Use of Acoustic Emission for the Detection of Brittle Rock Failure under Various Loading Rates

School of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an, Shaanxi 710054, China Key Laboratory ofWesternMine Exploitation andHazard Prevention withMinistry of Education, Xi’an, Shaanxi 710054, China School of Energy Engineering, Xi’an University of Science and Technology, Xi’an, Shaanxi 710054, China Department of Civil Engineering, Inha University, Incheon 402-751, Republic of Korea


Introduction
In recent years, the number of high-strength mining faces in Western China has increased.High-strength mining refers to a coal mining method with the mining intensity of fully mechanized top-coal caving and a large mining height, which has a high propulsion speed, large stope size, and high backstopping efficiency.e difference in the advance speed of the working face affects not only the transfer process of rock stress but also the speed of the loading and unloading processes.e probability of disaster induced by rock failure increases as the advancing speed increases in a working face [1].In addition, it was reported based on field monitoring data that rapid excavation at the working face can cause serious surface subsidence.
To examine the relationship between the advancing speed of the working face and the rock stress transfer mechanism, basic experimental studies have been carried out in the laboratory due to many difficulties related to onsite research.e advancing speed of the working face can be considered as the loading rate on a laboratory scale.e loading rate has a significant influence on the deformation characteristics and failure mechanism of rock [2].Li et al. [3] examined the growth of microcracks at different loading rates.Liang et al. [4], Liu et al. [5], Zhou et al. [6], Zhang et al. [7], and Kodama et al. [8] studied the effects of the strain rate on the mechanical properties of rock.Li et al. [9][10][11] analyzed the effect of the loading rate on the nonlinear mechanical properties of coal and suggested an efficient method to evaluate the impact performance of coal.
In addition, Daphalapurkar et al. [12], Lin et al. [13], and Cao and Lin [14] examined the effect of microcracks on the tensile properties of hard and brittle materials by numerical simulations.Yang et al. [15] conducted an experimental study on natural rock containing preexisting fissures using an "artificial customization technique."Yang et al. [16,17] and Zhang et al. [18] examined the effects of the shape and quantity of damage-induced fissures on the mechanical properties of brittle materials, of which regularly distributed initial fissures had been prefabricated artificially.In general, the damage-induced fissures in brittle materials are distributed in the form of open cracks and apertures, and microcracks are distributed randomly in a natural rock mass.Chen [19] and Wang et al. [20] produced damageinduced initial fissures within the rock samples by preloading.ey used an ultrasonic longitudinal wave velocity for quantitative characterization of the initial damage.Based on previous studies, uniaxial preloading is imposed on a brittle rock sample to generate initial damage in the form of microcracks in this study.In particular, the initial damage was characterized quantitatively using an acoustic emission technique.
e distribution of microcracks was analyzed visually using the acoustic emission positioning technique.Furthermore, a uniaxial compression test was conducted on the intact rock samples and the rock samples containing initial damage at a range of loading rates to determine the effect of the loading rate and initial damage on the mechanical properties of rock.From the experimental test result, a constitutive equation was constructed based on the damage mechanics.

Sample Preparation.
e rock type used in the present study was sandstone obtained from the Liuhuanggou Coal Mine, Yankuang Xinjiang, China.Quartz, ankerite, and anorthose are the main rock-forming minerals of the sandstone.e average longitudinal wave velocity and average density of sandstone were 4.4 km/s and 2800 kg/m 3 , respectively.
e sandstone samples were prepared, 500 × 1000 mm (diameter × length), in accordance with the recommendation suggested by the International Society for Rock Mechanics.To ensure the homogeneity of the sandstone samples, all samples were drilled from an intact sandstone block, and the sound wave velocity was obtained.Only the sandstone samples with the same wave velocity and a stable waveform were selected for further experimental testing. is means that the sandstone samples were intact and did not have notable fissures inside.Figure 1 shows the part of selected rock samples.Sandstone samples were separated into two groups, as shown in Table 1: Group 1 for an evaluation of the loading rate without preloading (i.e., no initial damage) and Group 2 for an evaluation of the loading rate after preloading with initial damage.

Testing Method. Acoustic emission (AE
) is a physical phenomenon of transient elastic waves produced by the rapid release of internal elastic energy due to rapid deformation and crack growth of hard and brittle materials when they are subjected to external or internal forces [21].Acoustic emission has a direct correspondence to the internal damage of a material.e damage level of a material can be estimated from the accumulative number of acoustic emission events because the new damage must be accompanied by the occurrence of acoustic emission [22].In addition, knowledge of the fracture mechanics shows that the fracture of hard and brittle materials is caused by internal defects.
e distribution of internal defects governs the failure behavior of a brittle material and its mechanical properties.
e acoustic emission technique can be used effectively to detect the generation of internal defects due to loading and its positioning.
In this study, the internal damage of rock due to preloading was characterized quantitatively by the accumulative number of acoustic emission events, and the location of  Preloading was performed at a loading rate of 0.2 kN/s and a maximum force limited to <200 kN. e loading rate was maintained for 3 min.e uniaxial compression test at di erent loading rates was conducted on the intact rock samples without preloading and the samples containing the initial damage due to preloading.Four di erent loading rates (i.e., 0.03, 0.05, 0.07, and 0.09 mm/min) were selected, as shown in Table 1.Four acoustic emission probes were attached to the rock specimen, as shown in Figure 2.

Positioning of Microcracks with Acoustic
Emission.e occurrence of the acoustic emission event is due mainly to the generation and growth of microcracks.Transient monitoring of the location where the acoustic emission event occurred can re ect the progressive evolution of the fracture.
e spatial distribution of microcracks, the direction, and spatial curved surface shape of crack growth within the rock samples can be observed visually.Figure 3 presents the location map of the acoustic emission events for Group 2 during preloading.
Figure 3 shows that AE events are concentrated at both ends of the rock samples and that the initial damage caused by preloading is distributed evenly within the rock samples, excluding the AE events caused by friction around 20 mm of the upper and lower ends.e preloading is a useful tool for simulating the distribution of internal microcracks within a rock specimen.

Quantitative Characterization of Initial Damage.
e longitudinal wave velocity and accumulative number of acoustic emission events can be used to characterize the level of rock damage quantitatively.In this study, the longitudinal wave velocity was obtained from the Group 2 samples containing microcracks due to preloading before and after loading.
e longitudinal wave velocity and acoustic emission test results (excluding the AE events around 20 mm of the upper and lower ends) were compared to select a more accurate characterization method for the initial damage.e results are summarized in Table 2.
Table 2 shows that the accumulated number of acoustic emission events produced by the four rock samples during the preloading process is 12∼14, and the decrease in longitudinal wave velocity is minor.Interestingly, the more the accumulated number of AE events, the greater the change in the longitudinal wave velocity.
is suggests that the AE event accompanies the increase in the number and density of microcracks and causes a signi cant reduction of the longitudinal wave velocity.
Variance analysis was conducted based on the test results to evaluate the validity among the accumulated number of AE events and longitudinal wave velocity as an indicator for better quantitative analysis.e variance is the degree of deviation from the average and is used to measure the uctuation size of a batch of data (i.e., the size of the data deviation from the average number), expressed as S 2 .When the number of specimens is identical, a greater variance indicates larger data uctuations.is also implies that the validity of the indicator becomes increasingly unstable as the variance increases.e variance can be calculated as follows: where n is the number of samples, X i is the individual, and X is the average of the sample.e normalization should be adopted for variance analysis to consider the inconsistency of data.e variance of the normalized data can be calculated as follows: e variances of the accumulated number of AE events and the longitudinal wave velocity were 0.006 and 0.357, respectively.erefore, the deviation obtained from the AE test was smaller than that of the longitudinal wave velocity.Hence, the AE test can be considered to be a good quantitative characterization method for initial damage.e rock samples undergo a compaction stage, elastic deformation stage, elastoplastic deformation stage (not obvious), and postpeak failure stage during uniaxial compression loading (Figures 4 and 5).e rock samples of Group 1 have similar stress-strain curves regardless of the loading rate because the stress and strain increase steadily until the stress falls suddenly due to brittle rock failure.

Brittle Rock Failure at Various Loading Rates
e rock samples of Group 2 with initial damage showed stress adjustment at a slow loading rate of 0.03 mm/min.e stress adjustment disappeared as the loading rate was increased.In addition, the stress decreased suddenly due to brittle rock failure.On the other hand, the strain at failure of Group 2 was slightly larger than that of Group 1 under the same loading rate. is suggests that the initial microcracks extend as the stress level increases, and a macroscopic fracture surface forms within the samples.In particular, the relatively large strain at failure of Group 1 can be caused by slipping of the macroscopic fracture surface within the rock samples when the loading rate is low.

Analysis for Intensity Characteristics.
Figure 6 shows the relationship between the loading rate and uniaxial compressive strength of the original rock samples without damage and rock samples with initial damage.
e uniaxial compressive strength increased with increasing the loading rate for both groups (Figure 6).For original rock samples, the UCS obtained from a minimum loading rate was approximately 77.4% of that obtained from the maximum loading rate.For rock samples with initial damage, the UCS obtained from the minimum loading rate was approximately 59% of that obtained from the maximum loading rate.e reason for the above phenomena can be understood by the rock composed of the physical medium and damage defects wrapped by the physical medium.When the loading rate was slow, the energy dissipated mainly for ssure growth, and the rock samples showed low compressive strength at a low loading rate, resulting in a fully developed ssure.As the loading rate increases, the ssures cannot develop fully, and microcracks do not interconnect due to the rapid deformation.In such cases, the energy is stored mainly in the physical medium in the form of elastic energy, which increases the uniaxial compressive strength of the rock samples.6).e compressive strengths of the rock samples containing microcracks are lower than those of the original rock samples.e deterioration e ect of the initial damage on the compressive strength di ered according to the loading rates.For a quantitative description of the deterioration e ect of the initial damage on the strength of a rock sample, the deterioration rate is de ned as follows: where K σ is the deterioration rate, R c is the uniaxial compressive strength of the original rock sample (MPa), and R cd is the uniaxial compressive strength of the damaged rock sample.e attenuation range of the rock samples' bearing capacity increases with increasing deterioration rate.On the other hand, the bearing capacity of the intact rock samples becomes similar with decreasing attenuation.e deterioration rate was obtained using (3) depending on the loading rate, and the results are presented in Figure 7.When the loading rate was low, the initial damage showed a less deterioration e ect on the rock samples.e deterioration rate increased with increasing loading rate.On the other hand, this phenomenon is not persistent; the deterioration rate decreases when the loading rate exceeds 0.07 mm/min.As the loading rate increases, the growth of microcracks is accelerated.erefore, the deterioration rate increases with increasing loading rate until the loading rate is slow enough to develop microcracks fully.e deterioration rate decreases because microcracks cannot be fully developed due to the rapid loading rate.8 and 9 show the maximum axial strain and corresponding elastic  Advances in Civil Engineering modulus of the original rock samples and the rock samples with initial damage at di erent loading rates.

Analysis for Deformation Characteristics. Figures
e maximum axial strain generally increases with increasing loading rate (Figure 8).When the loading rate is slow, slippage and dislocation are concentrated at the main crack area within the rock samples, and there is su cient time for crack growth.In such cases, the rock samples only need a small deformation to produce a dominant macrocrack and damage.When the loading rate is increased, the mesoscopic defects within the rock samples have no time to form a dominant crack but deformation of the physical medium, so larger deformation is necessary to cause complete fracture in the rock samples.e maximum axial strain of the rock samples with initial damage is larger than that of the original rock samples.
e initial damage enlarges the compaction stage and shortens the elastic stage, leading to an increase in axial strain.is means that the initial damage can improve the ductility of rock.
e elastic modulus increased with increasing loading rate and converges for the original rock samples (Figure 9).e elastic modulus increased with increasing loading rate for the rock samples with initial damage.
e nondeformability of the rock samples improved, and the elastic modulus increased.e di erence in elastic modulus between the two samples decreased with increasing loading rate.
is suggests that a faster loading rate weakens the deterioration e ect.To observe more clearly the deterioration e ect of initial micro ssures depending on the loading rate on the elastic modulus of the rock samples, the deterioration rate of the elastic modulus can be obtained by replacing the compressive strength in (3) with the elastic modulus, as shown in Figure 9. e deterioration rate of the elastic modulus decreases signi cantly when the loading rate is high.

Analysis of the Fracture Mode.
e loading rate and the initial damage have an important in uence on the strength and strain of rock samples.e di erent strength performance corresponds to the di erent failure characteristics.Figure 10 shows the typical failure mode of rock samples due to uniaxial compression depending on the loading rate.
e loading rate has a signi cant e ect on the failure mode of rock samples.When the loading rate was slow, the rock samples showed mainly splitting and stretch-draw fracture and two relatively large rock blocks formed after failure.As the loading rate increased, stretch-draw and shear fractures could be found, and the fracture intensity became severe.When the loading rate exceeded 0.07 mm/min, the rock samples were fractured completely in the form of rockburst, as shown in Figures 10(c) and 10(d).
is is consistent with the theoretical derivation in the literature [3].

Analysis for the Damage Mechanics of the Loading Rate Effect
As for the simplest model, the rock can be considered an elastic medium with a homogeneous, isotropic nature so that the mechanical properties of rock are only related to the state of stress.When the state of stress is unchanged, the forms of deformation and fracture will not change depending on the loading rate.On the other hand, the physical medium of the rock material is composed of various rock-forming minerals that contain microcracks.In addition, the mechanical properties of the rock samples with initial damage are in uenced heavily by the loading rate.
Based on the assumption that the intensity of the microbody follows the Weibull distribution for the addition of damage mechanics for a simple model, the probability density function becomes  Advances in Civil Engineering where λ is the scale parameter or the proportional parameter, k is the shape parameter greater than 0, and x is the random variable.
If the random variable is characterized by the parameter time t related to the loading rate, the physical meaning of the Weibull distribution is the probability of a microbody fracture when the loading time is t, and the damage variable D can be calculated using From ( 5), the damage variable increases with increasing loading time due to the growth of microcrack defects within the rock mass and slippage under the action of force: the shorter the loading time (the faster the loading rate), the better the integrity of the rock sample.Based on the assumption of equivalent strain, the relationship between the stress and the loading time can be de ned as Equation (6) shows that the stress increases with decreasing loading time. is is the theoretical explanation for the increase in the compressive strength of rock with increasing loading rate.
In addition, from the point of view of energy, some external energy can be stored in the physical medium in the form of elastic energy, and some is dissipated in the form of ssure growth.As reported elsewhere [22], when the crack length is ΔL, the energy consumption, W ΔL , is where σ t is the tensile stress at the crack tip, which can be considered the inherent properties of a material.e deformation of rock samples is caused mainly by fissure growth when the loading rate is slow.Because the dissipation energy is large and the absorbed elastic energy is lower, the rock samples show a simple failure mode.e fissure growth within the rock becomes slow when the loading rate is large, and the deformation of the physical medium governs the behavior of the rock sample.e elastic energy of the rock also increases with increasing loading rate, and it will be released suddenly after the peak strength is reached.In such cases, the rock samples show more intensive fracture in the form of rockburst.
In recent years, the advancing speed at the working face is very fast due to fully mechanized coal mining technology.High-speed advances bring significant economic benefits but also have a negative impact.erefore, it is important to understand the influence of the initial damage and loading rate on the mechanical properties of rock to prevent a disaster during mining.

Conclusion
To find a reasonable way to express damage, the characteristic by the number of acoustic emission events is used for the initial damage caused by rock precompression, and it is more accurate compared to the longitudinal wave velocity.
e acoustic emission monitoring shows that the prepressed rock samples produce randomly distributed microfissure damage, which is consistent with the field.
e original rock samples and the rock samples with initial damage underwent a compaction stage, elastic deformation stage, plastic deformation stage, and postpeak fracture stage under different loading rates.e existence of initial damage makes the compaction and plastic deformation stages of the rock samples longer.On the other hand, an increase in loading rate makes the compaction stage and the plastic deformation stage of the rock samples shorter, and the rock shows a purely brittle fracture.
e strength and peak strain of the original rock samples and the rock samples with initial damage increase almost linearly with increasing loading rate, and the initial damage plays a deterioration role on the strength and elastic modulus of the rock samples.e deterioration effect increases with increasing loading rate when the loading rate is slow and decreases when the loading rate is increased further.
e effect of the loading rate and initial damage on the mechanical properties of rock is a complex coupling process, in which the loading rate is more significant.
is study revealed failure of the rock samples from splitting fracture to stretch-draw and shear fractures with increasing loading rate and established a damage evolution equation considering the time effect.erefore, it is important to understand the influence of the initial damage and loading rate on the mechanical properties of rock to prevent the disasters during mining.

Figure 1 :
Figure 1: Sandstone samples for the experimental test.

Figure 2 :
Figure 2: Use of acoustic emission for the detection of microcracks.

Figure 3 :
Figure 3: Location map of acoustic emission events.(a) Location map for the initial damage events of rock sample #1; (b) location map for the initial damage events of rock sample #5; (c) location map for the initial damage events of rock sample #8; (d) location map for the initial damage events of rock sample #9.

Figure 8 :Figure 9 :
Figure 8: Relationship between the peak strain and loading rate.

Table 1 :
Grouping of the sandstone samples.
As shown in Section 2.1, sandstone samples in Group 2 were preloaded to produce the initial damage.A slow loading rate and maximum force were maintained to ensure the full development of ssures within the rock during preloading.

Table 2 :
AE events and reduction of the wave velocity due to preloading.
Figure 4: Stress-strain curve of Group 2 with initial damage.