Study on Characteristics of Energy Storage and Acoustic Emission of Rock Under Different Moisture Content

sustainability

Article Study on Characteristics of Energy Storage and Acoustic Emission of Rock under Different Moisture Content

Chuanming Li 1,2, Nan Liu 1,2,* , Wanrong Liu 3 and Ruimin Feng 4

1 Key Laboratory of Safety and High-Efﬁciency Coal Mining, Ministry of Education, Anhui University of Science and Technology, Huainan 232001, China; [email protected] 2 School of Mining and Safety Engineering, Anhui University of Science and Technology, Huainan 232001, China 3 School of Architecture & Civil engineering, Liaocheng University, Liaocheng 252059, China; [email protected] 4 Department of Civil Engineering, University of Arkansas, Fayetteville, AR 72701, USA; [email protected] * Correspondence: [email protected]

Abstract: In order to study the energy storage and sound emission characteristics of rocks under different water content, uniaxial compression test, cyclic loading, unloading test and sound emission test were carried out using RMT-150B rock mechanics test system and DS5 acoustic emission system. The results show that the total strain energy of saturated rock samples and the area of hysteresis loop are the largest in the same period number, which indicates that the presence of water can reduce the elastic limit of rock samples, making the rock very easy to deform and even damage. Acoustic emission tests show that the damage energy of water-bearing rocks is small. The higher the water

content, the smaller the peak damage energy. The bending energy index WET of the rock sample under saturated and natural state is smaller than that under dry state, which further indicates that the presence of water can reduce the elastic limit of the rock and soften it. The results can provide a basis for the prediction of underground engineering construction and rock failure instability. Citation: Li, C.; Liu, N.; Liu, W.; Feng, R. Study on Characteristics of Keywords: moisture content; sandstone; acoustic emission; energy storage Energy Storage and Acoustic Emission of Rock under Different Moisture Content. Sustainability 2021, 13, 1041. https://doi.org/10.3390/ 1. Introduction su13031041 In recent years, with the increase of intensity and depth of coal mining, dynamic dis- Academic Editor: Guang-Liang Feng asters such as rock burst seriously threaten production safety [1,2]. As water is common in Received: 9 December 2020 the coal mining environment and many deformations of engineering rock mass are related Accepted: 18 January 2021 to the water in the rock, and the elastic energy index is one of the critical measurement Published: 20 January 2021 indicators for the evaluation of impact tendency, accurate calculation of the elastic energy index is crucial to estimate the strength of coal rock impact tendency [3–5]. Therefore, the Publisher’s Note: MDPI stays neutral study of characteristics of mechanical properties and energy storage of rock under different with regard to jurisdictional claims in water-bearing conditions has very important engineering significance. published maps and institutional affil- The water inside the rock mass is the leading cause of rock softening and strength iations. reduction. Many scholars [6–9] have studied the influence of water content on rock deformation, strength characteristics, and energy storage characteristics. Z. Pan et al. [10] analyzed the influence of water content on compressive strength and elastic modulus of sandstone through loading and unloading tests. Eberhardt et al. [11] studied the fracture Copyright: © 2021 by the authors. damage mechanical behavior of brittle rock samples through uniaxial loading and unload- Licensee MDPI, Basel, Switzerland. ing tests and acoustic emission monitoring. Su [12] carried out uniaxial cyclic loading This article is an open access article and unloading tests on saturated diorite, and found that the energy storage capacity and distributed under the terms and brittleness of sandstone were greatly weakened and plasticity was significantly enhanced conditions of the Creative Commons after saturating water. Xia [13] found the energy dissipated and the number of cycles was Attribution (CC BY) license (https:// approximately linear. Zhang [14] studied the stress–strain curve and energy evolution creativecommons.org/licenses/by/ law of sandstone under different water content and found that the curve was sparse in 4.0/).

Sustainability 2021, 13, 1041. https://doi.org/10.3390/su13031041 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 1041 2 of 15

the saturated state, and the volume energy was small; and in the drying state, the curve was denser and the volume energy is the largest. Li [15] discusses the influence of water content and anisotropy on the strength and deformability of two meta-sedimentary rocks by triaxial compressive tests, and the experimental studies show that the anisotropy associated with bedding in rock specimens plays a weakening effect on the triaxial compressive strength for both tested rocks. Roshan [16] discussed the X-ray computed tomography which was conducted on the representative samples from each type of sandstone to assess the porosity, rock composition, and texture, and the experimental studies show that volume and effective porosity is more accurately correlated to mechanical properties. Meng [17] studied sedimentary rock and the models and correlations between moisture content and bursting potential are established, and the rock after peak strength of stress–strain curve represents brittleness and shear failure and has obvious strain softening behavior in the condition of dried or with small moisture content. Acoustic emission (A.E.) technology is capable of dynamically monitoring the genera- tion and expansion of micro-cracks in rock materials and reflecting the damage evolution process. Therefore, it has been widely used in geotechnical engineering such as coal mining, slopes, tunnels and bridges [18–20]. Mansurov et al. [21] used acoustic emission to measure the information of rock failure process and predict the failure type of rock. Xiao [22] studied the characteristic parameters of acoustic emission, and the plastic piecewise functions through the cyclic loading and unloading and acoustic emission experiments. Fu [23] conducted uniaxial compression tests and acoustic emission tests on the rock, and the results showed that the rock deformation rate has a good correspondence with the number of acoustic emission events. Liang et al. [24] studied the influence of the cyclic loading and unloading on the mechanical properties of the rock at the post-peak stage, and verified that the deformation behavior of the rock was in good agreement with the acoustic emission parameters. He et al. [25] studied the A.E. cumulative energy release phenomenon in the process of rock unloading, loading and failure. The aforementioned studies have greatly deepened the understanding of the law of energy changes in the process of rock instability and failure. However, the combined effect of periodic loads and water is common in actual underground engineering construction. Therefore, typical sandstone materials were selected to perform the uniaxial compression test, cyclic loading and unloading test, and acoustic emission test on rock samples with three different water content, and conduct research on the characteristics of mechanical properties and energy storage of the rock samples with water to provide a theoretical reference for rock fracture and instability.

2. Sample Preparation The white sandstone samples were produced from a sandstone mine in Renshou County, Sichuan Province, China. The main mineral components of white sandstone are quartz 60%, feldspar 20%, clay 15%, and a small amount of muscovite. All samples were manufactured in accordance with the standard of the International Society of Rock Mechanics and Rock Engineering. SC-200 core machine was ﬁrstly used to drill a cylindrical core with a diameter of 50 mm, and SCQ automatic stone cutter was then used to cut a sample with a length of 100 mm. Finally, the two ends of each specimen were polished to be smooth and parallel using SCQM automatic cutting and grinding machine. The specimens were divided into three groups: saturated state (a), natural state (b), and dry state (c). The average water content of the as-received sandstone is 0.202%. In order to obtain dry and saturated sandstone specimens, the white sandstone is dried and saturated with water, respectively. The sandstone specimens under two states are measured until the mass difference between the two consecutive times’ weighing is less than 0.05%. During tests, the rock samples under natural state are not processed; other rock samples are dried in an oven at 100 ◦C for 48 h, and then taken out, placed in a drying oven to cool to the room temperature, and ﬁnally weighed. When the change in weight is constant, the rock sample is considered to be completely dried, and an appropriate amount of rock sample Sustainability 2021, 13, 1041 3 of 15

will be selected as the drying group (c). The sample under the saturated state is prepared by using a proper amount of dried rock samples to absorb water by natural immersion method. Take out rock samples at regular intervals, wipe off the surface moisture of the rock sample with a towel, and weigh until the water content becomes stable. Figure1 shows the variation curve of the average water content of all saturated rock samples with the immersion time. It can be seen that white sandstone has strong water absorption, and the water content increases exponentially with the immersion time. In the initial stage of immersion (0–4 h), the water absorption rate is large, and the water content increases rapidly as time elapses; then (4–7 h) the water absorption rate gradually decreases, and the water content increases slowly; after more than 7 h, the average water content of the rock sample tends to stabilize, indicating that the sandstone is close to saturation with the average water content of 2.483%. The curve in Figure1 is the fitting equation with the correlation coefficient R2 of 0.9890. This equation is only applicable when white sandstone with φ50 mm and L100 mm is selected in this test. The variation of size and type of rock samples may change the fitting equation.

−t −t y = −0.0232e 1.6278 +3.6241e 0.1314 + 0.02549 (1)

Figure 1. Variation curve of average water content with time.

After being immersed for a certain period of time, the water content ω can be calculated according to the Equation (2)

M − M ω = 1 2 × 100% (2) M2

where ω is the water content of the rock; M1 is the mass of the sample after being immersed in water for t hours; M2 is the dry mass of the specimen. Figure2 shows part of the white sandstone specimens and test preparations. After the specimens were prepared, they were divided into 3 groups with 6 pieces for each group. Among them, 3 rock samples were subjected to the cyclic loading and unloading test, and the other 3 rock samples were subjected to the uniaxial compressive test. The average compressive strength was determined by the uniaxial compressive test, and the stress of Sustainability 2021, 13, 1041 4 of 15

each cycle loading were set with reference to this strength. As listed in Table1, the average water content of the natural group is 0.202%, the average water content of the saturated group is 2.483%, and the water content of the drying group is 0%.

Figure 2. Some white sandstone specimens and test preparation.

Table 1. Physical parameters of rock samples in different states.

No. Dry Gravity Moister Gravity Water Content ω/% Average Water Content ω/% a1 473.21 483.82 2.461 a2 473.71 484.18 2.418 2.481 a3 472.19 483.25 2.562 b1 470.61 471.56 0.202 b2 472.62 473.63 0.214 0.215 b3 470.86 471.98 0.231 c1 471.61 - 0 c2 462.82 - 0 0 c3 470.36 - 0

3. Test Equipment and Test Method This test device is composed of a stress loading system and an acoustic emission acquisition system. The stress loading system is the RMT-150B rock mechanics testing system, which can perform conventional mechanical performance tests on materials such as rock and concrete. The acoustic emission acquisition system is the DS5 acoustic emission system (acoustic emission, A.E.) which can collect parameters such as the number of A.E. event, energy, and arrival time. The test equipment is shown in Figure3.

Figure 3. Test equipment. Sustainability 2021, 13, 1041 5 of 15

In this test, RMT-150B rock mechanics system was tested by means of slope wave control force. The loading-unloading test in this manuscript was designed and completed according to the relevant articles of China’s national standard “Methods for test, monitoring and prevention of rock burst—part 1: method for classification and laboratory test method on bursting liability of roof strata GB/T 25217.1-2010” and “Methods for test, monitoring and prevention of rock burst—part 2: method for classification and laboratory test method on bursting liability of coal GB/T 25217.2-2010”, and some relevant scholarly researches [26,27]. The rate of loading and unloading is 0.5 MPa/s. To make data analysis simple, the force range is 0→5→0→10→0→15→0→20..., and repeat once for each interval until the rock sample is broken. In order to eliminate the influence of environmental noise on the acoustic emission test, Cai et al. [28] found that the frequency range of acoustic emission of rock is generally between 1 kHz and 500 kHz through experimental research. According to the test experience before, the preamplifier sampling frequency of the acoustic emission acquisition system was set to 40 dB, the threshold was set to 50 dB, and the range of sampling frequency was set to 1 kHz–400 KHz. The test loading and unloading path is shown in Figure4. Before the test, the acoustic emission probe was closely attached to the side surface of the rock sample with a coupling agent, so that the A.E. probe and the rock sample were optically coupled to ensure the effectiveness of the acoustic emission signal. During the experiment, pictures were taken to record.

Figure 4. The loading and unloading test path for white sandstone.

Since the average water content of the rock samples in the natural state is 0.202%, which is almost similar to that of the rock samples in the dry state, their elastic modulus and uniaxial compressive strength are not much different. The test was divided into two parts: uniaxial compression and cyclic loading and unloading. E can be determined from the linear part of the slope σ − ε, and the maximum stress of cyclic loading determines σc. The test loading conditions and value of mechanical parameters are listed in Table2. Sustainability 2021, 13, 1041 6 of 15

Table 2. Test loading conditions and mechanical parameters.

Elastic Peak Specimen Test Condition Sample State Loading Rate Loading Way Modulus Strength Number Uniaxial Moisture state 3.935 GPa 35.762 MPa 3 compression Natural state0.5 MPa/s Normal failure 5.461 GPa 54.783 MPa 3 failure Dry state 5.409 GPa 55.167 MPa 3 Moisture state - - 3 Cyclic loading 0→5 MPa→0→10 Natural state0.5 MPa/s - - 3 and unloading MPa→0→15 MPa ... Dry state - - 3

4. Analysis of Test Results 4.1. Energy Study During Rock Failure Energy accumulation, energy dissipation and energy release occur in the process of rock loading and unloading. The hysteresis loop appeared in the second cycle and beyond. The hysteresis loop area [29] representing the dissipated energy refers to the annular area enclosed by the loading curve formed by each cycle and the unloading curve formed by the previous cycle. According to the law of conservation of energy and the theorem of thermodynamics: as the recoverable strain energy, the elastic energy is reversible, while the irrecoverable strain energy is irreversible. The irrecoverable strain energy can be subdivided into two parts: plastic strain energy and dissipated energy. The relationship is as follows: U = U1 + U2 + U3 (3)

where U is the total energy produced by the external load on the rock specimen; U1 is the dissipated energy; U2 is the recoverable strain energy; and U3 is the plastic strain energy. The loading and unloading path is 0→A→B→C, and its distribution is shown in Figure5.

Figure 5. Energy schematic diagram. Sustainability 2021, 13, 1041 7 of 15

The test images of the three rock samples a2, b1, c2 were selected for analysis. Figure6 shows the stress–strain curves of the cyclic loading and unloading tests of rock samples under different water content; and they are well similar to each other. The cyclic loading and unloading curve is composed of three stages, including the compaction stage, elastic stage, plastic stage and failure stage, which is similar to that of the uniaxial compression test [30]. The rock sample a2 was cyclically destroyed at the 5th cycle with the peak strength of 25.455 MPa; the rock sample b1 was cyclically destroyed at the 6th cycle with the peak strength of 30.507 MPa; and the rock sample c2 was cyclically destroyed at the 8th cycle with the peak strength of 38.340 MPa. For the rock sample, after undergoing cyclic loading and unloading, the failure stress is less than the average value of the peak failure stress in the uniaxial compression test. It can be seen that the cyclic loading ultimately leads to the reduction of strength.

Figure 6. Cont. Sustainability 2021, 13, 1041 8 of 15

Figure 6. Stress–strain curves of rock samples under different water content.

In the cyclic loading process, the total strain energy is composed of recoverable strain energy and non-recoverable strain energy. According to the data in Table3, it can be seen that the total strain energy, recoverable strain energy and non-recoverable strain energy all increase with the increase of the cycle progression (stress). As the number of cycles increases, the area of the hysteresis loop increases accordingly. Under the same load cycle, the total strain energy, recoverable strain energy, dissipation energy (hysteresis loop area) and plastic strain energy of the rock sample increases with the water content of the rock sample. The total strain energy and hysteresis loop area of the saturated rock sample is the largest at the same load cycle, indicating that the presence of water can reduce the elastic limit of the rock and soften the rock. The more unrecoverable strain, the more energy is dissipated, which makes the rock sample easy to deform and fail. It can be seen that the water content has a signiﬁcant impact on the mechanical properties, instability and even failure of the rock samples [31]. Jia [32] reported that the water in rocks mainly exists as free water and bound water. On the one hand, pore water pressure on the rock mass-produced by the free water makes the end of micro-cracks of the rock mass under tensile stress; on the other hand, bound water adhered on the surface of rock mineral particles reduces the friction between the mineral particles and reduces the strength of the rock mass. Therefore, the strength of the rock mass decreases after water is immersed, the elastic limit of the rock is reduced, and the load failure vulnerability is intensiﬁed.

4.2. Analysis of Rock Failure Morphology The failure mode of a rock sample under different water content (a1, b1, c2) was shown in Figure7. After the 5th cycle of cyclic loading and unloading, the compressive strength of the saturated rock sample was 27.625 MPa; the rock sample presented a kind of combined failure mode of tensile failure accompanied by shear failure of the X-shaped conjugate inclined plane with a large number of broken rock blocks. After being loaded and unloaded in the 6th cycle, the compressive strength of the rock sample in the natural state was 30.507 MPa, and its failure mode was mainly X-shaped conjugate inclined plane shear failure and tensile failure, with a large number of broken rocks. After the 8th cycle of loading and unloading, the compressive strength of the dry rock sample was 38.340 MPa, and its failure mode was X-shaped conjugate inclined plane shearing. The number of rock blocks after the failure of the specimen was 3–6, with fewer broken blocks. The failure plane Sustainability 2021, 13, 1041 9 of 15

◦ ◦ ◦ angle of the rock (α1, α2, α3) are 74.8 ; 63.3 ; 58.9 . The failure plane angle of the saturated rock is larger than that of other two states. It shows that when the sample contains water, the failure mode of the rock sample is gradually excessive from shear failure to tensile failure, and the failure degree is more serious.

Table 3. Calculation results of energy at all cycles.

Total Strain Recoverable Unrecoverable Dissipated Plastic Strain Group Cyclic Loading Energy Energy Energy Energy Energy Number Times /kJ·m−3 1 2.042 0.610 1.432 - - 2 4.032 2.111 1.921 0.889 1.032 Saturated state 3 6.784 3.972 3.012 1.269 1.743 (a2) 4 10.073 6.154 3.919 2.048 1.871 5 15.078 2.764 1 1.578 0.561 1.017 - - 2 3.303 1.823 1.480 0.438 1.042 Natural state 3 5.645 3.511 2.134 1.001 1.133 (b10) 4 8.257 5.358 2.899 1.488 1.411 5 11.354 7.534 3.820 2.326 1.494 6 16.317 3.183 1 1.315 0.449 0.866 - - 2 3.031 1.612 1.419 0.334 1.085 3 5.051 3.145 1.906 0.767 1.139 4 7.554 4.951 2.603 1.238 1.365 Dry state (c2) 5 10.462 6.983 3.479 1.716 1.763 6 13.625 9.179 4.446 2.448 1.998 7 17.481 11.624 5.857 3.198 2.659 8 23.329 5.099

Figure 7. The macroscopic failure model of rock samples under different water content.

From the perspective of energy conversion, the deformation and failure of the rock is actually the result of energy input, accumulation, dissipation and release during the process of loading. There is a certain internal connection between deformation failure and energy [33]. Therefore, the strength of the rock sample is reduced after being immersed in water, which intensiﬁes the failure of the rock sample. With the increase of the water content, the failure mode of the rock sample tends to be complicated. Under the effect of Sustainability 2021, 13, 1041 10 of 15

water, the compressive strength of the rock sample decreases. The failure model gradually becomes the combined failure model of tensile and shear from the X-shear failure.

4.3. Study of Acoustic Emission Characteristics During Rock Failure The rock failure is a process of mutual conversion between energy absorption and energy release, and the acoustic emission event rate and cumulative event number can indicate the frequency and total amount of the internal crack formation and propagation in sandstone [34]. According to the data collected by the DS5 acoustic emission detection system, Figure8 is plotted to display the variation curve of the total acoustic emission energy and the total number of events of the rock sample under different conditions in the process of the loading and unloading. The acoustic emission curve of one rock sample under different water content (select a1, b2, and c2) was presented in Figure8. Comparing with the parallel test results, it can be seen that for the rock samples under three states of variation—curves of the stress, cumulative energy, acoustic event versus time of, are similar to each other, as well as the change law of the total acoustic emission curve and the total energy curve during the loading process. The total A.E. energy curve generally rises in a step-like manner. For all rock specimens, in the stress range of 0–5 MPa during the loading and unloading, the acoustic emission energy increased slowly. With the increase of the axial stress, the cumulative energy curve began to show the first apparent stage-like rise, indicating that the acoustic emission was relatively active which is mainly concentrated in the process of loading and unloading. When the acoustic emission signal activity was in a relatively calm phase, it is in the intermittent period of the two load cycles. At the last stage of loading, the slope of the cumulative energy curve and the increase of three states of rock samples was the largest, indicating that the acoustic emission activity was the highest at this time, and the expansion and complete penetration of cracks mainly occurred at this stage. Comparing with the parallel test results, it can be seen that the amount of released energy is positively correlated with the number of cycles, but the saturated rock sample was destroyed after the 5th cycle, and the natural state rock sample was destroyed after the 6th cyclic unloading, which indicates that the rock absorbs less energy and is destroyed after immersion. The higher the water content, the less destroy energy it will need. Comparing with the parallel test results, it can be seen that all rock specimens occurred acoustic events during each cycle of the cyclic loading and unloading. The acoustic events appear randomly as the number of cycles increased. The acoustic events tend to be stable during the intermittent period of two adjacent cycles, and the acoustic event fluctuates the most in the last cycle. It can be seen from Figure8 that the peak acoustic event of the saturated rock specimen is 74, and the peak value of cumulative energy (“mV·mS”, refers to the area below the signal detection envelope, which can reflect the relative energy or intensity of the event) is 13,642. At this time, the rock specimen is damaged at 25.455 MPa; the peak acoustic event of the rock specimen under the natural state is 97, and the peak value of cumulative energy is 48,764, and the rock specimen is broken at 30.507 MPa; the peak acoustic event of the dry rock sample is 164, and the peak value of cumulative energy is 60,241. At this time, the rock specimen is broken at 38.340 MPa. Sustainability 2021,, 13,, x 1041 FOR PEER REVIEW 1211 of of 16 15

(a) saturated state

(b) natural state

70,000 200 45 Stress–strain curve

) Acoustic event–strain curve 180 40 60,000

mS Cumulative AE energy–strain curve

 160 35

mV 50,000

( 140 30 120 40,000 25 100 30,000 20

80 Stress/MPa Acoustic event Acoustic 15 20,000 60

40 10 Cumulative AE energy Cumulative 10,000 20 5

0 0 0 0 100 200 300 400 500 600 700 800 Time /s

Figure 8. Curves of stress, cumulative energy and acoustic event with the time of rock samples under different states. Sustainability 2021, 13, 1041 12 of 15

Comparing with the parallel test results, it suggests that the accumulative acoustic emission energy gradually increases with the increase of strain. There is a positive correlation between strain and damage in the process of rock deformation, so the accumulative acoustic emission energy also has a certain relationship with the damage. Liu et al. [35] used the relationship between strain and accumulative acoustic emission energy obtained through experiments to obtain the relationship between damage and acoustic emission energy accumulation (Equations (4) and (5)) by theoretical derivating.

( n ) 1 1 1 1 1 n−1 w = ln E ε2 + Aε3 (4) s b a nγ 2 0 3

2n 1 o σ = E0ε + Aε 1 − [aexp(bws)] n (5)

where ws is the cumulative energy of acoustic emission; a and b are constants; n, A, E are material constants; γ is the dissipation rate of damage energy of the rock material; and ε is the strain. The process of the loading and unloading is associated with energy accumulation, energy dissipation, and energy release. Therefore, energy conversion can reflect the process of the development of internal defects to the final loss in the rock. There exists a certain relationship between energy dissipation and damage, which means that energy dissipation can reflect the damage degree of original strength [36,37]. Equations (4) and (5) suggest that the sample damage has an exponential relationship with the cumulative acoustic emission energy, and the cumulative acoustic emission energy can indirectly reflect the degree of damage. According to the cumulative energy relationship of acoustic emission of the rock samples under different water contents in Figure8, it can be known that the damage degree in the saturated state is large, while the damage degree in the dry state is weak. Liu et al. [38] reported that in the uniaxial compression process of the moisture rock sample, there are fewer micro-cracks, so less heat is absorbed. Through the above analysis, it can be concluded that the cumulative energy and the acoustic event appear in the initial stage of the cyclic loading and unloading. During the cyclic loading and unloading, the cumulative energy is more regular than the acoustic event. At the late stage of the cyclic loading and unloading, the cumulative energy suddenly increases significantly before the rock sample fails and becomes unstable, and the acoustic event also appears in the peak value in the last stage of the cyclic loading and unloading.

4.4. Analysis of Inﬂuence of Water Content on Energy Storage Characteristics of Rocks Rock impact tendency is one of the main factors affecting impact ground pressure and rock burst in coal mining. The elastic energy index is an index that uses the ratio of elastic energy to the dissipated energy of permanent deformation to measure the energy storage capacity of coal and rock and to predict the rock impact tendency; this index can represent the ability to accumulate elastic energy of the rock before failure, and can well indicate the possibility of rock impact tendency. In order to test and analyze the elastic energy index of the samples, loading and unloading tests were carried out on the samples, which were loaded into the range of 75~85% of the average uniaxial strength of the samples at the same sampling point at a speed ranging from 0.5 MPa/s to 1.0 MPa/s, and then unloaded at the same speed to the range of 1~5% of the uniaxial strength. In this way, the same sample is repeatedly loaded and unloaded, and the maximum value of each repeated loading should be increased by 5% of the average failure load compared with the previous one, until the sample is destroyed. The larger the value of WET, the stronger the tendency to impact [39]. According to the curve, the elastic energy index WET can be obtained as follows.

EE WET = (6) EP Sustainability 2021, 13, 1041 13 of 15

where EE is the stored elastic energy; Ep is the dissipated deformation energy. The saturated rock sample fails in the 5th cycle, the accumulated elastic energy EE is the recoverable strain energy of the 4th cycle, which is 6.154 kJ·m−3, and the dissipated variable performance EP is the irrecoverable strain energy of the 4th cycle, which is −3 3.919 kJ·m . Therefore, the WET = 1.571 can be calculated according to Equation (6). As for the rock sample in the natural state, it was damaged in the 6th cycle, the accumulated −3 elastic energy EE is the recoverable strain energy of the 5th cycle, which is 7.534 kJ·m , and the dissipated variable energy Ep is the irrecoverable strain energy of the 5th cycle, which is −3 3.820 kJ·m . Therefore, the WET = 1.972 can be calculated according to Equation (6), which is 25.5% higher than that of the saturated state. The rock sample in the dry state is damaged in the 8th cycle, the accumulated elastic energy EE is the recoverable strain energy of the −3 7th cycle, which is 11.624 kJ·m , and the dissipated variable energy EP is the irrecoverable −3 strain energy of the 7th cycle, which is 5.857 kJ·m . Therefore, the WET = 1.985 of the rock sample in the natural state can be calculated according to Equation (6), which is 26.3% higher than that in the saturated state. So, with the increase of water content, the elastic energy index WET gradually decreases, indicating that elastic strain energy accumulation of the rock sample becomes smaller when the rock sample contains water, which further indicates that the presence of water will soften the rock and reduce the elastic limit of the rock. The inﬂuence of water content on the mechanical properties and energy storage characteristics of rocks is very obvious.

5. Conclusions • In this paper, uniaxial compression tests, cyclic loading and unloading tests, and acoustic emission tests were carried out on white sandstone samples under different water content. The influence of water content on compressive strength, failure modes and acoustic emission signals was analyzed, and the following conclusions can be drawn: • As the number of cycles increases, the area of the hysteresis loop increases accordingly. Under the same load cycle, the total strain energy, recoverable strain energy, dissipation energy (hysteresis loop area) and plastic strain energy of the rock sample increase with the water content; and at the same load cycle, the total strain energy and the hysteresis loop area of the saturated rock are the largest. • Water has a certain influence on the deformation characteristics of rock samples. Saturated rock samples show tensile failure accompanied by X-shaped shear failure of the conjugate inclined plane; natural rock samples show combined failure mode of tensile failure and X-shaped shear failure of the conjugate inclined plane; and rock in the dry state shows X-shaped shear failure of the conjugate inclined plane. • Water has a significant influence on the characteristic parameters of acoustic emission of rock samples. The higher the water content of the rock sample, the less energy is required for destruction. At the end of the cycle loading and unloading, the cumulative energy suddenly increases, and the acoustic event also reaches the peak value in the last stage of the cycle loading and unloading. • With the increase of water content, the elastic energy index WET gradually decreases, indicating that the impact tendency of the rock sample becomes smaller when the rock sample contains water. It further shows that the presence of water will reduce the elastic limit of the rock and soften the rock. Water content of the rock has a significant influence on their mechanical properties and energy storage characteristics.

Author Contributions: Conceptualization, C.L., W.L. and R.F.; Formal analysis, N.L. and W.L.; Investigation, N.L.; Methodology, C.L., N.L., W.L. and R.F.; Resources, C.L. and W.L.; Validation, C.L., N.L., W.L. and R.F.; Visualization, N.L.; Writing—original draft, N.L. All authors have read and agreed to the published version of the manuscript. Sustainability 2021, 13, 1041 14 of 15

Funding: This research was supported by the Anhui Provincial Natural Science Foundation (2008085ME147), and open foundation from the Key Laboratory of Coal Mine Safety and Efficiently Caving of Ministry of Education (JYBSYS2018102). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to we tested in the laboratory. Conflicts of Interest: The authors declared no potential conflict of interest.

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