experimental research on mechanical and energy...
TRANSCRIPT
Research ArticleExperimental Research on Mechanical and EnergyCharacteristics of Reinforced Rock under Dynamic Loading
Xinxi Liu1 Yu Li 1 Fujun Zhao 2 Yanming Zhou1 Weiwei Wang1 and Shengnan Li1
1School of Civil Engineering Changsha University of Science amp Technology Changsha 410114 China2School of Resource Environment and Safety Engineering Hunan University of Science and Technology Xiangtan 411201 China
Correspondence should be addressed to Yu Li 1986740197qqcom
Received 31 July 2019 Revised 6 October 2019 Accepted 10 October 2019 Published 11 November 2019
Academic Editor Luca Landi
Copyright copy 2019 Xinxi Liu et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
-e properties of anchored surrounding rock may vary considerably under complex geological and stress conditions especiallydynamic loading in deep mining -erefore comprehensive study of the reinforced mechanism is required to prevent failuresassociated with deep mining In this paper with sandstone as matrix and steel bar as bolt the dynamic compression test ofreinforced rock was carried out by using a 50mm rod diameter split Hopkinson pressure bar (SHPB) test device -e mechanicaland energy characteristics of reinforced rock under dynamic loading were analyzed-e results show that the dynamic strength ofreinforced sample is greater than that of unreinforced sample and increases with the increase of the strain rate -e reflectedenergy and absorbed energy increase with the increase of incident energy while the transmitted energy increases slightly -ehigher the strain rate the larger the energy dissipation rate and the higher the degree of fragmentation It shows that the energydissipation characteristic reflects the internal damage process to some extent Compared with the results of unreinforced samplesthe reflected energy of reinforced samples significantly increases and the absorbed energy will significantly decrease It can be seenthat the bolt can reduce absorbed energy of surrounding rock thereby improving the stability of roadway surrounding rock -eresults may provide reference for the stability of deep roadway and support design
1 Introduction
Rockbolts are considered as a simple safe and economicalrock mass reinforcement technology which are widely usedin mines slopes tunnels and other geotechnical engi-neering and have achieved good economic and socialbenefits [1] Rockbolt performance and reinforcement areinfluenced by geological and stress conditions [2 3] espe-cially affected by impact loading which are suspected as thegreat challenges to the reinforcement mechanism andsupport design [4 5]
In recent decades many scholars carried out lots oflaboratory and numerical tests complemented by theoreticalanalysis to study the mechanism of anchored rock Inroadway support the anchor housing is often installed insections over a short section with one resin charge or usingan expansion head [6 7] Carranza-Torres [8] proposed aclosed-form solution of rockbolt reinforcement around
tunnels and numerical analysis confirmed that the bolt playsan important role in increasing the tunnel confining pres-sure and controlling the surrounding rock deformationZhao and Yang [9] designed the pull test of bolt with crackbased on the separation defect in the anchorage area andanalyzed the influence of crack on axial stress and shearstress distribution of bolt Zhang et al [10] analyzed themechanical properties of reinforced rock mass with cross-flaws and obtained that the compressive strength of cross-flaws rock is higher than that of single-flaw rock A newanalytical model that represents the behavior of reinforcedground near a circular underground opening in a homo-geneous uniform stress field has been developed by con-sidering the interaction behaviors between the groutedrockbolt and ground [11] Moosavi and Grayeli [12] sim-ulated rockbolt support problems by using the DDAmethodand mainly focused on the basic performance of the supportsystem Freeman [13] first proposed the concept of ldquoneutral
HindawiShock and VibrationVolume 2019 Article ID 4356729 11 pageshttpsdoiorg10115520194356729
pointrdquo by analyzing the full-length bonded anchor in the testtunnel which is widely recognized and applied but theposition of ldquoneutral pointrdquo is difficult to determine
In practical rock engineering rock mass is subjected tostatic load and will also be affected by dynamic loads [14]such as impact seismic explosion earthquake and blastingAt present some research studies have been carried out onthe dynamic mechanical response of rock [15ndash19] Li et al[16] analyzed the cracking of single-crack marble specimenunder impact loading based on experimental study For thedifficulty of studying the failure process of undergroundrock an experimental method is proposed to explore dy-namic failure process of prestressed rock specimen with acircular hole [17] Zhang et al [18] andHao et al [19] studiedthe effects of bedding on the dynamic and static properties ofcoal and rock respectively However few research studieshave been carried out on the dynamic response of therockbolt and reinforced surrounding rock [20ndash23] And dueto complicated geological and mining conditions a morecomplete understanding of the mechanical property ofreinforced rock is required-erefore in this study dynamiccompression tests of sandstones reinforced by using a steelbar were conducted -e mechanical and energy charac-teristics of the reinforced rock under dynamic loading wereinvestigated and the results may provide reference for thestability of deep roadway and support design
2 Specimen Preparation andExperimental Methods
21 Specimen Preparation -e sandstone used in the ex-periment was taken from Linyi Shandong Province ChinaAccording to the standard GBT50266-2013 [24] standardcylindrical samples were made (A-1 and A-2) Mechanicalparameters of the standard cylindrical specimen were ob-tained by using the RMT-150C rock mechanics test system(see Figure 1) -e compression test was carried out bydisplacement control with a loading rate of 0002mms Twodisplacement sensors with a range of 2mmwere used duringthe test to determine transverse deformation of sandstonesamples -e average compressive strength and elasticmodulus of the standard cylindrical specimen are 532MPaand 43GPa respectively Meanwhile the sandstone spec-imen was observed by using a scanning electron microscopewith SU3500 as shown in Figure 2 From the figure it isobserved that the internal microstructure of the rock is tightand mainly consists of quartz and feldspar
-e test samples shown in Figure 3(a) were used forunreinforced and reinforced tests and labeled as US and RSrespectively For example ldquoUS-1rdquo represents the 1 un-reinforced specimen and ldquoRS-1rdquo represents the 1 reinforcedspecimen -e sample size is 50mm in thickness and 50mmin diameter For the reinforced specimen the bolt arrange-ment is shown in Figure 3(b) A hole with a diameter of 3mmwas drilled through the center side of the specimen In thisexperiment a steel bar was used to simulate the rockbolt -esteel bar was inserted into the hole and anchored on the rockwith resin (the resin used is the same as in mine conditions)-e steel bar is 60mm long 2mm wide and 2mm thick with
the tensile strength of 600MPa shear strength of 400MPaand elastic modulus of 210GPa Since the SHPB test can onlydirectly control the impact pressure and cannot directly setdifferent strain rates the impact compression test was con-ducted under the impact pressure range of 035sim06MPa
22 Test System -e dynamic compression test of rock wascarried out by using a 50mm rod diameter split Hopkinsonpressure bar (SHPB) test device Figure 4 illustrates theschematic of the SHPB system which mainly consists of twoparts ie three bars (an incident bar with a length of 2m atransmitted bar with a length of 15m and an absorbing barwith a length of 05m) and a data acquisition subsystem Asemisine wave was generated by a special shape striker andused as the loading stress wave to ensure that the stress waseven before failure of the specimens [25 26] -e incidenttransmitted and absorbing bars were made of 40Cr alloysteel with a density of 7810 kgm3 longitudinal wave velocityof 5410ms and elastic modulus of 250GPa -e straingauge model on the incident and transmitted bars is BE120-5AA and the resistance value is 120Ω -e measurementbase has a length of 85mm and a width of 4mm -e KD6009 strain amplifier is used to collect data signals
A-2
A-1Stre
ss (M
Pa)
0
10
20
30
40
50
60
70
0004 0008 0012 0016 0020 00240000Strain
Figure 1 Mechanical properties of the sandstone
Figure 2 Electron microscopy of the sandstone
2 Shock and Vibration
According to the stress wave signals collected by straingauges on the incident and transmitted bars the stressstrain and strain rate of the specimen during impact loadingwere calculated based on the one-dimensional stress wavetheory and stress uniformity hypothesis -e calculationformula is as follows [25]
σ(t) AeEe
2AsεI(t) + εR(t) + εT(t)1113858 1113859 (1)
ε(t) Ce
Ls1113946
t
0εI(t) minus εR(t) minus εT(t)1113858 1113859dt (2)
_ε(t) Ce
LsεI(t) minus εR(t) minus εT(t)1113858 1113859 (3)
where σ(t) ε(t) and _ε(t) are the stress strain and strainrate respectively As and Ae are the area of the specimen and
the bar respectively Ee is the elastic modulus of bars εΙ(t)εR(t) and εT(t) are the incident wave reflected wave andtransmitted wave respectively Ls is the length of specimenCe is the wave velocity of bars
3 Experimental Results
31 Stress Equilibrium For dynamic compression tests it isnecessary to eliminate wave dispersion and inertia effect toensure the accuracy of test results -erefore the stressequilibrium at the two ends of the specimen before failurewas reached In this paper the typical stress wave signals ofsamples US-4 and RS-4 from the dynamic loading experi-ment are shown in Figure 5 With increase of loading timethe curve of the sum of the incident and reflected waves(In + Re) almost overlaps with that of the stress (Tr) in-dicating that the specimen is basically in a stress equilibrium
(a)
Rock
Bolt
Resin 50mm
50mm
25mm
(b)
Figure 3 Specimen preparation (a) -e unreinforced and reinforced samples (b) -e bolt arrangement
Damper
Absorbing bar Transmitted bar
Specimen
Strain gauge
Incident bar Cone-shaped striker
Gas gun
Gas valve
Compressednitrogen gas
Tr signal In amp Re signal
Wheatstonebridge
Ultradynamicstrain gauge
OscilloscopeData processing
system
Wheatstonebridge
Incident waveTransmitted wave
Reflected wave
Figure 4 Schematic of the SHPB system
Shock and Vibration 3
state during this dynamic loading process and the test dataare reliable
32 Stress-StrainCurve Characteristics -e strain signals onthe incident and transmitted bars were recorded by using theultradynamic strain gauge Based on equations (1) and (2)the strain signals on the incident and transmitted bars can beconverted into the stress and strain signals of the specimenduring dynamic loading -e stress-strain curves of samplesunder dynamic loading are shown in Figure 6
It can be seen from Figure 6 that the stress-strain curve ofthe specimen can be divided into the phase of linear elas-ticity plasticity and failure under dynamic loading Due tothe high impact velocity the phase of macro-microscopicdefect closure compaction is extremely short and there isbasically no sunken section in the stress-strain curve whichdirectly enters the phase of linear elasticity and the stressincreases linearly with the strain -en the phase of plas-ticity begins and the slope of the curve decreases Finally theultimate strength of the specimen is reached accompaniedby the failure of the specimen
33 Dynamic Compressive Strength -e mechanical pa-rameters of the specimens under impact loading are shownin Table 1 In order to analyze the effect of the loading rateand bolt on rock strength the test results are plotted asscatter plot as shown in Figure 7
Figure 7 shows that the dynamic compressive strength ofUS and RS samples increases with the increase of strain rateMoreover the dynamic elastic modulus of the specimen isdifferent under different strain rates (Figure 7) and thedynamic elastic modulus increases with the increase of strainrate It shows that the rock specimen has a strong correlationwith the strain rate-e dynamic compressive strength of RSsamples is slightly higher than that of US samples -eresults show that the strength and deformation ability ofrock are improved by applying rockbolt and reflecting theobvious correlation of strain rate
4 Energy Characteristics
41 Energy Calculation According to the energy balance[27] the absorbed energy of rock during impact loading canbe calculated using the following equation [28]
Wa WI minus WR + WT( 1113857 (4)
where Wa WI WR andWT are the absorbed energy in-cident energy reflected energy and transmitted energyrespectively WI WR andWT can be calculated using thefollowing equations [28]
WI EeAeCe 1113946t
0ε2I(t)dt (5)
WR EeAeCe 1113946t
0ε2R(t)dt (6)
WT EeAeCe 1113946t
0ε2T(t)dt (7)
-e results show that the absorbed energy of rock ismainly converted into the energy dissipation kinetic energyand other energy among which the energy dissipation ofspecimen fragmentation is more than 90 of the absorbedenergy [29]-erefore the absorbed energy is approximatelysubstituted for the energy dissipation of specimen frag-mentation in this study In order to measure the strength ofenergy dissipation of the US and RS specimens under dif-ferent loading rates it is generally characterized by theenergy dissipation rate which can be calculated as
N Wa
WI (8)
where N is the energy dissipation rate
42 Analysis of Energy-Time Curves Certainly the de-formation and destruction of rock is the whole process of theenergy dissipation and energy release [30ndash32] -erefore theenergy dissipation characteristics of samples during impactloading are analyzed from the viewpoint of energy Accordingto equations (4)ndash(7) the strain-time curves of specimen areobtained by the experiment -e energy-time curves of allsamples are plotted in Figures 8 and 9 by calculating
It can be seen from Figures 8 and 9 that the same phe-nomenon occurs for US and RS samples under impactloading -e incident energy reflected energy and absorbedenergy increase rapidly compared with the transmitted energywith the propagation of the stress wave and their valuesmaintain stable after reaching a certain value while thetransmitted energy-time curve is approximately a horizontalline Based on the stress-time curve and energy-time curve wecan find that the appearance of maximum absorption energyindicates the failure of the US and RS samples [33]
43 Energy ChangeCharacteristics Test results of the energydistribution of samples under impact loading are shown inTable 2 In order to analyze the effect of loading rate and bolton energy characteristics the test results are plotted asscatter plot as shown in Figures 10 and 11
Because the generation of incident energy is caused bythe impact between the striker bar and incident bar thevalue of incident energy is determined only by the velocity ofthe impact bar In this study loading rates are the singlefactor and the sample type (US and RS samples) has noeffect on the incident energy Figure 10(a) shows that thereflected energy of all samples increases linearly with theincrease of incident energy and the transmitted energyincreases slightly -e absorbed energy of specimen in-creases as a power function with the incident energy(Figure 10(b)) As can be seen from Table 2 most of theenergy is dissipated in the form of reflected wave with in-crease in the incident energy which is consistent with theresults of Li et al [34]
4 Shock and Vibration
Figure 11 shows that there is an exponential relationbetween the energy dissipation rate of samples and strainrate -e failure of sample becomes more severe with the
strain rate and the failure mode of sample develops fromcleavage to fragmentation -at is to say more energy wasused to generate new cracks in the samples with the
0 50 100 150 200
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200St
ress
(MPa
)
Time (μs)
InRe
TrIn + Re
(a)
Stre
ss (M
Pa)
InRe
TrIn + Re
50 100 150 2000Time (μs)
ndash250
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200
(b)
Figure 5 Typical dynamic stress equilibrium results at unreinforced and reinforced conditions (a) US-4 (b) RS-4
US-1US-2US-3
Stre
ss (M
Pa)
US-4US-5US-6
0004 0008 0012 00160000Strain
0
20
40
60
80
100
(a)
RS-1RS-2RS-3
RS-4RS-5RS-6
Stre
ss (M
Pa)
0002 0004 0006 0008 0010 0012 00140000Strain
0
20
40
60
80
100
(b)
Figure 6 Stress-strain curves of samples under dynamic loading (a) Unreinforced samples (b) Reinforced samples
Table 1 -e mechanical parameters of samples under dynamic loading
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
US-1 51 561 59 RS-1 49 590 63US-2 61 607 62 RS-2 69 692 67US-3 73 704 69 RS-3 80 779 74US-4 77 714 72 RS-4 87 805 76US-5 85 733 73 RS-5 93 880 88US-6 98 855 84 RS-6 105 994 94
Shock and Vibration 5
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
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pointrdquo by analyzing the full-length bonded anchor in the testtunnel which is widely recognized and applied but theposition of ldquoneutral pointrdquo is difficult to determine
In practical rock engineering rock mass is subjected tostatic load and will also be affected by dynamic loads [14]such as impact seismic explosion earthquake and blastingAt present some research studies have been carried out onthe dynamic mechanical response of rock [15ndash19] Li et al[16] analyzed the cracking of single-crack marble specimenunder impact loading based on experimental study For thedifficulty of studying the failure process of undergroundrock an experimental method is proposed to explore dy-namic failure process of prestressed rock specimen with acircular hole [17] Zhang et al [18] andHao et al [19] studiedthe effects of bedding on the dynamic and static properties ofcoal and rock respectively However few research studieshave been carried out on the dynamic response of therockbolt and reinforced surrounding rock [20ndash23] And dueto complicated geological and mining conditions a morecomplete understanding of the mechanical property ofreinforced rock is required-erefore in this study dynamiccompression tests of sandstones reinforced by using a steelbar were conducted -e mechanical and energy charac-teristics of the reinforced rock under dynamic loading wereinvestigated and the results may provide reference for thestability of deep roadway and support design
2 Specimen Preparation andExperimental Methods
21 Specimen Preparation -e sandstone used in the ex-periment was taken from Linyi Shandong Province ChinaAccording to the standard GBT50266-2013 [24] standardcylindrical samples were made (A-1 and A-2) Mechanicalparameters of the standard cylindrical specimen were ob-tained by using the RMT-150C rock mechanics test system(see Figure 1) -e compression test was carried out bydisplacement control with a loading rate of 0002mms Twodisplacement sensors with a range of 2mmwere used duringthe test to determine transverse deformation of sandstonesamples -e average compressive strength and elasticmodulus of the standard cylindrical specimen are 532MPaand 43GPa respectively Meanwhile the sandstone spec-imen was observed by using a scanning electron microscopewith SU3500 as shown in Figure 2 From the figure it isobserved that the internal microstructure of the rock is tightand mainly consists of quartz and feldspar
-e test samples shown in Figure 3(a) were used forunreinforced and reinforced tests and labeled as US and RSrespectively For example ldquoUS-1rdquo represents the 1 un-reinforced specimen and ldquoRS-1rdquo represents the 1 reinforcedspecimen -e sample size is 50mm in thickness and 50mmin diameter For the reinforced specimen the bolt arrange-ment is shown in Figure 3(b) A hole with a diameter of 3mmwas drilled through the center side of the specimen In thisexperiment a steel bar was used to simulate the rockbolt -esteel bar was inserted into the hole and anchored on the rockwith resin (the resin used is the same as in mine conditions)-e steel bar is 60mm long 2mm wide and 2mm thick with
the tensile strength of 600MPa shear strength of 400MPaand elastic modulus of 210GPa Since the SHPB test can onlydirectly control the impact pressure and cannot directly setdifferent strain rates the impact compression test was con-ducted under the impact pressure range of 035sim06MPa
22 Test System -e dynamic compression test of rock wascarried out by using a 50mm rod diameter split Hopkinsonpressure bar (SHPB) test device Figure 4 illustrates theschematic of the SHPB system which mainly consists of twoparts ie three bars (an incident bar with a length of 2m atransmitted bar with a length of 15m and an absorbing barwith a length of 05m) and a data acquisition subsystem Asemisine wave was generated by a special shape striker andused as the loading stress wave to ensure that the stress waseven before failure of the specimens [25 26] -e incidenttransmitted and absorbing bars were made of 40Cr alloysteel with a density of 7810 kgm3 longitudinal wave velocityof 5410ms and elastic modulus of 250GPa -e straingauge model on the incident and transmitted bars is BE120-5AA and the resistance value is 120Ω -e measurementbase has a length of 85mm and a width of 4mm -e KD6009 strain amplifier is used to collect data signals
A-2
A-1Stre
ss (M
Pa)
0
10
20
30
40
50
60
70
0004 0008 0012 0016 0020 00240000Strain
Figure 1 Mechanical properties of the sandstone
Figure 2 Electron microscopy of the sandstone
2 Shock and Vibration
According to the stress wave signals collected by straingauges on the incident and transmitted bars the stressstrain and strain rate of the specimen during impact loadingwere calculated based on the one-dimensional stress wavetheory and stress uniformity hypothesis -e calculationformula is as follows [25]
σ(t) AeEe
2AsεI(t) + εR(t) + εT(t)1113858 1113859 (1)
ε(t) Ce
Ls1113946
t
0εI(t) minus εR(t) minus εT(t)1113858 1113859dt (2)
_ε(t) Ce
LsεI(t) minus εR(t) minus εT(t)1113858 1113859 (3)
where σ(t) ε(t) and _ε(t) are the stress strain and strainrate respectively As and Ae are the area of the specimen and
the bar respectively Ee is the elastic modulus of bars εΙ(t)εR(t) and εT(t) are the incident wave reflected wave andtransmitted wave respectively Ls is the length of specimenCe is the wave velocity of bars
3 Experimental Results
31 Stress Equilibrium For dynamic compression tests it isnecessary to eliminate wave dispersion and inertia effect toensure the accuracy of test results -erefore the stressequilibrium at the two ends of the specimen before failurewas reached In this paper the typical stress wave signals ofsamples US-4 and RS-4 from the dynamic loading experi-ment are shown in Figure 5 With increase of loading timethe curve of the sum of the incident and reflected waves(In + Re) almost overlaps with that of the stress (Tr) in-dicating that the specimen is basically in a stress equilibrium
(a)
Rock
Bolt
Resin 50mm
50mm
25mm
(b)
Figure 3 Specimen preparation (a) -e unreinforced and reinforced samples (b) -e bolt arrangement
Damper
Absorbing bar Transmitted bar
Specimen
Strain gauge
Incident bar Cone-shaped striker
Gas gun
Gas valve
Compressednitrogen gas
Tr signal In amp Re signal
Wheatstonebridge
Ultradynamicstrain gauge
OscilloscopeData processing
system
Wheatstonebridge
Incident waveTransmitted wave
Reflected wave
Figure 4 Schematic of the SHPB system
Shock and Vibration 3
state during this dynamic loading process and the test dataare reliable
32 Stress-StrainCurve Characteristics -e strain signals onthe incident and transmitted bars were recorded by using theultradynamic strain gauge Based on equations (1) and (2)the strain signals on the incident and transmitted bars can beconverted into the stress and strain signals of the specimenduring dynamic loading -e stress-strain curves of samplesunder dynamic loading are shown in Figure 6
It can be seen from Figure 6 that the stress-strain curve ofthe specimen can be divided into the phase of linear elas-ticity plasticity and failure under dynamic loading Due tothe high impact velocity the phase of macro-microscopicdefect closure compaction is extremely short and there isbasically no sunken section in the stress-strain curve whichdirectly enters the phase of linear elasticity and the stressincreases linearly with the strain -en the phase of plas-ticity begins and the slope of the curve decreases Finally theultimate strength of the specimen is reached accompaniedby the failure of the specimen
33 Dynamic Compressive Strength -e mechanical pa-rameters of the specimens under impact loading are shownin Table 1 In order to analyze the effect of the loading rateand bolt on rock strength the test results are plotted asscatter plot as shown in Figure 7
Figure 7 shows that the dynamic compressive strength ofUS and RS samples increases with the increase of strain rateMoreover the dynamic elastic modulus of the specimen isdifferent under different strain rates (Figure 7) and thedynamic elastic modulus increases with the increase of strainrate It shows that the rock specimen has a strong correlationwith the strain rate-e dynamic compressive strength of RSsamples is slightly higher than that of US samples -eresults show that the strength and deformation ability ofrock are improved by applying rockbolt and reflecting theobvious correlation of strain rate
4 Energy Characteristics
41 Energy Calculation According to the energy balance[27] the absorbed energy of rock during impact loading canbe calculated using the following equation [28]
Wa WI minus WR + WT( 1113857 (4)
where Wa WI WR andWT are the absorbed energy in-cident energy reflected energy and transmitted energyrespectively WI WR andWT can be calculated using thefollowing equations [28]
WI EeAeCe 1113946t
0ε2I(t)dt (5)
WR EeAeCe 1113946t
0ε2R(t)dt (6)
WT EeAeCe 1113946t
0ε2T(t)dt (7)
-e results show that the absorbed energy of rock ismainly converted into the energy dissipation kinetic energyand other energy among which the energy dissipation ofspecimen fragmentation is more than 90 of the absorbedenergy [29]-erefore the absorbed energy is approximatelysubstituted for the energy dissipation of specimen frag-mentation in this study In order to measure the strength ofenergy dissipation of the US and RS specimens under dif-ferent loading rates it is generally characterized by theenergy dissipation rate which can be calculated as
N Wa
WI (8)
where N is the energy dissipation rate
42 Analysis of Energy-Time Curves Certainly the de-formation and destruction of rock is the whole process of theenergy dissipation and energy release [30ndash32] -erefore theenergy dissipation characteristics of samples during impactloading are analyzed from the viewpoint of energy Accordingto equations (4)ndash(7) the strain-time curves of specimen areobtained by the experiment -e energy-time curves of allsamples are plotted in Figures 8 and 9 by calculating
It can be seen from Figures 8 and 9 that the same phe-nomenon occurs for US and RS samples under impactloading -e incident energy reflected energy and absorbedenergy increase rapidly compared with the transmitted energywith the propagation of the stress wave and their valuesmaintain stable after reaching a certain value while thetransmitted energy-time curve is approximately a horizontalline Based on the stress-time curve and energy-time curve wecan find that the appearance of maximum absorption energyindicates the failure of the US and RS samples [33]
43 Energy ChangeCharacteristics Test results of the energydistribution of samples under impact loading are shown inTable 2 In order to analyze the effect of loading rate and bolton energy characteristics the test results are plotted asscatter plot as shown in Figures 10 and 11
Because the generation of incident energy is caused bythe impact between the striker bar and incident bar thevalue of incident energy is determined only by the velocity ofthe impact bar In this study loading rates are the singlefactor and the sample type (US and RS samples) has noeffect on the incident energy Figure 10(a) shows that thereflected energy of all samples increases linearly with theincrease of incident energy and the transmitted energyincreases slightly -e absorbed energy of specimen in-creases as a power function with the incident energy(Figure 10(b)) As can be seen from Table 2 most of theenergy is dissipated in the form of reflected wave with in-crease in the incident energy which is consistent with theresults of Li et al [34]
4 Shock and Vibration
Figure 11 shows that there is an exponential relationbetween the energy dissipation rate of samples and strainrate -e failure of sample becomes more severe with the
strain rate and the failure mode of sample develops fromcleavage to fragmentation -at is to say more energy wasused to generate new cracks in the samples with the
0 50 100 150 200
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200St
ress
(MPa
)
Time (μs)
InRe
TrIn + Re
(a)
Stre
ss (M
Pa)
InRe
TrIn + Re
50 100 150 2000Time (μs)
ndash250
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200
(b)
Figure 5 Typical dynamic stress equilibrium results at unreinforced and reinforced conditions (a) US-4 (b) RS-4
US-1US-2US-3
Stre
ss (M
Pa)
US-4US-5US-6
0004 0008 0012 00160000Strain
0
20
40
60
80
100
(a)
RS-1RS-2RS-3
RS-4RS-5RS-6
Stre
ss (M
Pa)
0002 0004 0006 0008 0010 0012 00140000Strain
0
20
40
60
80
100
(b)
Figure 6 Stress-strain curves of samples under dynamic loading (a) Unreinforced samples (b) Reinforced samples
Table 1 -e mechanical parameters of samples under dynamic loading
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
US-1 51 561 59 RS-1 49 590 63US-2 61 607 62 RS-2 69 692 67US-3 73 704 69 RS-3 80 779 74US-4 77 714 72 RS-4 87 805 76US-5 85 733 73 RS-5 93 880 88US-6 98 855 84 RS-6 105 994 94
Shock and Vibration 5
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
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Hindawiwwwhindawicom Volume 2018
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Electrical and Computer Engineering
Journal of
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Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
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Journal ofEngineeringVolume 2018
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Hindawiwwwhindawicom Volume 2018
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According to the stress wave signals collected by straingauges on the incident and transmitted bars the stressstrain and strain rate of the specimen during impact loadingwere calculated based on the one-dimensional stress wavetheory and stress uniformity hypothesis -e calculationformula is as follows [25]
σ(t) AeEe
2AsεI(t) + εR(t) + εT(t)1113858 1113859 (1)
ε(t) Ce
Ls1113946
t
0εI(t) minus εR(t) minus εT(t)1113858 1113859dt (2)
_ε(t) Ce
LsεI(t) minus εR(t) minus εT(t)1113858 1113859 (3)
where σ(t) ε(t) and _ε(t) are the stress strain and strainrate respectively As and Ae are the area of the specimen and
the bar respectively Ee is the elastic modulus of bars εΙ(t)εR(t) and εT(t) are the incident wave reflected wave andtransmitted wave respectively Ls is the length of specimenCe is the wave velocity of bars
3 Experimental Results
31 Stress Equilibrium For dynamic compression tests it isnecessary to eliminate wave dispersion and inertia effect toensure the accuracy of test results -erefore the stressequilibrium at the two ends of the specimen before failurewas reached In this paper the typical stress wave signals ofsamples US-4 and RS-4 from the dynamic loading experi-ment are shown in Figure 5 With increase of loading timethe curve of the sum of the incident and reflected waves(In + Re) almost overlaps with that of the stress (Tr) in-dicating that the specimen is basically in a stress equilibrium
(a)
Rock
Bolt
Resin 50mm
50mm
25mm
(b)
Figure 3 Specimen preparation (a) -e unreinforced and reinforced samples (b) -e bolt arrangement
Damper
Absorbing bar Transmitted bar
Specimen
Strain gauge
Incident bar Cone-shaped striker
Gas gun
Gas valve
Compressednitrogen gas
Tr signal In amp Re signal
Wheatstonebridge
Ultradynamicstrain gauge
OscilloscopeData processing
system
Wheatstonebridge
Incident waveTransmitted wave
Reflected wave
Figure 4 Schematic of the SHPB system
Shock and Vibration 3
state during this dynamic loading process and the test dataare reliable
32 Stress-StrainCurve Characteristics -e strain signals onthe incident and transmitted bars were recorded by using theultradynamic strain gauge Based on equations (1) and (2)the strain signals on the incident and transmitted bars can beconverted into the stress and strain signals of the specimenduring dynamic loading -e stress-strain curves of samplesunder dynamic loading are shown in Figure 6
It can be seen from Figure 6 that the stress-strain curve ofthe specimen can be divided into the phase of linear elas-ticity plasticity and failure under dynamic loading Due tothe high impact velocity the phase of macro-microscopicdefect closure compaction is extremely short and there isbasically no sunken section in the stress-strain curve whichdirectly enters the phase of linear elasticity and the stressincreases linearly with the strain -en the phase of plas-ticity begins and the slope of the curve decreases Finally theultimate strength of the specimen is reached accompaniedby the failure of the specimen
33 Dynamic Compressive Strength -e mechanical pa-rameters of the specimens under impact loading are shownin Table 1 In order to analyze the effect of the loading rateand bolt on rock strength the test results are plotted asscatter plot as shown in Figure 7
Figure 7 shows that the dynamic compressive strength ofUS and RS samples increases with the increase of strain rateMoreover the dynamic elastic modulus of the specimen isdifferent under different strain rates (Figure 7) and thedynamic elastic modulus increases with the increase of strainrate It shows that the rock specimen has a strong correlationwith the strain rate-e dynamic compressive strength of RSsamples is slightly higher than that of US samples -eresults show that the strength and deformation ability ofrock are improved by applying rockbolt and reflecting theobvious correlation of strain rate
4 Energy Characteristics
41 Energy Calculation According to the energy balance[27] the absorbed energy of rock during impact loading canbe calculated using the following equation [28]
Wa WI minus WR + WT( 1113857 (4)
where Wa WI WR andWT are the absorbed energy in-cident energy reflected energy and transmitted energyrespectively WI WR andWT can be calculated using thefollowing equations [28]
WI EeAeCe 1113946t
0ε2I(t)dt (5)
WR EeAeCe 1113946t
0ε2R(t)dt (6)
WT EeAeCe 1113946t
0ε2T(t)dt (7)
-e results show that the absorbed energy of rock ismainly converted into the energy dissipation kinetic energyand other energy among which the energy dissipation ofspecimen fragmentation is more than 90 of the absorbedenergy [29]-erefore the absorbed energy is approximatelysubstituted for the energy dissipation of specimen frag-mentation in this study In order to measure the strength ofenergy dissipation of the US and RS specimens under dif-ferent loading rates it is generally characterized by theenergy dissipation rate which can be calculated as
N Wa
WI (8)
where N is the energy dissipation rate
42 Analysis of Energy-Time Curves Certainly the de-formation and destruction of rock is the whole process of theenergy dissipation and energy release [30ndash32] -erefore theenergy dissipation characteristics of samples during impactloading are analyzed from the viewpoint of energy Accordingto equations (4)ndash(7) the strain-time curves of specimen areobtained by the experiment -e energy-time curves of allsamples are plotted in Figures 8 and 9 by calculating
It can be seen from Figures 8 and 9 that the same phe-nomenon occurs for US and RS samples under impactloading -e incident energy reflected energy and absorbedenergy increase rapidly compared with the transmitted energywith the propagation of the stress wave and their valuesmaintain stable after reaching a certain value while thetransmitted energy-time curve is approximately a horizontalline Based on the stress-time curve and energy-time curve wecan find that the appearance of maximum absorption energyindicates the failure of the US and RS samples [33]
43 Energy ChangeCharacteristics Test results of the energydistribution of samples under impact loading are shown inTable 2 In order to analyze the effect of loading rate and bolton energy characteristics the test results are plotted asscatter plot as shown in Figures 10 and 11
Because the generation of incident energy is caused bythe impact between the striker bar and incident bar thevalue of incident energy is determined only by the velocity ofthe impact bar In this study loading rates are the singlefactor and the sample type (US and RS samples) has noeffect on the incident energy Figure 10(a) shows that thereflected energy of all samples increases linearly with theincrease of incident energy and the transmitted energyincreases slightly -e absorbed energy of specimen in-creases as a power function with the incident energy(Figure 10(b)) As can be seen from Table 2 most of theenergy is dissipated in the form of reflected wave with in-crease in the incident energy which is consistent with theresults of Li et al [34]
4 Shock and Vibration
Figure 11 shows that there is an exponential relationbetween the energy dissipation rate of samples and strainrate -e failure of sample becomes more severe with the
strain rate and the failure mode of sample develops fromcleavage to fragmentation -at is to say more energy wasused to generate new cracks in the samples with the
0 50 100 150 200
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200St
ress
(MPa
)
Time (μs)
InRe
TrIn + Re
(a)
Stre
ss (M
Pa)
InRe
TrIn + Re
50 100 150 2000Time (μs)
ndash250
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200
(b)
Figure 5 Typical dynamic stress equilibrium results at unreinforced and reinforced conditions (a) US-4 (b) RS-4
US-1US-2US-3
Stre
ss (M
Pa)
US-4US-5US-6
0004 0008 0012 00160000Strain
0
20
40
60
80
100
(a)
RS-1RS-2RS-3
RS-4RS-5RS-6
Stre
ss (M
Pa)
0002 0004 0006 0008 0010 0012 00140000Strain
0
20
40
60
80
100
(b)
Figure 6 Stress-strain curves of samples under dynamic loading (a) Unreinforced samples (b) Reinforced samples
Table 1 -e mechanical parameters of samples under dynamic loading
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
US-1 51 561 59 RS-1 49 590 63US-2 61 607 62 RS-2 69 692 67US-3 73 704 69 RS-3 80 779 74US-4 77 714 72 RS-4 87 805 76US-5 85 733 73 RS-5 93 880 88US-6 98 855 84 RS-6 105 994 94
Shock and Vibration 5
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
state during this dynamic loading process and the test dataare reliable
32 Stress-StrainCurve Characteristics -e strain signals onthe incident and transmitted bars were recorded by using theultradynamic strain gauge Based on equations (1) and (2)the strain signals on the incident and transmitted bars can beconverted into the stress and strain signals of the specimenduring dynamic loading -e stress-strain curves of samplesunder dynamic loading are shown in Figure 6
It can be seen from Figure 6 that the stress-strain curve ofthe specimen can be divided into the phase of linear elas-ticity plasticity and failure under dynamic loading Due tothe high impact velocity the phase of macro-microscopicdefect closure compaction is extremely short and there isbasically no sunken section in the stress-strain curve whichdirectly enters the phase of linear elasticity and the stressincreases linearly with the strain -en the phase of plas-ticity begins and the slope of the curve decreases Finally theultimate strength of the specimen is reached accompaniedby the failure of the specimen
33 Dynamic Compressive Strength -e mechanical pa-rameters of the specimens under impact loading are shownin Table 1 In order to analyze the effect of the loading rateand bolt on rock strength the test results are plotted asscatter plot as shown in Figure 7
Figure 7 shows that the dynamic compressive strength ofUS and RS samples increases with the increase of strain rateMoreover the dynamic elastic modulus of the specimen isdifferent under different strain rates (Figure 7) and thedynamic elastic modulus increases with the increase of strainrate It shows that the rock specimen has a strong correlationwith the strain rate-e dynamic compressive strength of RSsamples is slightly higher than that of US samples -eresults show that the strength and deformation ability ofrock are improved by applying rockbolt and reflecting theobvious correlation of strain rate
4 Energy Characteristics
41 Energy Calculation According to the energy balance[27] the absorbed energy of rock during impact loading canbe calculated using the following equation [28]
Wa WI minus WR + WT( 1113857 (4)
where Wa WI WR andWT are the absorbed energy in-cident energy reflected energy and transmitted energyrespectively WI WR andWT can be calculated using thefollowing equations [28]
WI EeAeCe 1113946t
0ε2I(t)dt (5)
WR EeAeCe 1113946t
0ε2R(t)dt (6)
WT EeAeCe 1113946t
0ε2T(t)dt (7)
-e results show that the absorbed energy of rock ismainly converted into the energy dissipation kinetic energyand other energy among which the energy dissipation ofspecimen fragmentation is more than 90 of the absorbedenergy [29]-erefore the absorbed energy is approximatelysubstituted for the energy dissipation of specimen frag-mentation in this study In order to measure the strength ofenergy dissipation of the US and RS specimens under dif-ferent loading rates it is generally characterized by theenergy dissipation rate which can be calculated as
N Wa
WI (8)
where N is the energy dissipation rate
42 Analysis of Energy-Time Curves Certainly the de-formation and destruction of rock is the whole process of theenergy dissipation and energy release [30ndash32] -erefore theenergy dissipation characteristics of samples during impactloading are analyzed from the viewpoint of energy Accordingto equations (4)ndash(7) the strain-time curves of specimen areobtained by the experiment -e energy-time curves of allsamples are plotted in Figures 8 and 9 by calculating
It can be seen from Figures 8 and 9 that the same phe-nomenon occurs for US and RS samples under impactloading -e incident energy reflected energy and absorbedenergy increase rapidly compared with the transmitted energywith the propagation of the stress wave and their valuesmaintain stable after reaching a certain value while thetransmitted energy-time curve is approximately a horizontalline Based on the stress-time curve and energy-time curve wecan find that the appearance of maximum absorption energyindicates the failure of the US and RS samples [33]
43 Energy ChangeCharacteristics Test results of the energydistribution of samples under impact loading are shown inTable 2 In order to analyze the effect of loading rate and bolton energy characteristics the test results are plotted asscatter plot as shown in Figures 10 and 11
Because the generation of incident energy is caused bythe impact between the striker bar and incident bar thevalue of incident energy is determined only by the velocity ofthe impact bar In this study loading rates are the singlefactor and the sample type (US and RS samples) has noeffect on the incident energy Figure 10(a) shows that thereflected energy of all samples increases linearly with theincrease of incident energy and the transmitted energyincreases slightly -e absorbed energy of specimen in-creases as a power function with the incident energy(Figure 10(b)) As can be seen from Table 2 most of theenergy is dissipated in the form of reflected wave with in-crease in the incident energy which is consistent with theresults of Li et al [34]
4 Shock and Vibration
Figure 11 shows that there is an exponential relationbetween the energy dissipation rate of samples and strainrate -e failure of sample becomes more severe with the
strain rate and the failure mode of sample develops fromcleavage to fragmentation -at is to say more energy wasused to generate new cracks in the samples with the
0 50 100 150 200
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200St
ress
(MPa
)
Time (μs)
InRe
TrIn + Re
(a)
Stre
ss (M
Pa)
InRe
TrIn + Re
50 100 150 2000Time (μs)
ndash250
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200
(b)
Figure 5 Typical dynamic stress equilibrium results at unreinforced and reinforced conditions (a) US-4 (b) RS-4
US-1US-2US-3
Stre
ss (M
Pa)
US-4US-5US-6
0004 0008 0012 00160000Strain
0
20
40
60
80
100
(a)
RS-1RS-2RS-3
RS-4RS-5RS-6
Stre
ss (M
Pa)
0002 0004 0006 0008 0010 0012 00140000Strain
0
20
40
60
80
100
(b)
Figure 6 Stress-strain curves of samples under dynamic loading (a) Unreinforced samples (b) Reinforced samples
Table 1 -e mechanical parameters of samples under dynamic loading
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
US-1 51 561 59 RS-1 49 590 63US-2 61 607 62 RS-2 69 692 67US-3 73 704 69 RS-3 80 779 74US-4 77 714 72 RS-4 87 805 76US-5 85 733 73 RS-5 93 880 88US-6 98 855 84 RS-6 105 994 94
Shock and Vibration 5
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
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Active and Passive Electronic Components
VLSI Design
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Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
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Journal ofEngineeringVolume 2018
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Hindawiwwwhindawicom Volume 2018
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RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Figure 11 shows that there is an exponential relationbetween the energy dissipation rate of samples and strainrate -e failure of sample becomes more severe with the
strain rate and the failure mode of sample develops fromcleavage to fragmentation -at is to say more energy wasused to generate new cracks in the samples with the
0 50 100 150 200
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200St
ress
(MPa
)
Time (μs)
InRe
TrIn + Re
(a)
Stre
ss (M
Pa)
InRe
TrIn + Re
50 100 150 2000Time (μs)
ndash250
ndash200
ndash150
ndash100
ndash50
0
50
100
150
200
(b)
Figure 5 Typical dynamic stress equilibrium results at unreinforced and reinforced conditions (a) US-4 (b) RS-4
US-1US-2US-3
Stre
ss (M
Pa)
US-4US-5US-6
0004 0008 0012 00160000Strain
0
20
40
60
80
100
(a)
RS-1RS-2RS-3
RS-4RS-5RS-6
Stre
ss (M
Pa)
0002 0004 0006 0008 0010 0012 00140000Strain
0
20
40
60
80
100
(b)
Figure 6 Stress-strain curves of samples under dynamic loading (a) Unreinforced samples (b) Reinforced samples
Table 1 -e mechanical parameters of samples under dynamic loading
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
Specimenno
Strain rate(sminus 1)
Compressive strength(MPa)
Elastic modulus(GPa)
US-1 51 561 59 RS-1 49 590 63US-2 61 607 62 RS-2 69 692 67US-3 73 704 69 RS-3 80 779 74US-4 77 714 72 RS-4 87 805 76US-5 85 733 73 RS-5 93 880 88US-6 98 855 84 RS-6 105 994 94
Shock and Vibration 5
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
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Shock and Vibration
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Civil EngineeringAdvances in
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Submit your manuscripts atwwwhindawicom
Stre
ngth
(MPa
)
US specimensRS specimens
50
60
70
80
90
100
60 70 80 90 100 11050Strain rate (sndash1)
Figure 7 Dynamic strength under different strain rates
Incident energyReflected energy
Transmitted energyAbsorbed energy
Ener
gy (J
)
0
40
80
120
50 100 150 2000Time (μs)
(a)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(b)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
30
60
90
120
150
180
50 100 150 2000Time (μs)
(c)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
50 100 150 2000Time (μs)
(d)
Figure 8 Continued
6 Shock and Vibration
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
40
80
120
160
200
50 100 150 2000Time (μs)
(e)
Ener
gy (J
)
Incident energyReflected energy
Transmitted energyAbsorbed energy
0
50
100
150
200
250
50 100 150 2000Time (μs)
(f )
Figure 8 Energy-time curves of samples under impact loading (a) US-1 (b) US-2 (c) US-3 (d) US-4 (e) US-5 (f ) US-6
Ener
gy (J
)
50 100 150 2000Time (μs)
0
20
40
60
80
100
120
Incident energyReflected energy
Transmitted energyAbsorbed energy
(a)
Ener
gy (J
)
50 100 150 2000Time (μs)
0
40
80
120
160
Incident energyReflected energy
Transmitted energyAbsorbed energy
(b)
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(c)
Ener
gy (J
)
0
40
80
120
160
200
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(d)
Figure 9 Continued
Shock and Vibration 7
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
0
40
80
120
160
200
Ener
gy (J
)
50 100 150 2000Time (μs)
Incident energyReflected energy
Transmitted energyAbsorbed energy
(e)
50 100 150 2000Time (μs)
Ener
gy (J
)
200
150
100
250
50
0
Incident energyReflected energy
Transmitted energyAbsorbed energy
(f )
Figure 9 Energy-time curves of samples under impact loading (a) RS-1 (b) RS-2 (c) RS-3 (d) RS-4 (e) RS-5 (f ) RS-6
Table 2 Test results of the energy distribution of samples
Specimenno
Strain rate(sminus 1)
Incident energy(J)
Reflected energy(J)
Transmitted energy(J)
Absorbed energy(J)
Energy dissipationrate
US-1 51 11220 7676 963 2581 023US-2 61 13713 9178 1107 3428 025US-3 73 15624 9955 1138 4531 029US-4 77 15036 9754 1072 4210 028US-5 85 18451 11032 1146 6273 034US-6 98 20072 10807 1172 8093 040RS-1 49 10618 7816 767 2035 019RS-2 69 14135 10372 795 2968 021RS-3 80 16827 12125 832 3870 023RS-4 87 17862 12531 865 4466 025RS-5 93 19056 13100 811 5145 027RS-6 105 21315 14106 815 6394 030
Transmitted energy
US specimensRS specimens
US specimensRS specimens
Ener
gy (J
)
Reflected energy
0
20
40
60
80
100
120
140
120 140 160 180 200 220100Incident energy (J)
(a)
R2 = 0984
Wa = 0001WI2119
R2 = 0985
Wa = 00041WI17968
US specimensRS specimensFitting line
Abs
orbe
d en
ergy
(J)
20
40
60
80
120 140 160 180 200 220100Incident energy (J)
(b)
Figure 10 Relation between energy and incident energy (a)-e reflected and transmitted energy of specimens (b)-e absorbed energy ofspecimens
8 Shock and Vibration
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
increase of strain rate reflecting the obvious correlation ofstrain rate Comparing the energy characteristics of US andRS samples it is known that the absorbed energy andtransmitted energy of the unreinforced specimen arehigher than that of the reinforced specimen while thereflected energy of the unreinforced specimen is lower thanthat of the reinforced specimen (Figure 10) As shown inFigure 11 the energy dissipation rate increases with theincrease of strain rate and the increased rate of the un-reinforced specimen is slightly higher than that of thereinforced specimen Under the same strain rate comparedwith the unreinforced specimen the less the energy dis-sipation of the reinforced specimen the more difficult thecrack propagation and the smaller the destruction degreethe greater the fragment (Figure 11)
5 Discussion
With increasing coal mining depth and growing coaloutput the geological and mining conditions have changedcomplicated considerably [35] and roadway instability hasbeen a major concern for researchers Floor heave rooffalling off and splitting failure of roadway are often oc-curred Roadway stability is analyzed from the viewpoint ofenergy -e energy is dissipated in the form of wavepropagation in the rock A graph of wave propagation inthe interior of the reinforced specimen is shown in Fig-ure 12 When the incident energy comes from the rockthree components of the energy are divided namely theabsorbed energy reflected energy and transmitted energyFrom the performance of reinforced specimen as discussedin Sections3 and 4 it is indicated that the dynamic strengthand deformation ability of rock were enhanced by applyingrockbolt and the absorbed energy of the reinforcedspecimen was reduced -is is because the lateral confiningpressure σ3 is equivalently applied by inserting the bolt in
rock mass (Figure 12(b)) the material strength parametersof rock mass were improved [36] which improves thestrength of the rock mass and restricts the crack propa-gation -erefore at the same incident energy the moredifficult the crack propagation of reinforced sample theless the absorbed energy [37] When the roadway rein-forced by the rockbolt is subjected to dynamic loading therockbolt can share load increasing the strength of roadwaysurrounding rock so the deformation of roadway sur-rounding rock will be restricted Furthermore most ofenergy is transmitted in the form of reflected energy andlittle absorbed energy is used to break the reinforcedsurrounding rock so the roadway will retain stability
6 Conclusions
-e experimental investigation of steel bar-reinforcedsandstones under impact loading is presented in this paper-e strengths energy characteristics and failure patterns ofunreinforced and reinforced samples were studied -efollowing conclusions can be drawn based on this study
(1) -e bolt can share the compressive stress of rock-ecompressive strength of reinforced samples is greaterthan that of unreinforced samples under dynamicloading And the dynamic strength increases withthe increase of strain rate reflecting a strong cor-relation with the strain rate
(2) -e reflected energy and absorbed energy increasewith the increase of incident energy while thetransmitted energy increases slightly -e higher thestrain rate the larger the energy dissipation rate andthe higher the degree of fragmentation It shows thatthe energy dissipation characteristic reflects the in-ternal damage process to some extent
50 60 70 80 90 100 110
R2 = 096N = 001445e0028ε + 01679
US-6
US-5
US-4 US-3
US-2US-1
US specimensFitting line
Strain rate (sndash1)
020
025
030
035
040
N
(a)
R2 = 099N = 001427e0023ε + 0144
50 60 70 80 90 100 110
RS specimensFitting line
Strain rate (sndash1)
RS-6
RS-5RS-4
RS-3
RS-1
RS-2020
024
028
032
N
(b)
Figure 11 Relation between energy dissipation ratio and strain rate (a) US samples (b) RS samples
Shock and Vibration 9
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
(3) -e bolt has an important influence on the absorbedenergy and failure characteristics of rock Comparedwith unreinforced rock the lesser the absorbedenergy of reinforced rock the smaller the damagedegree Consequently the bolt can minimize failureof surrounding rock
Data Availability
-e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
-e authors declare that they have no conflicts of interestregarding the publication of this paper
Acknowledgments
-is work was supported by the Postgraduate Research andInnovation Project of Hunan Province (CX20190657) andthe National Natural Science Foundation of China(51674041 and 51474103)
References
[1] M Amini A Majdi and O Aydan ldquoStability analysis and thestabilisation of flexural toppling failurerdquo Rock Mechanics andRock Engineering vol 42 no 5 pp 751ndash782 2009
[2] C C Li ldquoField observations of rock bolts in high stress rockmassesrdquo Rock Mechanics and Rock Engineering vol 43 no 4pp 491ndash496 2010
[3] H Kang Y Wu F Gao J Lin and P Jiang ldquoFracturecharacteristics in rock bolts in underground coal mineroadwaysrdquo International Journal of Rock Mechanics andMining Sciences vol 62 no 6 pp 105ndash112 2013
[4] M C He J Wang X M Sun et al ldquoMechanics characteristicsand applications of prevention and control rock bursts of thenegative Poissons ratio effect anchorrdquo Journal of China CoalSociety vol 39 no 2 pp 214ndash221 2014
[5] M S Gao and N Zhang ldquoStudy of roadway support pa-rameters subjected to rock burst based on energy balancetheoryrdquo Journal of China University of Mining amp Technologyvol 36 no 4 pp 426ndash430 2007
[6] K Skrzypkowski W Korzeniowski K Zagorski andP Dudek ldquoApplication of long expansion rock bolt support inthe underground mines of Legnica-Głogow copper districtrdquoStudia Geotechnica et Mechanica vol 39 no 3 pp 47ndash572017
[7] K Skrzypkowski ldquoEvaluation of rock bolt support for PolishHard rock minesrdquo E3S Web of Conferences vol 35 p 8 2018
[8] C Carranza-Torres ldquoAnalytical and numerical study of themechanics of rockbolt reinforcement around tunnels in rockmassesrdquo Rock Mechanics and Rock Engineering vol 42 no 2pp 175ndash228 2009
[9] Y Zhao and M Yang ldquoPull-out behavior of an imperfectlybonded anchor systemrdquo International Journal of Rock Me-chanics and Mining Sciences vol 48 no 3 pp 469ndash475 2011
[10] B Zhang S Li K Xia et al ldquoReinforcement of rock mass withcross-flaws using rock boltrdquo Tunnelling and UndergroundSpace Technology vol 51 pp 346ndash353 2016
[11] Y Cai Y Jiang I Djamaluddin T Iura and T Esaki ldquoAnanalytical model considering interaction behavior of groutedrock bolts for convergence-confinement method in tunnelingdesignrdquo International Journal of Rock Mechanics and MiningSciences vol 76 pp 112ndash126 2015
[12] M Moosavi and R Grayeli ldquoA model for cable bolt-rock massinteraction integration with discontinuous deformationanalysis (DDA) algorithmrdquo International Journal of RockMechanics and Mining Sciences vol 43 no 4 pp 661ndash6702006
[13] T J Freeman ldquo-e behavior of fully-bonded rock bolts in theKielder experimental tunnelrdquo Tunnels Tunneling vol 10no 5 pp 37ndash40 1978
[14] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[15] 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
Rock
Incident wave
Bolt
Resin
(a)
(b)
σ3
σ1
σ3
Incident Reflection Transmission
Figure 12 Graph of wave propagates in reinforced roadway (a) Rockbolt reinforced roadway (b)Waves propagate in interior of reinforcedrock
10 Shock and Vibration
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[16] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a Split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017
[17] M Tao A Ma W Cao X Li and F Gong ldquoDynamic re-sponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017
[18] X Zhang X Ou F Gong and J Yang ldquoEffects of bedding onthe dynamic compressive properties of low anisotropy slaterdquoRock Mechanics and Rock Engineering vol 52 no 4pp 981ndash990 2019
[19] X J Hao W S Du Y D Jiang D Tannant Y Zhao andY Guo ldquoInfluence of bedding and cleats on the mechanicalproperties of a hard coalrdquo Arabian Journal of Geosciencesvol 11 no 9 p 200 2018
[20] Q H Wu L Chen B T Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo RockMechanics and Rock Engineering 2019
[21] M He C Li W Gong L R Sousa and S Li ldquoDynamic testsfor a constant-resistance-large-deformation bolt using amodified SHTB systemrdquo Tunnelling and Underground SpaceTechnology vol 64 pp 103ndash116 2017
[22] Y Z Wu J Y Chen J K Jiao et al ldquoDamage and failuremechanism of anchored surrounding rock with impactloadingrdquo Journal of China Coal Society vol 43 no 9pp 2389ndash2397 2018
[23] Q H Wu X B Li L Weng Q Li Y Zhu and R LuoldquoExperimental investigation of the dynamic response ofprestressed rockbolt by using an SHPB-based rockbolt testsystemrdquo Tunnelling and Underground Space Technologyvol 93 2019
[24] GBT 50266mdash2013 Standard for Tests Methods of EngineeringRock Mass Ministry of Housing and Urban-rural Develop-ment of the Peoplersquos Republic of China Beijing China 2013
[25] 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
[26] Z Zhou X Li A Liu and Y Zou ldquoStress uniformity of splitHopkinson pressure bar under half-sine wave loadsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 4 pp 697ndash701 2011
[27] K Skrzypkowski ldquoLaboratory testing of a long expansion rockbolt support for energy-absorbing applicationsrdquo E3S Web ofConferences vol 29 Article ID 00004 9 pages 2018
[28] B Lunberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Science amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[29] Z X Zhang S Q Kou L G Jiang and P-A LindqvistldquoEffects of loading rate on rock fracture fracture character-istics and energy partitioningrdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 745ndash7622000
[30] H P Xie R D Peng Y Ju et al ldquoOn energy analysis of rockfailurerdquo Chinese Journal Of Rock Mechanics And Engineeringvol 24 no 15 pp 2603ndash2608 2005
[31] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016
[32] Z Z Xie N Zhang Y X Yuan G Xu and Q Wei ldquoStudy onsafety control of composite roof in deep roadway based on
energy balance theoryrdquo Sustanability vol 11 no 13 p 36882019
[33] L Y Li H P Xie Y Ju X Ma and L Wang ldquoExperimentalinvestigations of releasable energy and dissipation energywithin rockrdquo Engineering Mechanics vol 28 no 3 pp 35ndash402011
[34] X Li Y Zou and Z Zhou ldquoNumerical simulation of the rockSHPB test with a special shape striker based on the discreteelement methodrdquo Rock Mechanics and Rock Engineeringvol 47 no 5 pp 1693ndash1709 2014
[35] H P Kang and J H Wang Rock Bolting4eory and CompleteTechnology for Coal Roadways China Coal Industry Pub-lishing House Beijing China 2007
[36] X G Zhu Q Yang and M T Luan ldquoStudy of reinforcementeffect of anchored rock masses and analytic constitutiveequation for rock boltrdquo Rock and Soil Mechanics vol 38no 3 pp 527ndash533 2007
[37] Y C You E B Li Y H Tan et al ldquoAnalysis on dynamicproperties and failure characteristics of salt rock based onenergy dissipation principlerdquo Chinese Journal of Rock Me-chanics and Engineering vol 36 no 4 pp 843ndash851 2017
Shock and Vibration 11
International Journal of
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Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom