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Physico-mechanical Behaviors of Granite Under Coupled Static and Dynamic Cyclic Loadings

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Abstract

The stress distribution around constructions in deep rock can be modified by dynamic disturbances, such as earthquakes. For this, we proposed a new loading method applied to granite sample under coupled static and dynamic cyclic loading (CSDCL) condition. The variations in P-wave velocity, gas permeability, and mechanical properties of granite before and after CSDCL are revealed. It shows that with increasing axial static stress, the dynamic cyclic loading amplitude and cycle number, P-wave velocity, uniaxial compressive strength (UCS) and elastic modulus decrease, whilst the permeability and Poisson’s ratio increase. It seems that variations in those parameters have a close relation with the exciting frequency. In this case, CSDCL is applied for crack development along the axial direction in the rock samples, and subsequently results in degradation of mechanical properties, delay of P-wave propagation, and increase of the transport paths. The results show that the permeability and Poisson’s ratio are likely to be more sensitive to the CSDCL, in particular under the axial static stress. The empirical relationships of the P-wave velocity with permeability, UCS, and elastic modulus are established for a pragmatic monitoring purpose. From design point of view, we have established the relationships of the disturbance factors to damage variable. Then the correlations of the damage variable to permeability, UCS, and elastic modulus are analyzed. The testing results in this context could facilitate our understanding of rock stability upon excavation subjected to dynamic disturbances.

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Abbreviations

CSDCL:

Coupled static and dynamic cyclic loading

UCS:

Uniaxial compressive strength

URS:

Uniaxial residual strength

ASS:

Axial static stress

FA:

Force amplitude

CN:

Cycle number

K :

Gas permeability of the samples

\(V_{1}\), \(V_{2}\) :

Volumes of upstream and downstream pressure vessel

\(\mu\) :

Viscosity factor of gas

\(\beta\) :

Compression factor of gas

\(L\) :

Length of the samples

\(A\) :

Cross-sectional area of the samples

\(\Delta t_{i}\) :

Time of the data point calculated from saturation

\(\Delta P_{i}\) :

Differential pressure at any time

\(\Delta P_{0}\) :

Initial pressure difference

\(E_{i}\) :

Extremum of the i force amplitude level

Max:

Function that finds the maximum value

\(P_{ij}\) :

P-wave velocity of j cycle number under i force amplitude level

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

Initial P-wave velocity

\(V_{i}\) :

Variance of i force amplitude level

\(\overline{{P_{i \cdot } }}\) :

Average of P-wave velocity at the i force amplitude level

\(D\) :

Damage variable

\(V_{d}\) :

P-wave velocity of the samples subjected to CSDCL

\(V_{0}\) :

P-wave velocity of the intact samples

References

  • Akesson U, Hansson J, Stigh J (2004) Characterisation of microcracks in the Bohus granite, western Sweden, caused by uniaxial cyclic loading. Eng Geol 72(12):131–142

    Google Scholar 

  • Alam AK, Niioka M, Fujii Y, Fukuda D, Kodama J (2014) Effects of confining pressure on the permeability of three rock types under compression. Int J Rock Mech Min Sci 65:49–61

    Google Scholar 

  • Amann F, Button ED, Evans KF, Gischig VS, Blümel M (2011) Experimental study of the brittle behavior of clay shale in rapid unconfined compression. Rock Mech Rock Eng 44(4):415–430

    Google Scholar 

  • Andy N, Hannu S, Brad F, David M, Conrad C, James C, Alex R (2017) Fault permeability and CO2 storage. Energy Proc 114:3229–3236

    Google Scholar 

  • Antonaci P, Bocca P, Masera D (2012) Fatigue crack propagation monitoring by acoustic emission signal analysis. Eng Fract Mech 81:26–32

    Google Scholar 

  • Baker GS, Steeples DW, Schmeissner CM (1999) In-situ, high-frequency P-wave velocity measurements within 1 m of the Earth’s surface. Geophysics 64(2):323–325

    Google Scholar 

  • Bagde M, Petroš V (2005) Fatigue properties of initial sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min Sci 42(2):237–250

    Google Scholar 

  • Bagde MN, Petros V (2009) Fatigue and dynamic energy behaviour of rock subjected to cyclical loading. Int J Rock Mech Min Sci 46(1):200–209

    Google Scholar 

  • Baud P, Zhu W, Wong TF (2000) In the brittle faulting regime, damage mechanics models predict that the uniaxial compressive strength scales with presence of water the confined brittle strength the pore will be denoted by Pt. J Geophys Res 105:371–389

    Google Scholar 

  • Bieniawski ZT, Bernede MJ (1979a) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials 1: suggested method for determination of the uniaxial compressive strength of rock materials. Int J Rock Mech Min Sci 16:137–138

    Google Scholar 

  • Bieniawski ZT, Bernede MJ (1979b) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials 2: suggested method for determination deformability of rock materials in uniaxial compression. Int J Rock Mech Min Sci 16:138–140

    Google Scholar 

  • Brace WF (2012) Permeability of crystalline rocks: new in situ measurements. J Geophys Res-Solid Earth 89(B6):4327–4330

    Google Scholar 

  • Cerfontaine B, Collin F (2018) Cyclic and fatigue behaviour of rock materials: review, interpretation and research perspectives. Rock Mech Rock Eng 51:391–414

    Google Scholar 

  • Chang SH, Lee CI (2004) Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission. Int J Rock Mech Min Sci 41(7):1069–1086

    Google Scholar 

  • Chen R, Xia KW, Dai F, Lu F, Luo SN (2009) Determination of dynamic fracture parameters using a semi-circular bend technique in split Hopkinson pressure bar testing. Eng Fract Mech 76(9):1268–1276

    Google Scholar 

  • Dai F, Huang S, Xia KW, Tan LZ (2010) Some fundamental issues in dynamic compression and tension tests of rocks using split Hopkinson pressure bar. Rock Mech Rock Eng 43(6):657–666

    Google Scholar 

  • Dai F, Xia K, Zuo JP, Zhang R, Xu NW (2013) Static and dynamic flexural strength anisotropy of Barre granite. Rock Mech Rock Eng 46:1589–1602

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B (1999) Quantifying progressive prepeak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 36(3):361brit

    Google Scholar 

  • Erarslan N (2016) Microstructural investigation of subcritical crack propagation and fracture process zone (FPZ) by the reduction of rock fracture toughness under cyclic loading. Eng Geol 208:181–190

    Google Scholar 

  • Erarslan N, Alehossein H, Williams DJ (2014) Tensile fracture strength of Brisbane tuff by static and cyclic loading tests. Rock Mech Rock Eng 47(4):1135–1151

    Google Scholar 

  • Erarslan N, Williams D (2012) Mechanism of rock fatigue damage in terms of fracturing modes. Int J Fatigue 43:76–89

    Google Scholar 

  • Frederic LP, Geraldine F (2007) Damage evaluation with P-wave velocity measurements during uniaxial compression tests on argillaceous rocks. Int J Geomech 7(6):431–436

    Google Scholar 

  • Fuenkajorn K, Phueakphum D (2010) Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng Geol 112(14):43–52

    Google Scholar 

  • Géraud Y (1994) Variations of connected porosity and inferred permeability in a thermally cracked granite. Geophys Res Lett 21(11):979–982

    Google Scholar 

  • Gholami R, Rasouli V (2014) Mechanical and elastic properties of transversely isotropic slate. Int J Rock Mech Eng 47(5):1763–1773

    Google Scholar 

  • Gong M, Smith I (2003) Effect of waveform and loading sequence on low-cycle compressive fatigue life of spruce. J Mater Civ Eng 15(February):93–99

    Google Scholar 

  • Gong SH, Sheng GM (2004) Effects of toughness of steel on seismic performance of building structures. Earthq Resist Eng 2004(03):41–47 (in Chinese)

    Google Scholar 

  • Gong FQ, Li XB, Liu XL (2011) Preliminary experimental study of characteristics of rock subjected to 3D coupled static and dynamic loads. Chin J Rock Mech Eng 30(6):1178–1190 (in Chinese)

    Google Scholar 

  • Guo Y, Yang C, Mao H (2012) Mechanical properties of Jintan mine rock salt under complex stress paths. Int J Rock Mech Min Sci 56:54–61

    Google Scholar 

  • Haimson BC, Kim CM (1971) Mechanical behaviour of rock under cyclic fatigue. In: Cording EJ (ed) Stability of rock slopes. Proceedings of the 13th symposium on rock mechanics. ASCE, New York, pp 845–863.

  • Hidalgo KP, Nordlund E (2013) Comparison between stress and strain quantities of the failure-deformation process of fennoscandian hard rocks using geological information. Rock Mech Rock Eng 46(1):41–51

    Google Scholar 

  • Heap M, Faulkner D, Meredith P, Vinciguerra S (2010) Elastic modulus evolution and accompanying stress changes with increasing crack damage: implications for stress changes around fault zones and volcanoes during deformation. Geophys J Int 183(1):225–236

    Google Scholar 

  • Hu DW, Zhou H, Zhang F, Shao JF (2010) Evolution of poroelastic properties and permeability in damaged sandstone. Int J Rock Mech Min Sci 47(6):962–973

    Google Scholar 

  • Hoek E (1964) Fracture of anisotropic rock. J S Afr I Min Metall 64(10):501–523

    Google Scholar 

  • Huang S, Xia KW, Dai F (2012) Establishment of a dynamic Mohr-Coulomb failure criterion for rocks. Int J Nonlinear Sci Numer Simul 13:55–60

    Google Scholar 

  • Kendrick J, Smith R, Sammonds P, Meredith P, Dainty M, Pallister J (2013) The influence of thermal and cyclic stressing on the strength of rocks from Mount St. Helens, Washington. Bull Volcanol 75(7):728

    Google Scholar 

  • Khandelwal M (2013) Correlating P-wave velocity with the physico-mechanical properties of different rocks. Pure Appl Geophys 170(4):507–514

    Google Scholar 

  • Kwon S, Cho WJ (2008) The influence of an excavation damaged zone on the thermal-mechanical and hydro-mechanical behaviors of an underground excavation. Eng Geol 101:110–123

    Google Scholar 

  • Le J, Manning J, Labuz J (2014) Scaling of fatigue crack growth in rock. Int J Rock Mech Min Sci 72:71–79

    Google Scholar 

  • Li N, Chen W, Zhang P, Swoboda G (2001) The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading. Int J Rock Mech Min Sci 38(7):1071–1079

    Google Scholar 

  • Li XB, Lok TS, Zhao J, Zhao PJ (2000) Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic stress-strain curves for rocks. Int J Rock Mech Min Sci 37(7):1055–1060

    Google Scholar 

  • Li XB, Gong FQ, Zhao J, Gao K, Yin TB (2010) Test study of impact failure of rock subjected to one dimensional coupled static and dynamic loads. Chin J Rock Mech Eng 29(2):251–260 (in Chinese)

    Google Scholar 

  • Li XB, Zhou ZL, Lok T, Hong L, Yin T (2008) Innovative testing technique of rock subjected to coupled static and dynamic loads. Int J Rock Mech Min Sci 45(5):739–748

    Google Scholar 

  • Li X, Gong F, Tao M, Dong L, Du K, Ma C, Yin T (2017) Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: a review. J Rock Mech Geot Eng 9(4):767–782

    Google Scholar 

  • Liu E, He S (2012) Effects of cyclic dynamic loading on the mechanical properties of initial rock samples under confining pressure conditions. Eng Geol 125:81–91

    Google Scholar 

  • Liu JR, Li BY, Tian W, Wu XG (2018) Investigating and predicting permeability variation in thermally cracked dry rocks. Int J Rock Mech Min Sci 103:77–88

    Google Scholar 

  • Liu ZB, Shao JF, Hu D, Xie SY (2016) Gas permeability evolution with deformation and cracking process in a white marble under compression. Transport Porous Med 111(2):441–455

    Google Scholar 

  • Ma L, Liu X, Wang M, Xu H, Hua R, Fan P, Jiang S, Wang G, Yi Q (2013) Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 62:34–41

    Google Scholar 

  • Martin CD (1993) The strength of massive Lac du Bonnet granite around underground openings[D]. University of Manitoba, Manitoba

    Google Scholar 

  • Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min 31(6):643–659

    Google Scholar 

  • Meng Q, Zhang M, Han L, Pu H, Nie T (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

    Google Scholar 

  • Min KB, Rutqvist J, Tsang CF, Jing L (2005) Thermally induced mechanical and permeability changes around a nuclear waste repository—a far-field study based on equivalent properties determined by a discrete approach. Int J Rock Mech Min Sci 42:765–780

    Google Scholar 

  • Mu WQ, Li LC, Yang TH, Yu GF, Han YC (2019) Numerical investigation on a grouting mechanism with slurry-rock coupling and shear displacement in a single rough fracture. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-019-01535-w

    Article  Google Scholar 

  • Ohya S (1986). In-situ P and S wave velocity measurement. In: Proceedings of specialty conference on use of in-situ tests in geotechnical engineering, geotechnical special publication no. 6, American Society of Civil Engineers

  • Pardoen B, Talandier J, Collin F (2016) Permeability evolution and water transfer in the excavation damaged zone of a ventilated gallery. Int J Rock Mech Min Sci 85:192–208

    Google Scholar 

  • Ray SK, Sarkar M, Singh TN (1999) Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone. Int J Rock Mech Min Sci 36(4):543–549

    Google Scholar 

  • Ren X, Chen J, Li J, Slawson TR, Roth MJ (2011) Microcracks informed damage models for brittle solids. Int J Solids Struct 48:1560–1571

    Google Scholar 

  • Ramamurthy T (1993a) Strength and modulus responses of anisotropic rocks. Compressive Rock Eng 1:313–329

    Google Scholar 

  • Ramamurthy T (1993b) Strength, modulus responses of anisotropic rocks. In: Hudson JA (ed) Compressive rock engineering, vol 1. Pergamon, Oxford, pp 313–329

    Google Scholar 

  • Sun JP, Zhao ZY (2010) Effects of anisotropic permeability of fractured rock masses on underground oil storage caverns. Tunn Undergr Sp Tech 25:629–637

    Google Scholar 

  • Sun H, Sun Q, Deng WN, Zhang WQ, Lu C (2017) Temperature effect on microstructure and P-wave propagation in Linyi sandstone. Appl Therm Eng 115:913–922

    Google Scholar 

  • Tan X, Konietzky H, Fruhwirt T (2014) Laboratory observation and numerical simulation of permeability evolution during progressive failure of brittle rocks. Int J Rock Mech Min Sci 68:167–176

    Google Scholar 

  • Trippetta F, Collettini C, Meredith P, Vinciguerra S (2013) Evolution of the elastic modulus of seismogenic triassic evaporites subjected to cyclic stressing. Tectonophysics 592:67–79

    Google Scholar 

  • Viete DR, Ranjith PG (2006) The effect of CO2 on the geomechanical and permeability behaviour of brown coal: implications for coal seam CO2 sequestration. Int J Coal Geol 66:204–216

    Google Scholar 

  • Villaescusa E, Thompson A, Windsor C (2019) Probabilistic estimate of rock mass static and dynamic demands for underground excavation stabilisation. J Rock Mech Geotech Eng 11(3):481–493

    Google Scholar 

  • Vinegar HJ, Waxman MH (1988) In-situ induced polarization method for determining formation permeability. United States Patent 47438541988-05-10

  • Vinciguerra S, Trovato C, Meredith PG, Benson PM (2005) Relating seismic velocities, thermal cracking and permeability in Mt. Etna and Iceland basalts. Int J Rock Mech Min Sci 42:900–910

    Google Scholar 

  • Wang Y, Ma L, Fan P, Chen Y (2016) A fatigue damage model for rock salt considering the effects of loading frequency and amplitude. Int J Min Sci Tech 26(5):955–958

    Google Scholar 

  • Wang Z, Li S, Qiao L, Zhang Q (2015) Finite element analysis of the hydro-mechanical behavior of an underground crude oil storage facility in granite subject to cyclic loading during operation. Int J Rock Mech Min Sci 73:70–81

    Google Scholar 

  • Wang Z, Li S, Qiao L, Zhao J (2013) Fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. Rock Mech Rock Eng 46(6):1603–1615

    Google Scholar 

  • Xia KW, Nasseri MHB, Mohanty B, Lu F, Chen R, Luo SN (2008) Effects of microstructures on dynamic compression of Barre granite. Int J Rock Mech Min Sci 45:879–887

    Google Scholar 

  • Xia KW, Huang S, Dai F (2013) Evaluation of the frictional effect in dynamic notched semi-circular bend tests. J Rock Mech Min Sci 62:148–151

    Google Scholar 

  • Xia KW, Yao W (2015) Dynamic rock tests using split Hopkinson (Kolsky) bar system—a review. J Rock Mech Geotech Eng 7:27–59

    Google Scholar 

  • Xiao JQ, Ding DX, Jinag FL, Xu G (2010a) Fatigue damage variable and evolution of rock subjected to cyclic loading. Int J Rock Mech Min Sci 47:461–468

    Google Scholar 

  • Xiao J, Ding D, Xu G, Jiang F (2009) Inverted S-shaped model for nonlinear fatigue damage of rock. Int J Rock Mech Min Sci 46(3):643–648

    Google Scholar 

  • Xiao J, Feng X, Ding D, Jiang F (2010b) Investigation and modeling on fatigue damage evolution of rock as a function of logarithmic cycle. Int J Numer Anal Meth Geomech 35:1127–1140

    Google Scholar 

  • Xue L, Qin SQ, Sun Q, Wang YY, Lee LM, Li WC (2014) A study on crack damage stress thresholds of different rock types based on uniaxial compression tests. Rock Mech Rock Eng 47:1183–1195

    Google Scholar 

  • Yan CB (2007) Blasting cumulative damage effects of underground engineering rock mass based on sonic wave measurement. J Cent South Univ Technol 14(2):230–235

    Google Scholar 

  • Yang SQ, Ranjith P, Huang YH, Yin PF, Jing HW, Gui YL, Yu QL (2015) Sandstone under triaxial cyclic loading. Geophys J Int 201:662–682

    Google Scholar 

  • Yang SQ, Tian W, Ranjith P (2017) Experimental investigation on deformation failure characteristics of crystalline marble under triaxial cyclic loading. Rock Mech Rock Eng 50(11):2871–2889

    Google Scholar 

  • Zhang WH, Qiu ZH, Yu GS (2004) Analysis of brittle dynamic damage in dam and rock foundation due to earthquake. Chin J Rock Mech Eng 23(8):1311–1317 (in Chinese)

    Google Scholar 

  • Zhao BY, Ma ZY, Liang B, Jin CY (2009) Seismic analysis of underground structures based on damaged plasticity model. Rock Soil Mech 30(5):1515–1521 (in Chinese)

    Google Scholar 

  • Zhou ZL, Li XB, Zou Y, Jiang YH, Li GN (2014) Dynamic Brazilian tests of granite under coupled static and dynamic loads. Rock Mech Rock Eng 47:495–505

    Google Scholar 

  • Zhu JB, Liao ZY, Tang CA (2016) Numerical SHPB tests of rocks under combined static and dynamic loading conditions with application to dynamic behavior of rocks under in situ stresses. Rock Mech Rock Eng 49:3935–3946

    Google Scholar 

  • Zhu WC, Bai Y, Li XB (2012) Numerical simulation on rock failure under combined static and dynamic loading during SHPB tests. Int J Impact Eng 49(2):142–157

    Google Scholar 

  • Zhu W, Tang C (2006) Numerical simulation of Brazilian disk rockfailure under static and dynamic loading. Int J Rock Mech Min Sci 43(2):236–252

    Google Scholar 

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Acknowledgements

The authors are grateful for the constructive comments and suggestions provided by anonymous reviewers and Professor Kaiwen Xia in Toronto University, Canada. This work was supported by The National Key Research and Development Program of China (Nos. 2018YFC0809600, 2018YFC0809601), National Natural Science Foundation of China (Nos. 51779252, 51479193), and Major Technological Innovation Projects of Hubei (No. 2017AAA128).

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

    Fujian Yang, Dawei Hu, Hui Zhou & Jingjing Lu

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

    Fujian Yang, Dawei Hu, Hui Zhou & Jingjing Lu

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Yang, F., Hu, D., Zhou, H. et al. Physico-mechanical Behaviors of Granite Under Coupled Static and Dynamic Cyclic Loadings. Rock Mech Rock Eng 53, 2157–2173 (2020). https://doi.org/10.1007/s00603-019-02040-y

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