dynamicbehaviorandenergyevolutioncharacteristicofdeep...

Research ArticleDynamic Behavior and Energy Evolution Characteristic of DeepRoadway Sandstone Containing Weakly Filled Joint atVarious Angles

Qinyong Ma ,1,2,3 Qingqing Su ,1,2,3 and Pu Yuan 1,2,3

1State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mine,Anhui University of Science and Technology, Huainan, Anhui 232001, China2Engineering Research Center of Underground Mine Construction, Ministry of Education of China,Anhui University of Science and Technology, Huainan, Anhui 232001, China3School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan, Anhui 232001, China

Correspondence should be addressed to Qingqing Su; [email protected]

Received 20 May 2020; Revised 10 July 2020; Accepted 31 July 2020; Published 24 August 2020

Academic Editor: Fengqiang Gong

Copyright © 2020 Qinyong Ma 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.

Dynamic impact tests were carried out by implying split-Hopkinson pressure bar (SHPB) apparatus under three-dimensionalstress state to investigate the influences of weakly filled joint at seven kinds of angles on dynamic behavior and energy evolutioncharacteristic of deep roadway sandstone (985 m below the surface). )e results indicated that rebound strain phenomenon wasobvious and the growth rate of stress was in two kinds of phased variations. Dynamic peak strain was inversely proportional tojoint angle under three different strain rates. Dynamic compressive strength, elastic deformation modulus, and plastic defor-mation modulus were in similar variable tendencies with incremental joint angles, showing firstly decrease to minimum value atjoint angle of 45° and then increase to maximum value at joint angle of 90°. Moreover, the sensitivity of plastic deformationmodulus to joint angle was obviously inferior to that of elastic deformation modulus when joint angle increased from 0° to 45°.Furthermore, both elastic deformation modulus and plastic deformation modulus were independent of strain rate, which wascontrary to dynamic compressive strength and dynamic peak strain. Additionally, absorption energy release rate was introducedand defined to describe energy release and conversion characteristics of joint specimens. )e changed trend of energy reflectioncoefficient was completely opposite to that of energy transmission coefficient and absorbed energy release rate. Absorbed energydensity was linearly decreased with incremental joint angle and was increased with the increase of strain rate.

1. Introduction

Deepmining was the inevitable trend of future development.Deep rock mass, which was affected by geological tectonicmovement and human activity, contained various defects,such as joints, flaws, and fractures. As a kind of filledfracture, weakly filled joint universally existed in naturalrock masses, resulting in degraded mechanical properties ofdeep rock masses and reduced stability of undergroundstructures. And joint angle was a critical parameter in jointgeometry, with notable influences on energy evolutioncharacteristic and rock-breaking efficiency. Moreover, dy-namic disturbance and stress state were significant factors

affecting the mechanical properties of deep rock masses[1–4]. Hence, it was a tremendous necessity to investigate theeffects of weakly filled joint at various angles on dynamicbehavior and energy evolution characteristic of deepsandstone under three-dimensional stress state to providescientifically guidance for practical projects.

Numerous efforts had been devoted to investigatingmechanical behaviors of intact rock specimens under staticor dynamic loading with various stress states [5–10]. And therewere relatively few studies that investigated the effects ofpreexisting defects on deformation features and crack coa-lescence categories of rockmass. Gong et al.’s [11] experimentalsimulation investigated the rockburst characteristics in deep

HindawiAdvances in Civil EngineeringVolume 2020, Article ID 8817107, 12 pageshttps://doi.org/10.1155/2020/8817107

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https://doi.org/10.1155/2020/8817107

circular tunnels by utilizing a true triaxial system under fourdifferent initial stresses and revealed the mechanism of rock-burst induced by spalling damage. )e diameter of hole andlateral stress had significant influences on rockburst. Wu et al.[12] studied the dilatancy, acoustic emission, and failurecharacteristics of rock specimens with two preexisting flawsunder uniaxial and triaxial loading states. Moreover, the crackevolution and failure features were closely related to loadingrate and confining pressure. Bai et al. [13] carried out triaxialtests in laboratory to solve ice–rock coupled problem of redsandstone with two preexisting ice-filled fissures. )e rela-tionship between shear strength (σ1 − σ3) and confining stresswas nonlinear, which was opposite to peak strength, elasticmodulus, and shear strength parameters. Wang et al. [14]studied the strength and the failure mode of a heterogeneousrock mass by combining numerical simulation and acousticemission technology under conventional triaxial compression.Confining pressure could inhibit the development of tensilecracks, but facilitate the coalescence of shear cracks. Bothdiscretized virtual internal bond model and element partitionmethod were utilized by Yang et al. [15] to simulate and getinsight into failure sequences of rock with single flaw ormultiple flaws under unloading conditions. )e fracturingprocesses and failure modes were significantly influenced byconfiguration of randomized flaws, whereas the amount offlaws could slightly affect acoustic emission counts. Li et al. [16]combined experimental analysis with theoretical derivation todescribe stress distribution around the circular and ellipticalhole contained in specimens under axial compression andfound that digital image correlation technology could wellreflect crack coalescence processes at different stress stages. Liuet al. [17] proposed a damage constitutive model to analyzedeformation and strength properties of rock with intermittentjoints under cyclic axial compression. Yang et al. [18] con-sidered that U-shaped variation in peak strength and elasticmodulus of nonpersistent jointed rock specimens was obviouswith incremental joint inclination, and shear slipping crackseasily occurred at the sidewalls of circular hole. Si and Gong[19] considered that the weakening effect was positively relatedto unloading rate and confining pressure. However, a higherunloading rate would lead to a weaker rockburst, and a moresevere rockburst resulted from a higher confining pressure.)efailure mode transformation, i.e., shear failure in triaxialcompression tests transformed to tension failure in triaxialunloading compression tests, was the central reason for theweakening of strength.

However, aside from static loadings, dynamic loadingswere universally distributed in deep underground engi-neering. And various defects in rock masses performedsignificant effects on mechanical behaviors and energyevolution characteristics. Han et al. [20] found that flawinclination angle and ligament angle remarkably affecteddynamic compressive strength and dynamic deformationproperties, respectively. Liu et al. [21] comparatively ana-lyzed energy consumption properties of vertical bedded andparallel bedded coal-rock and observed that more energywould be needed by vertical bedded coal-rock for the samefractal dimension. Yuan et al. [22] investigated the effect ofjoint angle on zonal disintegration under coupled high in

situ axial stress and blasting load and found that the numberof cracks after blasting and released strain energy had similarvariable tendency. Li et al. [23] carried out a series of dy-namic tests to study the influences of joint roughness co-efficient on wave energy attenuation and introduced a newmethod based on stress wave energy to calculate seismicquality factor, which was simpler than traditional approachdependent on stress–strain curves. Wang et al. [24] theo-retically analyzed the effects of various parameters of stresswave and joint gap width on energy transmission coefficient.)ere was an optimal incident angle of stress wave tomaximize the transmission coefficient and a critical width ofjoint gap existed for effective propagation of stress wave. Liet al. [25] found that, under coupled dynamic and staticloads, the influences of axial pressure and incident energy onthe mechanical parameters of flawed granite were signifi-cant. With the increase of axial pressure, the energy ab-sorption rate of granite with single flaw increased first andthen decreased, which was inversely proportional to impactpressure. Chen et al. [26] found that the interference ofdetachment wave was adverse to achieve stress equilibriumof specimen and could be avoided by adopting two straingauges mounted on the incident bar at different locations toseparate the detachment wave and reflected wave in triaxialSHPB tests. Additionally, in terms of rock masses with filledjoint, the propagation mechanisms of stress wave were thecentral issues of scholars. Zou et al. [27] derived the solutionsin time domain for plane wave propagation across filled jointbased on Maxwell and Kelvin models and considered thatthe stiffness and the viscosity of joints, incident angle, andduration of incident waves had notable effects on propa-gation and attenuation of stress wave. Cai et al. [28] adoptedtheoretical analysis with the displacement discontinuitymodel to describe the effects of stiffness, spacing, andnumber of parallel fractures on wave attenuation and foundthat the ratio of fracture spacing to wavelength was a de-termining factor for the dependence of transmission coef-ficient on fracture spacing and number. Zhu et al. [29] foundthat the displacement and stress discontinuity model couldwell characterize the seismic response of the filled joint andthe incident angle, joint stiffness. )e nondimensional jointviscosity and the impedance ratio of the filled joint hadsignificant effects on reflection coefficient and transmissioncoefficient. Li et al. [30] demonstrated theoretically thatsimilar variable tendencies of transmitted wave were ob-tained for parallel joints and single joint under differentincident angles and frequencies, and the number of jointswas inversely proportional to transmission coefficient.

It could be safely accepted that weakly filled joint atvarious angles had notable influences on dynamic behaviorand energy evolution mechanism of rock masses. Manyengineering accidents were caused by neglecting the dra-matic change of lithology around the weakly filled joints.However, insufficient researches had been conducted on thedynamic behavior and energy evolution mechanism of rockmasses possessing weakly filled joint with various angles. Inthe present study, a series of dynamic compressive tests werecarried out to investigate the influences of weakly filled jointat seven kinds of angles on dynamic properties and energy

2 Advances in Civil Engineering

evolution characteristics of deep roadway sandstone (985 mbelow the surface) under three-dimensional stress statecoupled with three different strain rates. )e variations indynamic stress–strain curves, dynamic compressivestrength, dynamic peak strain, elastic deformation modulus,plastic deformation modulus, typical energy–time curves,absorbed energy release rate, absorbed energy density, en-ergy transmission coefficient, and energy reflection coeffi-cient were analyzed in detail.

2. Testing Specimens andExperimental Methods

2.1. Preparation of Testing Specimens. Specimens containingweakly filled joint were made of sandstone and gypsum,divided into seven types according to joint angle α, i.e., 0°,15°, 30°, 45°, 60°, 75°, and 90°, as shown in Figure 1(a) andFigure 1(b). )e joint angle α was defined as the acute angleformed by joint and cross section of specimen. And thesandstone was selected from a roadway 985 m below thesurface of a coal mine located in Huainan, Anhui province ofChina, which was composed of quartz (85%), microcline(6.8%), muscovite (4.6%), albite (2.2%), and small amount ofother minerals (1.4%) as determined by XRD analyses, asdisplayed in Figure 1(c). Firstly, intact cylinder core withoutobvious defects was drilled from a sandstone block; then thecylinder specimens were cut into two parts on the basis ofdesigned joint angle by rock cutting machine. Secondly,prefabricated joints with a thickness of 4 ± 1mm (samethickness as cutter blade) were made of gypsum (the weightratio of gypsum to water was 2:1). )e joint and pairedsandstone pieces were cemented by gypsum. Finally, bothends of specimens were grinded and polished to controlunevenness and nonperpendicularity less than 0.2mm. )equalified jointed specimens were with size of 50mm indiameter and 50mm in height following the method sug-gested by the International Society for Rock Mechanics(ISRM) [31].

2.2. Testing Equipment. )e dynamic tests were conductedby employing a modified SHPB apparatus coupled withconfining pressure system and data processing system. )emodified SHPB equipment was consisted of an axial com-pressive system, elastic bars (i.e., an incident bar, a trans-mitted bar, and an absorbing bar), a cone-shaped striker, alaunch device, and a laser speedometer. )e elastic bars wereall made of high-strength alloy steel with Young’s modulus Eof 210GPa, density of 7900 kg/m3, and P-wave propagationvelocity of 5100m/s. Data acquisition and processing systemwas composed of bridge boxes, an oscilloscope, a dynamicresistance strain gauge, a chronograph, a computer, andstrain gauges mounted on elastic bars. )e experimentalprocedure could be described as follows: (1) )e confiningpressure system was carefully debugged, and an appropriateamount of Vaseline was daubed to eliminate as muchfrictional force as possible between interior surface ofconfining pressure chamber and elastic bars. (2) Jointedspecimen was put into confining pressure chamber of

confining pressure system and sandwiched the jointedspecimen between incident bar and transmitted bar. (3) )econfining pressure was applying until the jointed specimenwas loaded with 1MPa, and then the axial precompressivestress was also loaded with 1MPa, which could effectivelyavoid the failure of specimen with weakly filled joint prior todynamic loading. We had determined that the active con-fining pressure and axial precompressive stress were both1MPa after many tests. )e reasons behind this determi-nation were stated as follows. Weak cementation actionbetween rock matrix and joint plane made the jointedspecimen separated locally along cementation planes underlower axial precompressive stress. Although the jointedspecimen had not reach static compressive strength at thismoment, considerable influence of prior local separation onstress wave propagation had formed under dynamic loading.(4) Gas pressure was adjusted to generate desired strain rate,and the pressure switch was opened to accelerate the cone-shaped striker hitting the incident bar with the strain rate _εaround of 30 s−1, 85 s−1, and 105 s−1, respectively. Simulta-neously the elastic stress pulses were captured and displayedby oscilloscope, dynamic resistance strain gauge, and thestrain gauges mounted on the incident bar and transmittedbar. (5) Finally, fragments of specimen were collected aftertest, and the confining pressure chamber was cleared.

2.3. Stress Equilibrium. Stress equilibrium prior to failure, asan essential assumption to ensure valid test dates, wassignificantly important to jointed specimens. A cone-shapedstriker, which was conducive to generate a slowly rising halfsine wave, was utilized to provide sufficient loading time forstress equilibrium of jointed specimens. In terms of jointedspecimen, typical impulse waveform and dynamic stressequilibrium were displayed by Figure 2. )e half sine wavewith an approximate duration of 400 μs was smooth, whichimplied that the dispersion effect of stress wave could beneglected. And the sum of incident stress and reflected stresswas closely inconsistent with transmitted stress, especiallyfor the section of stress equilibrium curves before reachingpeak value. Hence, jointed specimens could well satisfy therequirement of stress equilibrium under the condition ofstatic–dynamic coupling loading in the present SHPB tests.Based on one-dimensional stress wave propagation theory,the axial stress σ(t), strain ε(t), and strain rate _ε(t)of jointedspecimens could be calculated through “three-wave analysis”[32].

3. Dynamic Mechanical Behavior

3.1. Stress–Strain Relationship. Typical stress–strain curvesfor jointed specimens were presented in Figure 3. Based onthe occurrence of filled joints [33], specimens with a jointangle of 0°, 15°, 30°, and 45° were entitled as category I jointedspecimens, and specimens containing a joint angle of 60°,75°, and 90° were called after category II jointed specimens.And representative stress–strain curves of category I jointedspecimens and category II jointed specimens were shown inFigure 3(a). In general, the stress–strain curves of jointed

Advances in Civil Engineering 3

specimens could be sequentially divided into three stages(i.e., elastic stage, plastic stage, and unloading stage)according to the evolutionary characteristics of stress–straincurve. Moreover, the notable differences of stress–straincurves between the two categories of jointed specimens wereperformed in plastic stage and unloading stage. )e plasticstage of category I jointed specimens could be furthersubdivided as the first plastic section AB and the secondplastic section BC. Similar as the plastic stage PQ of categoryII jointed specimens, the first plastic section AB also per-formed remarkably rising trend with a considerable slope,whereas the second plastic section BC was keeping slowlyascending tendency. It was indicated that the deformationcapacity of category I jointed specimens was vastly superiorto that of category II jointed specimens. Furthermore, thestresses of the first unloading section QR for category IIjointed specimens would fall dramatically, which generallyshowed the growth rate of “fast-fast” two sections charac-teristics, while slight decline of stresses for category I jointed

specimens firstly occurred after reaching maximum stressand then plunged linearly, with the growth rate of “fast-slow-slow-fast” four sections characteristics. FromFigures 3(b)–3(d), the failure mode of category I jointedspecimens was obviously plastic failure feature. Conversely,there had been dramatically growing tendency of the brittlefailure feature for category II jointed specimens as jointangle increased from 60° to 90°. )e plastic feature of cat-egory I jointed specimens and the brittle behavior of cate-gory II jointed specimens were both notable under higherstrain rate.

Moreover, the rebound strain phenomenon was ob-served in both category I jointed specimens and category IIjointed specimens. )e reasons behind the phenomenonmight be as follows. From Figure 4, the ultimate failuremodes of jointed specimens were the separation betweenjoint and sandstone matrix. )e crack coalescence andpropagation in jointed specimens were restrained underthree-dimensional stress state, which was conducive to the

Reflected wave

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Figure 2: (a) Typical wave form of electrical signal and (b) dynamic stress equilibrium of jointed specimen.

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Figure 1: Physical pictures of jointed specimens and XRD diffraction pattern of sandstone. (a) Specimen with a joint angle of 30°. (b)Specimen with a joint angle of 60°. (c) XRD diffraction pattern of sandstone.


accumulation of elastic deformation energy in jointedspecimens. )e release of elastic deformation energy gath-ered in sandstone matrix was the primary cause of the re-bound strain phenomenon [34].

3.2.Effects of JointAngle andStrainRate onDynamic Strength.)e relationship of dynamic compressive strength ofintact specimens and jointed specimens against jointangle and strain rate was plotted in Figure 5. In general,the dynamic compressive strengths of jointed specimenwere lower than those of intact specimens and wereproportional to strain rate. For a constant strain rate, themaximum value of dynamic compressive strength hasoccurred at joint angle of 90°, which was slightly smallerthan the dynamic compressive strength of intact

specimen, while the joint angle of 45° minimized thedynamic compressive strength. When the strain rate wasat around 105s−1, the average dynamic strength of intactsandstone specimen and jointed specimen in thedescending order was 151.05MPa, 132.18MPa,107.24MPa, 81.02MPa, 80.39MPa, 71.16MPa,62.72MPa, and 49.46MPa, with multiple relationshipsfrom 1.14 times to 3.05 times. It was implied that jointangle had a strong effect on dynamic strength of sand-stone. Moreover, dynamic compressive strength of jointedspecimens was linearly decreased as the joint angle in-creased from 0° to 45° and then significantly increased tomaximum value with the mounting joint angle from 60° to90°, which was changed in V-shape. And the higher thestrain rate was, the more obvious the V-shaped changewas.

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Figure 3: Stress–strain curves of intact specimens and jointed specimens. (a) Subsection methods of stress–strain curve; (b) the averagestrain rate _ε � 30 s− 1; (c) the average strain rate _ε � 85 s− 1; and (d) the average strain rate _ε � 105 s− 1.


3.3. Effects of Joint Angle and Strain Rate on Dynamic PeakStrain. )e tendencies of dynamic peak strain of specimensunder three kinds of strain rates were shown in Figure 6.Dynamic peak strain under an average strain rate of 85s−1 or105s−1 was gradual decline as joint angle increased from 0° to90°, which was obviously different to that under one-di-mensional stress state [35]. However, the dynamic peakstrain performed slight fluctuation under the average strainrate of 30s−1, which might be resulted from that the lowerincident energy generated marginal damage and deforma-tion to jointed specimen under three-dimensional stressstates. Hence, the deformation characteristics of joint

specimens were not entirely revealed, which resulted in anunapparent variation tendency of dynamic peak strain.Moreover, the dynamic peak strain of intact specimens wasthe minimum and was slightly lower than that of specimenwith a joint angle of 90°, while the maximum value of dy-namic peak strain for jointed specimens has occurred at jointangle of 0°. )ese phenomena could be explained as follows.Weakly filled joint with a certain thickness was compressivelarge deformation material compared with sandstone matrixand brought about a great influence on dynamic peak strain,especially for specimens with a smaller joint angle.)ere wasa large part of dynamic peak strain that came from the

0°

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Figure 4: )e failure modes of specimens with various joint angles under the strain rate of 85s−1.

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Figure 5: Relationship between dynamic compressive strength andjoint angle under three different strain rates.


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ain

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Figure 6: Relationship between dynamic peak strain and jointangle under three different strain rates.


compression deformation of weakly filled joint. And thecompression deformation of weakly filled joints increasedwith the decrease of joint angle. Obviously, the compressiondeformation of joint reached the maximum value at jointangle α � 0 °, whereas the minimum value appeared at jointangle of 90°.

3.4. Effects of Joint Angle and Strain Rate on DeformationModulus. Elastic deformation modulus E1 and plastic de-formation modulus E2 were defined to describe elastic andplastic deformation behaviors of jointed specimensaccording to previous research of sandstone materials, asshown in Figure 7. Elastic deformation modulus E1 wasequal to the slope of the straight line between the pointcorresponding to 50% peak stress and coordinate origin.And plastic deformation modulus E2 was equal to the slopeof the straight line between the point corresponding to peakstress and the point corresponding to 50% peak stress. )edependence of elastic deformation modulus E1 and plasticdeformation modulus E2 on joint angle was presented inFigure 8. Conspicuous change of E1 for jointed specimenspossessing weakly filled joint at various angles was notobserved as the strain rate increased from 30s−1 to 105s−1,but performed regularly prominent fluctuation with variablejoint angle. Notably, E2 with the strain rate of 30s−1 wasminor greater than that when the strain rate was at around85s−1 or 105s−1. )e reasons behind this phenomenon wereas follows. )e ability of three-dimensional stress state torestrain plastic deformation was more considerable, whichimplied that plastic deformation of jointed specimens didnot reach maximum value under smaller strain rate, and thegrowth rate of stress was greater than that of strain. Con-sequently, it was accepted practically that E1 and E2 wereboth independent of strain rate but were sensitive to jointangle.

Subsequently, the variable tendency of E1 and E2 versusjoint angle was stated in detail under the strain rate of 85s−1,as presented in Figure 8. )e maximum and minimumvalues of E1, respectively, occurred at intact specimen andspecimen containing a joint angle of 45°, with a variablerange from 24.82GPa to 69.07GPa. )e average value of E1for intact specimens was 1.74 times, 2.78 times, and 1.09times as much as that of specimens containing a joint angleof 0°, 45°, and 90°, separately. Moreover, V-shaped variabletrend of E1 was apparently demonstrated for jointed spec-imens. It was indicated that E1 decreased linearly when jointangle increased from 0° to 45° and then increased to max-imum value dramatically with incremental joint angle from45° to 90°. Similarly, the variable range of E2 was from3.84GPa to 31.77GPa. )e average maximum value of E2was occupied by intact specimen, which was 5.76 times, 8.27times, and 1.17 times as much as that of specimens pos-sessing a joint angle of 0°, 45°, and 90°, respectively. Whenjoint angle increased from 0° to 45°, the values of E2 forjointed specimens were all far less than those of intactspecimens. And the value of E2 performed a slight reductionwhen α≤ 45° and increased remarkably from 3.84GPa to27.19GPa when α≥ 45°. It meant that weakly filled joint

could conspicuously decline the value of E2, whereas E2 wasmarginally influenced by joint angle when α≤ 45°. Conse-quently, E1 and E2 of jointed specimens were lower thanthose of intact specimens and presented different sensitiv-ities to joint angle. )e value of E1 was dependent on jointangle, while the value of E2 was significantly affected by jointangle only when α> 45° and was insensitive to joint anglewhen α≤ 45°.

4. Energy Evolution Characteristic

Energy dissipation was the internal mechanism for dynamicbehavior of rock mass. Weakly filled joint had significanteffects on stress wave propagation and energy dissipationbehavior [36]. Analyses of energy transmission and trans-formation path were instrumental in ensuring stability and

0.5εcd

0.5σcd

β

E1 = tanβ

εcd0

γ E2 = tanγ

σcd

Elastic stage Plastic stage Failure stage

Figure 7: Defining method of elastic deformation modulus andplastic deformation modulus of jointed specimens.

1.74 times

2.78 times

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Test values,Test values,Test values,Test values,Test values,Test values,

E1

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Figure 8: )e variable tendency of E1 and E2 versus joint angleunder three different strain rates.


safety of underground engineering in design, construction,and service stage, especially for underground cavities sur-rounded by jointed rock masses. Conventionally, energyreflection coefficient RW and energy transmission coefficientTW were defined as the ratio of reflected energy WR andtransmitted energy WT to incident energy WI, respectively.And absorbed energy density WD was described as the ratioof absorbed energy W to the volume of jointed specimens.Additionally, absorption energy release phenomenon ofjointed specimens was observed under three-dimensionalstress state in present study. Hence, released absorbed energyΔW and absorbed energy release rateWRR were introduced toelaborate the storage and release behavior of absorbed energy,which were defined as the difference between maximum valueand final value of absorbed energy and the ratio of absorbedenergy release amountΔW to absorbed energyW, respectively.In addition, only the energy evolution time curves were an-alyzed in detail under the strain rate of 30 s−1 and 105 s−1,because similar energy evolution characteristics were observedunder the strain rate of 85 s−1 and 105 s−1.

4.1. Typical Energy–Time Curves. Energy–time curves pos-sessing a joint angle of 15°, 45°, and 75° were selected as thetypical representatives under the strain rate of 30s−1 and105s−1, as plotted in Figure 9. It could be seen that theshapes of energy evolution–time curves for incident energywere consistent with each other. However, beyond incidentenergy, there were distinct differences in evolutionarycharacteristics of energy–time curves for reflected energy,transmitted energy, and absorbed energy. Absorbed energyrelease phenomenon was more notable under lower strainrate than that under higher strain rate. For specimen with ajoint angle of 15°, absorbed energy reached the maximumvalue and then decreased, whereas the value of incidentenergy and reflected energy tended to be a constant. It wasinferred that the released absorbed energy was mainlyconverted into transmitted energy from energy evolu-tion–time curves. Moreover, the release phenomenon ofabsorbed energy was only observed under the strain rate of30s−1 for specimen containing a joint angle of 45°, whichhas implied that specimen containing a joint angle of 45°still had certain bearing capacity after failure under three-dimensional stress state. )e decline section of absorptionenergy was corresponding to the rising section of reflectionenergy, as well as absorbed energy would keep a constantafter reaching its peak value under higher strain rate, whichcould be considered that released energy was predomi-nantly transformed into reflected energy. Furthermore, thereleased phenomena of absorbed energy were observed forspecimen containing a joint angle of 75° under three dif-ferent strain rates coupled with three-dimensional stressstate. And similar conversion paths of released energy werediscerned, which was entitled section I with durationaround 40 μs from 280 μs to 320 μs and section II withduration around 80 μs from 320 μs to 400 μs. )e releasedabsorbed energy was mainly altered into transmitted en-ergy in section I and reflected energy in section II,respectively.

Absorbed energy released phenomenon could beexplained as follows. Preloading axial compressive stress andactive confining stress propelled energy accumulation injointed specimens. Under lower incident energy, the elasticand plastic energy gathered in jointed specimen was notenough to make specimens loss capacity ability, whichbrought about the release of elastic energy in absorbedenergy. And the relative proportion of released absorbedenergy in absorbed energy was on incline with higher in-cident energy. It was implied that the incremental incidentenergy accelerated the deterioration and damage of jointedrock masses and leaded to the reduction of residual elasticenergy.

In terms of specimen with a joint angle of 15°, the in-creased rate of transmitted energy under the strain rate of30s−1 was slower than that under the strain rate of 105s−1.)e growth rate of reflected energy was the slowest under thestrain rate of 30s−1, which was alien to the evolutionarytendency of reflected energy under the strain rate of 105s−1.And the increase rate of absorbed energy was always thefastest prior to reaching the maximum value. Moreover, forspecimen with a joint angle of 45°, incident energy remainedconstant after reaching the maximum value at around280 μs.)e increase rate of reflected energy was always fasterthan that of transmitted energy and absorbed energy, whiletransmitted energy with a slowest growth rate has accountedfor a much small part in incident energy and would be inplateaus period after reaching its maximum value, whichindicated that specimen with a joint angle of 45° was easy tobe damaged under dynamic loading. Furthermore, forspecimen possessing a joint angle of 75°, the increased rate oftransmitted energy was the fastest compared with reflectedenergy and absorbed energy. Notably, reflected energy waseven larger than absorbed energy in later stage of ener-gy–time curve under three-dimensional stress state, whichdemonstrated that the available energy for rock breaking wasless than the energy returned to incident bar.

4.2. Absorbed Energy Release Rate and Absorbed EnergyDensity. )e relationship between absorbed energy releaserateWRR and joint angle was presented in Figure 10. Similarvariable tendency of absorbed energy release rate was ob-served, which slightly decreased to minimum value first andthen dramatically increased to maximum value. )ere was acritical joint angle tominimize or maximize absorbed energyrelease rate, which was approximate to the joint angle of 45°and 90°, respectively. )e absorbed energy release rate underthe strain rate of 30s−1 was almost always larger than thatunder the strain rate of 85s−1 or 105s−1, except for that ofspecimen with a joint angle of 90°. While the difference ofabsorbed energy release rate under the strain rate of 85s−1

and 105s−1 was insignificant for jointed specimens. )emechanism behind these phenomena could be summarizedas follows. )e lower incident energy resulted in slightdamage of jointed specimens under three-dimensional stressrate, which was instrumental in the storage and release ofelastic energy, while jointed specimens were seriouslydamaged by higher incident energy, especially for weakly


filled joint, without excess elastic energy being released.From Figure 11, there was an obvious linear relationshipbetween absorption energy density and joint angle [37]. Andthe absorption energy density was decreased linearly withthe increase of joint angle under the strain rate of 85s−1 or105s−1, whereas a minor variation was exposed withmounting joint angle under the strain rate of 30s−1. )esephenomena could be explained as follows. )e degree ofcompression failure of joint decreased with the increase ofjoint angle, and crack propagation in jointed specimens wasconfined by three-dimensional stress state, which leaded to agradual decrease in absorbed energy utilized for jointed rockbreaking. However, lower incident energy was not enough todestroy jointed specimens under three-dimensional stressstate, the degree of crack initiation and propagation wassimilar for specimens containing weakly filled joint atvarious angles, with a modest variety in absorbed energydensity.

4.3. Energy Transmission Coefficient and Energy ReflectionCoefficient. Figures 12 and 13 characterized the changingtrajectory of energy reflection coefficient RW and energytransmission coefficient TW against joint angle under three

Test values, ε· = 30s–1 Test values, ε· = 85s–1





0

20

40

60

80

WRR

(%)

15 30 45 60 75 900Joint angle (°)

Figure 10: )e variable tendency of WRR with joint angle underthree different strain rates.

Ener

gy (J

)

Δ∆W

Maximum value

Final value

Time (μs)0 100 200 300 400

WIWR

WTW

0

5

10

15

(a)

Energy Conversion

0 100 200 300 400Time (μs)

WIWR

WTW

Ener

gy (J

)

0

5

10

15

(b)

Section I Section II

Energy conversion

0 100 200 300 400Time (μs)

WIWR

WTW

Ener

gy (J

)

0

5

10

15

(c)

Ener

gy (J

)

Time (μs)0 100 200 300 400

WIWR

WTW

120

0

20

40

60

80

100

(d)

0 100 200 300 400Time (μs)

WIWR

WTW

Ener

gy (J

)

0

20

40

60

80

100

(e)

0 100 200 300 400Time (μs)

WIWR

WTW

Ener

gy (J

)

125

0

25

50

75

100

(f )

Figure 9: Typical energy–time curves. (a) and (d) for specimen with a joint angle of 15° under strain rate of 30 s−1 and 105 s−1, respectively;(b) and (e) for specimen with a joint angle of 45° under strain rate of 30 s−1 and 105 s−1, respectively; and (c) and (f) for specimen with a jointangle of 75° under strain rate of 30 s−1 and 105 s−1, respectively.


different strain rates, respectively. Notably synchronousascending tendency of energy reflected coefficient was dis-covered when joint angle increased from 0° to 45°, which wasopposite to that when joint angle increased from 45° to 90°.)e value of energy reflection coefficient under the strainrate of 105s−1 was marginally larger than that under thestrain rate of 85s−1, but conspicuously larger than that underthe strain rate of 30s−1. )e variable trend of energytransmission coefficient was completely contrary to that ofenergy reflection coefficient through comparative analysis ofFigures 12 and 13 [38]. )e reasons could be epitomized asfollows. Jointed specimens were consolidated, compacted,

and still in elastic state under three-dimensional stress statecoupled with the strain rate of 30s−1, which would contributeto the propagation of transmission wave. Conversely, underthe conditions of higher strain rate, crack initiation andpropagation in jointed specimens would inevitably countagainst the propagation of transmission wave. However, thehigher the strain rate was, the more abundant the crackdeveloped, leading to the increase of energy reflectionsurface, which in turn resulted in an increase in the energyreflection coefficient.

5. Conclusions

Dynamic impact tests were conducted by employing SHPBapparatus to investigate the effects of weakly filled joint atseven kinds of angles on dynamic behavior and energyevolution characteristic of sandstone under three-dimen-sional stress state. Summative conclusions were reached asfollows.

(1) Rebound strain phenomenon was observed fromstress–strain curves of jointed specimens. )e stressgenerally showed the growth rate of “fast-slow-slow-fast” four sections characteristics for specimenscontaining a joint angle of 0°, 15°, 30°, and 45°, withobvious plastic failure feature, whereas for specimenspossessing a joint angle of 60°, 75°, and 90°, the stressdisplayed the growth rate of “fast-fast” two sectionscharacteristics, showing typical brittle failurebehavior.

(2) Dynamic compressive strength, elastic deformationmodulus, and plastic deformation modulus were allchanged in V-shape with the incremental joint anglefrom 0° to 90°, whose maximum value and minimumvalue occurred at 45° and 90°, respectively. However,dynamic peak strain was gradually descending with

W = –0.00038α + 0.052, R2 = 0.946

W = –0.0026α + 0.35, R2 = 0.929

W= –0.0013α + 0.44, R2 = 0.977

Test valuesTest valuesTest values

Average values, ε. = 30s–1



15 30 45 60 75 900Joint angle α (°)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

W (J

/cm

3 )

Figure 11: Variation in W with joint angle under three differentstrain rates.

0

10

20

30

40

50

60

70

80

90

R W (%

)





15 30 45 60 75 900Joint angle (°)

Figure 12: Variation in RW with joint angle under three differentstrain rates.

0

10

20

30

40

50

60

70

80

90

100

T W (

%)





15 30 45 60 75 900Joint angle (°)

Figure 13: Variation in TW with joint angle under three differentstrain rates.


the mounting joint angle. Both elastic deformationmodulus and plastic deformation modulus wereindependent of strain rate, which was opposite todynamic compressive strength and dynamic peakstrain. )e value of elastic deformation modulus wasdependent on joint angle. While the value of plasticdeformation modulus was significantly affected byjoint angle only when α> 45° and was insensitive tojoint angle when α≤ 45°.

(3) )e value of energy reflection coefficient under thestrain rate of 105s−1 was marginally larger than thatunder the strain rate of 85s−1 and conspicuouslylarger than that under the strain rate of 30s−1, withinverted V-shaped change, which was completelycontrary to the variable trend of energy transmissioncoefficient and absorbed energy release rate. And thereleased absorption energy was mainly convertedinto transmitted energy and reflected energy fromenergy evolution–time curves. Absorbed energydensity was linearly decreased with incremental jointangle and was increased with the increase of strainrate.

Data Availability

)e datasets generated and analyzed during the currentstudy are available from the corresponding author on rea-sonable request.

Conflicts of Interest

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

Acknowledgments

)is research received financial support from the NationalNatural Science Foundation of China (no. 51774011).)anks are due to the State Key Laboratory of MiningResponse and Disaster Prevention and Control in Deep CoalMine and Engineering Research Center of UndergroundMine Construction, Ministry of Education of China, AnhuiUniversity of Science and Technology, for providing theexperiment conditions.

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