Abstract
To address the unclear instability mechanism of a rock mass under a complex stress path and considering the widely recognized research methods with energy as the main line, this study systematically analyzes the evolution of the pre-peak strain energy of diorite under triaxial loading and unloading paths using laboratory tests and numerical simulations. First, the characteristic parameter data were obtained by laboratory tests to study the effects of different loading and unloading rates on the pre-peak strain energy accumulation of diorite. Second, the influence of different unloading confining pressure rates and times and axial loading rates on the nonlinear strain energy accumulation characteristics of diorite were studied using a strain energy self-suppression evolution model. As a result, the large difference between the promotion and self-repression effects of the strain energy accumulation mechanism before the peak strength accurately revealed the strain energy accumulation phenomenon. The ultimate strain energy accumulation capacity of diorite increased with the unloading confining pressure timing and axial loading rate and decreased with the unloading confining pressure rate. Moreover, a higher unloading confining pressure rate activated the promotion and self-repression effects of the strain energy accumulation mechanism, whereas a larger unloading confining pressure timing and axial loading rate weakened them.
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References
Akdag S, Karakus M, Nguyen GD, Taheri A (2022) Strain burst vulnerability criterion based on energy-release rate. Eng Fract Mech 237:107232. https://doi.org/10.1016/j.engfracmech.2020.107232.
Akdag S, Karakus M, Nguyen GD, Taheri A, Bruning T (2021) Evaluation of the propensity of strain burst in brittle granite based on post-peak energy analysis. Undergr Space 6:1–11. https://doi.org/10.1016/j.undsp.2019.08.002
An XX, Hu ZP, Zhang L, Liu AL, Zhang YH, Li FT (2022) Nonlinear energy evolution characteristics of diorite examined by triaxial loading-unloading and acoustic emission tests. Materials 15: 6434. https://doi.org/10.3390/ma15186434.
Bratov V, Petrov Y (2007) Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth. Int J Solids Struct 44(7):2371–2380. https://doi.org/10.1016/j.ijsolstr.2006.07.013
Chau KT (1992) Non-normality and bifurcation in a compressible pressure sensitive circular cylinder under axi-symmetric tension and compression. Int J Solids Struct 29(7):801–824. https://doi.org/10.1016/0020-7683(92)90017-n
Diederichs MS (2007) The 2003 Canadian geotechnical colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44:1082–1116. https://doi.org/10.1139/T07-033
Farhadian H (2021) A new empirical chart for rockburst analysis in tunnelling: tunnel rockburst classification (TRC). Int J Min Sci Technol 31:603–610. https://doi.org/10.1016/j.ijmst.2021.03.010
Gao L, Gao F, Zhang ZZ, Xing Y (2020) Research on the energy evolution characteristics and the failure intensity of rocks. Int J Min Sci Technol 30(5):705–713. https://doi.org/10.1016/j.ijmst.2020.06.006
Gong FQ, Ni YX, Jia HY (2022) Effects of specimen size on linear energy storage and dissipation laws of red sandstone under uniaxial compression. Bull Eng Geol Env 801(9):386. https://doi.org/10.1007/s10064-022-02881-y
Guo JQ, Zhang HY, Sun FY, Fan JQ, Shi XY (2022a) Experimental investigation of nonlinear energy evolution and failure characteristics of granite under different water content states. Geofluids 2022:7969009. https://doi.org/10.1155/2022/7969009
Guo WY, Zhang DX, Zhao TB, Li YR, Zhao YQ, Wang CW, Wu WB (2022b) Influence of rock strength on the mechanical characteristics and energy evolution law of gypsum-rock combination specimen under cyclic loading-unloading condition. Int J Geomech 22:04022034. https://doi.org/10.1061/(asce)gm.1943-5622.0002276
Han Y, Ma HL, Yang CH, Li H, Yang J (2021) The mechanical behavior of rock salt under different confining pressure unloading rates during compressed air energy storage (CAES). J Petrol Sci Eng 196: 107676. https://doi.org/10.1016/j.petrol.2020.107676.
Hirata T, Imoto M (1991) Multifractal analysis of spatial distribution of micro earthquakes in the Kanto region. Geophys J Int 107:155–162. https://doi.org/10.1111/j.1365-246X.1991.tb01163.x
Khan NM, Ma LQ, Gao KW, Hussain S, Liu W, Xu YJ, Yuan QP, Gu J (2021) Prediction of an early failure point using infrared radiation characteristics and energy evolution for sandstone with different water contents. Bull Eng Geol Env 80(9):6913–6936. https://doi.org/10.1007/s10064-021-02345-9
Lai XP, Zhang S, Cui F, Wang ZY, Xu HC, Fang XW (2020) Energy release law during the damage evolution of water-bearing coal and rock and pick-up of AE signals of key pregnancy disasters. Chin J Rock Mech Eng 39(03): 433–444. https://kns.cnki.net/kcms/detail/42.1397.O3.20200316.1213.001.html.
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. https://doi.org/10.1016/j.enggeo.2017.08.006
Li P, Cai MF, Wang PT, Guo QF, Miao SJ, Ren FH (2021) Mechanical properties and energy evolution of jointed rock specimens containing an opening under uniaxial loading. Int J Miner Metall Mater 28(12):1875–1886. https://doi.org/10.1007/s12613-020-2237-3
Li TT, Pei XJ, Wang DP, Huang RQ, Tang H (2019a) Nonlinear behavior and damage model for fractured rock under cyclic loading based on energy dissipation principle. Eng Fract Mech 206:330–341. https://doi.org/10.1016/j.engfracmech.2018.12.010
Li XB, Chen ZH, Weng L, Li CJ (2019) Unloading responses of pre-flawed rock specimens under different unloading rates. Trans Nonferrous Met Soc China 29(7):1516–1526. https://doi.org/10.1016/S1003-6326(19)65059-4
Liu WL, Yan EC, Dai H, Du Y, Xiao WB, Zhang S (2020) Study on characteristic strength and energy evolution law of Badong formation mudstone under water effect. Chin J Rock Mech Eng 39(02):311–326. https://kns.cnki.net/kcms/detail/42.1397.O3.20191107.1131.001.html.
Liu XX, Li Y, Wang WW (2022) Study on mechanical properties and energy characteristics of carbonaceous shale with different fissure angles under dry–wet cycles. Bull Eng Geol Env 81(8):319. https://doi.org/10.1007/s10064-022-02823-8
Luo Y, Gong HL, Xu K, Pei CH, Wei XQ, Li X P (2022) Progressive failure characteristics and energy accumulation of granite with a pre-fabricated fracture during conventional triaxial loading. Theor Appl Fract Mech 118: 103219. https://doi.org/10.1016/j.tafmec.2021.103219.
Manouchehrian A, Cai M (2016) Simulation of unstable rock failure under unloading conditions. Can Geotech J 53:22–34. https://doi.org/10.1139/cgj-2015-0126
Martin CD, Christiansson R (2009) Estimating the potential for spalling around a deep nuclear waste repository in crystalline rock. Int J Rock Mech Min Sci 46:219–228. https://doi.org/10.1016/j.ijrmms.2008.03.001
Meng QB, Zhang MW, Zhang ZZ, Han LJ, Pu H (2018) Experimental research on rock energy evolution under uniaxial cyclic loading and unloading compression. Geotech Test J 41(4):717–729. https://doi.org/10.1520/GTJ20170233
Mousavi SZS, Tavakoli H, Moarefvand P, Rezaei M (2019) Assessing the effect of freezing-thawing cycles on the results of the triaxial compressive strength test for calc-schist rock. Int J Rock Mech Mining Sci 123:104090. https://doi.org/10.1016/j.ijrmms.2019.104090.
Mousavi SZS, Tavakoli H, Moarefvand P, Rezaei M (2020) Evaluating the variations of density and durability index of schist rock under the effect of freezing-thawing cycles. J Mining Eng 14(45): 1–12. https://doi.org/10.22034/ijme.2020.37382.
Pan PZ, Miao ST, Wu ZH, Feng XT, Shao CG (2020) Laboratory observation of spalling process induced by tangential stress concentration in hard rock tunnel. Int J Geomech 20:04020011. https://doi.org/10.1061/(asce)gm.1943-5622.0001620
Pan Y, Li AW (2013) Rapid iterative incremental model of the intermittent chaos of deep hole developing in coal-gas outburst. Int J Min Sci Technol 23(2):287–292. https://doi.org/10.1016/j.ijmst.2013.04.005
Peng K, Shi SW, Zou QL, Mou JH, Yu J, Zhang YJ, Cheng YY (2020) Characteristics of energy storage and dissipation of coal under one-time cyclic load. Energy Science and Engineering 8(9):3117–3135. https://doi.org/10.1002/ese3.738
Qin T, Duan YW, Sun HR, Liu HL, Wang L (2019) Energy evolution and acoustic emission characteristics of sandstone specimens under unloading confining pressure. Shock Vib 2019:1612576. https://doi.org/10.1155/2019/1612576
Wang G, Zhang L, Xu M, Liang ZY, Rang LB (2019) Energy damage evolution mechanism of non-across jointed rock mass under uniaxial compression. Chin J Geotech Eng 41(04): 639–647. https://kns.cnki.net/kcms/detail/32.1124.TU.20180815.1425.016.html.
Wang GL, Cao TC, Wen XX, Fan S, Zhang L (2021a) Evolution law of self-suppression of peak energy of single jointed sandstone. J Chin Coal Soc 46(S1):211–221. https://kns.cnki.net/kcms/detail/11.2190.TD.20201011.0802.001.html.
Wang H, Dyskin A, Dight P, Pasternak E, Hsieh A (2020) Review of unloading tests of dynamic rock failure in compression. Eng Fract Mech 225:106289. https://doi.org/10.1016/j.engfracmech.2018.12.022.
Wang HT, He MM, Pang F, Chen YS, Zhang ZQ (2021b) Energy dissipation-based method for brittleness evolution and yield strength determination of rock. J Petrol Sci Eng 200:108376. https://doi.org/10.1016/j.petrol.2021.108376.
Wang W, Duan XL, Jia Y, Cao YJ, Zhu QZ, Liu SF (2022a) Deformation characteristics, gas permeability and energy evolution of low-permeability sandstone under cyclic loading and unloading path. Bull Eng Geol Env 81(9):369. https://doi.org/10.1007/s10064-022-02858-x
Wang YC, Tang CA, Tang LX, Zhang SC, Li LM (2022b) Duan WS (2022) Microseismicity characteristics before and after a rockburst and mechanisms of intermittent rockbursts in a water diversion tunnel. Rock Mech Rock Eng 55:341–361. https://doi.org/10.1007/s00603-021-02666-x
Xie HX, Li XH, Shan CH, Xie Z, Yu LQ (2023) Study on the damage mechanism and energy evolution characteristics of water-bearing coal samples under cyclic loading. Rock Mech Rock Eng 56(2):1367–1385. https://doi.org/10.1007/s00603-022-03136-8
Yang DJ, Hu JH, Ding XT (2020) Analysis of energy dissipation characteristics in granite under high confining pressure cyclic load. Alex Eng J 59(5):3587–3597. https://doi.org/10.1016/j.aej.2020.06.004
Yu Y, Zhu BT, Guo HS, Chen BR, Geng DX (2021) Warning index associated with rock burst in deeply buried tunnels. Int J Geomech 21:04021211. https://doi.org/10.1061/(asce)gm.1943-5622.0002135
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. https://doi.org/10.1007/s11440-020-01028-1
Zhang M, Lin MQ, Zhu HQ, Zhou DH, Wang LK (2018) An experimental study of the damage characteristics of gas-containing coal under the conditions of different loading and unloading rates. J Loss Prev Process Ind 55:338–346. https://doi.org/10.1016/j.jlp.2018.07.006
Zhang Y, Feng XT, Yang CX, Zhang XW, Sharifzadeh M, Wang ZF (2019) Fracturing evolution analysis of Beishan granite under true triaxial compression based on acoustic emission and strain energy. Int J Rock Mech Min Sci 117:150–161. https://doi.org/10.1016/j.ijrmms.2019.03.029
Zhang Z, Gao F (2012) Research on nonlinear characteristics of rock energy evolution under uniaxial compression. Chin J Rock Mech Eng 31(06):1198–1207
Zhang Z, Gao F (2015) Experimental investigation on the energy evolution of dry and water-saturated red sandstones. Int J Min Sci Technol 25(3):383–388. https://doi.org/10.1016/j.ijmst.2015.03.009
Zhang ZZ, Deng M, Bai JB, Yu XY, Wu QH, Jiang LS (2020) Strain energy evolution and conversion under triaxial unloading confining pressure tests due to gob-side entry retained. Int J Rock Mech Mining Sci 126:104184. https://doi.org/10.1016/j.ijrmms.2019.104184.
Zhao K, Yu X, Zhou Y, Wang Q, Wang JQ, Hao JL (2020) Energy evolution of brittle granite under different loading rates. Int J Rock Mech Mining Sci 132:104392. https://doi.org/10.1016/j.ijrmms.2020.104392.
Zhao Y, Dang S, Bi J, Wang CL, Gan F (2022) Influence of complex stress path on energy characteristics of sandstones under triaxial cyclic unloading conditions. Int J Geomech 22(6):04022076. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002413
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This study is supported by-Joint Fund of Hanjiang to Weihe River Valley Water Diversion Project, China (2021JLM-49) and National Natural Science Foundation of Shaanxi Province (2022JQ-435). Their support is gratefully acknowledged.
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An, X., Su, Y., Tao, L. et al. Analysis of pre-peak strain energy storage transformation mechanism of diorite under triaxial loading–unloading paths. Bull Eng Geol Environ 82, 270 (2023). https://doi.org/10.1007/s10064-023-03310-4
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DOI: https://doi.org/10.1007/s10064-023-03310-4