Mechanical response and dilatancy characteristics of deep marble under different stress paths: A sight from energy dissipation

Abstract

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock. This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m. Various uniaxial and triaxial tests at different strain rates, along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths. Subsequently, a new empirical dilatancy coefficient is proposed based on the energy dissipation method. The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing, and plastic failure characteristics of marble under triaxial compression are gradually strengthened. Furthermore, compared to the constant confining pressure, the volume expansion is relatively lower under unloading condition. The energy dissipation is closely linked to the process of dilatancy, with a rapid increase of dissipated energy coinciding with the beginning of dilatancy. A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve, of which change trend is consistent with the actual dilatancy response in marble under different stress paths. The existing empirical and theoretical dilatancy models are analyzed, which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Keywords

deep marble / stress paths / dilatancy / energy dissipation / empirical dilatancy coefficient

References

[[1]] Bridgman P W. Volume changes in the plastic stages of simple compression [J]. Journal of Applied Physics, 1949, 20(12): 1241-1251,

[[2]] Cook N G W. An experiment proving that dilatancy is a pervasive volumetric property of brittle rock loaded to failure [J]. Rock Mechanics, 1970, 2(4): 181-188,

[[3]] Paterson M S, Wong T F. . Experimental rock deformation the brittle field [M], 2005 2nd. Berlin Springer

[[4]] Song Z-x, Zhang J-w, Dong X-k, et al.. Time-dependent behaviors and volumetric recovery phenomenon of sandstone under triaxial loading and unloading [J]. Journal of Central South University, 2022, 29(12): 4002-4020,

[[5]] Walton G, Arzúa J, Alejano L R, et al.. A laboratory-testing-based study on the strength, deformability, and dilatancy of carbonate rocks at low confinement [J]. Rock Mechanics and Rock Engineering, 2015, 48(3): 941-958,

[[6]] Labaune P, Rouabhi A, Tijani M, et al.. Dilatancy criteria for salt cavern design: A comparison between stress-and strain-based approaches [J]. Rock Mechanics and Rock Engineering, 2018, 51(2): 599-611,

[[7]] Ban L-r, Du W-s, Qi C-zhi. A peak dilation angle model considering the real contact area for rock joints [J]. Rock Mechanics and Rock Engineering, 2020, 53(11): 4909-4923,

[[8]] Chen Y-y, Xiao P-w, Li P, et al.. Formation mechanism of rockburst in deep tunnel adjacent to faults: Implication from numerical simulation and microseismic monitoring [J]. Journal of Central South University, 2022, 29(12): 4035-4050,

[[9]] Zheng Z, Feng X-t, Yang C-x, et al.. Post-peak deformation and failure behaviour of Jinping marble under true triaxial stresses [J]. Engineering Geology, 2020, 265: 105444,

[[10]] Feng X-t, Xu H, Qiu S-l, et al.. In situ observation of rock spalling in the deep tunnels of the China Jinping underground laboratory (2400 m depth) [J]. Rock Mechanics and Rock Engineering, 2018, 51(4): 1193-1213,

[[11]] Zheng Z-q, Kong Q-x, Xiao M-l, et al.. Dilatancy and multi-scale failure characteristics of a foliated rock under triaxial confinement unloading conditions [J]. Engineering Failure Analysis, 2024, 160: 108168,

[[12]] Wang X, Wu Y-x, Lu Y, et al.. Strength and dilatancy of coral sand in the South China Sea [J]. Bulletin of Engineering Geology and the Environment, 2021, 80(10): 8279-8299,

[[13]] Cai W-q, Zhu H-h, Liang W-h, et al.. A post-peak dilatancy model for soft rock and its application in deep tunnel excavation [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2023, 15(3): 683-701,

[[14]] Meng Q-b, Liu J-f, Ren L, et al.. Experimental study on rock strength and deformation characteristics under triaxial cyclic loading and unloading conditions [J]. Rock Mechanics and Rock Engineering, 2021, 54(2): 777-797,

[[15]] Ding Q-l, Ju F, Mao X-b, et al.. Experimental investigation of the mechanical behavior in unloading conditions of sandstone after high-temperature treatment [J]. Rock Mechanics and Rock Engineering, 2016, 49(7): 2641-2653,

[[16]] Zheng Z-q, Liu H-z, Zhuo L, et al.. Experimental study on the dilatancy and energy evolution behaviors of red-bed rocks under unloading conditions [J]. Materials, 2023, 16(17): 5759,

[[17]] DAI Bing, ZHAO Guo-yan, DONG Long-jun, et al. Mechanical characteristics for rocks under different paths and unloading rates under confining pressures [J]. Shock and Vibration, 2015: 578748. DOI: https://doi.org/10.1155/2015/578748.

[[18]] Li X-r, Lv W-t, Liang J-p, et al.. Influence of excavation inner diameter on the unloading deformation and failure characteristics of surrounding rock [J]. Rock Mechanics and Rock Engineering, 2024, 57: 5193-5205,

[[19]] Li B, Ding Q-f, Xu N-w, et al.. Mechanical response and stability analysis of rock mass in high geostress underground powerhouse caverns subjected to excavation [J]. Journal of Central South University, 2020, 27(10): 2971-2984,

[[20]] Cai W, Dou L-m, Ju Y, et al.. A plastic strain-based damage model for heterogeneous coal using cohesion and dilation angle [J]. International Journal of Rock Mechanics and Mining Science, 2018, 110: 151-160,

[[21]] Walton G, Diederichs M S. A new model for the dilation of brittle rocks based on laboratory compression test data with separate treatment of dilatancy mobilization and decay [J]. Geotechnical and Geological Engineering, 2015, 33(3): 661-679,

[[22]] Alejano L R, Alonso E. Considerations of the dilatancy angle in rocks and rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(4): 481-507,

[[23]] Detournay E. Elastoplastic model of a deep tunnel for a rock with variable dilatancy [J]. Rock Mechanics and Rock Engineering, 1986, 19(2): 99-108,

[[24]] Yuan S C, Harrison J P. An empirical dilatancy index for the dilatant deformation of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(4): 679-686,

[[25]] Walton G, Diederichs M S, Alejano L R, et al.. Verification of a laboratory-based dilation model for in situ conditions using continuum models [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2014, 6(6): 522-534,

[[26]] Li F, You S, Ji H-g, et al.. Strength and energy exchange of deep sandstone under high hydraulic conditions [J]. Journal of Central South University, 2020, 27(10): 3053-3062,

[[27]] Ulusay R. . The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014 [M], 2015 Cham Springer International Publishing,

[[28]] Zha E-s, Zhang Z-t, Zhang R, et al.. Long-term mechanical and acoustic emission characteristics of creep in deeply buried Jinping marble considering excavation disturbance [J]. International Journal of Rock Mechanics and Mining Sciences, 2021, 139: 104603,

[[29]] Zou C-j, Cheng Y, Li J-chun. Strain rate and size effects on the brittleness indexes of Carrara marble [J]. International Journal of Rock Mechanics and Mining Sciences, 2021, 146: 104860,

[[30]] Lu W-b, Yang J-h, Yan P, et al.. Dynamic response of rock mass induced by the transient release of in situ stress [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 53: 129-141,

[[31]] Si X-f, Gong F-q, Luo Y, et al.. Experimental simulation on rockburst process of deep three-dimensional circular cavern [J]. Rock and Soil Mechanics, 2018, 39(2): 621-634 (in Chinese)

[[32]] Dai B, Zhao G-y, Konietzky H, et al.. Experimental investigation on damage evolution behaviour of a granitic rock under loading and unloading [J]. Journal of Central South University, 2018, 25(5): 1213-1225,

[[33]] Liu J-f, Wang L, Pei J-l, et al.. Experimental study on creep deformation and long-term strength of unloading-fractured marble [J]. European Journal of Environmental and Civil Engineering, 2015, 19(sup1): s97-s107,

[[34]] Liu X-h, Zheng Y, Guo J-y, et al.. Deformation and failure characteristics of loading and unloading rock based on volume crack strain [J]. Frontiers in Earth Science, 2022, 10: 911823,

[[35]] Guo J-q, Huang W-f, Liu X-r, et al.. Rock dilation criteria development based on releasable strain energy [J]. Journal of China Coal Society, 2019, 44(7): 2094-2102 (in Chinese)

[[36]] Guo J-q, Yang Q-d, Lu X-f, et al.. Research on generalized unified strength theory of rock (mass) failure[J]. Journal of China Coal Society, 2021, 46(12): 3869-3882 (in Chinese)

[[37]] Huang D, Li Y-rong. Conversion of strain energy in triaxial unloading tests on marble [J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 66: 160-168,

[[38]] Xie H-p, Li L-y, Peng R-d, et al.. Energy analysis and criteria for structural failure of rocks [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2009, 1(1): 11-20,

[[39]] Zhao X G, Cai M. A mobilized dilation angle model for rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2010, 47(3): 368-384,