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Time-Dependent Behavior of Jinping Deep Marble Taking into Account the Coupling Between Excavation Damage and High Pore Pressure

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Abstract

During the operation of the Jinping II hydropower station, the rocks surrounding the headrace tunnels have undergone failure because of the time-dependent creep effect that occurs due to the high geostress present and seepage. However, a few studies of the creep deformation of deep rocks have taken into account the coupling effect between excavation damage and pore pressure. This paper reports the results of a series of triaxial creep experiments conducted on Jinping deep marble in which the coupling between excavation damage and high pore pressure was studied. The results show that the magnitude of the creep deformation, the long-term strength, and failure mode of the excavation-damaged marble vary considerably with pore pressure. That is, the pore pressure has a significant effect on the marble. A new nonlinear viscoelastic-plastic damage (VEPD) model incorporating the effect of pore pressure was subsequently developed based on the experimental data. The values of the parameters appearing in the model were then obtained using a method of Universal Global Optimization. Good consistency is found between our theoretical predictions and test data which indicates that the VEPD model can be reliably used to simulate and predict the complete creep process in excavation-damaged deep rocks. It also gives a good account of the effect of pore pressure on the creep behavior. As a result, the model provides us with a better understanding of the long-term stability of underground engineering projects.

Highlights

  • The coupling between excavation damage and high pore pressure was investigated during creep deformation of deep marble.

  • The time-dependent behavior and mechanism of excavation-damaged marble subjected to various pore pressures were analyzed.

  • A new creep model that is applicable to excavation-damaged deep marble was proposed.

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Abbreviations

\(\alpha\) :

Material constant

\(\beta\) :

Material constant

\(b\) :

Material constant

\(\tilde{c}\) :

The effective cohesive strength of the rock

\(d\) :

Material constant

\(D\) :

Creep damage factor

\(\varepsilon_{{{\text{ij}}}}\) :

Total strain

\(\varepsilon_{ij}^{{\text{e}}}\) :

The strain component of the Hooke element in 3D

\(\varepsilon_{ij}^{{{\text{ve}}}}\) :

The strain component of the modified Kelvin element in 3D

\(\varepsilon_{ij}^{{{\text{vp}}}}\) :

The strain component of the nonlinear viscoplastic element in 3D

\(E^{{\text{H}}}\) :

Elasticity parameter of the Hooke element

\(E^{{\text{K}}}\) :

Elasticity parameter of the modified Kelvin element

\(\eta^{{{\text{ve}}}}\) :

Viscosity coefficient of the modified Kelvin element

\(\eta^{{{\text{vp}}}}\) :

Viscosity coefficient of the nonlinear viscoplastic element

\(F\) :

Yield function

\(\tilde{\varphi }\) :

The effective friction angle of the rock

\(g\) :

Plastic potential function

\(G^{{\text{K}}}\) :

The shear modulus of the modified Kelvin element

\(G^{{\text{H}}}\) :

The shear modulus of the Hooke element

\(\gamma\) :

The bulk density of the rock

\(H\) :

The burial depth of the rock

\(H^{ * }\) :

Step function

\(K^{{\text{H}}}\) :

The bulk modulus of the Hooke element

\(m\) :

Material constant

\(\lambda\) :

Material parameter controlled by the stress level

\(\varpi\) :

Material constant

\(\kappa\) :

Lateral pressure coefficient

\(\varsigma\) :

Stress concentration coefficient

\(P_{{\text{w}}}\) :

Pore pressure

\(\tilde{S}_{ij}\) :

The effective deviatoric stress tensor

\(t\) :

Creep time

\(\sigma_{ij}\) :

Total stress tensor

\(\tilde{\sigma }_{ij}\) :

The effective stress tensor

\(\tilde{\sigma }_{{\text{m}}}\) :

The effective spherical stress tensor

\(\tilde{\sigma }_{t}\) :

The effective tensile strength of the rock

\(\tilde{\sigma }_{ij}^{{\text{e}}}\) :

The effective stress tensor of the Hooke component

\(\tilde{\sigma }_{ij}^{{{\text{ve}}}}\) :

The effective stress tensor of the modified Kelvin component

\(\tilde{\sigma }_{ij}^{{{\text{vp}}}}\) :

The effective stress tensor of the nonlinear viscoplastic component

\(\sigma_{{\text{s}}}\) :

The creep yield strength subjected to a certain stress state

\(\sigma_{{\text{s}}}^{{\text{P}}}\) :

The creep yield strength subjected to the coupling between a certain stress and pore pressure

\(\delta_{ij}\) :

Kronecker delta function

References

  • Aydan Ö, Tokashiki N, Genis M (2012) Some considerations on yield (failure) criteria in rock mechanics ARMA 12–640. In: Proceedings of the 46th US rock mechanics/geomechanics symposium, Chicago, vol 640, p 10

  • Bian K, Liu J, Zhang W, Zheng XQ, Ni SH, Liu ZP (2019) Mechanical behavior and damage constitutive model of rock subjected to water-weakening effect and uniaxial loading. Rock Mech Rock Eng 52(1):97–106

    Article  Google Scholar 

  • Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–164

    Article  Google Scholar 

  • Brantut N, Heap MJ, Meredith PG, Baud P (2013) Time-dependent cracking and brittle creep in crustal rocks: a review. J Struct Geol 52(5):17–43

    Article  Google Scholar 

  • Cai M, Kaiser PK, Tasaka Y, Maejima T, Morioka H, Minami M (2004) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41:833–847

    Article  Google Scholar 

  • Cerasi P, Lund E, Kleiven ML, Stroisz A, Pradhan S, Kjøller C, Frykman P, Fjær E (2017) Shale creep as leakage healing mechanism in CO2 sequestration. Energy Procedia 114(7):3096–3112

    Article  Google Scholar 

  • Chen J, Jiang Q, Hu YR, Qin WM, Li SJ, Xiong J (2020) Time-dependent performance of damaged marble and corresponding fractional order creep constitutive model. Arab J Geosci 13:1150

    Article  Google Scholar 

  • Chen F (2012) rheological strength aging model of hard brittle fracture rock in high dam zone and engineering application. Dissertation, Shandong University

  • Debernardi D, Barla G (2009) New viscoplastic model for design analysis of tunnels in squeezing conditions. Rock Mech Rock Eng 42(2):259–288

    Article  Google Scholar 

  • Fahimifar A, Karami M, Fahimifar A (2015) Modifications to an elasto-visco-plastic constitutive model for prediction of creep deformation of rock samples. Soils Found 55(6):1364–1371

    Article  Google Scholar 

  • Fan QZ, Li SC, Gao YF (2007) Experimental study on creep properties of soft rock under triaxial compression. Chin J Rock Mech Eng 26(7):1381–1385

    Google Scholar 

  • Feng GL, Feng XT, Chen BR, Xiao YX, Yu Y (2015) A microseismic method for dynamic warning of rockburst development processes in tunnels. Rock Mech Rock Eng 48:2061–2076

    Article  Google Scholar 

  • Feng XT, Yao ZB, Li SJ, Wu SY, Yang CX, Guo HS, Zhong S (2018) In situ observation of hard surrounding rock displacement at 2400-m-deep tunnels. Rock Mech Rock Eng 51(3):873–892

    Article  Google Scholar 

  • Fujii Y, Kiyama T, Ishijima Y, Kodama J (1999) Circumferential strain behavior during creep tests of brittle rocks. Int J Rock Mech Min Sci 36(3):323–337

    Article  Google Scholar 

  • Ge XR, Hou MX (2012) Principle of in-situ 3D rock stress measurement with borehole wall stress relief method and its preliminary applications to determination of in-situ rock stress orientation and magnitude in Jinping hydropower station. Sci China Technol Sci 55(4):939–949

    Article  Google Scholar 

  • Grgic D (2016) Constitutive modelling of the elastic–plastic, viscoplastic and damage behaviour of hard porous rocks within the unified theory of inelastic flow. Acta Geotech 11:95–126

    Article  Google Scholar 

  • Heap MJ, Baud P, Meredith PG, Bell AF, Main IG (2009) Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res 114:B07203

    Google Scholar 

  • Heap MJ, Baud P, Meredith PG, Vinciguerra S, Bell AF, Main IG (2011) Brittle creep in basalt and its application to time-dependent volcano deformation. Earth Planet Sci Lett 307(1):71–82

    Article  Google Scholar 

  • Herrmann J, Rybacki E, Sone H, Dresen G (2019) Deformation experiments on Bowland and Posidonia Shale-part II: creep behavior at in situ pc–T conditions. Rock Mech Rock Eng 52(2):755–779

    Article  Google Scholar 

  • Hou RB, Zhang K, Tao J, Xue XR, Chen YL (2019) A nonlinear creep damage coupled model for rock considering the effect of initial damage. Rock Mech Rock Eng 52:1275–1285

    Article  Google Scholar 

  • Hu B, Yang SQ, Xu P (2018) A nonlinear rheological damage model of hard rock. J Cent South Univ 25(7):1665–1677

    Article  Google Scholar 

  • Huang SL, Feng XT, Zhou H, Zhang CQ (2010) Study of aging failure mechanics and triaxial compression creep experiments with water pressure coupled stress of brittle rock. Rock Soil Mech 31(11):3441–3451

    Google Scholar 

  • ISRM (1983) Suggested methods for determining the strength of rock materials in triaxial compression: revised version. Int J Rock Mech Min Sci Geomech Abstr 20(6):285–290

    Article  Google Scholar 

  • Jia SP, Zhang LW, Wu BS, Yu HD, Shu JX (2018) A coupled hydro-mechanical creep damage model for clayey rock and its application to nuclear waste repository. Tunn Undergr Space Technol 74:230–246

    Article  Google Scholar 

  • Jiang HF, Liu DY, Huang W, Xia YC, Liu FY (2014a) Creep properties of rock under high confining pressure and different pore water pressures and a modified Nishihara model. Chin J Geotech Eng 36(3):443–451

    Google Scholar 

  • Jiang HF, Liu DY, Huang W, Liu FY (2014b) Influence of high pore water pressure on creep properties of rock under high confining pressure. J Chin Coal Soc 39(7):1248–1256

    Google Scholar 

  • Jiang Q, Zhong S, Pan PZ, Shi YE, Guo HG, Kou YY (2020) Observe the temporal evolution of deep tunnel’s 3D deformation by 3D laser scanning in the Jinchuan No. 2 Mine. Tunn Undergr Space Technol 97(1):03237

    Google Scholar 

  • Keneti A, Sainsbury BA (2018) Characterization of strain-burst rock fragments under a scanning electron microscope—an illustrative study. Eng Geol 246:12–18

    Article  Google Scholar 

  • Komurlu E (2018) Loading rate conditions and specimen size effect on strength and deformability of rock materials under uniaxial compression. Int J Geo Eng 9:17

    Article  Google Scholar 

  • Kranz RL (1983) Microcracks in rocks: a review. Tectonophysics 100(1):449–480

    Article  Google Scholar 

  • Li LQ, Xu WY, Wang W, Guo YQ, Zhao HB (2010) Estimation of long-term strength for Xiangjiaba sandstone based on creep tests. Eng Mech 27(11):127–143

    Article  Google Scholar 

  • Li SJ, Feng XT, Li ZH, Chen BR, Zhang CQ, Zhou H (2012) In situ monitoring of rockburst nucleation and evolution in the deeply buried tunnels of Jinping II hydropower station. Eng Geol 137–138(7):85–96

    Article  Google Scholar 

  • Li HB, Liu MC, Xing WB, Shao S, Zhou JW (2017) Failure mechanisms and evolution assessment of the excavation damaged zones in a large-scale and deeply buried underground powerhouse. Rock Mech Rock Eng 50(7):1883–1900

    Article  Google Scholar 

  • Li SJ, Xie ZK, Xiao YX, Feng GL, Pan PZ, Wang ZF (2021) Review of international research on rock in situ rockmass behavior in deep underground research laboratory. J Cent South Univ (sci Technol) 52(8):2491–2509

    Google Scholar 

  • Liu DY, Jiang HF, Li DS, Zhao BY (2014) Creep properties of rock under high confining pressure and high water pore pressure. J Cent South Univ (sci Technol) 45(6):1916–1923

    Google Scholar 

  • Liu HZ, Xie HQ, He JD, Xiao ML, Zhuo L (2017) Nonlinear creep damage constitutive model for soft rocks. Mech Time Depend Mater 21(1):73–96

    Article  Google Scholar 

  • Liu X, Li D, Han C (2020) A nonlinear damage creep model for sandstone based on fractional theory. Arab J Geosci 13(6):246

    Article  Google Scholar 

  • Malan DF (2002) Manuel rocha medal recipient simulating the time-dependent behaviour of excavations in hard rock. Rock Mech Rock Eng 35(4):225–254

    Article  Google Scholar 

  • Malan DF, Vogler UW, Drescher K (1997) Time-dependent behaviour of hard rock in deep level gold mines. J South Afr Inst Min Metall 97(3):135–147

    Google Scholar 

  • Mansouri H, Ajalloeian R (2018) Mechanical behavior of salt rock under uniaxial compression and creep tests. Int J Rock Mech Min Sci 110:19–27

    Article  Google Scholar 

  • Martino JB, Chandler NA (2004) Excavation-induced damage studies at the underground research laboratory. Int J Rock Mech Min Sci 41(8):1413–1426

    Article  Google Scholar 

  • Meng Q, Zhang M, Han L, Pu H, Li H (2016) Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression. Arab J Geosci 9(8):527

    Article  Google Scholar 

  • Ömer A, Ito T, Özbay U, Kwasniewski M, Shariar K, Okuno T, Özgenoğlu A, Malan DF, Okada T (2014) ISRM suggested methods for determining the creep characteristics of rock. Rock Mech Rock Eng 47(1):275–290

    Article  Google Scholar 

  • Ortlepp WD (1997) Rock fracture and rockbursts: an illustrative study (vol 9). South Afr Inst Min Metall, 126 monograph series M9

  • Pan Y, Wang ZQ, Wu M (2006) Plastic analysis of surrounding rock of tunnel based on strain nonlinear hardening and nonlinear softening. Rock Soil Mech 27(7):1038–1042

    Google Scholar 

  • Paraskevopoulou C, Perras M, Diederichs M, Loew S, Lam T, Jensen M (2018) Time-dependent behaviour of brittle rocks based on static load laboratory tests. Geotech Geol Eng 36(1):337–376

    Article  Google Scholar 

  • Perzyna P (1966) Fundamental problems in viscoplasticity. Adv Appl Mech 9(2):244–368

    Google Scholar 

  • Pu SY, Zhu ZD, Song L, Song WL, Peng YY (2020) Fractional-order visco-elastoplastic constitutive model for rock under cyclic loading. Arab J Geosci 13(9):326

    Article  Google Scholar 

  • Sainoki A, Tabata S, Mitri HS, Fukuda D, Kodama J (2017) Time-dependent tunnel deformations in homogeneous and heterogeneous weak rock formations. Comput Geotech 92:186–200

    Article  Google Scholar 

  • Scheidegger AE (1970) Stochastic models in hydrology. Water Resour Res 6(3):750–755

    Article  Google Scholar 

  • Shao JF, Zhu QZ, Su K (2003) Modeling of creep in rock materials in terms of material degradation. Comput Geotech 30:549–555

    Article  Google Scholar 

  • Shao JF, Chau KT, Feng XT (2006) Modeling of anisotropic damage and creep deformation in brittle rocks. Int J Rock Mech Min Sci 43(4):582–592

    Article  Google Scholar 

  • Sone H, Zoback MD (2014) Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress. Int J Rock Mech Min Sci 69(3):120–132

    Article  Google Scholar 

  • Sun J (2007) Rock rheological mechanics and its advance in engineering applications. Chin J Rock Mech Eng 26(6):1081–1106

    Google Scholar 

  • Tan TK, Kang WF (1980) Locked in stresses, creep and dilatancy of rocks, and constitutive equations. Rock Mech 13(1):5–22

    Article  Google Scholar 

  • The Professional Standards Compilation Group of People’s Republic of China (2020) Chinese industry standard SL/T 264–2020: code for rock tests in water and hydropower projects. Ministry of Water Resources of the PRC, Beijing

  • Vakili A (2016) An improved unified constitutive model for rock material and guidelines for its application in numerical modelling. Comput Geotech 80:261–282

    Article  Google Scholar 

  • Wan Y, Chen GQ, Sun X, Zhang GZ (2021) Triaxial creep characteristics of red sandstone subjected to freeze-thaw cycles under different water content and its damage model. Chin J Geotech Eng 43(8):1463–1472

    Google Scholar 

  • Wang JX, Hu LS, Ye C, Tang YQ, Yang P (2010) Triaxial permeability test of marble under complex stress path. Rock Soil Mech 31(8):2389–2398

    Google Scholar 

  • Wang W, Tian ZY, Zhu QZ, Li XH, Xu WY (2015) Study of statistical damage constitutive model for rock considering pore water pressure. Chin J Rock Mech Eng 34(S2):3676–3682

    Google Scholar 

  • Wang R, Zhuo Z, Zhou HW, Liu JF (2017) A fractal derivative constitutive model for three stages in granite creep. Results Phys 7:2632–2638

    Article  Google Scholar 

  • Wang L. (2017) Research on time-dependent mechanical behavior and creep model of marble from Jinping I underground powerhouse. Dissertation, Sichuan University

  • Wasantha PLP, Darlington WJ, Ranjith PG (2013) Characterization of mechanical behaviour of saturated sandstone using a newly developed triaxial apparatus. Exp Mech 53:871–882

    Article  Google Scholar 

  • Wu F, Liu JF, Wang J (2015) An improved Maxwell creep model for rock based on variable-order fractional derivatives. Environ Earth Sci 73(11):6965–6971

    Article  Google Scholar 

  • Xie HP, Chen ZD (1989) Analysis of rock fracture micro-mechanism. J China Coal Soc 2:57–67

    Google Scholar 

  • Xie YG, Jiang HF, Li J, Xue KX (2016) Nonlinear creep model for deep rock under high stress and high pore water pressure condition. J Eng Sci Technol Rev 9(2):39–46

    Article  Google Scholar 

  • Xu DJ (1980) The rheological behaviour of the weak rock mass and the method of determining long-term strength. Rock Soil Mech 1:37–50

    Google Scholar 

  • Xu T, Tang CA, Zhao J, Li LC, Heap MJ (2012) Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys J Int 189(3):1781–1796

    Article  Google Scholar 

  • Yan BQ, Guo QF, Ren FH, Cai MF (2020) Modified Nishihara model and experimental verification of deep rock mass under the water-rock interaction. Int J Rock Mech Min Sci 128:104250

    Article  Google Scholar 

  • Zha ES, Zhang ZT, Zhang R, Wu SY, Li CB, Ren L, Gao MZ, Zhou JF (2021) Long-term mechanical and acoustic emission characteristics of creep in deeply buried jinping marble considering excavation disturbance. Int J Rock Mech Min Sci 139:104603

    Article  Google Scholar 

  • Zhang CQ, Zhou H, Feng XT (2011) An index for estimating the stability of brittle surrounding rock mass: FAI and its engineering application. Rock Mech Rock Eng 44(4):401–414

    Article  Google Scholar 

  • Zhang ZP, Xie HP, Zhang Ru, Zhang ZT, Gao MZ, Jia ZQ, Xie J (2019) Deformation damage and energy evolution characteristics of coal at different depths. Rock Mech Rock Eng 52(5):1491–1503

    Article  Google Scholar 

  • Zhang ZT, Xie HP, Zhang R, Gao MZ, Ai T, Zha ES (2020) Size and spatial fractal distributions of coal fracture networks under different mining-induced stress conditions. Int J Rock Mech Min Sci 132:104364

    Article  Google Scholar 

  • Zhao NY, Jiang HF (2021) Mathematical methods to unloading creep constitutive model of rock mass under high stress and hydraulic pressure. Alex Eng J 60:25–38

    Article  Google Scholar 

  • Zhao YL, Wang YX, Wang WJ, Wan W, Tang JZ (2017) Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int J Rock Mech Min Sci 93:66–75

    Article  Google Scholar 

  • Zhao J, Feng XT, Zhang XW, Yang CX, Zhou YY (2018) Time-dependent behaviour and modeling of Jinping marble under true triaxial compression. Int J Rock Mech Min Sci 110:218–230

    Article  Google Scholar 

  • Zhao J, Feng XT, Zhang XW, Yang CX (2019) Brittle and ductile creep behavior of Jinping marble under true triaxial stress. Eng Geol 258:105157

    Article  Google Scholar 

  • Zheng MZ, Li SJ, Zhao HB, Huang X, Qiu SL (2021) Probabilistic analysis of tunnel displacements based on correlative recognition of rock mass parameters. Geosci Front 12(4):101136

    Article  Google Scholar 

  • Zhou H, Jia Y, Shao JF (2008) A unified elastic–plastic and viscoplastic damage model for quasi-brittle rocks. Int J Rock Mech Min Sci 45(8):1237–1251

    Article  Google Scholar 

  • Zhou HW, Wang CP, Mishnaevsky L, Duan ZQ, Ding JY (2013) A fractional derivative approach to full creep regions in salt rock. Mech Time Depend Mater 17:413–425

    Article  Google Scholar 

  • 7D Soft High Technology Inc (2009) Auto2Fit User Manual. 7D Soft High Technology Inc, Beijing

    Google Scholar 

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Acknowledgements

The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (Grant nos. 51879261, U1765206, and 52125903) and the innovation group project of the Natural Science Foundation of Hubei Province (ZRQT2020000114).

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Xiang Huang, Shaojun Li, Dingping Xu & Pengzhi Pan

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiang Huang

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  1. Xiang Huang
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  4. Pengzhi Pan
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Correspondence to Shaojun Li or Dingping Xu.

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Huang, X., Li, S., Xu, D. et al. Time-Dependent Behavior of Jinping Deep Marble Taking into Account the Coupling Between Excavation Damage and High Pore Pressure. Rock Mech Rock Eng 55, 4893–4912 (2022). https://doi.org/10.1007/s00603-022-02912-w

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