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Energy Evolution and Brittleness Analysis of Sandstone Under Confining Pressure Unloading

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Abstract

Excavation and unloading operations in underground rock engineering can cause strong disturbances to the original in situ stress, potentially leading to disasters such as spalling and rockburst. To address the inadequacy of strength analysis research, this study employs the energy analysis method. By analysing the relationship between different confining pressure unloading paths, a series of constant deviatoric stress direct and cyclic unloading triaxial tests were conducted to obtain the energy evolution process. Based on this, the energy evolution mechanism of the unloading confining pressure test path was revealed, and the influence of this path on the brittleness of the specimen was discussed. The research results indicate that confining pressure unloading leads to active energy release, triggering energy imbalance release and energy transfer mechanisms, which generate tensile and shear fractures, respectively, leading to energy dissipation. Throughout the entire test process, energy dissipation mainly comes from the elastic energy stored in the specimen before the unloading point, while the external work is relatively small. The elastic energy ratio continuously decreases from the unloading point. In addition, different triaxial confining pressure unloading tests can be regarded as the coupling of two stress path mechanisms: when the stress deviation remains unchanged, the spherical stress decreases, and when the stress deviation changes, the spherical stress remains unchanged. Furthermore, tensile microcracks weaken the brittleness before the peak and enhance it after the peak. The research results can guide the construction schemes of rock underground engineering.

Highlights

  • The unloading of confining pressure leads to the active release of energy, triggering energy imbalance release and energy transfer mechanisms, which generate tensile and shear fractures, respectively.

  • During the unloading of confining pressure, the dissipation of energy primarily originates from the elastic energy stored in the specimen before the unloading point, with less contribution from external work.

  • Different triaxial unloading tests can be considered as the coupling of three energy mechanisms, namely energy saturation, energy imbalance release, and energy transfer mechanism.

  • The tensile microcracks generated during the unloading process of the specimen have weakened the brittleness before the peak and enhanced it after the peak.

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Data availability

Some or all data, models, or codes that support the fndings of this study are available from the corresponding author (hliucumt@163.com) upon reasonable request.

References

  • Abi E, Yuan H, Cong Y, Wang Z, Jiang M (2023) Experimental study on the entropy change failure precursors of marble under different stress paths. Ksce J Civ Eng 27(1):356–370

    Article  Google Scholar 

  • Bouibes A, Zaoui A, Tunega D (2013) Bonds, bands and elasticity of smithsonite rock. Solid State Commun 166:76–82

    Article  ADS  CAS  Google Scholar 

  • Chen ZH, Huang LQ, Li XB, Weng L, Wang SF (2020) Influences of the height to diameter ratio on the failure characteristics of marble under unloading conditions. Int J Geomech 20(9)

  • Ding ZW, Jia JD, Tang QB, Li XF (2022) Mechanical properties and energy damage evolution characteristics of coal under cyclic loading and unloading. Rock Mech Rock Eng 55(8):4765–4781

    Article  ADS  Google Scholar 

  • Dong XJ, Karrech A, Basarir H, Elchalakani M, Seibi A (2019) Energy dissipation and storage in underground mining operations. Rock Mech Rock Eng 52(1):229–245

    Article  ADS  Google Scholar 

  • Duan SQ, Jiang Q, Xu DP, Liu GF (2020) Experimental study of mechanical behavior of interlayer staggered zone under cyclic loading and unloading condition. Int J Geomech 20(3):4019187

    Article  Google Scholar 

  • Duan SQ, Jiang Q, Liu GF, Xiong JC, Gao P, Xu DP, Li MY (2021) An insight into the excavation-induced stress paths on mechanical response of weak interlayer zone in underground cavern under high geostress. Rock Mech Rock Eng 54(3):1331–1354

    Article  ADS  Google Scholar 

  • Duan SQ, Jiang XQ, Jiang Q, Xiong JC, Li CY (2023) Theoretical solution and failure analysis of water pressure on lining of deep-buried non-circular hydraulic tunnel based on the equivalent hydraulic radius method. Eng Fail Anal 148:107163

    Article  Google Scholar 

  • Feng XT, Pei SF, Jiang Q, Zhou YY, Li SJ, Yao ZB (2017) Deep fracturing of the hard rock surrounding a large underground cavern subjected to high geostress: in situ observation and mechanism analysis. Rock Mech Rock Eng 50(8):2155–2175

    Article  ADS  Google Scholar 

  • Feng X, Xu H, Qiu S, Li S, Yang C, Guo H, Cheng Y, Gao Y (2018) In situ observation of rock spalling in the deep tunnels of the china jinping underground laboratory (2400 m depth). Rock Mech Rock Eng 51(4):1193–1213

    Article  ADS  Google Scholar 

  • Feng XT, Xu H, Yang CX, Zhang XW, Gao YH (2020) Influence of loading and unloading stress paths on the deformation and failure features of jinping marble under true triaxial compression. Rock Mech Rock Eng 53(7):3287–3301

    Article  ADS  Google Scholar 

  • Gao FQ, Yang L (2021) Experimental and numerical investigation on the role of energy transition in strainbursts. Rock Mech Rock Eng 54(9):5057–5070

    Article  ADS  Google Scholar 

  • Gong FQ, Yan JY, Li XB, Luo S (2019) A peak-strength strain energy storage index for rock burst proneness of rock materials. Int J Rock Mech Min 117:76–89

    Article  Google Scholar 

  • Gong F, Zhang P, Luo S, Li J, Huang D (2021) Theoretical damage characterisation and damage evolution process of intact rocks based on linear energy dissipation law under uniaxial compression. Int J Rock Mech Min 146:104858

    Article  Google Scholar 

  • Guo YT, Wang L, Chang X (2019) Study on the damage characteristics of gas-bearing shale under different unloading stress paths. PLoS ONE 14(11):e224654

    Article  Google Scholar 

  • He MC, Miao JL, Feng JL (2010) Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions. Int J Rock Mech Min 47(2):286–298

    Article  Google Scholar 

  • He MM, Huang BQ, Zhu CH, Chen YS, Li N (2018) Energy dissipation-based method for fatigue life prediction of rock salt. Rock Mech Rock Eng 51(5):1447–1455

    Article  ADS  Google Scholar 

  • Huang R, Huang D (2010) Experimental research on affection laws of unloading rates on mechanical peoperties of Jinping marble under high geostress. Chin J Rock Mech Eng 29(1):21–33 (in Chinese)

    MathSciNet  Google Scholar 

  • Huang D, Li YR (2014) Conversion of strain energy in triaxial unloading tests on marble. Int J Rock Mech Min 66:160–168

    Article  Google Scholar 

  • Huang D, Huang R, Zhang Y (2012) Experimental investigations on static loading rate on mechanical properties and energy mechanism of coarse crystal grain marble under uniaxial. Chin J Rock Mech Eng 31(02):245–255 (in Chinese)

    CAS  Google Scholar 

  • Huang T, Wang L, Li J, Zhang B, Wang X, Xu X (2022) Study on mechanical properties and fracture surface characteristics of argillaceous sandstone under different stress paths. Sci Rep-Uk 12(1)

  • Jia ZQ, Li CB, Zhang R, Wang M, Gao MZ, Zhang ZT, Zhang ZP, Ren L, Xie J (2019) Energy evolution of coal at different depths under unloading conditions. Rock Mech Rock Eng 52(11):4637–4649

    Article  ADS  Google Scholar 

  • Jiang Q, Su G, Feng X, Chen G, Zhang M, Liu C (2019) Excavation optimization and stability analysis for large underground caverns under high geostress: a case study of the Chinese laxiwa project. Rock Mech Rock Eng 52(3):895–915

    Article  ADS  Google Scholar 

  • Lai Y, Zhao K, He Z, Yu X, Yan Y, Li Q, Shao H, Zhang X, Zhou Y (2023) Fractal characteristics of rocks and mesoscopic fractures at different loading rates. Geomech Energy Envir 33:100431

    Article  Google Scholar 

  • Li XB, Cao WZ, Zhou ZL, Zou Y (2014) Influence of stress path on excavation unloading response. Tunn Undergr Sp Tech 42:237–246

    Article  Google Scholar 

  • Li DY, Sun Z, Xie T, Li XB, Ranjith PG (2017) Energy evolution characteristics of hard rock during triaxial failure with different loading and unloading paths. Eng Geol 228:270–281

    Article  Google Scholar 

  • Li Z, Wang L, Lu Y, Li W, Wang K, Fan H (2019) Experimental investigation on true triaxial deformation and progressive damage behaviour of sandstone. Sci Rep-Uk 9(1):93386

    ADS  Google Scholar 

  • Li CC, Zhao T, Zhang Y, Wan W (2022a) A study on the energy sources and the role of the surrounding rock mass in strain burst. Int J Rock Mech Min 154:105114

    Article  Google Scholar 

  • Li Y, Zhao T, Li Y, Chen Y (2022b) A five-parameter constitutive model for hysteresis shearing and energy dissipation of rock joints. Int J Min Sci Techno 32(4):737–746

    Article  Google Scholar 

  • Li Z, Suo J, Fan J, Fourmeau M, Jiang D, Nelias D (2023) Damage evolution of rock salt under multilevel amplitude creep–fatigue loading with acoustic emission monitoring. Int J Rock Mech Min 164:105346

    Article  Google Scholar 

  • Luo S, Gong F (2023) Evaluation of energy storage and release potentials of highly stressed rock pillar from rockburst control perspectives. Int J Rock Mech Min 163:105324

    Article  Google Scholar 

  • Mcsaveney MJ, Davies TR (2009) Surface energy is not one of the energy losses in rock comminution. Eng Geol 109(1–2):109–113

    Article  Google Scholar 

  • Meng QB, Zhang MW, Han LJ, Pu H, Nie TY (2016) Effects of acoustic emission and energy evolution of rock specimens under the uniaxial cyclic loading and unloading compression. Rock Mech Rock Eng 49(10):3873–3886

    Article  ADS  Google Scholar 

  • Meng QB, Liu JF, Ren L, Pu H, Chen YL (2021) Experimental study on rock strength and deformation characteristics under triaxial cyclic loading and unloading conditions. Rock Mech Rock Eng 54(2):777–797

    Article  ADS  Google Scholar 

  • Meng QB, Liu JF, Huang BX, Pu H, Wu JY, Zhang ZZ (2022) Effects of confining pressure and temperature on the energy evolution of rocks under triaxial cyclic loading and unloading conditions. Rock Mech Rock Eng 55(2):773–798

    Article  ADS  Google Scholar 

  • Munoz H, Taheri A, Chanda EK (2016) Fracture energy-based brittleness index development and brittleness quantification by pre-peak strength parameters in rock uniaxial compression. Rock Mech Rock Eng 49(12):4587–4606

    Article  ADS  Google Scholar 

  • Naji AM, Rehman H, Emad MZ, Ahmad S, Kim J, Yoo H (2019) Static and dynamic influence of the shear zone on rockburst occurrence in the headrace tunnel of the Neelum Jhelum hydropower project, Pakistan. Energies 12:2124

    Article  Google Scholar 

  • Peng K, Wang YQ, Zou QL, Liu ZP, Mou JH (2019) Effect of crack angles on energy characteristics of sandstones under a complex stress path. Eng Fract Mech 218:106577

    Article  Google Scholar 

  • Peng K, Shi SW, Zou QL, Wen ZJ, Wang YQ, Jiang ZB, Zheng CS (2021) Quantitative characteristics of energy evolution of gas-bearing coal under cyclic loading and its action mechanisms on coal and gas outburst. Rock Mech Rock Eng 54(6):3115–3133

    Article  ADS  Google Scholar 

  • Qiu S, Feng X, Zhang C, Zhou H, Sun F (2010) Experimental research on mechanical properties of deep-buried marble under different unloading rates of confining pressures. Chin J Rock Mech Eng 29(09):1807–1817 (in Chinese)

    Google Scholar 

  • Qiu SL, Feng XT, Xiao JQ, Zhang CQ (2014) An experimental study on the pre-peak unloading damage evolution of marble. Rock Mech Rock Eng 47(2):401–419

    Article  ADS  Google Scholar 

  • Rahimzadeh KI, Ameri M, Molladavoodi H (2018) Shale brittleness evaluation based on energy balance analysis of stress-strain curves. J Petrol Sci Eng 167:1–19

    Article  Google Scholar 

  • Rehbock SM, Jesel T (2018) Fault induced rock bursts and micro-tremors —experiences from the Gotthard base tunnel. Tunn Undergr Sp Tech 81:358–366

    Article  Google Scholar 

  • Ren F, Zhu C, He M (2020) Moment tensor analysis of acoustic emissions for cracking mechanisms during schist strain burst. Rock Mech Rock Eng 53(1):153–170

    Article  ADS  Google Scholar 

  • Si XF, Gong FQ (2020) Strength-weakening effect and shear-tension failure mode transformation mechanism of rockburst for fine-grained granite under triaxial unloading compression. Int J Rock Mech Min 131:104347

    Article  Google Scholar 

  • Sun LN, Zhang LM, Cong Y, Song YD, He KQ (2021) The meso-fracturing mechanism of marble under unloading confining pressure paths and constant axial stress. Sci Rep-Uk 11(1)

  • Tarasov B, Potvin Y (2013) Universal criteria for rock brittleness estimation under triaxial compression. Int J Rock Mech Min 59:57–69

    Article  Google Scholar 

  • Tarasov BG, Stacey TR (2017) Features of the energy balance and fragmentation mechanisms at spontaneous failure of class i and class ii rocks. Rock Mech Rock Eng 50(10):2563–2584

    Article  ADS  Google Scholar 

  • Wang Y, Feng WK, Hu RL, Li CH (2021) Fracture evolution and energy characteristics during marble failure under triaxial fatigue cyclic and confining pressure unloading (fc-cpu) conditions. Rock Mech Rock Eng 54(2):799–818

    Article  ADS  Google Scholar 

  • Wang Y, Zhao QH, Xiao YG, Hou ZQ (2020) Influence of time-lagged unloading paths on fracture behaviors of marble using energy analysis and post-test ct visualization. Environ Earth Sci 79(10)

  • Wasantha PLP, Ranjith PG, Shao SS (2014) Energy monitoring and analysis during deformation of bedded-sandstone: use of acoustic emission. Ultrasonics 54(1):217–226

    Article  CAS  PubMed  Google Scholar 

  • Xie H, Ju Y, Li L (2005) Criteria for strength and structural failure of rocks based onenergy dissipation and energy release principles. Chin J Rock Mech Eng 24(17):3003–3010 (in Chinese)

    Google Scholar 

  • Yan ZL, Dai F, Zhu JB, Xu Y (2021) Dynamic cracking behaviors and energy evolution of multi-flawed rocks under static pre-compression. Rock Mech Rock Eng 54(9):5117–5139

    Article  ADS  Google Scholar 

  • Yang R, Ma DP, Yang YJ (2019) Experimental investigation of energy evolution in sandstone failure during triaxial unloading confining pressure tests. Adv Civ Eng 2019:7419752

    Google Scholar 

  • Zhang WJ, Chen YM, Zhan LT (2006) Loading/unloading response ratio theory applied in predicting deep-seated landslides triggering. Eng Geol 82(4):234–240

    Article  Google Scholar 

  • Zhang Y, Feng XT, Yang CX, Zhang XW, Sharifzadeh M, Wang ZF (2019a) Fracturing evolution analysis of beishan granite under true triaxial compression based on acoustic emission and strain energy. Int J Rock Mech Min 117:150–161

    Article  Google Scholar 

  • Zhang Y, Feng XT, Zhang XW, Wang ZF, Sharifzadeh M, Yang CX (2019b) A novel application of strain energy for fracturing process analysis of hard rock under true triaxial compression. Rock Mech Rock Eng 52(11):4257–4272

    Article  ADS  Google Scholar 

  • Zhang LM, Cong Y, Meng FZ, Wang ZQ, Zhang P, Gao S (2021) Energy evolution analysis and failure criteria for rock under different stress paths. Acta Geotech 16(2):569–580

    Article  Google Scholar 

  • Zhang D, Wang Z, Zhang L, Wang X (2023) Crack propagation behavior in sandstone during unloading confining pressure under different seepage pressures. J Cent South Univ 30(8):2657–2670

    Article  MathSciNet  Google Scholar 

  • Zhao G, Wang D, Gao B, Wang S (2017) Modifying rock burst criteria based on observations in a division tunnel. Eng Geol 216:153–160

    Article  Google Scholar 

  • Zhao K, Yu X, Zhou Y, Wang Q, Wang J, Hao J (2020) Energy evolution of brittle granite under different loading rates. Int J Rock Mech Min 132:104392

    Article  Google Scholar 

  • Zhao Y, Bi J, Wang CL, Liu PF (2021) Effect of unloading rate on the mechanical behavior and fracture characteristics of sandstones under complex triaxial stress conditions. Rock Mech Rock Eng 54(9):4851–4866

    Article  ADS  Google Scholar 

  • Zhou XP, Zhang YX, Ha QL (2008) Real-time computerized tomography (ct) experiments on limestone damage evolution during unloading. Theor Appl Fract Mec 50(1):49–56

    Article  Google Scholar 

Download references

Acknowledgements

The financial and general supports for this research provided by the National Key Research and Development Plan (Nos. 2016YFC0501103) and the National Natural Science Foundation of China (Nos. 51804298).

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Authors and Affiliations

  1. School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

    Yinda Li, Liu Han & Tao Shang

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  1. Yinda Li
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  2. Liu Han
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Correspondence to Liu Han.

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Li, Y., Han, L. & Shang, T. Energy Evolution and Brittleness Analysis of Sandstone Under Confining Pressure Unloading. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-024-03818-5

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