Kshng Li ,Shngqi Yng *,Chunxio Liu ,Yun Chn ,Gungli Zhng ,Qing M

a State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering,China University of Mining and Technology,Xuzhou 221116,China

b School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou 221116,China

c College of Water Conservancy and Civil Engineering,Shandong Agricultural University,Tai’an 271018,China

d School of Civil and Transportation Engineering,Hebei University of Technology,Tianjin 300401,China

e State Key Laboratory of Hydroscience and Engineering,Tsinghua University,Beijing 100084,China

Keywords:

ABSTRACT This study aims to investigate the mechanical response and acoustic emission (AE) characteristic of preflawed sandstone under both monotonic and multilevel constant-amplitude cyclic loads.Specifically,we explored how coplanar flaw angle and load type impact the strength and deformation behavior and microscopic damage mechanism.Results indicated that being fluctuated before rising with increasing fissure angle under monotonic loading,the peak strength of the specimen first increased slowly and then steeply under cyclic loading.The effect of multilevel cyclic loading on the mechanical parameters was more significant.For a single fatigue stage,the specimen underwent greater deformation in early cycles,which subsequently stabilized.Similar variation pattern was also reflected by AE count/energy/b-value.Crack behaviors were dominated by the fissure angle and load type and medium-scale crack accounted for 74.83%-86.44% of total crack.Compared with monotonic loading,crack distribution of specimen under cyclic loading was more complicated.Meanwhile,a simple model was proposed to describe the damage evolution of sandstone under cyclic loading.Finally,SEM images revealed that the microstructures at the fracture were mainly composed of intergranular fracture,and percentage of transgranular fracture jumped under cyclic loading due to the rapid release of elastic energy caused by high loading rate.

1.Introduction

Geological hazards associated with rock dynamics,such as landslides,collapse of mining areas,destabilization of coal pillars,rock bursts,sudden fall of large rocks,often happen during underground/slope excavations [1].Activities like drilling,blasting,mechanical excavation,truck haulage,mine seismic,back-filling,earthquake,compressed air energy storage and pumped storage power of closed/abandoned mines can produce seismic waves and periodic cyclic stresses [2].Hence,the rock masses in both underground and slope engineering usually suffer from permanently dynamic and cyclic stress disturbance.Being a typical discontinuous and highly non-homogeneous natural material,rock masses contain extensive internal flaws such as pores,joints and fissures[3],which are more subject to failure under periodic stress.In the previous several decades,the mechanical behavior and fracture mechanism of pre-flawed rock under static loading have been extensively reported [4,5].However,there are relatively limited investigations on the fatigue characteristics of these rocks.

Based on the loading path,fatigue tests were divided into two main categories,namely,constant/variable-amplitude loading.For most investigations,the values for amplitude and mean stress are constant during the fatigue experiment.These studies mainly analyzed the effect of the loading parameters,including waveform,frequency,maximum stresses,amplitude and cycle number,on specimen’s strength and deformation[6].Generally,there is a basic consensus in the literature on the fatigue behaviors of rock as follows: (1) the sinusoidal signal is the most similar to the dynamic waveform resulting from earthquakes or rock burst,and(2)deformation parameter and fatigue life rose with increasing amplitude or upper limit stress.For the investigation of dynamic frequency,most lab-experiment results suggested that the strength and deformation of the specimen were improved or dropped with increasing frequency [7,8];however,partial data indicated that there was a non-linear relationship between frequency and fatigue mechanical parameters [9].

Recent studies have shown that multilevel cyclic loading may match the actual stress conditions of rock engineering in the field[10].Similarly,the field monitoring data also demonstrated that the rock mass was subjected to multi-level fatigue loading [11].For instance,the roads,railroads and bridges are exposed to multilevel cyclic loading due to the varying number and loads of vehicles [12];blasting or mining earthquakes generates nonconstant-amplitude fatigue loading on the surrounding rock structures in underground engineering [13];the cyclic loading on the slopes during open pit mining is multi-stress level as the mining depth increases[14];the forces exerted on the rocks during water level rise and fall usually are regarded as a kind of fatigue loading for water diversion tunnels,and their impact on the hydraulic engineering is multi-level [15];the rock mass in the surroundings of salt caverns is frequently exposed to multilevel cyclic loading due to the periodic injection and production activities of gas in underground gas storage [16].Considering the rock mass from the above-mentioned engineering suffered from complex dynamic stress disturbance,the multilevel constant or non-constant amplitude fatigue tests were conducted on the rocks collected from the field in the laboratory.In the present literature review,we compiled previous laboratory investigations in which multilevel fatigue tests were reported (Table 1) [17-27].From Table 1,it is concluded that(1)multi-level fatigue tests are mainly divided into two categories (constant-amplitude and variable stress limit,and constant stress limit and increasing-amplitude),(2) uniaxial loading is used for the fatigue tests in most studies,(3) granite,sandstone,marble and rock salt are the commonly investigated rock types,and(4)the impacts of loading parameters,external environment and structural plane on the fatigue characteristics of rock are widely investigated.Following detailed literature reviews,it is distinct that the object of most studies about rock fatigue test mainly is intact specimen,however,experimental data on fatigue behaviors of the pre-flawed rock are relatively limited.Moreover,the effects of both monotonic and multi-level fatigue loading on the mechanical behavior and fracture mechanism for rock remain unclear.

Table 1 Brief summary of representative laboratory fatigue experiments on brittle geomaterials under complex cyclic paths.

In this study,sandstone was used as the experimental material to investigate the monotonic and fatigue mechanical response of specimen containing two coplanar flaws with various fissure angles.Furthermore,the AE signals during the whole test were monitored and a simple model was proposed based on the statistical damage mechanics and geometric damage theory,to describe qualitatively and quantitatively the damage evolution of preflawed sandstone respectively.Finally,the fractured surface of failed specimen was observed using scanning electron microscopy(SEM) to reveal their microscopic damage mechanism.Organization of the paper is described as follows: Section 1 highlights the importance of fatigue loading for rock engineering,reviews the literatures in which fatigue behaviors of the rock are reported,and remarks the limitations of the existing investigations.Section 2 briefly describes the experimental methodology including basic properties and preparation of specimen and test procedures.The mechanical properties of pre-flawed rock under monotonic loading are presented in Section 3.Section 4 provides a detailed analysis of the mechanical response and damage evolution for pre-flawed sandstone under multilevel cyclic loading.Section 5 compares the findings of this study with those reported in the literature,and explores microscopic damage mechanism of sandstone under different load types by SEM images.Finally,the final concluding remarks of the investigation are given in Section 6.

2.Experimental methodology

2.1.Sandstone material

The sandstones used for this experiment were obtained from Zigong,Sichuan Province,China.For the sandstone material,the connected porosity is 15.99% and the bulk density is 2240 kg/m3.The sandstone was comprised of quartz (38.2%),sodium feldspar(32.5%),calcite (17.1%) and chlorite (12.2%).The volume share of each pore group was as follows: 61.95% for macropores(d≥20 μm),29.31% for small pores (0.1≤d＜20 μm),and 8.74%for micropores (d＜0.1 μm).The SEM images indicated that tested sandstone was mainly composed of mineral grains,pores and micro-cracks,and the grains were connected to each other by large number of cements (Fig.1).

Fig.1.Microscopic characteristics of sandstone material used in this study.

The massive sandstones were made into standard cylinders(diameter: 50 mm;height:100 mm).The standard intact sandstones were cut into samples containing two open coplanar fissures using a high pressure water-jet,and the open fissure parameters were described as: the values for length and width were 12 and 2 mm,respectively (Fig.2);the angle values were designed to be 0°,30°,45°,60°,75° and 90°,respectively;the length of the rock bridge was 12 mm.

Fig.2.Geometry of two coplanar open fissures in yellow sandstone samples.(For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

2.2.Testing system description

The mechanical experiments in the present study were performed on the rock triaxial testing system,as shown in Fig.3.The detailed parameters for this test system are as follows: the stiffness of the loading frame is 20 GN/m,and the maximum values of axial force and confining pressure 2 MN and 60 MPa,respectively.Furthermore,we placed the 4 probes in sample surface to monitor the AE signal in real time during the whole test.The setting parameters of the AE system are as follows: the threshold value is 40 dB and the sampling rate is 500 kHz.

Fig.3.Rock triaxial testing system.

2.3.Experimental procedure

The mechanical experiments in this study were divided into two sections based on the stress path(Fig.4).Firstly,conventional uniaxial compression tests were performed on pre-flawed sandstone samples at a displacement control of 0.05 mm/min(Fig.4a).Secondly,multilevel constant-amplitude cyclic loading tests were conducted on pre-flawed sandstone specimens(Fig.4b).

Fig.4.Stress paths in this study.

The fatigue experiments consisted of two procedures: (1) The axial stress was loaded to 2 MPa at a constant loading rate of 0.05 mm/min.(2) Then,multilevel cyclic loading was applied to the sandstone specimens,and the dynamic frequency and waveform of cyclic loading were 0.2 Hz and cosine respectively.During the whole loading,30 cycles were applied in each stress level and the minimum and maximum cyclic stress were increased by 4 MPa for each loading stage until the specimen failed.

The stress-strain data and AE signals of the sandstone specimens were monitored in real time during the whole test duration.After the end of the test,the microstructure at the fracture of the failed specimen was observed using a high magnification SEM.

3.Results of monotonic loading experiment

Fig.5 shows the stress-strain curves of the pre-flawed sandstone samples under monotonic loading.From Fig.5a,the peak stress exhibited slight fluctuation followed by a dramatic rise as coplanar fissure angle increased.Furthermore,it was observed that the fissure angle had no distinct influence on the curve morphology in pre-peak portion.Specifically,these specimens underwent initial deformation,elastic deformation,nonlinear deformation,post-peak failure stages.Conversely,the fissure angle distinctly affected the curves of post-peak stage.At this stage,the stress fluctuation phenomenon due to the propagation and coalescence of new/existing cracks were only observed for specimens with smaller pre-existing fissure angle.Moreover,it was found that the specimens had not immediately lost its load bearing capacity completely after reaching the peak strength.It was noteworthy that peak radial-strain of the specimen appeared to be larger and was more sensitive to stress compared to peak axial-strain.This was due to the fact that radial-strain variation after the yielding stage reflected the internal weakening course of rock materials.As evident from Fig.5b,specimens showed obvious dilatation after undergoing the elastic and volumeinvariant stages.

Fig.5.Impact of coplanar flaw angle on stress-strain curves of sandstone exposed to monotonic loading.

Fig.6 shows that the parameters characterizing strength and deformation of pre-flawed sandstone specimens.As evident in Fig.6a,the uniaxial compressive strength of sandstone slightly fluctuated and then dramatically rose as fissure angle increased.When the flaw angle was increased from 0° to 75°,the preexisting fissure had least impact on the specimen’s strength,ranging from 17.30 to 19.34 MPa.The sandstone with 90°coplanar fissure angle had the highest uniaxial compressive strength of 36.50 MPa.As the flaw angle increased,the peak axial strain presented a trend of decreasing and then rising (Fig.6b).The peak axial strains were the minimum and maximum values of 4.42×10-3and 6.72×10-3respectively when the coplanar flaw angle was 45° and 90°.The variation in elastic modulus coincided with in peak strength (Fig.6c).Specifically,the elastic modulus showed slight fluctuation (α=0°-75°) and then obviously rose to 5.99 GPa (α=90°).Finally,we found that the Poisson’s ratio of the sample has little correlation with fissure angle (Fig.6d).

Fig.6.Variation of strength and deformation parameters of sandstone with different pre-existing flaw angles.

Fig.8 presented the ultimate failure mode of the pre-flawed specimen under uniaxial monotonic loading,which is clearly different from the that of the intact specimens (Fig.7).Specifically,it showed combined shear-tension failure mode for intact specimens;for pre-fissured specimens,the cracks initiation was found from the pre-existing flaw tips,and the propagation,coalescence and penetration behaviors of the cracks were distinctly related to the coplanar fissure angle.

For the specimens with α=0°,30° and 45°,the cracks first appeared at the pre-existing flaw tips and subsequently the wing cracks propagated towards specimen ends,and indirect/direct cracks coalescence between the two inner tips was found.For the specimens with α=60°,they displayed shear failure,and the two distinct wing cracks initiating from the flaw’s outer tips propagated to the specimen ends and cracks initiating from inner tips of flaws directly coalesced.For the specimens with α=75° and 90°,crack propagation traces were observed in and around tips of the pre-existing fissure,and crack coalescence phenomenon was not found at the rock bridge,and numerous far-field/secondary cracks were noted.The ultimate failure patterns of the pre-flawed sandstone were determined by a combination of farfield cracks and the main cracks originating from the pre-flaw tips.Therefore,the crack initiation,propagation and coalescence phenomena were highly related to the coplanar pre-flaw angles.Further,the stress-strain responses were dependent on the crack coalescence types at the tips of pre-existing fissures in the specimen.

4.Results of fatigue loading experiment

4.1.Overall stress-strain responses

The complete stress-strain curves of the pre-flawed sandstone under multilevel cyclic loading are presented in Fig.9.The curves were similar in form for all specimens.Specifically,as the loading time increased,the unloading and loading curves did not overlap,instead forming a distinct hysteresis loop,which showed that the irreversible plastic deformation produced inside the specimen.We observed that the hysteresis curves displayed a trend from dense to sparse with rise of the stress level.This was because the new/existing cracks propagated gradually,leading to an increase in the irreversible damage inside the rock samples as the loading increased,especially when the maximum cyclic stress exceeded the yield limit of sandstone material.It is further found that apart from last fatigue stage,the hysteresis loops showed a trend of‘‘sparse-dense” with increasing cycle number for a single stage,and this trend became more distinct when the specimen was in the yield phase.This was attributed to that the sudden rise in stress levels in the first few cycles caused significant plastic deformation of specimen,and nevertheless,with increase of cycle number,the new/existing cracks were partially closed.For last stage of fatigue loading,the stress-strain curves displayed two forms,namely‘‘progressively sparse” and ‘‘sparse-dense-sparse”,which were obviously different from those previous stages.It is dependent on the properties of the sample itself and fatigue loading parameters(such as amplitude,frequency,stress limits and confining pressure,etc.).

Fig.9.Influence of pre-existing flaw angle on axial,lateral,and volumetric stress-strain curves of sandstone exposed to multilevel cyclic loading.

To better reflect the impact of axial and lateral strains on sandstone’s volume variation,the volumetric strain (εv) was calculated in this study according to Eq.(1).

where ε1and ε3are the axial and lateral strains of rock specimen,respectively.

As can be seen from Fig.9,the evolution pattern of volumetric strain for pre-flawed sandstone showed good agreement with that of axial and lateral strains.Furthermore,the stress-volume strain curves indicated that the pre-flawed specimens produced a significant dilatation before rock failure.

Fig.9 also revealed that(1)most of the specimens failed due to the maximum axial cyclic stress abruptly rose,and (2) the postpeak curves linearly dropped,and specimens showed obvious brittle failure.The fatigue mechanical and deformation parameters are listed in Table 2.The peak strength,fatigue life and fatigue stages for the pre-flawed samples showed first a slight rise followed by a jump with increasing pre-existing fissure angle.The three parameters mentioned above obtained minimum value (18.29 MPa,92,4)and maximum value(38.06 MPa,240,8)when the coplanar flaw angle was 0°and 90°,respectively.It demonstrated that flaw angle had remarkable influence on strength,deformation and fracture behaviors of sandstone under multilevel cyclic loading.

Table 2 The mechanical properties of sandstone specimens containing two coplanar fissures subjected to fatigue loading conditions.

4.2.Fatigue deformation characteristics

The strain evolution process of pre-flawed sandstones under multilevel cyclic loading are given in Fig.10.The sample’s deformation increased in a stepped pattern as the maximum cyclic stress rose.Specifically,the above three strains displayed a threestage developing trend,i.e.,slowly rising,steadily rising,and rapidly rising,which was similar to the creep deformation laws of rock materials.For single fatigue stage,axial strain rose quickly at a couple of earlier cycles and then the growth rate slowed down.The above phenomenon was attributed to that axial force dramatically rose as a result of the fatigue stage climbed,leading to the creation,propagation and coalescence of new/existing cracks.However,following a few cycles of loading,partial cracks were closed due to fatigue loads.Furthermore,we also noticed that the volume of all the samples changed from compression to expansion at the last fatigue stage.

Fig.10.Evolution of axial,lateral,and volumetric strain of sandstone with various pre-existing flaw angles under multilevel constant-amplitude cyclic loading.

Fig.11 shows the enlarged parts of the time-strain curves for pre-flawed sandstone samples.It revealed that (1) for a single stage,the deformation varied periodically with increasing loading time,which was closely associated with the force applied on the specimen,and(2)the lateral strains changed relatively slight compared with the axial and volumetric strains during the early stages of fatigue loading,and rose dramatically in the last few stages.

Fig.11.Enlarged parts of the strain evolution process of partially pre-flawed sandstone.

Fig.12 presents the maximum axial strains of sample at each fatigue stage.The maximum axial strain showed a linear rise with increasing stress level.It is noteworthy that despite the positive correlation between the angle of coplanar flaw and the fatigue mechanical parameters of the specimen,their axial deformation was not strongly related to the fissure angle.Further,it was observed that axial strain during fatigue loading stages was dependent on initial axial strain (the strain value obtained after monotonic loading to the first lower stress limit).

Fig.12.Variation of maximum axial strain of sandstone containing two coplanar flaws with cyclic loading stage.

Fig.13.Evolution of AE counts for multilevel constant-amplitude cyclic loading tests on yellow sandstone containing different fissure angles.

Fig.14.Evolution of AE energy for multilevel constant-amplitude cyclic loading tests on yellow sandstone containing different fissure angles.

The axial strain rate could exhibit the damage behavior of brittle materials including rocks.Thus,the axial strain rate values per fatigue stage were calculated in the study,as shown in Table 3.The formula is shown below.

Table 3 Axial deformation rate for sandstone samples containing different flaw angles per cycle subjected to multilevel cyclic loading,s-1.

The difference in axial strain rates for specimens containing different pre-flaw angles varied widely,even not in the same order of magnitude.Similarly,the rates corresponding to different fatigue stages of the same specimen also changed greatly.For example,the strain rates for specimen with α=0° were 1.01×10-6s-1and 1.11×10-4s-1at the first stress level and the fourth stress level,respectively.

The evolution laws of the axial strain rate were followed in a similar form for every sample.In other words,except for last fatigue stage,the rates gradually increased and was proportional to the maximum cyclic stress,indicating that the damage inside specimen rose progressively.In the last fatigue stage,there was jump in the strain rate which was notably higher than those calculated from other stages.This phenomenon was attribute to the rapid propagation/coalescence of the existing microcracks eventually forming macroscopic cracks at this stage.

4.3.AE characteristics

4.3.1.AE counts and energy

The AE parameters were found to be effective in reflecting the damage conditions inside the rock material during the whole loading period.Figs.13 and 14 display the relation between axial stress,AE counts,energy and loading time,respectively.As expected,AE counts and energy showed similar trends as the loading time increased,and hence,both of these parameters were analyzed together in this work.The AE counts/energy showed a progressively active trend as mean cyclic stress climbed.Concretely,the higher AE event number gradually increased with rising stress level,indicating that the damage inside specimens presented progressive evolution characteristic.

For the single fatigue loading stage before specimen failure,AE count/energy displayed the identical trend.AE count/energy presented a relatively active state at the first few cycles,and progressively calmed down as cycle number increased.When the mean cyclic stress increased for a level from one to another,the AE signal became active again.This phenomenon could be explained that(1)the instantaneous axial compression led to weak crystals fracture and grain boundary sliding inside the specimen,causing frequent AE events at the initial cycles,and (2) with increasing cycle number,the weak crystals were completely destroyed and the strong crystals play an important role in bearing external force,resulting in a decrease in AE activity.At the last fatigue stage,the AE count/energy always displayed a highly active state until the samples lost its load-bearing capacity,showing that the propagation/coalescence of cracks inside the specimen mainly occurred at this stage.

4.3.2.AE spectrum frequency analysis

Besides the AE event parameters,the AE signals also include a variety of frequencies,among which peak frequency is extremely sensitive to the crack behaviors including number,type,dimension.Thus,the peak frequency distribution of pre-flawed samples in the whole fatigue test was analyzed,as presented in Fig.15,to explore its damage evolution process.The peak frequency of AE signal is opposite to the crack dimension,i.e.,low frequencies correspond to larger cracks (b＞100 μm),median frequencies correspond to medium size cracks (10 μm≤b≤100 μm) and high frequencies correspond to smaller cracks (b＜10 μm).The letterbrefers to the crack opening,which is actually the crack width.The distribution pattern of AE peak frequencies was consistent for samples with different coplanar flaw angles as the loading time increased.In detail,in the first several loading stages,the AE signals were mainly dominated by low and medium frequencies,and high frequency signals were rarely detected;as the maximum cyclic stress increased,peak frequencies of the three categories for AE signals(namely,low,medium and high frequencies)all showed an increasing trend,especially the medium-frequency part.It was further demonstrated that the specimen’s damage rose over time during the loading.Furthermore,we observed that the AE signals were mainly distributed at the sudden loading stress rise and the last stage of fatigue loading,suggesting further evidence that the fracture behavior of the cracks mainly occurred during this time period.This was in line with the evolution characteristic of AE count/energy.

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The percentages of the three types of peak frequencies are listed in Table 4.The AE signal was mainly dominated by medium frequency,accounting for 74.83%-86.44% of the all AE signal.It illustrated that the fracture behavior of these specimens was controlled by medium size cracks.As the pre-existing fissure angle increased,the proportions of low-frequency signals first dropped and subsequently rose,indicating that the coplanar flaw angle had impact on the larger cracks.

4.3.3.b-value analysis

Due to the fact that fatigue tests are conducted in a closed environment,crack propagation cannot be observed.To remedy these limitations,previous studies usually analyzed the variation laws of theb-value to characterize the crack propagation inside the specimen.The concept of AEb-value was first originated in seismology and later introduced into the rock mechanics field,which is calculated by the following equation [23].

whereNis the total AE ring counts for each statistical interval;AdBthe maximum amplitude of AE event;andathe empirical constant.

Generally,increasingbvalue means that the proportion of small AE events rises,and fracture inside the specimen is dominated by the smaller scale fracture;conversely,the proportion of large AE events increases,and larger scale fracture occurs inside the specimen.In case thebvalue fluctuates with a given range,indicating a progressive propagation of cracks.

Fig.16 gives the evolution patterns ofb-value for all pre-flawed samples subjected to multilevel fatigue loading.The trend ofbvalue variation was basically similar for these specimens.For single fatigue stage except the last one,theb-value first rose and then stabilized.This was because the stress suddenly increased between the two fatigue stages,causing rapid propagation of cracks inside the specimen,and these cracks partially closed as the number of cycles increased.In the last stage,theb-value initially fluctuated and then dropped linearly.At this time,the cracks inside the specimen entered the non-stable propagation stage,and the cracks with various scales propagated dramatically,which showed an obvious fluctuation trend for theb-value.The samples were subjected to high axial cyclic stress and the internal cracks propagated quickly and aggregated to form a macro fracture surface,resulting in a linear drop in theb-value.This indicated that the sandstone samples were about to be fractured.

Fig.16.Evolution of b-value for multilevel constant-amplitude cyclic loading tests on yellow sandstone containing different pre-existing fissure angles.

4.3.4.Evolution of crack classification

The average frequency(AF)and rise angle(RA)in the AE indicators were first used for the identification and characterization of damage state of concrete materials,and are key parameters for determining the failure mode of concrete.Similarly,these two parameters can also effectively characterize failure mode of rock material.Previous studies showed that highRAvalue for shear crack and highAFvalue for tensile crack.TheAFandRAare calculated as shown below [28].

whereAECis the ring counts;DTthe duration time;RTthe rise time;andAdBthe maximum amplitude.The units ofAFandRAare kHz and ms/V,respectively.

Fig.17 depicts the principle drawing of the classification method for cracks in the sample based on theAFandRAvalues.It can be found that a straight line passing through the origin divides the whole area into 2 parts,the upper area is the tensile region and the lower area is the shear region.However,the dividing line betweenRAandAFis usually determined empirically,which makes the results highly uncertain.Zhang and Deng [29]found that the slope of this dividing line was approximately 100/1-500/1 for brittle material.On this basis,we also referred to several recent studies on the rock materials [23].Finally,the slope was determined as 100/1 in this study.

Fig.17.Schematic diagram of crack classification based on AE waveform parameters [28].

Fig.18.Crack classification results of sandstone with two pre-existing coplanar flaws based on RA and AF value.

Fig.19.The proportion of tensile/shear cracks for sandstones with different preexisting flaw angles during failure.

The crack classification results of rock sample with various preexisting flaw angles are presented in Figs.18 and 19.TheRA-AFvalues of the pre-fissured sandstone specimens were mainly distributed along the longitudinal axis,which implied that tensile cracks of the rock specimen subjected to uniaxial cyclic loading developed.The proportion of tensile cracks and shear cracks distinctly depended on the coplanar flaw angle.As the coplanar flaw angle increased,the percentages of shear cracks exhibited a trend of dropping and then rising,and the percentages of tensile cracks showed the opposite law.Apart from the specimen containing 0°pre-flaw angle,the percentages of tensile crack were 64.42%,81.63%,71.49%,77.70%,and 64.32% for samples with 30°,45°,60°,75°,and 90° fissure angle,respectively.This illustrates that the lack of lateral restraint for the specimen under uniaxial compression conditions contributes to the dominance of their tensile cracks.

4.4.Macroscopic failure modes

Fig.20 displays the macro-failure modes of pre-fissured samples exposed to multilevel constant-amplitude fatigue loading.For the specimens with α=0°and α=30°,two pre-existing coplanar fissures dramatically influenced the initiation and propagation direction of cracks,and cracks initiating at the tips of the preexisting flaws failed to propagate to the two ends of the specimen.Besides,secondary cracks and far-field cracks with random distribution were found on specimen surface.When angle value of the pre-existing flaw increased to 45°,the cracks propagated from two tips of pre-existing flaw to sample’s ends,with the direction changing from parallel to the pre-existing coplanar fissures to vertical.Furthermore,there were direct coalescence of cracks and surface spalling of rock particles at the rock bridge.Meanwhile,for specimens with α=60°,there was a single complete shear crack parallel to the pre-existing fissures,implying a significant induction of failure mode by pre-existing flaws,which also occurred in the samples with α=75°.However,when the direction of axial stress conformed to that of pre-existing flaws,the number of cracks observed around two flaws obviously reduced and the shear cracks were dominant,which showed that this coplanar angle had less impact on crack behavior than others.In conclusion,the ultimate failure modes of specimens exposed to multilevel constantamplitude fatigue loading were remarkably influenced by the pre-existing coplanar fissure angle.

Fig.20.Ultimate failure modes of sandstone with two pre-existing coplanar fissures exposed to multilevel cyclic loading.

4.5.Coupled damage analysis of fractured rocks

For the rocks including both micro flaws and macro fissures,the rock’s damage caused by these two types of flaws is usually calculated separately and then coupled to calculate the total damage variables.Fig.21 gives the calculation of the coupled damage variables for fractured rocks.In this study,we recorded the damage variable for rocks containing only macro pre-existing fissures asD1,and the damage variable for rocks containing only micro-flaws asD2.The calculation methodology for the above two types of damage variables is presented separately in the following.

Fig.21.Calculation of the coupled damage variable of fractured rock.

For damage caused by macro fissures,this damage variable is obtained based on geometric damage theory.Since the specimen is subjected to uniaxial compression,we ignore the projection of the two pre-existing fissures in the other 2 directions.Thus,the damage variableD1is expressed as:

whereAfissureis the total effective area obtained by the projection of the two pre-existing fissures along the axial direction;andAtotalthe total area of the specimen end,which is 1962.5 mm2(πR2=3.14×252) in this study.Table 5 lists the total projected area of the pre-existing fissures along axial direction and the calculated values ofD1.

Table 5 The damage value (D1) caused only by macro fissures of the pre-flawed sandstone samples.

For the damage caused by microscopic flaws in the specimen,statistical damage mechanics in this work is used to study this damage variable since the micro-flaws inside the rock are randomly distributed.It is assumed that the strength of microscopic unit inside the specimen obeys the Weibull distribution.The damage variableD2in this part can be expressed by Eq.(7).

whereFis the distributed variable of microscopic element’s intensity;andmandF0the Weibull parameters describing the centralization and intensity magnitude of the microscopic elements,respectively.

Previous studies usually regardedFas uniaxial stress or strain,followed by a linear fitting approach to determine the parametersF0andm.Obviously,there are certain deficiencies for this method.Liu and Dai [30] adopted the D-P strength criterion to determine the variableF(Eq.(8))and proposed an analytical method to determine the parametersmandF0(Eqs.(9) and (10)).

whereI1is the first invariant of the stress tensor,whose value is equal to σ1;J2the second invariant of the stress deviator,whose value is equal tothe material coefficient;and φ the internal friction angle.

whereEis the elastic modulus of the rock material;σpand εpthe stress and strain at the peak point of the stress-strain curves,respectively;andFpthe distributed variable at the peak point and its value is.

Based on the Lemaitre strain equivalence assumption,a simple damage model for fractured rocks considering coupling effects was established.Its coupled damage variables (D12) are:

Substitute Eqs.(6) and (7) into Eq.(11) to obtain the coupled damage model of the pre-fissured rocks under uniaxial compression:

Fig.22 shows the coupled damage evolution curves of the preflawed sandstone during the whole loading process.As evident in Fig.22,the initial coupling damage values ranged from 0.052 to 0.528 and dropped progressively with increasing coplanar fissure angle.We also found that the specimen’s damage showed a gradual increasing trend overall.The coupled fatigue damage value abruptly increased when the mean cyclic stress rose.In the early and middle stages of fatigue loading,the damage variables first increased and then stabilized with the increasing number of cycles.In the later stages of fatigue loading,the coupled damage values rose significantly and continuously as the number of cycles increased.This was similar to the strain evolution laws of the specimen.

Fig.22.Coupling damage evolution of sandstone with different pre-existing coplanar flaw angles.

From the whole loading process,the fatigue damage rate of the specimen displayed the obvious ‘‘deceleration-stabilization-accel eration” three-stage variation pattern.In the first stage of fatigue loading,the micro-flaws inside the specimen were compacted and the specimen produced larger plastic damage.In the subsequent several fatigue stages,the fatigue damage rate decreased and stabilized due to the compaction of the initial micro-defects.In the last two fatigue stages,the cracks propagated quickly and sample produced macroscopic cracks,at which time the damage rate jumped obviously.Ultimately,the macroscopic cracks coalesced with each other and the specimen failed.

5.Discussions

In the present study,we investigated the deformation,strength and fracture behaviors of the sandstone with two pre-existing coplanar flaws under both monotonic and multilevel fatigue loading,respectively,to better explicate the impacts of load types and flaw angles on the sandstone properties.In this section,based on above experimental investigation data,we compared relevant characteristics of sandstone with various flaw angles exposed to two types of loads and observed the microstructure of fractured surface to explore its damage mechanism from the microscopic aspect,the findings of which provided a reference for further investigations.

5.1.Comparison of mechanical behaviors of specimen under monotonic and cyclic loading

Fig.23 compares the peak strength and axial strain of sandstone samples with two coplanar flaws under monotonic and multilevel cyclic loading.Previous studies reported that load types and flaw geometry parameters considerably impacted the geological characteristics and fracture behaviors of rock materials[31].The experimental data in this study,in general,support this conclusion with peak strength and axial strain for pre-flawed samples under multilevel fatigue loading being higher than the corresponding values under monotonic loading (Fig.23).Similarly,Peng et al.[32]observed that triaxial compressive strength of sandstone was lower than the fatigue strength;Yang et al.[33]also reported that geological parameters of red sandstone under monotonic loading were lower than the corresponding values under cyclic loading at low confining pressures.The reasons for these test results may be explained by the following views.In this work,we considered that maximum cyclic loading without exceeding fatigue threshold values led to better closure of initial microcracks/pores inside sandstone specimen;in other words,the lower fatigue loading improved its pore characteristics,which led to a slight rise in the strength.

Fig.23.Comparison of mechanical parameters of pre-flawed sandstone samples under both monotonic and multilevel cyclic loading.

Satisfactorily,our opinion is supported by literatures from rock/concrete materials.Yang et al.[33]believed that local yielding of the rock occurred under low cyclic loading,and the extruded and crushed materials filled the internal pores of the specimens and strengthened the support structure of the rocks.Chen et al.[34]discovered that cyclic loading caused the specimens to exhibit different degrees of strengthening by conducting uniaxial fatigue tests on sandstone,limestone and concrete specimens in the elastic deformation stage.In addition,by measuring the specimen’s porosity,they revealed that the cyclic loading applied to the specimens in the elastic stage reduced its porosity,and the more the number of cycles,the more obvious the reduction in porosity.Fei et al.[35]demonstrated that the fatigue strength and life of reinforced concrete beams under‘‘low-medium-high”stress level fatigue loading were significantly higher than that under high fatigue loading.

It is of concern that most of the findings indicated that fatigue loading significantly decreased rock’s mechanical properties compared to monotonic loading [36].The present study,however,obtained the opposite conclusion to it.The root causes for the conflicting results were: (1) the multi-level constant-amplitude fatigue tests were performed on the sandstone samples in the study,which were obviously different from the loading paths of conventional fatigue test;(2)the cycle number at each stress level in this study was designed to be a constant value(only 30 times);and(3)the original structures of the rock specimen were different,especially the microstructure.

5.2.Comparison of crack behaviors of specimen under monotonic and cyclic loading

In this section,we compared in detail the macroscopic failure modes of specimens containing different pre-existing flaw angles under conventional uniaxial compression and multilevel constant-amplitude cyclic loading,aiming to explore the impacts of loading types and fissure angles on its fracture behavior.From Figs.8 and 20,we observed that the macroscopic damage images of samples with same flaw angle under different loading showed similar patterns and the ultimate failure modes of sandstone with different flaw angles differed greatly,indicating that the macroscopic failure modes of the specimens were determined mainly by the pre-existing flaw angle,and the load type had little effect on them.However,the surface of failed specimens under multilevel cyclic loading had more far-field cracks and secondary cracks,which were mainly far from two pre-existing coplanar fissures,distributed randomly and short in length.

We tried to put forward two perceptions to explain the above phenomenon.On the one hand,higher frequency fatigue loading acted on sandstone,causing rapid accumulation and release of compression energy inside rock specimen,leading to the more crack initiation between crystals and inside crystals.The SEM images supported our opinion and revealed a significant increase in the proportion of transgranular cracks and intragranular cracks at the fracture of specimens under fatigue loading compared to specimens under monotonic loading.On the other hand,when specimens reached the peak stress,the function of these two loading methods presented notable differences: the specimens lost bearing capacity instantaneously under monotonic loading,while the specimens were subjected to peak cyclic stress disturbances several times under multilevel fatigue loading,resulting in a more lasting loading process,and thus,there would be more far-field cracks.The microstructure images at the fracture demonstrated that the sample’s cracks showed an increase and the scale of crack network was larger under fatigue loading.Besides,Figs.13-15 displayed that the AE count/energy showed active state and the peak frequency distribution concentrated in the last fatigue stage,which demonstrated the reasonableness of the above points.In a word,the pre-existing coplanar fissure angles were the main culprits to transform the failure modes of specimen compared to other factors,and the influence of multilevel constant-amplitude cyclic loading on the fracture behavior of samples was mainly reflected in the damage to microstructure and the failure process.

5.3.Microscopic damage mechanisms of pre-flawed specimens

This study adopted high magnification SEM to observe the microscopic features at the fracture,such as mineral,structure,and configuration,thus exploring its microscopic damage mechanism.Figs.24 and 25 illustrated the SEM images at the specimen fracture under both monotonic and cyclic loading,respectively,which revealed the almost identical microstructural features of failure surface,i.e.,they all consisted of minerals,pores,inclusions,dislocations,intergranular fractures,transgranular fractures,and cleavage fractures.We found that no matter what kind of loading the specimen was subjected to,there were always three types of microcracks within and between the mineral crystals at the specimen fracture,namely,intergranular fracture,transgranular fracture,and intragranular fracture.To be specific,intergranular fracture refers to the extension of cracks along grain boundaries;transgranular fracture refers to the extension of crack through the interior of crystal;and intragranular fracture refers to the appearance of microcracks within the crystal.

As evident in Fig.24,the microcracks at the fractured surface of specimens under monotonic loading were dominated by intergranular cracks,followed by intragranular cracks,with a smaller number of transgranular cracks.These clean and fresh cracks had a clear propagation direction and contained no inclusions,which was caused by the simple stress acting on rock masses directly.In addition,the number and width of microcracks at the fracture initially showed no significant change and then dramatically increased as the pre-existing fissure angle increased,which was strongly associated with the energy dissipation inside specimens during the loading.As shown in Fig.25,the microcracks at the fracture under multilevel cyclic loading were still dominated by intergranular cracks.The microstructures of the specimens under fatigue loading were more complex compared with that under monotonic loading,which was manifested as the increase in the number,length,and width of microcracks,the variety of crack propagation paths,and the rise in the proportion of transgranular cracks.This was probably attributed to the fact that under monotonic loading,the loading rate used in the test (v=0.05 mm/min)belonged to static loading range,and the elastic energy stored inside the specimen during the elastic stage was released along the relatively weaker crystal boundary;under cyclic loading,owing to higher loading frequency,the paths of the elastic energy release were complicated,and part of the energy was rapidly released from the interior of crystal where the energy release rate was the fastest.Besides,we discovered obvious cleavage fractures and dislocations,showing that these specimens produced greater damage under cyclic loading.Similarly,the number,length,and width of cracks highly rose with larger fissure angle.

Fig.24.SEM images of the fractured surface of failed sandstone containing two coplanar fissures exposed to monotonic loading.

The analysis of microstructural characteristics of the specimen fracture demonstrated the significant role of loading types and coplanar flaw angles on its microscopic damage mechanism,which in turn affected the strength and deformation behaviors.In addition,intergranular fracture was the most important damage form during damage evolution process,followed by transgranular fracture,and the contribution of intragranular fracture to specimen failure was extremely low.Thus,an indepth understanding of the microstructural characteristics of rocks is vital for elaborating the fracture mechanisms of rock structures.

5.4.Implications,limitations and future direction

The rock masses in the slope and underground engineering usually contain numerous fissures,joints and pores,as shown in Fig.26[14,37,38].As may be expected,these rock masses are subjected to frequent dynamic disturbances due to human activities besides static loading.However,little information was available on the fractured rock under complex fatigue loading.In this work,the mechanical behaviors,AE responses and microscopic damage characteristics of pre-flawed sandstone under both monotonic and multilevel cyclic loading were investigated.Results showed that the flaw angle in the range of 0° to 75° had little effect on the mechanical behaviors of the sandstone under monotonic loading;the peak strength of specimens changed slightly (flaw angle:0°-30°) and then obviously rose with increasing flaw angle under cyclic loading.Thus,the natural flaws with smaller angle especially below 30°should be given extra attention in the filed engineering.Furthermore,the pre-existing fissure angle determined the macroscopic failure modes of the rock specimens,while the load types had no dramatic influence on them,with the difference that more secondary cracks and far-field cracks were observed on the specimens subjected to fatigue loading.We found that theses cracks and main cracks together determined the failure patterns.Thus,the presence of these cracks,which are essential for rock failure,should not be ignored.Understanding the evolution and precursory features of AE signals is vital for earlier warnings for geologic disasters.Real-time AE monitoring revealed that under multilevel fatigue loading,the AE signals were only active at the early period of each fatigue stage,and then gradually calmed down.At the last stage of fatigue loading,the AE ringing count/energy surged due to crack coalescence,theb-value dropped significantly and the high frequency signals were frequently detected.This indicated that four AE indicators could be effective in predicting the failure of rock structures.The peak frequency is probably the major indicator for geo-hazards warning due to its strong sensitivity to the crack evolution process.

Fig.26.Flaws observed from slopes and underground engineering [14,37,38].

The findings of this study are promising to promote the insight into the fracture mechanisms of fractured rock mass,but there are still some limitations.Firstly,the fatigue tests in this work are conducted using multilevel cyclic loading with variable lower limit,which is obviously different from the other fatigue loading paths designed in the previous studies and more compatible with the real stress situations,but the fatigue loading applied to rock mass are complex and diverse in practical engineering.Secondly,the object of this study is rocky slope,and thus,uniaxial compression test is performed owing to the lower depth;however,most underground engineering are in triaxial stress state,and even the confining pressure is extremely high.Finally,due to various factors,initial damage exists in the rock masses,and this investigation reveals the fatigue characteristics of the sandstone containing two coplanar flaws comprehensively,but the geometrical parameters of fissures and the spatial relationship between fissures in the rock masses are extremely complex.Future works should strive to overcome above limitations and investigate how variation in flaws or external conditions correlate with the mechanical behaviors of rock material.

6.Conclusions

In this work,both monotonic and multilevel constantamplitude fatigue tests were conducted on sandstone containing two coplanar flaws with various angles,respectively.Real-time AE monitoring and fracture surface observing were utilized to explore the microscopic damage mechanisms of the pre-flawed samples.Finally,a simple model was established to quantitatively describe the damage evolution of the specimens during whole loading period.The findings from the study are summarized with the following conclusions.

(1) Compared with monotonic loading,fatigue mechanical parameters of the specimens exposed to multilevel cyclic loading were correlated with flaw angle.More specifically,the specimen’s strength first fluctuated and then rose significantly as the fissure angle increased under monotonic loading,while dynamical parameters gradually rose under multilevel cyclic loading.Moreover,the strength and deformation for the latter were found to be slightly higher than for the former.

(2) The specimen’s deformation displayed a distinct rise in the first few cycles,for single fatigue stage,and then became stable.Similarly,AE signal was initially active and then turned stable.This indicates that the internal damage of the specimen primarily generates at the steep rise in cyclic stress levels and the early part of each fatigue stage.AE count/energy exhibited a decreasing trend with the increasing of fissure angle.Besides,the maximum cyclic stress presented a positive linear relationship with the axial strain rate,which suggested that the damage inside the specimen was a progressive process.

(3) The medium-frequency AE signals were always dominant during fatigue tests,indicating the scale of cracks inside the specimen was moderate.Based onAF-RAvalue and final damage images,on the one hand,the pre-existing fissures played a strong inducing role for failure mode and the crack evolution behavior and ultimate failure mode depended on flaw angle;on the other hand,long-term multilevel cyclic loading aggravated the internal damage of rock samples,resulting in more cracks.

(4) SEM images indicated that microstructures at the fracture were dominated by intergranular fracture,followed by transgranular fracture and intragranular fracture.The load types had an obvious effect on the microscopic characteristics compared with flaw angle.The number and width of cracks especially transgranular fracture inside rock subjected to multilevel cyclic loading were significantly higher than those exposed to monotonic loading.Accelerated energy release due to high dynamic loading rate might be the major reason for the rise in the density of transgranular cracks.

Acknowledgment

This work was financially supported by the National Natural Science Foundation of China (Nos.42077231 and 51574156).