Research ArticleInfluence of Deviatoric Stress on the Deformation and DamageEvolution of Surrounding Rock under Unloading Conditions

Gongyu Hou,1,2 Jinping Liang ,1 Haoyong Jing,1 Jinxin Tan,1 Yongkang Zhang,1

Xi Yang,1 and Xin Xie1

1School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China2School of Mining Engineering and Geology, Xinjiang Institute of Engineering, Urumqi 830091, China

Correspondence should be addressed to Jinping Liang; bqt1800605051@student.cumtb.edu.cn

Received 7 January 2020; Revised 24 June 2020; Accepted 17 August 2020; Published 4 September 2020

Academic Editor: Yuri S. Karinski

Copyright © 2020 Gongyu Hou et al. .is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

.e study of the deformation and damage evolution behaviour of surrounding rock under excavation unloading conditions is ofvital importance for a deep understanding of the mechanism of roadway failure. In this study, unloading testing using a partiallyhollow thick-walled cylinder cement mortar specimen with dimensions of 280mm (height)× 200mm (outer diameter)× 60mm(inner diameter) and a solid height of 60mm at the bottom was performed to investigate the deformation response and damagefailure evolution characteristics of the surrounding rock. .e experimental results showed that the higher deviatoric stress levelaccelerated the damage development caused by the unloading effect and improved the expansion rate of the internal cracks, whichled to a higher radial strain rate, total strain, and acoustic emission hits. When deviatoric stress increased to a relatively higherlevel, the radial strain rates were highly unstable, and the surrounding rock near or at the opening free surface was damaged locallyand regionally. During the failure process of the specimen, the generation of the deformation and damage in the unloading stagewas more alive (as indicated by the growth rate). Nevertheless, the main deformation and damage to the surrounding rock weregenerated and accumulated in the maintaining stage after unloading.

1. Introduction

Tunnel/roadway engineering construction is an unloadingprocess in a three-dimensional state. With the removal ofradial stress and the increase of tangential stress, this processwill cause varying degrees of disturbance to an in situ stressfield. .e disturbed rock masses near or at an opening cavesurface often suffer from unloading and creep that can resultin rock spalling [1], large squeezing deformation [2], androck bursting [3–5] during or after an excavation, whichcould cause serious injuries for underground engineeringfacilities and workers [6]. A large number of studies haveshown that evaluation of the performance of rock damagethresholds, that is, crack closure, crack initiation, and crackdamage stresses, is significantly affected by different loadingconditions and rock internal structure [7–9]. Clearly, it isvital to study the deformation, failure, and damage evolutionof roadway surrounding rocks under unloading conditions.

Owing to the particularity and complexity of under-ground engineering, the in situ measurement of the rockmass is difficult and the test conditions are not generallyavailable, especially in a deep-buried area. .erefore, in thepast few decades, researchers have carried out a largenumber of theoretical studies [10], numerical simulations[11, 12], and laboratory scale experiments [13–15] to studythe rock mechanics and damage failure evolution. Usinggrain-based distinct element model, Mahdi et al. [11] studiedmicrocracking behaviour of precracked Barre granite. Wenget al. [13] investigated the stability of underground exca-vations under high in situ stress conditions, and several rocksamples with a minitunnel were prepared and subjected tomonotonic axial and coupled static–dynamic loading untilfailure. Munoz et al. [14] investigated the effects of cyclicloading on the deformational characteristics of both thenonlocalized damage zone (NLDZ) and the localizeddamage zone (LDZ) of rock in the postpeak regime. At

HindawiShock and VibrationVolume 2020, Article ID 3158209, 14 pageshttps://doi.org/10.1155/2020/3158209

present, much attention has been paid to the study ofdamage and failure mechanism by AE techniques.

After acoustic emission (AE) techniques were first in-troduced into rock mechanics studies [16] and the Kaisereffect was discovered [17], the AE techniques began to beapplied to investigate earthquake [18], in situ stress mea-surement [19], determination of fracture initiation stress[20], and rock burst prediction [21]. Focusing on the damageevaluation, Kim et al. [20] compared two damage evaluationmethods (stress-strain and AE) and suggested that AEmethods were the best choice for damage estimation. Yanget al. [22] obtained the damage and failure evolutioncharacteristics of limestone under triaxial confining pres-sure. Based on AE parameters and their determinationmethods, Zhang et al. [23] established damage variables andcompared the AE characteristics of rock salt, granite, andmarble during damage process. .ese studies play an im-portant role in understanding the mechanical behaviour ofsurrounding rock and maintaining the stability of sur-rounding rock.

To simulate the stress state of rock mass in roadwayexcavation more effectively, researchers proposed a methodto evaluate the stability of circular roadway by using thick-walled cylindrical (TWC) structure model specimens[24, 25]. .is was a simple and reliable test method to in-vestigate the effect of roadway excavation, which can sim-ulate the hoop effect and stress gradient of roadway. It hasbeen widely used in laboratory tests to study the mechanicalresponse and supporting characteristics of rock mass[26–31], which greatly promoted the understanding ofroadway/tunnel failure mechanism. Due to the difficulty ofsystem development, most previous studies used thisstructural model to study damage of roadway under loadingconditions, and few researchers carried out damage andstrength studies under unloading conditions. Nevertheless,few experimental studies focused on the deformation,damage failure mechanism, and AE characteristics of thesurrounding rock during or after an excavation unloading..erefore, a series of unloading tests for partially hollowthick-walled cylinder (PHTWC) cement mortar specimenswere carried out using the roadway/tunnel excavationunloading model testing system, which combined with thestrain test system and acoustic emission monitoring system..e deformations at different space-time positions of thesurrounding rock and the time-frequency-domain charac-teristics of the AE signals, for example, the AE hits, am-plitude, and frequency, were monitored during the entiretest process..e effects of different in situ stress levels on thedeformation response and the damage failure evolutioncharacteristics of the surrounding rock after excavation wereanalyzed according to the experimental results.

2. Materials and Methods

2.1. Testing Method. In the laboratory, the emphasis was onstudying the degree of influence of the secondary stress fieldon the surrounding rock deformation and the damage afterbeing removed by an excavated body. .e process ofroadway excavation unloading was simulated “actually.”.e

“actually” term meant that the mechanical process and theprinciple of this modeling testing were in accordance withthe simplification of the mechanical model of the elastic-plastic solution of the circular roadway at the time of testing..e roadway excavation was the process of the “excavatedbody” being taken out. After excavation, the original stressvalue dropped to zero and the surrounding rock shrank anddeformed.

2.2. Testing System. A roadway/tunnel excavation unloadingmodel testing system that was equipped with a strainmeasurement system and an AE measurement system wasused to achieve the simulation of the in situ stress envi-ronment and the roadway excavation. .e testing systemwas also used to investigate the deformation and AE re-sponse of the surrounding rock during excavation [29, 31],as shown in Figure 1. It should be noted that the testingsystem used in this research could achieve independentloading and unloading for the axial, external, and internalstresses. During the test, the inner and outer cavities of thespecimen were isolated with rubber sleeve and filled withsilicone oil. .rough the independent control of the servovalve in the inner and outer cavities, the pipe connecting theinner and outer cavities was pressurized to achieve the in-dependent control of the internal and external pressure. .einternal pressure relief process was completed by sending anegative opening command to the corresponding servovalve through the controller.

.e static strain gauge (model DH3818Y) used in thisstudy (see Figure 1(b)), equipped with a 24-bit Σ − Δ(A/D)

analog-to-digital converter, could achieve continuous andaccurate dynamic and static sampling. .e storage batterycontinuously supplied power to the strain gauge, avoidingthe noise caused by the AC power supply during the test.Eight strain gauges (numbered #1 to #8) were distributed indifferent positions inside the specimen to obtain radial strainof the corresponding locations, as shown in Figure 2(a).

Acoustic emission acquisition equipment (model DS5-8B) was used to collect waveform and state information of 8channels synchronously in real time (Figure 1(c)). Fourcylindrical high oil pressure resistant AE broadband ceramicsensors (model RS-5A) with operating frequency range from50 kHz to 100 kHz were mounted on the outer wall of thespecimen, as shown in Figure 2. As a coupling agent, siliconegrease reduced the signal attenuation and enhanced thesignal transmission between the specimen and sensor bycoating on the contact between them. .e trigger thresholdand the sampling rate were set to 30 dB and 3MHz/s, re-spectively. .erefore, the AE response could be obtainedeffectively during the process of roadway excavation.

2.3. Specimen Preparation. .e PHTWC specimens had aheight of 280mm, an outer diameter of 200mm, and aninner diameter of 60mm, and the specimens were made ofcement mortar material. To create an unexcavated rock massahead of the excavation face, a solid with a height of 60mmwas left at the bottom of the specimens. .at is, the hollowheight was 220mm (Figure 3). Core specimens

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(φ50×100mm) that were made of cement mortar with thesame mix ratio as the PHTWC samples were tested. It wasfound that the mechanical properties of the core specimens

were similar to those of the sandstone. .e physical andmechanical parameters of cement mortar and sandstone areshown in Table 1.

2.4. Testing Program. .e axial stress and internal and ex-ternal confining stresses were increased to the designedlevels (10, 20, and 30MPa) with a constant loading rate of0.1MPa/s, following the experimental paths plotted inFigure 4, held on 10min to allow for stress field homoge-nisation, then, released internal pressure to produce thedifference of external stress and internal stress (hereaftercalled deviatoric stress), created free surface around the cave,and, finally, held on 8min to investigate the deformation andAE response after unloading.

3. Experiment Results

3.1. Characteristics Analysis of Fracture. In Figure 5, pho-tographs of three typical representative specimens corre-sponding to the initial confining stress level can be observed..e figure illustrates the fact that a relatively high stress leveltriggered the failure. When the stresses were 10MPa and20MPa, the coalescence of fractures and faults on themacroscopic scale occurred. In contrast, no large dilationand volume changes of the surrounding rock appearedtoward the direction of the opening free surface induced bystress. When the stress increased to 30MPa, this resulted in a

Hydraulic hoist

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Figure 1: Illustration of the tunnel excavation unloading test system: (a) the unloading test machine; (b) the strain monitoring system;(c) the AE monitoring system.

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bulky piece of a slab and slices that were characterized bythinner edges and a thicker middle section peeling off fromthe inner sidewalls, as shown in Figures 5(c)–5(f).

It should be noted that the failure mode, caused by highdeviatoric stress in unloading, was similar to the bulgingfailure at the tunnel face (Figure 5(d)) and the rock burst insitu field that had been observed by researchers [32], whichdiffered from the failure mode under the loading conditions,such as axial, uniaxial, and triaxial. It was evident fromFigure 6(c) that most of the deformation was observed in the

maintaining stage after unloading during the failure of thespecimen. .is signified that the maintaining stage afterunloading was the main damage stage. Similarly, numerousstudies have shown that a rockburst would occur in a periodafter unloading at a relatively high unloading speed [33–35].To confirm this postulation, the AE technique was adoptedto investigate the damage evolution characteristics duringthe test process.

3.2. Characteristics Analysis of Deformation. To clearly de-scribe the stage test results during the entire test process, theprocess was divided into four sections: (I) loading stage, (II)maintaining stage after loading, (III) unloading stage, and(IV) maintaining stage after unloading. .e strain responsefor each test after unloading is given in Figures 6 and 7. Itwas found from Figure 6 that the radial strain increased withthe increase of the initial confining stress. When the stresswas 10MPa or 20MPa, the radial strain response trends atthe same position during the testing process were essentiallythe same; that is, the radial strain in the unloading stage wasproduced quickly, and the strain growth rate in the main-tenance stage after unloading slowed down. However, thedeformation after unloading was still very large, which led tothe strain response in the unloading stage not being obviousin the diagram when the local stress increased to 30MPa. Itshould be noted that a small deformation was detected in theunexcavated rock mass ahead of the excavation face, and itwas often found in previous studies that the rock mass in acertain range ahead of the excavation face produced a smalldeformation under the influence of excavation unloading[36]. .e strain values of the #5 to #8 strain gauges weresignificantly higher than those of the #1 to #4 strain gauges,respectively, indicating that the surrounding rock of theinner hollow free sidewalls might be more susceptible toexcavation. Similarly, the farther away the excavation surfacewas, the greater the radial deformation was, and the

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Table 1: Mechanical and physical parameters of cement mortarmaterial and sandstone.

Rock type CS (MPa) E (GPa) ] ρ(g·cm− 3)

Cement mortar 25.0 10.2 0.19 1.97Sandstone 20∼170 4.9∼ 78.5 0.02∼ 0.2 2.1

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4 Shock and Vibration

experimental results were in accordance with the supportingtheory of the excavation surface spatial effect on the rockmass around the excavation surface [37].

.e slope of the strain curve was called the strain rate inthis study, which indicated the speed of the deformation perunit time. It could indirectly reflect the friction and theintensity of the spatial relative position change betweenparticles in the specimen [38], which could be written asfollows:

_εr �Δεr

Δt, (1)

where _εr is the radial strain rate, Δεr is the radial strainincrement, and Δt is the time interval (in seconds).

.e larger the strain rate was, the faster the deformationper unit time was. As can be seen from Figure 7, theunloading effect led to a rapid increase in deformation, andthe corresponding strain curve slope was high. During theunloading stage, the strain rate increased dramatically andthen decreased sharply. .e strain rate generally increasedwith the increase of the initial confining stress. Afterunloading, the radial strain continued to increase and thestrain rate was very small. No obvious failure of the specimenoccurred when the stress was 10MPa or 20MPa. Never-theless, when the stress increased to 30MPa, the strain ratewas still high and the deformation increased rapidly. Duringthis period, the #5 strain gauge failed and the maximumstrain value was 18.2×10−3ε. .erefore, it was speculatedthat a large amount of damage accumulation occurredduring the maintenance stage after the unloading, resultingin a large fracture of the sample, which is described inSection 4. It was noted that the strain rate of different straingauges changed in an unstable manner during a period of

time after unloading. In addition, when the strain rate ofsome strain gauges increased suddenly at the same time, thedeformation increased suddenly (Figure 7(c)), at 954 s and1015 s. .ese phenomena showed that the friction and theintensity of the spatial relative position change betweenparticles in the specimen were strengthened.

3.3. AE Characteristics. .e AE events carried importantinformation about the internal change of the material andthey could reflect the fracture development and damagefracture behaviour in the rock material. Based on this, itbecame an important research method to predict the stress,deformation, damage, and failure evolution of rock throughAE events.

3.3.1. AE Time-Domain Evolution. .eAE hit was one of theAE parameters used to indicate the density and intensity ofthe AE activity [39]. To systematically compare the AEsignals and the mechanical parameters of the test process,the AE signal and stress-strain signal were recorded at thesame time at each test, so the AE and stress-strain infor-mation could correspond to each other.

Figure 8 shows the complete histograms of the AE hitsfor three typical specimens during the entire testing process..e total recorded times were 1181 s, 1265 s, and 1367 s. .echaracteristics of the AE hit signals during the entire testprocess included the four stages I–IV.

(1) At the initial loading stage, the AE signals increasedwith the increasing load due to the loading adjust-ments and the closing of the original microcracksand microholes. .is phenomenon has also beenfound in true triaxial loading experiments [34].

Confining stress of 10MPa Confining stress of 20MPa Confining stress of 30MPa

Figure 5: Photographs of the inner wall under initial confining stress of (a) 10, (b) 20, and (c) 30MPa. Comparison of failure fragments inthe field and test, (d) the face of the tunnel [32], (e) and (f) failure fragments of specimen.

Shock and Vibration 5

(2) At the maintenance stage after loading, the numberof AE hits dropped and then stayed at a low level, andthe density decreased correspondingly.

(3) At the unloading stage, a quiescent period of AEsignals occurred first. .en, the AE hits decreasedafter a rapid increase (Figures 8(b), 8(d), and 8(f)).During the two stages beforehand, a large amount ofstrain energy accumulated in the specimens. .esubsequent removal of the internal confining stressin a short period of time could result in the corre-sponding AE hits increasing suddenly and thenumber of cracks increasing rapidly. .e number ofAE hits was still maintained at the level above thepreunloading stage, and the number of crackscontinued to increase. In addition, it was clear thatthe AE hits for the unloading stage were significantlyhigher than those of the loading stage..e unloadingstage was the active stage of AE, and the active degree

increased with the increase of the initial confiningstress.

(4) At the maintaining stage after unloading, when thestress was 10MPa or 20MPa, the active degree of AEdecreased, but the active degree of AE was signifi-cantly higher than that in the maintaining stage afterloading.When the stress was 30MPa, a large numberof AE hits occurred, the AE was still highly active inthis stage, and there were three events of sharp risingand decreasing. Until the end, the hits remained at arelatively high level. .e number of AE hits wasclosely related to the number of cracks in thespecimen [40]. .is meant that after unloading, themicrocracks in the surrounding rock continued toproduce, develop, interact, and converge into frac-tures..at is, the unloading effect continued to affectthe surrounding rock after unloading. .is alsoexplained the phenomenon of rock burst occurring

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Figure 6: Radial deformation during unloading stage and maintaining after unloading. .e unloading stage of different initial confiningstress ((a) 10, (b) 20, and (c) 30MPa) lasted for 6 s, 10 s, and 12 s, respectively. .e maintaining stage of which lasted for 480 s.

6 Shock and Vibration

after a period of time after unloading at a fasterunloading speed [33–35].

As presented in Figure 8, the number of AE hits was lowand high for the low initial confining stress and high initialconfining stress. .e larger the initial confining stress was,the greater the unloading damage was, which could cause theincrease of the crack propagation speed and number ofcracks. When the specimens were under relatively low initialconfining stress (10MPa and 20MPa), the maximumAE hitsoccurred during the unloading stage. Nevertheless, when thestress increased to a relatively high stress (30MPa), themaximum AE hits occurred during the maintaining stageafter unloading. It should be noted that the fracture of thespecimen that was caused by the stress level was not relatedto the time. When the stress level was constant, theunloading capacity of the main rupture of the specimen wascertain. .at is, the greater the in situ stress was, the higherthe relative unloading capacity was when the main fractureoccurred. .e reason for this phenomenon may be that thegreater the level of in situ stress was, the higher the degree of

compaction of the specimen was. .e corresponding in-crease of the critical stress was caused by cracking at thecrack tip, and the relative time of the occurrence of the mainfracture was delayed.

3.3.2. AE Frequency-Domain Evolution. .e AE waveformwas transformed by fast Fourier transformation (FFT) inorder to obtain the frequency spectrum information cor-responding to the typical AE hits of the entire testingprocess. .e amplitudes and the peak frequency charac-teristics of three typical specimens under different confiningstresses are presented in Figure 9, which can be used toprovide additional quantitative information about theunloading. It should be noted that the amplitude and thepeak value corresponded to the AE hits at any time, whichcould be regarded as corresponding to the four stages:

(1) At the initial loading stage, high-frequency and low-frequency values appeared sporadically with highamplitude.

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Figure 7: Radial strain rates during unloading stage and maintaining after unloading in different initial confining stress ((a) 10, (b) 20, and(c) 30MPa).

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(2) At the maintaining stage after loading, the peakfrequency value and the amplitude activities of the AEsignals were characterized by a sparse distribution.

(3) At the unloading stage, the deviatoric stress in-creased gradually, and the peak frequency value ofAE signals was characterized by a dense high am-plitude distribution. .e number of high-frequency

and low-frequency signals increased, and the am-plitude signals clearly increased. .is indicated thatthe cracks for different scales in the specimen in-creased, and the small cracks had accelerated de-velopment into large-scale fractures.

(4) At the maintaining stage after unloading, thenumber of high-frequency and low-frequency

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8 Shock and Vibration

signals continued to increase, as did the high am-plitude signals.

.e peak frequency and the amplitudewere distributed in acertain range (45–100dB, 0–600 kHz) during the testingprocess under different initial confining stresses. It was seenthat a high confining stress led to a wider frequency band andhigher amplitudes. Additionally, the AE signals were charac-terized by a dense frequency-amplitude distribution. To fa-cilitate the data analysis, a frequency-amplitude distributionthat was recorded from the entire testing process of threetypical specimens was obtained, as presented in Figure 10.Among the points of the frequency-amplitude distribution, itwas evident from Figure 10 that the amplitude value of thehigh-frequency (>200kHz) was much smaller than that of thelow-frequency (<200kHz). In addition, the amplitude of thehigh-frequency and low-frequency increased with the initialincrease of the confining stress. It was obvious that there weretwo main frequency bands below 200kHz, including the rangeof 40–100kHz and the other range of about 140–190kHz.

4. Damage Estimation Based on AE

4.1. AE Parameter. To facilitate the data analysis, wetransformed the histograms of AE hits from the unloading

stage to maintaining stage into a continuous waveform curvein Figure 11. Bruning et al. [9] found that on the eve of therock burst, the AE hits experienced a fast increase while itrapidly decreased after that. Su et al. [41] found that, in theprocess of true triaxial rock burst, the AE hits decreasedrapidly after the spalling phenomenon of the free surface.Until the particle ejection, the number of AE hits increasedrapidly to a high value again and then decreased. Hu et al.[21] also found that the phenomenon of particle ejection andspalling on the opening free surface corresponds to the risingpoint of AE hits during the rockburst process of borehole.Similarly, it was also found that AE hits enhanced sharply atthe moment of the rockburst [42–44]. .erefore, combinedwith the failure characteristics of the specimen (Figure 5(c)),it was inferred that during the unloading andmaintenance ofthe 30MPa confining stress, spalling or particle ejectionoccurred at the corresponding three high value points of theAE hits. .e damage parameter was proposed in order toinvestigate the damage evolution of the surrounding rockduring the entire test process, as described in Section 4.2.

.e changes of the AE amplitude and the strain rateduring unloading under the confining stress of 30MPa arepresented in Figure 12. .ere was a good correspondencebetween the AE signal and the strain rate during this period.We found that the amplitude and the strain rate first

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(kH

z)A

mpl

itude

(dB)

0 200 400 600 800 12001000Time (s)

(b)

30

25

35

20

15

10

5

0

p 0 –

p1 (

MPa

)

Peak frequency

AmplitudeI II III IV 120

100

80

60454003002001000 Pe

ak fr

eque

ncy

(kH

z)A

mpl

itude

(dB)

0 200 400 600 800 140012001000Time (s)

(c)

Figure 9: Peak frequency and amplitude of AE signals during the whole test process under different initial confining stress ((a) 10, (b) 20, (c)30MPa).

Shock and Vibration 9

increased and then decreased with the increase of the in-ternal and external pressure difference during unloading..e appearance of a high strain rate was accompanied by a

high and dense amplitude signal. It was found that theamplitude of the AE signal was directly related to the size ofthe AE event.

4.2. Damage Parameter. .e damage parameter was intro-duced to quantify the relative damage of the four stagesinvolved in the test process and to investigate the progressiveevolution process of the damage, and it was obtained withthe following equation:

DSB �Ωt

Ωm

, (2)

where DSB is the damage parameter corresponding to therelative damage of specimens at any time. Ωt is the cu-mulative amount of AE hits (or energy) from the start ofloading to a certain time of the PHTWC specimen.Ωm is thecumulative amount of AE hits (or energy) throughout thewhole testing process. .e range of values for the damageparameter DSB was 0 to 1, that is, 0≤DSB ≤ 1. It should benoted that 0 represented the cumulative amount of damage

100

90

80

70

60

50

Am

plitu

de (d

B)

0 100 200 300 400 500 600Peak frequency (kHz)

(a)

100

90

80

70

60

50

Am

plitu

de (d

B)

0 100 200 300 400 500 600Peak frequency (kHz)

(b)

100

90

80

70

60

50

Am

plitu

de (d

B)

0 100 200 300 400 500 600Peak frequency (kHz)

(c)

Figure 10: Peak frequency-amplitude distributions under different initial confining stress ((a) 10, (b) 20, (c) 30MPa).

3000

2500

2000

1500

1000

500

0

AE

hits

(103 )

C t = 1015s

t = 882sA

B

t = 954s

900 1000 1100 1200 1300 1367Time (s)

Figure 11: .e curve of AE hits evolution after unloading underconfining stress of 30MPa.

10 Shock and Vibration

to the initial state of the test, and 1 was the amount ofdamage that accumulated at the end of the test, not nec-essarily the cumulative amount of AE in the failure state ofthe test piece. It is also important to note that the damage inthis study referred to relative damage, which was used toinvestigate the damage evolution during the entire testingprocess for different initial confining stresses.

Equation (2) was used to establish the hypothesis that thecumulative AE hits were related to the internal damage of thespecimen, so the damage evolution curves of the entiretesting process for three different initial confining stresseswere collected, as shown in Figure 13. It can be seen from thediagram that although the confining stress was different, thetrends were essentially the same, but the damage ratio ofeach stage was changed. .e slope of the damage curve fromthe OA segment increased gradually. .e slope of thedamage curve from the AB segment was reduced slowly..eslope of the damage curve from the BC segment was thelargest, which meant that the damage per unit time was verylarge, although the proportion of total damage was verysmall. When the initial confining stress was 20MPa, thedamage ratio in the unloading stage was higher than thatwhen the stress was 10MPa. .e longer the unloading timewas, the greater the relative accumulation damage was..erewas no obvious failure (Figures 5(a), 5(b)) in the specimenafter unloading, which meant that the amount of relativedamage in the maintenance stage after unloading was rel-atively lower. .e slope of the CD segment decreased, but itstill stayed at a high level, especially under high stress. Inaddition, the relative damage of this stage was much higherthan the other two stresses for the stress of 30MPa.

Overall, as the pressure level increased, points A–C onthe damage curve moved down. .is meant that the ratio ofthe damage in the maintaining stage after unloading in-creased, even became as high as 90% when the initialconfining stress was 30MPa. .is showed that most of thedamage occurred and accumulated in the maintenance stageafter unloading. .is verified that the unloading effect

continued to influence the surrounding rock afterunloading.

4.3. b-Value Analysis. .e change of the b-value was closelyrelated to the crack scale and the stress level, which could beused to measure the development of the crack [20]. .eevolution of the b-value with the time sequence in theunloading stage and the postunloading maintenance stagewas investigated to deduce the crack development during theprocess of specimen failure (initial confining stress 30MPa)..e famous G-R relationship [45] from seismology was usedto calculate the b-value with the following equation:

logN10 � a − bM, (3)

whereM is the magnitude of the earthquake, which could bereplaced by the amplitude (AdB) divided by 20 in the AEexperiment. N is the cumulative number of earthquakes inthe magnitude interval set in this study, which was thenumber of AE events. a and b are constants. During theprocess of changing with the time sequence, when the b-value tended to increase, the proportion of small eventsincreased. In contrast, when the b-value tended to decrease,the proportion of large events increased.

In this study, the magnitude interval was set to 0.01 dBand the b-value was calculated using the least-squaremethod. A large number of studies have shown that thedifferent values of the calculated parameters will affect thestatistical calculation results of a b-value. But, the variationtrend is consistent as time goes on [20].

Figure 14(a) shows the rapid initiation of large newcracks corresponding to the lower initial b-value ofunloading and the initiation of small cracks correspondingto the increase of the b-value with unloading. .is crackinitiation implied that large cracks appeared at the beginningof unloading, and then small cracks initiation and accu-mulation occurred. During this period, it was noted that theb-value experienced a decline. .is indicated that smallcracks accumulated and propagated, which resulted in largecracks. .is corresponded to the variation of the amplitudeand strain rate, as shown in Figure 12. Additionally, theamplitude was relatively high at the beginning of unloading.At 879 s, the amplitude reached the maximum value. Fur-thermore, at 882 s, a dense amplitude of AE signals and alarge number of AE hits suddenly appeared. .is indicatedthat more cracks existed and cracks expanded into largecracks. In general, the b-value increased with the increase ofthe internal and confining pressure difference.

.e variation of the b-value during the maintenancestage after unloading was shown in Figure 14(b). .ere weretwo sudden decreases of the b-value, which meant that smallcracks propagate into large cracks. During the process, thepropagation of small cracks led to a continuous and unstableincrease of the large fracture, and small cracks continued toincrease and propagate, resulting in the emergence of largecracks. At the end of the maintaining stage, the b-value waskept at a high level and the small crack was steadily gen-erated. .is corresponded well to the AE hits (Figures 8(e),

80

70

60

50

Am

plitu

de (d

B)

t = 879s

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Stra

in ra

te (s

–1)

876 878 880 882 884 886Time (s)

Amplitude

Strain rate

Figure 12: Amplitude and radial strain rate of unloading stageunder confining stress of 30MPa.

Shock and Vibration 11

8(f)), and large numbers of AE hits appeared at about 954 sand 1015 s.

5. Conclusions

(1) At the unloading stage, the strain rates and the AEhits for different stress levels were characterized bydecreasing after an initial increase. At the main-taining stage after unloading, when the specimenswere under a relatively low initial confining stress(10MPa, 20MPa), the radial strain rates were verysmall. In contrast, when the stress increased to arelatively high stress (30MPa), the rates were un-stable, which implied that the local and regionaldamage failures of the surrounding rocks near or atthe opening free surface were occurring.

(2) It was seen that the rock failure behaviour wastriggered by a relatively high deviatoric stress level inthis study. .e higher stress level accelerated thedamage development caused by the unloading effectand increased the expansion rate of the internalcracks, so the AE hits increased.

(3) .e amplitudes of the high-frequency or low-frequencyincreased with the initial increase of the confining stress.In addition, the amplitude value of the high-frequency(>200kHz) was much smaller than that of the low-frequency (<200kHz). Two main frequency bands be-low 200kHz were presented, including the range of40–100kHz and the range of about 140–190kHz.

(4) For a faster unloading rate condition, large cracksoccurred at the beginning of unloading, followed by

1.0

0.8

0.6

0.4

0.2

0.0

Dam

age p

aram

eter

(DSB

)

OA→IAB→II

BC→IIICD→IV

10MPa D

C

B

A

O0 300 600 900

Time (s)

(a)

20MPa D

C

B

A

O

OA→IAB→II

BC→IIICD→IV

0 400 800 1200Time (s)

(b)

30MPa D

CBA

O

OA→IAB→II

BC→IIICD→IV

0 400 800 1200Time (s)

(c)

30MPa C

B

A

O

OA→IAB→II

BC→IIICD→IV

0 400 800Time (s)

Zoomed-in view 0.06

0.04

0.02

0.00

(d)

Figure 13: Damage evolution based on AE response under different initial confining stress ((a) 10, (b) 20, (c) 30MPa).

Macrocracks are dominantMicrocracks are forming

Microcracks are dominantMacrocracks are forming

(III) Unloading stage1.6

1.8

2.0

2.2

2.4

2.6

b-va

lue

(a)

Macrocracksare dominant

Microcracksare dominant

Macrocracks are dominantMicrocracks are forming

(IV) Maintaining stage2.1

2.2

2.3

2.4

b-va

lue

(b)

Figure 14: Variation of b-value in the process of failure under confining stress of 30MPa: (a) unloading stage and (b) maintaining stage afterunloading.

12 Shock and Vibration

small cracks initiation and accumulation. .e evo-lution of the squeezing deformation and the failureoccurred along with the increase of the unloadingdamage. Based on the proposed damage parameter,the damage mainly occurred in the maintenancestage after unloading. .at is, the unloading effectcontinued to affect the surrounding rock afterunloading.

Data Availability

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

Conflicts of Interest

.e authors declare that there are no conflicts of interest.

Acknowledgments

.is work was supported by the National Key Project ofNational Natural Science Foundation and Shenhua GroupCorporation Limited of China (U1361210) and the NationalNature Science Foundation of China (51574247).

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14 Shock and Vibration