A damage model of rock mass energy conversion efficiency based on DIC and AE

Abstract

To address the lack of a unified energy mapping framework for energy release and damage evolution in rocks, uniaxial compression tests were conducted on sandstone with typical pore configurations. Using acoustic emission (AE) and digital image correlation (DIC) techniques to characterize the energy release characteristics and strain evolution laws during rock fracture process. Based on the principle of energy conservation, the energy conversion efficiency α is defined to correlate AE energy with stored strain energy, and an energy type damage factor D is introduced to quantify the damage accumulation process. The results indicate that when D < 0.4, the damage evolution is relatively stable; When D ≥ 0.4, the damage rapidly intensifies, indicating the failure of the specimen. The study also found a significant time lag between AE energy release and macroscopic deformation, which is consistent with the law in engineering practice that microseismic activity precedes monitoring displacement response. Furthermore, a Lemaitre damage model incorporating α was established, which can effectively characterize the nonlinear evolution process of sandstone from elastic deformation to complete failure. Finally, an energy based rockburst warning index based on α and D was discussed, providing technical path for identifying high-risk areas and preventing rockburst disasters in mining engineering.

Keywords

Acoustic emission / Digital image correlation / Energy conversion efficiency / Lemaitre damage model / Rockburst warning

References

[1] Rong H, Li NN, Zhang HW, Sun DQ, Huo BJ. Insights into fundamental problems of rockburst under the modern structure stress field. Sci Rep 2022; 12(1):20299.

[2] He MC, Cheng T, Qiao YF, Li HR. A review of rockburst: Experiments, theories, and simulations. J Rock Mech Geotech Eng 2023; 15(5):1312—53.

[3] Li TZ, Zhang LM, Gong WP, Tang HM. Cyclic freezing—thawing induced rock strength degradation, crack evolution, heave and settlement accounted for by a DEM model. Int J Rock Mech Min Sci 2023; 170:105498.

[4] Hoek E, Brown ET. The Hoek—Brown failure criterion and GSI—2018 edition. J Rock Mech Geotech Eng 2019; 11(3):445-63.

[5] Cheng HM, Yang XB, Zhang ZW, Li WL, Ning ZX. Damage evaluation and precursor of sandstone under the uniaxial compression: Insights from the strain—field heterogeneity. PLoS One 2021; 16(12):e0262054.

[6] Lin Q, Wan B, Wang Y, Lu YH, Labuz JF. Unifying acoustic emission and digital imaging observations of quasi—brittle fracture. Theor Appl Fract Mech 2019; 103:102301.

[7] Wei LK, Yuan Q, Ren YW, Jiang DY, Zhang DD, Liu YL, et al. Analysis of failure mechanics and energy evolution of sandstone under uniaxial loading based on DIC technology. Front Earth Sci 2022; 10:814292.

[8] Fan J, Zhu X. Systematic detection and evaluation of cracking behavior of flawed brittle sandstones with AE and 3D—DIC techniques. PLoS One 2024; 19(9):e0309381.

[9] Pan JL, Wu X, Guo QF, Xi X, Cai MF. Uniaxial experimental study of the deformation behavior and energy evolution of conjugate jointed rock based on AE and DIC methods. Adv Civ Eng 2020; 2020(1):8850250.

[10] Wang YC, Tang CA, Cai M, Tang LX, Ma TH, Zhang SC, et al. Microseismicity evolution related to two extremely intense rockbursts in a water diversion tunnel. Int J Rock Mech Min Sci 2023; 164:105359.

[11] Chen J, Huang HQ, Rui YC, Pu YY, Zhang S, Li Z, et al. Enhancing microseismic/acoustic emission source localization accuracy with an outlier—robust kernel density estimation approach. Int J Min Sci Technol 2024; 34(7):943-56.

[12] Urbancic TI, Meighan L, Viegas G, Baig A. Seismic efficiency, overshoot and enhanced dynamic weakening of fractures. Fifth EAGE Passive Seism Work 2014:p1-2.

[13] Boroumand N, Eaton DW. Comparing energy calculations — hydraulic fracturing and microseismic monitoring. 74th EAGE Conf Exhib Incorporating EUROPEC 2012; 2012.p.293—00090.

[14] Hao QJ, Zhang ZP, Wang XZ, Zhang R, Zhang AL, Zhang LB, et al. Study on mechanical properties and acoustic emission response of deep granite under hydro—mechanical coupling. Therm Sci 2023; 27(1 Part B):631—8.

[15] Dong LJ, Zhu HY, Yan F, Bi SJ. Risk field of rock instability using microseismic monitoring data in deep mining. Sensors 2023; 23(3):1300.

[16] Si GY, Cai W, Wang SY, Li X. Prediction of relatively high—energy seismic events using spatial—temporal parametrisation of mining—induced seismicity. Rock Mech Rock Eng 2020; 53(11):5111—32.

[17] Yu JX, He HS, Liu ZQ, He XZ, Zhou FW, Song ZH, et al. Analysis of spatiotemporal characteristics of microseismic monitoring data in deep mining based on ST—DBSCAN clustering algorithm. Processes 2025; 13(8):2359.

[18] Trifu CI, Shumila V. Microseismic monitoring of a controlled collapse in field II at ocnele mari, Romania. Pure Appl Geophys 2010; 167(1):27-42.

[19] Liang BF, Fu YL, Lin M, et al. Seismic efficiency: from hydraulic fracturing—acoustic emission laboratory experiments of shale based on energy budget. Geoenergy Sci Eng 2025; 252:213917.

[20] Xing TZ, Zhu HB, Song YM. Experimental study on rock deformation localization using digital image correlation and acoustic emission. Appl Sci 2024; 14(12):5355.

[21] Salvoni M. Rock damage assessment in a large unstable slope from microseismic monitoring—MMG century mine case study. 2017. p.105-134.

[22] Lemaitre J. A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 1985; 107(1):83-9.

[23] Kim JS, Lee KS, Cho WJ, Choi HJ, Cho GC. A comparative evaluation of stress—strain and acoustic emission methods for quantitative damage assessments of brittle rock. Rock Mech Rock Eng 2015; 48(2):495-508.

[24] Khazaei C, Hazzard J, Chalaturnyk R. Damage quantification of intact rocks using acoustic emission energies recorded during uniaxial compression test and discrete element modeling. Comput Geotech 2015; 67:94-102.

[25] Olgaard DL, Brace WF. The microstructure of gouge from a mining—induced seismic shear zone. Int J Rock Mech Min Sci Geomech Abstr 1983; 20(1):11-9.

[26] Zhao Y, Yang TH, Zhang PH, Zhou JR, Yu QL, Deng WX. The analysis of rock damage process based on the microseismic monitoring and numerical simulations. Tunn Undergr Space Technol 2017; 69:1-17.

[27] Chen J, Shi WH, Rui YC, Du JS, Pan XK, Peng X, et al. Research on a dynamic early warning model for gas outbursts using adaptive fractal dimension characterization. Int J Min Sci Technol 2025; 35(8):1245—57.