Research ArticleExperimental Investigation of the Anomalously Low FrictionPhenomena in Blocky Rock Systems

Yehui Shi1 Hao Lu 2 Shuxin Deng3 Chenghua Xu1 and Helan Cheng1

1Tunnel and Underground Engineering Research Center of Jiangsu Province (TERC) Nanjing 210041 China2State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact -e Army Engineering University of PLANanjing 210094 China3School of Mechanical Engineering Nanjing University of Science and Technology Nanjing 210094 China

Correspondence should be addressed to Hao Lu 465576221qqcom

Received 9 August 2020 Accepted 12 September 2020 Published 10 October 2020

Academic Editor Peixin Shi

Copyright copy 2020 Yehui Shi 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

Rock masses can be regarded as a blocky rock system After a disturbance load is applied the anomalously low friction phe-nomenon may take place and cause geological disasters A series of impact experiments on granite blocks were conducted toinvestigate the anomalously low friction phenomena Vertical vibration Fourier frequency spectrum and horizontal motionswere investigated It can be found that the tensile phases of vertical vibration can reduce the maximum static friction forcenamely the shear strength e quasi-resonance operating mode of the rock blocks was observed During the stress wavepropagation the vibration in the loading direction tends to transfer from high frequency to low frequency and the modes of stresswave propagation do not depend on disturbance energies e observed translational and rotational motions were due to theinitial shear force which is less than the friction force with no disturbance load Stability of the blocky rock system is very sensitiveto the initial stress state In the subcritical state friction force reduction can easily break the equilibrium of forces along the contactsurface and even a slight disturbance may make the horizontal motions happen which may lead to geological disasters with greatenergy release

1 Introduction

When an external disturbance load is applied on rockmasses friction between adjacent rock blocks in the or-thogonal direction to the disturbance load may be signifi-cantly reduced or even completely disappeared which isknown as an anomalously low friction phenomenon [1 2]e phenomenon may lead to serious geological disasterssuch as the large-scope tunnel deformations [3ndash5] and slip-type rock bursts [6ndash8] in the surrounding rock massesaround tunnels ese disturbance-induced geological di-sasters can pose considerable threats to construction safetyand the stability of underground engineering

Natural rock masses can be considered as assemblies ofrock blocks of different sizes [9ndash11] e generalized faultsbetween adjacent rock blocks can involve quite a wide rangeof scale levels from microscopic scale levels to macroscopic

scale levels Effective strengths of these faults are much lowerthan the rock blocks which makes the faults turn into slipsurfaces And the effective strengths will be further reduceddue to the anomalously low friction phenomena after ex-ternal disturbances which can be caused by a nearbyblasting [4 12] a construction disturbance [13 14] anearthquake [15 16] and so on

A simple rock block model as shown in Figure 1 is takento analyse the geological disasters induced by the anoma-lously low friction phenomena [2 17 18] Kurlenya et al[19 20] studied the anomalously low friction phenomena inblock media from various geomaterials and found thatsignificant displacements of the working blocks occur atabsolute values of plus actions which are much smaller thanthe corresponding friction forces Kocharyan et al [21]utilized drop-weight apparatuses to apply disturbance forcesand investigate the dynamic response of a blocky system It

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8893786 10 pageshttpsdoiorg10115520208893786

was not conducive for precise control of the loading processMoreover the displacements in the loading direction weredifficult to obtain using superimposed blocky model in priorexperimental studies [18 21 22] In the present paper weused an electrodynamic vibration exciter to provide theshock loading and a digital image correlation (DIC) methodbased on high-speed photography to perform quantitativein-plane deformation measurement Under vertical impactdisturbance loads the anomalously low friction phenomenawere investigated Vertical vibration Fourier frequencyspectrum and horizontal motion were obtained emechanism of the disturbance-induced residual displace-ments and rock bursts due to the anomalously low frictionphenomena was discussed

2 Experimental Methods

21 Experimental Model Experimental system is depictedin Figure 2 All the five granite blocks were cut from anintact rock e dimensions of these rock blocks are160mm times 125mm times 125mm Mass of a single graniteblock is 68 kg P-wave velocity Cp is 4300ms Density ofthe granite is ρ 2720 kgm3 e rock blocks stackedvertically (see Figure 2(b)) and marked 1 to 5 from top tobottom

22 Loading System As plotted in Figure 2(a) an electro-dynamic vibration exciter including a flexible stinger and aforce transducer is fixed upon the top block to providevertical disturbance forces e electrodynamic vibrationexciter can convert electrical energy into impact energy toprovide precise and controllable excitation force of ampli-tude up to 1000N With the load delay control system toaccurately control the impact load start time the exciter canachieve accurate adjustment of 0ndash200ms at any time in-terval e stinger transmits force in the stiff axial directionand flexes laterally to reduce input side loads to the top rock

block is uniaxial force delivered by the flexible stingerincreases the accuracy of the measurement e forcetransducer along with the exciter can measure the inputforces applied to the block system Figure 3 shows the time-history curves of vertical disturbance force p(t) Uponcalucation the integral of p(t) and the impulse I can beobtained as

I 1113946infin

0p(t)dt (1)

Initial velocity of the top rock block is assumed to be 0and the duration is considered to be extremely short (seeFigure 3) us the disturbance energy W can be expressedas follows

W 12m

1113946infin

0p(t)dt

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

2

I2

2m (2)

where p(t) is the time-history function of the disturbingforce and m is the mass of a single block

23 Measuring System Digital image correlation (DIC)method is a noncontact and full-field measurementtechnique [23] which is very suitable to obtain full-fielddisplacement and strains Due to extremely relaxed en-vironmental requirements DIC method is widely appliedduring mechanical experiments [24] A high-speedcamera is often used to capture high-resolution digitalimages at ultrahigh speeds which can provide a betterobservation and understanding previously invisible pro-cesses and phenomena In our experiments a PHOTRONFASTCAM SA-Z High-Speed Camera with a maximumframe rate of 20000 fps and a maximum resolution of1024 times 1024 pixels was used to record the motions of theblock system As shown in Figure 2(c) two LED lightswere used for easy pixel capture Images with 1024 times 512pixels taken at 1000 fps were obtained After recording the

Rock formation boundaryFaultsDisturbance source

Disturbanceforce

Rockblocks

Ground stress

Figure 1 Schematic diagram of disturbance-induced geological disasters

2 Advances in Civil Engineering

(a)

Control computerfor vibration exciter

Power amplifier

Signal generator Rubber pads

Rock blocks

Electric vibration exciterand force transducer

Spray paint

LED light

1

2

3

4

5

High-speed camera

Control computer forhigh-speed camera

Figure 2 Experiment apparatus (a) schematic diagram (b) photograph of rock blocks (c) photograph of DIC measurement system

50 60 70 80

0

200

400

600

800

1000

Ver

tical

dist

urba

nce f

orce

(N)

Time (ms)

350 mJ250 mJ

150 mJ50 mJ

Figure 3 Time-history curves of vertical disturbance force with different disturbance energies

Advances in Civil Engineering 3

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(a)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(b)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 250 300ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 4 Vertical displacements of rock blocks with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ Positivevalues indicate the compression displacements while negative ones do the opposite

4 Advances in Civil Engineering

digital images of the blocks during vertical disturbances adigital image correlation and evaluation software com-putes the motion of each image point by comparing thedigital images before and after deformation [25]

3 Experimental Results

31 Vertical Vibration As shown in Figure 4 the verticaldisplacements of five rock blocks were obtained by usingDIC method After the disturbance load was applied the

vertical vibration of the blocky system consisted of twophases [1] the forced vibration phase and the free vibrationphase Compression displacements were observed in theforced vibration phase When the disturbance load endedthere should be a remarkable tensile displacement in the freevibration phase Vertical vibration gradually stopped withthe dissipation of energies

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasede blocky system entered a quasi-resonance operating

0 50 100 150 200 250 300 350 4000

10

20

30

40

50

60

70

80

Block 1Block 2Block 3

Block 4Block 5Fitting results

Max

imum

tens

ile d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 5 Relations between the maximum tensile displacements and disturbance energies

00 01 02 03 04 05 060

1

2

3

4

5

350 mJ300 mJ250 mJ

150 mJ100 mJ50 mJ

10 mJ5 mJFitting results

Li

A iradicW

Figure 6 Attenuation of the maximum tensile displacement with distance to disturbance source

Advances in Civil Engineering 5

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(a)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(b)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 25000051015202530

Spec

tral

den

sity

(μm

Hz)

Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 7 Spectral density of vertical displacement with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ

6 Advances in Civil Engineering

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

(a)

Control computerfor vibration exciter

Power amplifier

Signal generator Rubber pads

Rock blocks

Electric vibration exciterand force transducer

Spray paint

LED light

1

2

3

4

5

High-speed camera

Control computer forhigh-speed camera

Figure 2 Experiment apparatus (a) schematic diagram (b) photograph of rock blocks (c) photograph of DIC measurement system

50 60 70 80

0

200

400

600

800

1000

Ver

tical

dist

urba

nce f

orce

(N)

Time (ms)

350 mJ250 mJ

150 mJ50 mJ

Figure 3 Time-history curves of vertical disturbance force with different disturbance energies

Advances in Civil Engineering 3

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(a)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(b)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 250 300ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 4 Vertical displacements of rock blocks with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ Positivevalues indicate the compression displacements while negative ones do the opposite

4 Advances in Civil Engineering

digital images of the blocks during vertical disturbances adigital image correlation and evaluation software com-putes the motion of each image point by comparing thedigital images before and after deformation [25]

3 Experimental Results

31 Vertical Vibration As shown in Figure 4 the verticaldisplacements of five rock blocks were obtained by usingDIC method After the disturbance load was applied the

vertical vibration of the blocky system consisted of twophases [1] the forced vibration phase and the free vibrationphase Compression displacements were observed in theforced vibration phase When the disturbance load endedthere should be a remarkable tensile displacement in the freevibration phase Vertical vibration gradually stopped withthe dissipation of energies

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasede blocky system entered a quasi-resonance operating

0 50 100 150 200 250 300 350 4000

10

20

30

40

50

60

70

80

Block 1Block 2Block 3

Block 4Block 5Fitting results

Max

imum

tens

ile d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 5 Relations between the maximum tensile displacements and disturbance energies

00 01 02 03 04 05 060

1

2

3

4

5

350 mJ300 mJ250 mJ

150 mJ100 mJ50 mJ

10 mJ5 mJFitting results

Li

A iradicW

Figure 6 Attenuation of the maximum tensile displacement with distance to disturbance source

Advances in Civil Engineering 5

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(a)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(b)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 25000051015202530

Spec

tral

den

sity

(μm

Hz)

Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 7 Spectral density of vertical displacement with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ

6 Advances in Civil Engineering

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(a)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(b)

ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

0 50 100 150 200 250 300Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 250 300ndash80ndash60ndash40ndash20

02040

Ver

tical

disp

lace

men

t (μm

)

Time (ms)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 4 Vertical displacements of rock blocks with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ Positivevalues indicate the compression displacements while negative ones do the opposite

4 Advances in Civil Engineering

digital images of the blocks during vertical disturbances adigital image correlation and evaluation software com-putes the motion of each image point by comparing thedigital images before and after deformation [25]

3 Experimental Results

31 Vertical Vibration As shown in Figure 4 the verticaldisplacements of five rock blocks were obtained by usingDIC method After the disturbance load was applied the

vertical vibration of the blocky system consisted of twophases [1] the forced vibration phase and the free vibrationphase Compression displacements were observed in theforced vibration phase When the disturbance load endedthere should be a remarkable tensile displacement in the freevibration phase Vertical vibration gradually stopped withthe dissipation of energies

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasede blocky system entered a quasi-resonance operating

0 50 100 150 200 250 300 350 4000

10

20

30

40

50

60

70

80

Block 1Block 2Block 3

Block 4Block 5Fitting results

Max

imum

tens

ile d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 5 Relations between the maximum tensile displacements and disturbance energies

00 01 02 03 04 05 060

1

2

3

4

5

350 mJ300 mJ250 mJ

150 mJ100 mJ50 mJ

10 mJ5 mJFitting results

Li

A iradicW

Figure 6 Attenuation of the maximum tensile displacement with distance to disturbance source

Advances in Civil Engineering 5

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(a)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(b)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 25000051015202530

Spec

tral

den

sity

(μm

Hz)

Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 7 Spectral density of vertical displacement with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ

6 Advances in Civil Engineering

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

digital images of the blocks during vertical disturbances adigital image correlation and evaluation software com-putes the motion of each image point by comparing thedigital images before and after deformation [25]

3 Experimental Results

31 Vertical Vibration As shown in Figure 4 the verticaldisplacements of five rock blocks were obtained by usingDIC method After the disturbance load was applied the

vertical vibration of the blocky system consisted of twophases [1] the forced vibration phase and the free vibrationphase Compression displacements were observed in theforced vibration phase When the disturbance load endedthere should be a remarkable tensile displacement in the freevibration phase Vertical vibration gradually stopped withthe dissipation of energies

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasede blocky system entered a quasi-resonance operating

0 50 100 150 200 250 300 350 4000

10

20

30

40

50

60

70

80

Block 1Block 2Block 3

Block 4Block 5Fitting results

Max

imum

tens

ile d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 5 Relations between the maximum tensile displacements and disturbance energies

00 01 02 03 04 05 060

1

2

3

4

5

350 mJ300 mJ250 mJ

150 mJ100 mJ50 mJ

10 mJ5 mJFitting results

Li

A iradicW

Figure 6 Attenuation of the maximum tensile displacement with distance to disturbance source

Advances in Civil Engineering 5

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(a)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(b)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 25000051015202530

Spec

tral

den

sity

(μm

Hz)

Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 7 Spectral density of vertical displacement with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ

6 Advances in Civil Engineering

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(a)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(b)

00051015202530

Spec

tral

den

sity

(μm

Hz)

0 50 100 150 200 250Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(c)

0 50 100 150 200 25000051015202530

Spec

tral

den

sity

(μm

Hz)

Frequency (Hz)

Block 1Block 2Block 3

Block 4Block 5

(d)

Figure 7 Spectral density of vertical displacement with different disturbance energies (a) 50mJ (b) 150mJ (c) 250mJ (d) 300mJ

6 Advances in Civil Engineering

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

mode as a whole if the disturbance energies were largeenough (see Figures 4(c) and 4(d)) in this state the frictionbetween adjacent blocks can be dramatically reduced or evencompletely disappeared [18] Vertical vibration of the blockysystem in quasi-resonance operating mode can last longerand will not immediately stop

As plotted in Figure 5 the relations between the max-imum tensile displacements and disturbance energies can beexpressed as

Ai ki

W

radic

ki minus0788i + 4628(3)

where Ai(i 1 2 3 4 5) is the maximum tensile displace-ments ki(i 1 2 3 4 5) is the fitting coefficient and W isthe disturbance energy

From equation (3) the attenuation of Ai with distance todisturbance source (the center point on the top surface ofblock 1) can be deduced as follows

AiW

radic minus0788Li

h+ 4234 (4)

where h 0125m is the height of a single rock block andLi (i minus 05)h is the distance to disturbance source Fig-ures 5 and 6 show that the fitting results of equations (3) and(4) match the experimental results well

32 Fourier Frequency Spectrum of Vertical Displacemente Fourier frequency spectra of vertical displacement areplotted in Figure 7 Frequency spectral density of block 1had a wide distribution and more high-frequency waveswere included in the wave packets of block 1 ese high-frequency waves attenuated significantly with increase in thedistance to disturbance source In blocks 4 and 5 themajority was the low-frequency waves It meant that in theprocess of stress wave propagation in the blocky rock systemthe vibration in the loading direction tended to transfer from

ndash20

ndash10

0

10

20

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)H

oriz

onta

ldi

spla

cem

ent (μm

)

(a)

ndash20ndash10

01020

0 50 100 150 200 250 300 350 400

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(b)

0 50 100 150 200 250 300 350 400

ndash20ndash10

01020

Block 1Block 2Block 3

Block 4Block 5

Time (ms)

Hor

izon

tal

disp

lace

men

t (μm

)

(c)

Figure 8 Horizontal displacements of rock blocks with different disturbance energies (a) 150mJ (b) 250mJ (c) 350mJ

Advances in Civil Engineering 7

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

high frequency to low frequency Figure 7 also shows thatwith the increase of disturbance energies the local maxi-mum frequencies of vertical displacements will not changeand only the amplitude frequency increases us distur-bance energies cannot change the modes of stress wavepropagation e propagation modes only depend on thestructural characteristics of the blocky rock system

33 Horizontal Motions As plotted in Figure 8 horizontaldisplacements were observed which were mainly due tothe translational and rotational motions of rock blocksWhen W 150mJ the horizontal displacements werenegligible (see Figure 8(a)) When W 350mJ the hor-izontal displacements could reach a maximum value of2371 μm (see Figure 8(c)) As W increased the transla-tional and rotational motions became more significante amplitudes of horizontal displacements attenuatedfrom block 1 to 5 with the increase in distance todisturbance source

e interfaces of the rock blocks are not absolutely flate slight fluctuations of the interfaces may cause initialshear force which is less than the friction force when nodisturbance load is applied Under the disturbance load ifdisturbance energies are large enough the vertical tensiledisplacements may significantly reduce the maximum staticfriction force If the maximum static friction force is lowerthan the initial shear force the translational and rotationalmotions of rock blocks take place and will last for quite along time relative to the loading time (see Figure 3)Maximum horizontal displacements of rock blocks areshown in Figure 9 which can reflect the degree of frictionreduction As the disturbance energies increase it is obviousthat the low friction effect becomes more significant

34 Reduced Friction Force To estimate the reduced frictionforce the blocky rock system is simplified into a multiple-degree-of-freedom mass-spring-dashpot system [1] Basedon such a consideration the nonlinear mechanical behaviorof adjacent rock blocks can be simulated with a KelvinndashVoigtmodel Assume that the relationship between the reducedfriction force and the maximum tensile displacement is

ΔNi k0Ai (5)

where k0 is an equivalent spring coefficient and depends oninherent properties of the contact surfaces From equations(3)ndash(5) the reduced friction force can be expressed as

ΔFi μΔNi μk0Ai μk0W

radic4234 minus 0788

Li

h1113874 1113875 (6)

ehorizontal motions depend on the equilibrium of theshear force Ti and friction force Fi Before the disturbanceload Ti leFi and the blocky rock system is stable After theimpact load is applied the tensile displacements of adjacentrock blocks lead to friction reduction Once the condition ofTi gtFi minus ΔFi is met the block starts to slip horizontally eshear motions of blocks can reduce friction coefficient μwhich causes a further reduction of friction forces and finallyleads to geological disasters of different scales

4 Discussion

As analyzed above the critical condition for rock blocks tostart a horizontal motion can be expressed as Ti Fi minus ΔFie critical disturbance energy can be easily derived fromequations (3) and (6) as follows

W kprimexc

μk0ki

1113888 1113889

2

(1 minus β)2 (7)

150 200 250 300 350

0

5

10

15

20

25

Block 1Block 2Block 3

Block 4Block 5

Hor

izon

tal d

ispla

cem

ent (μm

)

Disturbance energy (mJ)

Figure 9 Maximum horizontal displacements of rock blocks

8 Advances in Civil Engineering

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

where kprime and xc are the elastic coefficient and critical dis-placement of friction constitutive curves respectively Fi

kprimexc is the shear strength β is the ratio of shear force to shearstrength β TiFi Obviously 0le βle 1

Equation (7) shows the dependence of the disturbanceenergy on the initial stress state It is noteworthy that whenβ⟶ 1 W⟶ 0 is means even a slight disturbance maymake the horizontal motions happen which may lead togeological disasters with great energy release Triggeringmechanism of geological disasters is clear External dis-turbances cause tensile displacements of adjacent rockblocks which reduces the normal stress and friction force ofthe contact surfaces In the subcritical state (β⟶ 1)friction force reduction can easily break the equilibrium offorces along the contact surface e mechanism can explainthe remotely triggered earthquake [26] which can beconsidered as a larger-scale slip motion than a rock burst in atunnel

Besides the impact loads the anomalously low frictionphenomena can also be induced by ocean tides [27] orhydraulic fracturing [28] Elevated pore pressures reduce theeffective stress of contact surfaces which causes the frictionreduction In addition there may be a cumulative weakeningeffect on the friction coefficient as the external disturbancesoccur frequently

5 Conclusions

Based on the structural hierarchy theory rock masses can beregarded as a blocky rock systemWhen a disturbance load isapplied anomalously low friction phenomenon may takeplace and cause geological disasters To investigate theanomalously low friction phenomena a series of impactexperiments on granite blocks were conducted by using anelectrodynamic vibration exciter and a digital image cor-relation (DIC) method based on high-speed photography

With the increase of disturbance energies the ampli-tudes of the vertical displacements significantly increasedand the tensile phases of vertical vibration may reduce themaximum static friction force namely the shear strengthe blocky system entered a quasi-resonance operatingmode as a whole if the disturbance energies were largeenough In the process of stress wave propagation in theblocky rock system the vibration in the loading directiontends to transfer from high frequency to low frequency andthe modes of stress wave propagation do not correlate verymuch with disturbance energies e observed translationaland rotational motions were due to the initial shear forcewhich is locked by the friction force when no disturbanceload is applied External disturbances reduce the frictionforce and weaken the constraint is causes the horizontalmotions of the work block e low friction effect becomesmore significant with larger disturbance energies

Stability of the blocky rock system is very sensitive to theinitial stress state External disturbances cause tensile dis-placements of adjacent rock blocks which reduces thenormal stress and friction force of the contact surfaces Inthe subcritical state friction force reduction can easily breakthe equilibrium of forces along the contact surface and even

a slight disturbance may make the horizontal motionshappen which may lead to geological disasters with greatenergy release

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e present study was supported by the Opening Project ofTunnel and Underground Engineering Research Center ofJiangsu Province (TERC) e authors also acknowledge thefinancial support of the National Natural Science Founda-tion of China (Grant no 51909120)

References

[1] G W Ma X M An and M Y Wang ldquoAnalytical study ofdynamic friction mechanism in blocky rock systemsrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 5 pp 946ndash951 2009

[2] L Li W Li J Tang and J Lv ldquoInfluence of bidirectionalimpact loading on anomalously low-friction effect in blockrock mediardquo Advances in Civil Engineering vol 2018 ArticleID 9156304 9 pages 2018

[3] V V Adushkin and A A SpivakGeomechanics of Large-ScaleExplosions Nedra Publishers Moscow Russian 1993

[4] S K Guha Induced Earthquakes Springer Science amp BusinessMedia Berlin Germany 2013 httpsbooksgooglecombookshl=zh-CNamplr=ampid=IW4yBwAAQBAJampoi=fndamppg=PP12ampdq=Induced+Earthquakes+guhaampots=RrCLt_DYQ-ampsig=4RYZyDEYdYCXuFSNREakma79Yv8

[5] K Sarkarinejad and B Zafarmand ldquoStress state and move-ment potential of the Kar-e-Bas fault zone Fars Iranrdquo Journalof Geophysics and Engineering vol 14 no 4 pp 998ndash10092017

[6] F Meng H Zhou Z Wang et al ldquoExperimental study offactors affecting fault slip rockbursts in deeply buried hardrock tunnelsrdquo Bulletin of Engineering Geology and the Envi-ronment vol 76 no 3 pp 1167ndash1182 2017

[7] H Zhou F Meng C Zhang D Hu F Yang and J LuldquoAnalysis of rockburst mechanisms induced by structuralplanes in deep tunnelsrdquo Bulletin of Engineering Geology andthe Environment vol 74 no 4 pp 1435ndash1451 2015

[8] J Pan S Liu S Wang and Y Xia ldquoA new theoretical view ofrockburst and its engineering applicationrdquo Advances in CivilEngineering vol 2018 Article ID 4683457 12 pages 2018

[9] M A Sadovskiy ldquoNatural lumpiness of rocksrdquo DokladyAkademii Nauk SSSR vol 247 no 4 pp 829ndash831 1979

[10] M V Kurlenya V N Oparin and A A Eremenko ldquoRelationof linear block dimensions of rock to crack opening in thestructural hierarchy of massesrdquo Journal of Mining Sciencevol 29 no 3 pp 197ndash203 1993

[11] C-Z Qi Q-H Qian M-Y Wang and J Dong ldquoStructuralhierarchy of rock masses and mechanism of its formationrdquo

Advances in Civil Engineering 9

Journal of Rock Mechanics and Geotechnical Engineeringvol 24 pp 2838ndash2846 2005

[12] L-T Xie P Yan W-B Lu M Chen and G-H WangldquoEffects of strain energy adjustment a case study of rockfailure modes during deep tunnel excavation with differentmethodsrdquo KSCE Journal of Civil Engineering vol 22 no 10pp 4143ndash4154 2018

[13] P Yan Z Zhao W Lu Y Fan X Chen and Z ShanldquoMitigation of rock burst events by blasting techniques duringdeep-tunnel excavationrdquo Engineering Geology vol 188pp 126ndash136 2015

[14] T Liu H Wang X Su K Li S Liu and F Guo ldquoInstabilitymechanism of cavity-bearing formation under tunnel exca-vation disturbancerdquo Advances in Civil Engineering vol 2020Article ID 9038421 15 pages 2020

[15] A Demirci S Ozden T Bekler D Kalafat and A Pınar ldquoAnactive extensional deformation example 19 may 2011 Simavearthquake (Mw 58) Western Anatolia Turkeyrdquo Journalof Geophysics and Engineering vol 12 no 4 pp 552ndash5652015

[16] G Papathanassiou S Valkaniotis A Ganas N Grendas andE Kollia ldquoe november 17th 2015 Lefkada (Greece) strike-slip earthquake field mapping of generated failures and as-sessment of macroseismic intensity ESI-07rdquo EngineeringGeology vol 220 pp 13ndash30 2017

[17] N I Aleksandrova ldquoPendulum waves on the surface of blockrock mass under dynamic impactrdquo Journal of Mining Sciencevol 53 no 1 pp 59ndash64 2017

[18] M V Kurlenya V N Oparin and V I Vostrikov ldquoPen-dulum-type waves Part II experimental methods and mainresults of physical modelingrdquo Journal of Mining Sciencevol 32 no 4 pp 245ndash273 1996

[19] M V Kurlenya V N Oparin and V I VostrikovldquoAnomalously low friction in block mediardquo Journal of MiningScience vol 33 no 1 pp 1ndash11 1997

[20] M V Kurlenya V N Oparin and V I Vostrikov ldquoEffect ofanomalously low friction in block mediardquo Journal of AppliedMechanics and Technical Physics vol 40 no 6 pp 1116ndash11201999

[21] G G Kocharyan A A Kulyukin V K MarkovD V Markov and D V Pavlov ldquoSmall disturbances andstress-strain state of the Earthrsquos crustrdquo Physical Meso-mechanics vol 8 no 1-2 pp 21ndash33 2005

[22] N I Aleksandrova A G Chernikov and E N Sher ldquoEx-perimental investigation into the one-dimensional calculatedmodel of wave propagation in block mediumrdquo Journal ofMining Science vol 41 no 3 pp 232ndash239 2005

[23] Y Seo G R Chehab and Y R Kim ldquoPost-peak character-ization of asphalt concrete using DIC methodrdquo KSCE Journalof Civil Engineering vol 10 pp 1ndash7 2006

[24] H Wu G Zhao W Liang E Wang and S Ma ldquoExperi-mental investigation on fracture evolution in sandstonecontaining an intersecting hole under compression using DICtechniquerdquo Advances in Civil Engineering vol 2019 ArticleID 3561395 12 pages 2019

[25] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strainmeasurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 Article ID 062001 2009

[26] D P Hill P A Reasenberg A Michael et al ldquoSeismicityremotely triggered by the magnitude 73 Landers Californiaearthquakerdquo Science vol 260 no 5114 pp 1617ndash1623 1993

[27] H Houston ldquoLow friction and fault weakening revealed byrising sensitivity of tremor to tidal stressrdquo Nature Geosciencevol 8 no 5 pp 409ndash415 2015

[28] L W Shen D R Schmitt and R Schultz ldquoFrictional sta-bilities on induced earthquake fault planes at fox CreekAlberta a pore fluid pressure dilemmardquo Geophysical ResearchLetters vol 46 no 15 pp 8753ndash8762 2019

10 Advances in Civil Engineering