as the response variable eLURR (Y) is defined as follows

4 Shock and Vibration

Y X+

Xminus

(3)

where X+ and Xminus are the response rate under loading andunloading conditions respectively and are defined asfollows

X limΔP⟶0

ΔRΔP

(4)

where ΔP and ΔR denote the increments of load P andresponse R respectively

For the elastic phase the response rate X+ Xminus andthus Y 1 However X+ gtXminus occurs when the load exceedsthe elastic limit and thus Ygt 1emore severe the damageof the material the larger the Y value When the systemapproaches instability Y⟶infin

Based on the assumption that the damage at the fracturelimit obeys the Weibull distribution on the mesoscale

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

0

20

40

60

80

100

120St

ress

(MPa

)

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(a)

0

20

40

60

80

100

140

160

120

Stre

ss (M

Pa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(b)

Figure 4 Cyclic impact stress-strain curves of mortar under different air pressures (a) CC-1 (air pressure of 026MPa) (b) CC-2 (airpressure of 028MPa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

006

0

005

5

3rd

1st2nd

0

20

40

60

80

10

30

50

70

Stre

ss (M

Pa)

4th5th

(a)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

3rd4th

1st2nd

0

20

40

60

80

100

Stre

ss (M

Pa)

(b)

Figure 5 Cyclic impact stress-strain curves of concrete under different air pressures (a) HC-1 (air pressure of 026MPa) (b) HC-2 (airpressure of 028MPa)

Shock and Vibration 5

[30ndash32] Zhang et al [33 34] established a relationshipbetween Y and the damage variable D as follows

D 1 minus exp1 minus Y

mY1113874 1113875 (5)

where m is the Weibull index

e loading and unloading section secant slopes of thestress-strain curve were used to calculate the LURR allowingfor the damage degree of the specimen following eachimpact to be determined (Figure 8)

e first impact was the most damaging for both themortar and concrete samples In particular damage to themortar specimens CC-1 and CC-2 was 073 and 070

0

20

40

60

80

100

120

140

160

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

Stre

ss (M

Pa)

(R2 = 09940)σS = minus28003n + 167875

(R2 = 09893)σS = minus31956n + 154164

(a)

HC-1HC-2Fitting curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Number of cycles

Stre

ss (M

Pa)

(R2 = 07639)σS = minus70337n + 835026

(R2 = 09016)σS = minus14372n + 107798

(b)

Figure 6 Relation between peak stress and the number of cyclic impacts (a) Mortar (b) Concrete

00

20

40

60

80

100

120

Ener

gy u

sage

ratio

()

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

(R2 = 09953)σS = minus2607n + 10549

(R2 = 09937)σS = minus2968n + 13230

(a)

00

10

20

30

40

50

60

70

80

Ener

gy u

sage

ratio

()

0 1 2 3 54

HC-1HC-2Fitting curve

Number of cycles

(R2 = 08920)σS = minus0849n + 5199

(R2 = 09712)σS = minus2239n + 10208

(b)

Figure 7 Relation between the energy utilization ratio and number of cyclic impacts (a) Mortar (b) Concrete

6 Shock and Vibration

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

Figure 5 shows that at an air pressure of 026MPa nosignificant increases were observed in the strength of thefirst four impact times of the concrete specimen Howeverthe fifth impact time is associated with an obvious decreaseand the specimen has no bearing capacity e elasticmodulus decreased with the increase in impact time At anair pressure of 028MPa the strength associated with thesecond impact was reduced significantly e elasticmodulus exhibited an obvious reduction with increasingimpact time

32 Relation between Peak Stress and Number of CyclicImpacts Figure 6 presents the relation between the mortarand concrete peak stress and the number of cyclic impacts

e mortar and concrete peak stress continuouslydecreased with the increasing impact time indicating thecontinuous deterioration of the bearing capacity e peakstress of mortar specimens varies with the impact pressure(Figure 6(a)) while the slopes of the two curves are almostequal As the number of cyclic impacts increased the peakstress reduction rate of mortar stabilized Following thefourth impact time the peak stress of specimen CC-1decreased from 12026MPa to 2237MPa (8140) whilethe peak stress of specimen CC-2 decreased from14240MPa to 5815MPa (5916) Despite its low impactpressure specimen CC-1 exhibited a marked decrease inpeak stress

Specimens HC-1 and HC-2 had air pressures of026MPa and 028MPa respectively (Figure 6(b)) withthe slope of HC-2 curve double that of HC-1 Morespecifically a rise in the impact number increased theimpact pressure which consequently resulted in a steeperreduction of the concrete peak stress After repeatedimpacts the peak stress of specimen HC-1 decreased from7492MPa to 4093MPa (4537) while that of specimenHC-2 decreased from 8761MPa to 4654MPa (4688)e two specimens exhibit an almost equal reduction inpeak stress

e fitting degree of the mortar specimen is higher thanthat of concrete Although the homogeneity of the concretespecimens could be ensured by the use of large-sizespecimens the dispersion of test data was still relativelylarge Under the same impact pressure the initial peakstress of the mortar was greater than that of concrete eabsolute value of the mortar slope was also larger than thatof concrete indicating the sensitivity of the mortar peakstress to the impact time Moreover the two mortar curvesare parallel while those of concrete intersect e resultsdemonstrate the greater sensitivity of the peak stress to theimpact pressure

33RelationbetweentheEnergyUtilizationRatioandNumberof Cyclic Impacts e energy carried by the incident andtransmission waves and energy utilization rate betweenloading and unloading were determined as follows

WI E0AC0 1113946t

0ε2Idt

WT E0AC0 1113946t

0ε2Tdt

η WT

WI

middot 100

(2)

where WI WT and η are the incident energy transmissionenergy and energy utilization ratio respectively Figure 7depicts the relation between the energy utilization ratio ofmortar and concrete and number of cyclic impacts

e curves in Figures 6 and 7 exhibit similar trends eenergy utilization ratio of both the mortar and concretespecimens decreased as the number of impact cycles in-creased e energy utilization ratio of the mortar specimenvaries with impact pressure (Figure 7(a)) while the slopes ofthe two curves are almost equal In particular under the twoimpact pressures the rate of reduction of the mortar peakstress is almost equal to the increase in cyclic impact timesFollowing the fourth impact time the energy utilization ratioof specimen CC-1 decreased from 789 to 024 (9696)while that of specimen CC-2 decreased from 1050 to164 (8438) e energy utilization ratio of specimensCC-1 and CC-2 decreased greatly following the repeatedimpacts is indicates close to complete breakage of thespecimen

e slope of the specimen HC-2 curve is 264 times thatof HC-1 (Figure 7(b)) revealing that the higher the impactnumber the greater the impact pressure and the steeper thereduction in the energy utilization ratio of the concretesamples After repeated impacts the energy utilization ratioof specimen HC-1 decreased from 471 to 074 (8429)while that of specimen HC-2 decreased from 750 to 097(8707) e reduction ranges are almost equal Moreoverthe fitting degree of the mortar sample is greater than that ofconcrete

Under the same impact pressure the initial energyutilization ratio of mortar was higher than that of concretee absolute value of the mortar slope is larger than that ofconcrete indicating that the energy utilization ratio ofmortar is more sensitive to the impact times Furthermorethe two mortar curves are parallel while those of concreteintersect is demonstrates that the energy utilization ratioof concrete is more sensitive to the impact pressure

34 Relation between Damage Degree and Number of CyclicImpacts e load-unload response ratio (LURR) was ini-tially proposed by Yin Xiangchu [29] who extracted thedamage degree of the target medium based on the concept ofldquothe change of physical quantityrdquo e LURR is used toquantify the damage of the medium e common axialstress is employed as the LURR load variable and thecorresponding strain is used as the response variable eLURR (Y) is defined as follows

4 Shock and Vibration

Y X+

Xminus

(3)

where X+ and Xminus are the response rate under loading andunloading conditions respectively and are defined asfollows

X limΔP⟶0

ΔRΔP

(4)

where ΔP and ΔR denote the increments of load P andresponse R respectively

For the elastic phase the response rate X+ Xminus andthus Y 1 However X+ gtXminus occurs when the load exceedsthe elastic limit and thus Ygt 1emore severe the damageof the material the larger the Y value When the systemapproaches instability Y⟶infin

Based on the assumption that the damage at the fracturelimit obeys the Weibull distribution on the mesoscale

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

0

20

40

60

80

100

120St

ress

(MPa

)

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(a)

0

20

40

60

80

100

140

160

120

Stre

ss (M

Pa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(b)

Figure 4 Cyclic impact stress-strain curves of mortar under different air pressures (a) CC-1 (air pressure of 026MPa) (b) CC-2 (airpressure of 028MPa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

006

0

005

5

3rd

1st2nd

0

20

40

60

80

10

30

50

70

Stre

ss (M

Pa)

4th5th

(a)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

3rd4th

1st2nd

0

20

40

60

80

100

Stre

ss (M

Pa)

(b)

Figure 5 Cyclic impact stress-strain curves of concrete under different air pressures (a) HC-1 (air pressure of 026MPa) (b) HC-2 (airpressure of 028MPa)

Shock and Vibration 5

[30ndash32] Zhang et al [33 34] established a relationshipbetween Y and the damage variable D as follows

D 1 minus exp1 minus Y

mY1113874 1113875 (5)

where m is the Weibull index

e loading and unloading section secant slopes of thestress-strain curve were used to calculate the LURR allowingfor the damage degree of the specimen following eachimpact to be determined (Figure 8)

e first impact was the most damaging for both themortar and concrete samples In particular damage to themortar specimens CC-1 and CC-2 was 073 and 070

0

20

40

60

80

100

120

140

160

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

Stre

ss (M

Pa)

(R2 = 09940)σS = minus28003n + 167875

(R2 = 09893)σS = minus31956n + 154164

(a)

HC-1HC-2Fitting curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Number of cycles

Stre

ss (M

Pa)

(R2 = 07639)σS = minus70337n + 835026

(R2 = 09016)σS = minus14372n + 107798

(b)

Figure 6 Relation between peak stress and the number of cyclic impacts (a) Mortar (b) Concrete

00

20

40

60

80

100

120

Ener

gy u

sage

ratio

()

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

(R2 = 09953)σS = minus2607n + 10549

(R2 = 09937)σS = minus2968n + 13230

(a)

00

10

20

30

40

50

60

70

80

Ener

gy u

sage

ratio

()

0 1 2 3 54

HC-1HC-2Fitting curve

Number of cycles

(R2 = 08920)σS = minus0849n + 5199

(R2 = 09712)σS = minus2239n + 10208

(b)

Figure 7 Relation between the energy utilization ratio and number of cyclic impacts (a) Mortar (b) Concrete

6 Shock and Vibration

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

Y X+

Xminus

(3)

where X+ and Xminus are the response rate under loading andunloading conditions respectively and are defined asfollows

X limΔP⟶0

ΔRΔP

(4)

where ΔP and ΔR denote the increments of load P andresponse R respectively

For the elastic phase the response rate X+ Xminus andthus Y 1 However X+ gtXminus occurs when the load exceedsthe elastic limit and thus Ygt 1emore severe the damageof the material the larger the Y value When the systemapproaches instability Y⟶infin

Based on the assumption that the damage at the fracturelimit obeys the Weibull distribution on the mesoscale

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

0

20

40

60

80

100

120St

ress

(MPa

)

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(a)

0

20

40

60

80

100

140

160

120

Stre

ss (M

Pa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

005

5

3rd4th

1st2nd

(b)

Figure 4 Cyclic impact stress-strain curves of mortar under different air pressures (a) CC-1 (air pressure of 026MPa) (b) CC-2 (airpressure of 028MPa)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

006

0

005

5

3rd

1st2nd

0

20

40

60

80

10

30

50

70

Stre

ss (M

Pa)

4th5th

(a)

000

0

000

5

001

0

001

5

002

0

002

5

003

0

Strain

003

5

004

0

004

5

005

0

3rd4th

1st2nd

0

20

40

60

80

100

Stre

ss (M

Pa)

(b)

Figure 5 Cyclic impact stress-strain curves of concrete under different air pressures (a) HC-1 (air pressure of 026MPa) (b) HC-2 (airpressure of 028MPa)

Shock and Vibration 5

[30ndash32] Zhang et al [33 34] established a relationshipbetween Y and the damage variable D as follows

D 1 minus exp1 minus Y

mY1113874 1113875 (5)

where m is the Weibull index

e loading and unloading section secant slopes of thestress-strain curve were used to calculate the LURR allowingfor the damage degree of the specimen following eachimpact to be determined (Figure 8)

e first impact was the most damaging for both themortar and concrete samples In particular damage to themortar specimens CC-1 and CC-2 was 073 and 070

0

20

40

60

80

100

120

140

160

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

Stre

ss (M

Pa)

(R2 = 09940)σS = minus28003n + 167875

(R2 = 09893)σS = minus31956n + 154164

(a)

HC-1HC-2Fitting curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Number of cycles

Stre

ss (M

Pa)

(R2 = 07639)σS = minus70337n + 835026

(R2 = 09016)σS = minus14372n + 107798

(b)

Figure 6 Relation between peak stress and the number of cyclic impacts (a) Mortar (b) Concrete

00

20

40

60

80

100

120

Ener

gy u

sage

ratio

()

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

(R2 = 09953)σS = minus2607n + 10549

(R2 = 09937)σS = minus2968n + 13230

(a)

00

10

20

30

40

50

60

70

80

Ener

gy u

sage

ratio

()

0 1 2 3 54

HC-1HC-2Fitting curve

Number of cycles

(R2 = 08920)σS = minus0849n + 5199

(R2 = 09712)σS = minus2239n + 10208

(b)

Figure 7 Relation between the energy utilization ratio and number of cyclic impacts (a) Mortar (b) Concrete

6 Shock and Vibration

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

[30ndash32] Zhang et al [33 34] established a relationshipbetween Y and the damage variable D as follows

D 1 minus exp1 minus Y

mY1113874 1113875 (5)

where m is the Weibull index

e loading and unloading section secant slopes of thestress-strain curve were used to calculate the LURR allowingfor the damage degree of the specimen following eachimpact to be determined (Figure 8)

e first impact was the most damaging for both themortar and concrete samples In particular damage to themortar specimens CC-1 and CC-2 was 073 and 070

0

20

40

60

80

100

120

140

160

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

Stre

ss (M

Pa)

(R2 = 09940)σS = minus28003n + 167875

(R2 = 09893)σS = minus31956n + 154164

(a)

HC-1HC-2Fitting curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Number of cycles

Stre

ss (M

Pa)

(R2 = 07639)σS = minus70337n + 835026

(R2 = 09016)σS = minus14372n + 107798

(b)

Figure 6 Relation between peak stress and the number of cyclic impacts (a) Mortar (b) Concrete

00

20

40

60

80

100

120

Ener

gy u

sage

ratio

()

0 1 2 3 4

CC-1CC-2Fitting curve

Number of cycles

(R2 = 09953)σS = minus2607n + 10549

(R2 = 09937)σS = minus2968n + 13230

(a)

00

10

20

30

40

50

60

70

80

Ener

gy u

sage

ratio

()

0 1 2 3 54

HC-1HC-2Fitting curve

Number of cycles

(R2 = 08920)σS = minus0849n + 5199

(R2 = 09712)σS = minus2239n + 10208

(b)

Figure 7 Relation between the energy utilization ratio and number of cyclic impacts (a) Mortar (b) Concrete

6 Shock and Vibration

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

accounting for 7842 and 7735 of the maximum damagerespectively (Figure 8(a)) In the subsequent cyclic impactsthe increase in damage of specimen CC-1 was relativelyminimal with a damage increment less than 011 When thedamage reached 093 the load was unbearable e damageincrement of specimen CC-2 approached 0 at the secondimpact while at the third and fourth impact the damageincrement of the specimen increased rapidly When thedamage reached 090 the specimen could not bear the loade maximum damage increment of the last three impactswas 012

e damage of concrete specimens HC-1 and HC-2 atthe first impact was observed as 078 and 070 accounting for7798 and 6800 of the maximum damage respectively(Figure 8(b)) During the subsequent cyclic impacts thedamage accumulation of the two specimens exhibited slightfluctuations e maximum damage increment of HC-1 wasobserved as 0072 while that of HC-2 was 0018 e twospecimens were unable to bear their loads once the damagereached 092 and 090 respectively

e results demonstrate the strong similarity betweenthe damage evolution trends of the mortar and concretespecimens under cyclic impact loads At the initial impactthe damage was greater than 07When the damage exceeded09 the specimen no longer had a bearing capacity uswhen the damage degree of the first impact was greater than07 the effects of the impact times and pressure on themortar and concrete damage evolution were relatively small

4 Conclusion

e current paper is based on the assumption that rockbursts are typically followed by continuous multiple shocksFilling materials mortar and concrete were selected as the

research objects to investigate the mechanical properties ofmortar and concrete under cyclic impacts e followingconclusions were determined

(1) e SHPB testing of large-size specimens revealedthe improvement of the waveform shape and thereduction in the wave dispersion via the applicationof a rubber sheet as the pulse shaper Followingrepeated impacts the peak stress of the mortar andconcrete specimens was reduced is indicatesobvious fatigue characteristics

(2) Although the large-size concrete specimens couldmaintain a certain level of homogeneity the dis-persion was relatively largee peak stress of mortarwas sensitive to the impact time while that ofconcrete was sensitive to impact pressure

(3) As the number of cycles increased the energy uti-lization ratio of the mortar and concrete specimensdecreased Under the same impact pressure theinitial energy utilization ratio of mortar was higherthan that of concrete Furthermore the energy uti-lization ratio of mortar was sensitive to the impacttime while that of concrete was more sensitive to theimpact pressure

(4) Trends in the damage evolution of mortar andconcrete were in strong agreement under the cyclicimpact load e impact pressure had a minimaleffect on the damage evolution

Data Availability

e experimental data used to support the findings of thisstudy are available from the corresponding author uponrequest

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4

CC-1CC-2

Number of cycles

Dam

age d

egre

e

(a)

HC-1HC-2

00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5Number of cycles

Dam

age d

egre

e(b)

Figure 8 Relation between damage degree and number of impact cycles t (a) Mortar (b) Concrete

Shock and Vibration 7

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 41831278 51579081 and51709184) and Central Public-Interest Scientific InstitutionBasal Research Fund (Grant no Y118008)

References

[1] Y Jiang Y Zhao HWang et al ldquoA review of mechanism andprevention technologies of coal bumps in Chinardquo Journal ofRock Mechanics and Geotechnical Engineering vol 9 no 1pp 180ndash194 2017

[2] X Pang Y Jiang Y Zhao and J Zhu ldquoStudy on risk analysisand control technology of coal bumprdquo Procedia Environ-mental Sciences vol 12 pp 831ndash836 2012

[3] S Qin J J Jiao C A Tang et al ldquoInstability leading to coalbumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof systemrdquo International Journal of Solids andStructures vol 43 no 25-26 pp 7407ndash7423 2006

[4] Y L Tan X S Liu B Shen et al ldquoNew approaches to testingand evaluating the impact capability of coal seam with hardroof andor floor in coal minesrdquo Geomechanics and Engi-neering vol 14 no 4 pp 367ndash376 2018

[5] S H Li W C Zhu L L Niu et al ldquoDynamic characteristicsof green sandstone subjected to repetitive impact loadingphenomena and mechanismsrdquo Rock Mechanics and RockEngineering vol 51 no 6 pp 1921ndash1936 2018

[6] Q Qian and X Zhou ldquoFailure behaviors and rock defor-mation during excavation of underground cavern group forjinping I hydropower stationrdquo Rock Mechanics and RockEngineering vol 51 no 8 pp 2639ndash2651 2018

[7] K DuM Tao X Li et al ldquoExperimental study of slabbing androckburst induced by true-triaxial unloading and local dy-namic disturbancerdquo Rock Mechanics and Rock Engineeringvol 49 no 9 pp 3437ndash3453 2016

[8] G Zhu L Dou A Cao et al ldquoAssessment and analysis ofstrata movement with special reference to rock burst mech-anism in island longwall panelrdquo Journal of Central SouthUniversity vol 24 no 12 pp 2951ndash2960 2017

[9] K A Heasley and I B Tulu ldquoUsing LaModel to analyze coalbumpsrdquo International Journal of Mining Science and Tech-nology vol 28 no 5 pp 729ndash737 2018

[10] Z Li Y Xue S Li et al ldquoRock burst risk assessment in deep-buried underground caverns a novel analysis methodrdquoArabian Journal of Geosciences vol 13 no 11 2020

[11] L Weng L Huang A Taheri and X Li ldquoRockburst char-acteristics and numerical simulation based on a strain energydensity index a case study of a roadway in Linglong goldmine Chinardquo Tunnelling and Underground Space Technologyvol 69 pp 223ndash232 2017

[12] Q Jiang X Feng T Xiang et al ldquoRockburst characteristicsand numerical simulation based on a new energy index a casestudy of a tunnel at 2500m depthrdquo Bulletin of EngineeringGeology and the Environment vol 69 no 3 pp 381ndash388 2010

[13] B Hopkinson ldquoA method of measuring the pressure pro-duced in the detonation of high explosives or by the impact ofbulletsrdquo Philosophical Transactions of the Ｒoyal Society ofLondon Series A Containing Papers of a Mathematical orPhysical Character vol 89 pp 411ndash413 1914

[14] G I Taylor ldquoe testing of materials at high rates of loadingrdquoJournal of the Institution of Civil Engineers vol 26 no 8pp 486ndash519 1946

[15] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949

[16] D J Frew M J Forrestal and W Chen ldquoA split Hopkinsonpressure bar technique to determine compressive stress-straindata for rock materialsrdquo Experimental Mechanics vol 1no 41 pp 40ndash46 2001

[17] X B Li T S Lok and J Zhao ldquoDynamic characteristics ofgranite subjected to intermediate loading raterdquo Rock Me-chanics and Rock Engineering vol 38 no 1 pp 21ndash39 2005

[18] P Wang P Wang T Yin et al ldquoDynamic properties ofthermally treated granite subjected to cyclic impact loadingrdquoRock Mechanics and Rock Engineering vol 52 no 4pp 991ndash1010 2019

[19] J Zhou and LGe ldquoEffect of strain rate andwater-to-cement ratioon compressive mechanical behavior of cement mortarrdquo Journalof Central South University vol 22 no 3 pp 1087ndash1095 2015

[20] H-b Du F Dai Y Xu Y Liu and H-n Xu ldquoNumericalinvestigation on the dynamic strength and failure behavior ofrocks under hydrostatic confinement in SHPB testingrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 108 pp 43ndash57 2018

[21] N Wu J Fu Z Zhu and B Sun ldquoExperimental study on thedynamic behavior of the Brazilian disc sample of rock ma-terialrdquo International Journal of Rock Mechanics and MiningSciences vol 130 p 104326 2020

[22] N Wu Z Zhu C Zhang et al ldquoDynamic behavior of rockjoint under different impact loadsrdquo KSCE Journal of CivilEngineering vol 23 no 2 pp 541ndash548 2019

[23] X T Wu S S Hu B Y Yang et al ldquoAn improvement inmeasuring the dynamic properties of concrete material by thetraditional SHPB techniquerdquo Journal of Hefei University ofTechnology vol 1 pp 63ndash66 2004

[24] C Chree ldquoe equations of an isotropic elastic solid in polarand cylindrical Co-ordinates their solution and applicationrdquoTransactions of the Cambridge Philosophical Society vol 14pp 250ndash369 1889

[25] L Pochhammer ldquoUeber die fortpflanzungsgeschwindigkeitenkleiner schwingungen in einem unbegrenzten isotropenkreiscylinderrdquo Journal fur die reine und angewandte Math-ematikPY vol 81 pp 324ndash336 1876

[26] Y G Wang and L L Wang ldquoStress wave dispersion in large-diameter SHPB and its manifold manifestationsrdquo Journal ofBeijing Institute of Technology vol 3 pp 247ndash253 2004

[27] O S Lee S H Kim and Y H Han ldquoickness effect of pulseshaper on dynamic stress equilibrium and dynamic defor-mation behavior in the polycarbonate using SHPB techniquerdquoJournal of Experimental Mechanics vol 21 no 1 pp 51ndash602006

[28] J Zhu S Hu and L Wang ldquoAn analysis of stress uniformityfor concrete-like specimens during SHPB testsrdquo InternationalJournal of Impact Engineering vol 36 no 1 pp 61ndash72 2009

[29] X Yin L Zhang H Zhang et al ldquoLURrsquos twenty years and itsperspectiverdquo Pure and Applied Geophysics vol 163 no 11-12pp 2317ndash2341 2006

[30] X H Xu S P Ma M F Xia et al ldquoDamage evaluation anddamage localization of rockrdquogteoretical and Applied FractureMechanics vol 42 no 2 pp 131ndash138 2004

[31] Y-J Wei M-F Xia F-J Ke X-C Yin and Y-L BaildquoEvolution-induced catastrophe and its predictabilityrdquo Mi-croscopic and Macroscopic Simulation Towards Predictive

8 Shock and Vibration

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9

Modelling of the Earthquake Process vol 157 no 11-12pp 1945ndash1957 2000

[32] W Weibull ldquoA statistical distribution function of wide ap-plicabilityrdquo Transactions of the ASME Journal of AppliedMechanics vol 2 no 18 pp 293ndash297 1951

[33] L Zhang H Yu and X Yin ldquoFailure potential evaluation inengineering experiments using loadunload response ratiomethodrdquo Pure and Applied Geophysics vol 170 no 1-2pp 237ndash245 2013

[34] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

Shock and Vibration 9