energies Article A New Bursting Liability Evaluation Index for Coal –The Effective Elastic Strain Energy Release Rate Zhiguo LU 1,2,*, Wenjun JU 1,2, Fuqiang GAO 3, Youliang FENG 1,2, Zhuoyue SUN 1,2, Hao WANG 4 and Kang YI 1,5 1 Coal Mining and Designing Branch, China Coal Research Institute, Beijing 100013, China; [email protected] (W.J.); [email protected] (Y.F.); [email protected] (Z.S.); [email protected] (K.Y.) 2 Coal Mining and Designing Department, Tiandi Science and Technology Co Ltd, Beijing 100013, China 3 National Key Laboratory of Coal Mining and Clean Utilization, China Coal Research Institute, Beijing 100013, China; [email protected] 4 School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China; [email protected] 5 School of Resource and Safety Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China * Correspondence: [email protected]; Tel.: +86-1352-050-5296 Received: 2 September 2019; Accepted: 26 September 2019; Published: 30 September 2019 Abstract: Because both faults and cleats exist in coal, sharp stress drops occur during loading when coal is deformed. These drops occur during the pre-peak stage and are accompanied by sudden energy releases. After a stress drop, the stress climbs slowly following a zigzag path and the energy accumulated during the pre-peak stage is unstable. A stress–strain curve is the basic tool used to evaluate the bursting liability of coal. Based on energy accumulation in an unsteady state, the pre-peak stress–strain curve is divided into three stages: pre-extreme, stress drop, and re-rising stage. The energy evolution of the specimen during each stage is analyzed. In this paper, an index called the effective elastic strain energy release rate (EESERR) index is proposed and used to evaluate the coal’s bursting liability. The paper shows that the propagation and coalescence of cracks is accompanied by energy release. The stress climb following a zigzag path prolongs the plastic deformation stage. This causes a significant difference between the work done by a hydraulic press during a laboratory uniaxial compression experiment and the elastic strain energy stored in the specimen during the experiment, so the evaluation result of the burst energy index would be too high. The determination of bursting liability is a comprehensive evaluation of the elastic strain energy accumulated in coal that is released when the specimen is damaged. The index proposed in this paper fully integrates the energy evolution of coal samples being damaged by loading, the amount of elastic strain energy released during the sample failure divided by the failure time is the energy release rate. The calculation method is simplified so that the uniaxial compressive strength and elastic modulus are included which makes the new index more universal and comprehensive. Theoretical analysis and physical compression experiments validate the reliability of the evaluation. Keywords: bursting liability; unstable energy accumulation; effective elastic strain energy; stress drop 1. Introduction Safety and efficiency are two of the major goals in mining [1]. As coal mine production and mining depths in China increase, coal burst accidents are occurring more frequently. According to statistics, the number of coal mines susceptible to coal bursts in China has increased from 32 in 1985 to 177 in 2016. The dust produced by coal burst accidents seriously affects the working environment [2]. Energies 2019, 12, 3734; doi:10.3390/en12193734 www.mdpi.com/journal/energies Energies 2019, 12, 3734 2 of 15 This seriously threatens efficient production and the safety of workers and mine infrastructure [1–5]. A considerable number of research projects on coal bursts have made significant progress on predicting the occurrence of coal bursts and numerous theories and prediction indexes have been proposed. These indexes include the Turchaninov index [6], Russenes index [7], Hoek index [8], and a brittleness index (σc/σt)[2]. In addition, the technology for measuring coal burst precursors has also advanced including hardware and software for monitoring acoustic [9] and thermal infrared [10,11] and for monitoring microseismicity [12,13]. Exploiting mineral resources, particularly when done by underground mining, causes stress redistribution and rock can fail suddenly when the imposed load exceeds the rock’s ultimate bearing capacity. A coal burst (also called a rock burst, a coal bump, and other names) is a strong underground dynamic disaster caused by the sudden release of elastic strain energy from the surrounding rock [14–17]. Energy accumulations and their release are the important factors that must be studied to evaluate mine workings for coal burst liability and intensity. Conventional coal burst indexes based on energy theory include an energy release rate index [18], a burst energy index (KE)[19], an elastic energy index (WET)[20], and the burst energy release index (BERI) [21]. Weng et al. [22] proposed a strain energy density index based on strain energy accumulations and their release. It was developed from numerical simulations in which the surrounding rocks with high strain energy density were suddenly damaged by the rapid release of that energy. This caused a coal burst. Brady et al. [23] and Jiang et al. [24] emphasized the influence of energy evolution in the pre-peak stage. The local energy release rate (LERR) was determined by calculating the differences between strain energies before and after brittle failure. Xu et al. [25] defined the ratio of the LERR to the limit energy storage rate (LESR) as the coal burst energy release rate based on energy evolution during coal failure. This was used as an index to evaluate bursting liability. Further analysis of the energy accumulation shows that more than half of the energy in the surrounding rock is stored as elastic strain energy. The energy is either dissipated during inelastic deformation, like shearing, or released instantaneously in the form of kinetic energy when the rock fractures. The sudden release of energy is what causes coal bursts [26]. Miao et al. [27] considered the accumulation of elastic strain energy to be the primary factor behind coal bursts and high stress to be the external cause for the accumulation and sudden release of elastic strain energy. Zhang et al. [28,29] pointed out that the elastic strain energy stored in the coal is the main source of the energy released during a coal burst. After a detailed analysis of energy transformation and the release of different forms of energy during coal burst, Yang et al. [30] proposed an elastic deformation energy release rate index that considered energy dynamic release time. The instantaneous release of energy caused by the sudden failure of coal is the internal cause of coal bursts. Energy evolution is closely related to coal deformation and failure. Zheng [31] generated a mathematical model for dynamic deformation of rock and provided analytical solutions for different deformation modes. Zheng pointed out that rock failure is the result of energy transformation and dissipation in time and space. The shape of the stress–strain curves at the pre-peak and post-peak stages can reflect the stress and deformation state of rock; this is useful for understanding energy evolution [32,33]. Numerous uniaxial compression tests on coal samples show that stress drops in the pre-peak stage (which is equivalent to the energy suddenly released), demonstrating that the energy was in an unstable state at that stage. Based on these stress drops, this paper proposes a new energy index. This index, called the effective elastic strain energy release rate (EESERR) index, fully reflects the evolution of the energy in the coal samples during the sequence of events comprising loading, failure, and the dynamic release time of energy after failure. The index encapsulates the bursting liability of material caused by the release rate of elastic strain energy. The index’s calculation method is simplified and the uniaxial compressive strength (UCS) and elastic modulus of the material are included. Theoretical and experimental verification show that this index is comprehensive and can be applied universally. Energies 2019, 12, x FOR PEER REVIEW 3 of 15 Energiesmodulus2019 of, 12 the, 3734 material are included. Theoretical and experimental verification show that this index3 of 15 is comprehensive and can be applied universally. 2. Materials and Methods 2.1. Uniaxial Compression Test Coal samples were collected from the No. 4 coal seam in the Tashan coal mine, Datong, Shanxi Province, China.China. AllAll the the coal coal specimens specimens tested tested were were cylinders cylinders 50 mm 50 inmm diameter in diameter and 100 and mm 100 height. mm Uniaxialheight. Uniaxial compression compression tests were tests conducted were conducted in the laboratory in the withlaboratory a hydraulic with pressa hydraulic using displacement press using 5 controldisplacement and a loadingcontrol and rate ofa loading 10− mm rate/s. Theof 10 test−5 mm/s. equipment The test is shown equipment in Figure is shown1. Displacements, in Figure 1. loads,Displacements, and other loads, data wereand other recorded data and were the recorded samples’ and mechanical the samples’ parameters mechanical such parameters as peak strength such andas peak elastic strength modulus and wereelastic obtained modulus during were theobtained tests. during the tests. Figure 1. Test equipment. 2.2. Pre-peak Pre-Peak Stress