Acoustic emission and fragment fractal characteristics of rock burst tendency coal samples under different strain rate loads
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摘要: 现有研究针对岩石受载破坏过程的声发射特征和试件碎片分形特征进行了相关分析，并取得了一定成果，但针对冲击倾向煤样在不同应变率单向受载条件下破坏程度的定量描述及与加载应变率定量关系的研究较少。针对该问题，基于MTS−C64.106型电液伺服系统对原煤试件在单轴静态载荷基础上施加不同应变率载荷试验，试验中采用PCI−2卡型声发射卡对试件受载破裂过程开展实时监测，同时应用分形理论对试件破裂碎片进行处理分析，定量评价试件破碎程度及与载荷应变率的关系。结果表明：① 在静态载荷基础上，试件破坏的峰值强度随着应变率动载荷的升高而逐渐上升。② 随着加载应变率增大，声发射总体数量减少，高能声发射事件增多，声发射振铃计数和能量幅值经历缓增−急增−突增的一致转变过程。③ 试件受载的能量输入速率与声发射振铃计数、内部撞击数增长趋势基本一致，即也会经历缓增−急增−突增的变化。④ 声发射与震动强弱正相关的常数随加载应变率增大而减小，与高低能震动数之比负相关的常数随加载应变率增大而增大；原煤试件的破坏模式会发生剪切破坏−劈裂破坏−爆裂破坏的转变。⑤ 当加载应变率较低时，试件主要是上半部分破坏，应变率增大后由试件中部逐渐向下半部分延伸破坏，原煤试件在动载应变率作用下的破坏过程主要是裂纹的脆性扩展行为。⑥ 试件冲击碎片质量分维与加载应变率呈二次函数关系，即存在加载应变率极值使试件破坏程度达到最大，试验显示该值为2.8×10−3 s−1。Abstract: At present, the correlation analysis between the acoustic emission characteristics of the rock failure process and the fractal characteristics of sample fragments has been carried out. Some achievements have been obtained. But the quantitative description of the failure degree of coal samples with rock burst tendency under the condition of unidirectional loading with different strain rates and the quantitative relationship between the failure degree and the loading strain rate are few. In order to solve this problem, based on the MTS-C64. 106 electro-hydraulic servo system, the raw coal samples are subjected to uniaxial static load with different strain rates. In the test, the PCI-2 acoustic emission card is used to monitor the fracture process of the samples under load in real-time. The fractal theory is used to analyze the fracture fragments of the samples. The relationship between the fracture degree of the samples and the load strain rate is quantitatively evaluated. The results show the following points. ① On the basis of static load, the peak strength of sample failure increases with the increase of strain rate dynamic load. ② With the increase of the loading strain rate, the total number of AE decreases, and the number of high-energy AE events increases. The AE ringing count and energy amplitude undergo a consistent transition process of "slow increase-rapid increase-sudden increase." ③ The loading energy input rate of the sample is basically consistent with the increasing trend of acoustic emission ringing count and internal impact number. It will also experience the change of "slow increase-rapid increase-sudden increase." ④ The constant for the positive correlation between acoustic emission and vibration strength decreases with increasing loading strain rate. The constant which is negatively related to the ratio of the number of high and low energy vibrations, increases with increasing loading strain rate. The failure mode of the raw coal sample will experience a "shear failure - splitting failure - bursting failure" transformation. ⑤ When the loading strain rate is low, the upper part of the sample is destroyed. When the strain rate increases, the sample is gradually destroyed from the middle to the lower part. The failure process of the raw coal sample under the action of dynamic strain rate is mainly the brittle propagation behavior of cracks. ⑥ The fractal dimension of the impact fragment mass of the sample has a quadratic function relationship with the loading strain rate. There is an extreme value of the loading strain rate that maximizes the damage to the sample, with the test showing a strain rate extreme value of 2.8×10−3 s−1.
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图 3 不同应变率载荷加载作用下的应力−应变曲线
Figure 3. Stress-strain curves under loading modes with different strain rates
图 4 不同应变率载荷加载下声发射振铃计数、能量特征
Figure 4. Ringing count and energy characteristics of AE under different strain rate loading
图 7 不同载荷应变率与碎片分维关系
Figure 7. Relationship between fractal dimension of fragments and different loads strain rate
表 1 煤矿载荷的应变率界定标准
Table 1. Strain rate definition criterion of loadings in coal mine
指标 静态载荷 准动态载荷 动态载荷 应变率/s−1 <10−5 10−5～10−3 >10−3 变化率/（MPa·s−1） <0.1 0.1～10 >10 
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表 2 试件基本参数
Table 2. Basic parameters of samples
编号 高度/mm 直径/mm 质量/g 横截面积/cm2 体积/cm3 密度/(g·cm−3) 编号 高度/mm 直径/mm 质量/g 横截面积/cm2 体积/cm3 密度/(g·cm−3) 1−1 99.14 49.43 257.4 19.18 190.15 1.35 2−5 101.51 48.85 261.3 18.73 190.15 1.37 1−2 100.53 48.59 250.3 18.53 186.32 1.34 2−6 99.83 49.25 237.2 19.04 190.08 1.25 1−3 98.59 48.91 246.6 18.78 185.14 1.33 2−7 95.64 48.89 243.4 18.76 179.45 1.36 1−4 99.35 48.72 254.4 18.63 185.12 1.37 2−8 97.95 49.07 242.6 18.90 185.14 1.31 1−5 101.78 49.01 247.3 18.86 191.91 1.29 补1 100.35 48.94 243.0 18.80 188.68 1.29 1−6 99.55 48.99 259.7 18.84 187.55 1.38 补2 96.96 48.93 231.5 18.79 182.23 1.27 1−7 101.64 49.13 260.0 18.95 192.59 1.35 补3 100.90 49.07 250.5 18.90 190.72 1.31 1−8 101.47 48.76 248.7 18.66 189.38 1.31 补4 95.52 49.01 230.5 18.86 180.11 1.28 2−1 100.66 49.21 268.3 19.01 191.35 1.40 补5 92.55 49.02 241.1 18.86 174.58 1.38 2−2 100.63 48.72 253.7 18.63 187.50 1.35 补6 95.80 48.95 226.3 18.81 180.19 1.26 2−3 99.83 48.93 277.6 18.79 187.62 1.48 补7 100.35 48.98 253.0 18.83 188.98 1.34 2−4 100.72 48.87 275.3 18.75 188.83 1.46 补8 99.63 48.94 243.4 18.80 187.32 1.30
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表 3 不同应变率加载下a，b
Table 3. The a and b values under different strain rate loading
序号 应变率/s−1 a b 1 8.33×10−6 5.053 15 0.431 13 2 1.67×10−4 4.860 07 0.432 89 3 2.50×10−3 4.484 21 0.441 75
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表 4 不同加载条件下冲击碎片质量百分比
Table 4. Quality percentage of coal fragment under different loadings
序号 应变率/s−1 指标 粒径/mm ＜1 1～2 2～5 5～10 10～20 20～40 ≥40 1 8.33×10−6 质量/g 4.66 2.67 7.27 13.43 30.98 192.79 0 质量分数/% 1.85 1.06 2.89 5.33 12.30 76.56 0 2 4.17×10−5 质量/g 4.94 2.96 7.93 10.62 37.76 182.14 0 质量分数/% 2.01 1.20 3.22 4.31 15.33 73.94 0 3 8.34×10−5 质量/g 3.22 4.51 4.93 30.85 113.33 81.22 0 质量分数/% 1.35 1.89 2.07 12.96 47.61 34.12 0 4 1.67×10−4 质量/g 2.26 1.14 4.17 6.11 152.18 81.91 0 质量分数/% 0.91 0.46 1.68 2.47 61.42 33.06 0 5 3.34×10−4 质量/g 7.78 2.58 10.27 12.72 97.49 50.04 58.33 质量分数/% 3.25 1.08 4.29 5.32 40.75 20.92 24.38 6 1.00×10−4 质量/g 3.58 4.47 4.85 8.24 19.75 58.98 147.75 质量分数/% 1.45 1.81 1.96 3.33 13.38 23.82 59.67 7 2.50×10−3 质量/g 4.69 2.46 17.91 23.75 32.27 115.87 48.86 质量分数/% 1.91 1.00 7.29 9.66 13.13 47.14 19.88 8 5.00×10−3 质量/g 2.93 2.49 15.44 18.87 24.61 138.42 40.17 质量分数/% 1.21 1.02 6.36 7.77 10.13 56.98 16.54
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表 5 不同加载条件下冲击碎片分维计算结果
Table 5. Fractal dimension results of rock burst fragments under different loadings
序号 应变率/s−1 拟合方程 相关性系数 d 1 8.33×10−6 lnU=1.410 79 ln(Mmax/M)+0.083 42 0.912 11 1.410 79 2 4.17×10−5 lnU=1.443 94 ln(Mmax/M)+0.112 19 0.949 44 1.443 94 3 8.34×10−5 lnU=1.496 79 ln(Mmax/M)+0.356 45 0.911 38 1.496 79 4 1.67×10−4 lnU=1.949 09 ln(Mmax/M)+2.177 44 0.970 31 1.949 09 5 3.34×10−4 lnU=2.172 51 ln(Mmax/M)+1.077 02 0.958 35 2.172 51 6 1.00×10−3 lnU=2.464 55 ln(Mmax/M)+0.974 85 0.876 45 2.464 55 7 2.50×10−3 lnU=2.515 53 ln(Mmax/M)+1.214 67 0.961 32 2.515 53 8 5.00×10−3 lnU=1.803 63 ln(Mmax/M)+0.834 79 0.854 87 1.803 63
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