Index of loading rate dependency of class I and class II rocks behavior in uniaxial compressive and Brazilian tensile tests

Abstract

Understanding time-dependency of rock is indispensable for geotechnical applications to estimate long-term deformation and stability of underground structures. This paper introduced a comparison between uniaxial compressive (UC) and Brazilian tensile test (BT) behavior for class I and class II rocks using constant loading rate (CLR) and alternative loading rate (ALR) method, which includes the similarity and otherness of complete stress-strain curves, peak strength, loading rate effect and elastic modulus of two types of test; and time-dependency was also quantitatively analyzed. The results show that the stress—strain curves have a similar law; the correlation coefficient k between UC and BT strength for different rocks is 0.0424–0.1394, and the two strengths can convert to each other; there is a linear relationship between tensile and elastic modulus, with an obvious time-dependency, and the two moduli also can convert to each other; the constant n was taken as index of loading rate dependency for rock, and analyzed the relation to the loading condition, testing environment. The constant n can quantitatively assess the long-term stability of underground structures. A constitutive equation based on n value was proposed to simulate the experimental data for four rocks and the calculated results are fitted very well.

Keywords

underground structures / class I and class II rocks / uniaxial compression / Brazilian tension / time-dependency

References

[1] HashibaK, FukuiK. Index of loading-rate dependency of rock strength [J]. Rock Mechanics and Rock Engineering, 2015, 48(2): 859-865

[2] ZhangH, TangY, RenT, et al. . Time dependency for generalized relaxation compliance of rock [J]. Bulletin of Engineering Geology and the Environment, 2022, 81(5): 1-9

[3] SanoO, ItoI, TeradaM. Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression [J]. Journal of Geophysical Research: Solid Earth B, 1981, 86(10): 9299-9311

[4] HashibaK, FukuiKIndex of time-dependency for rock and its application for the assessment of the long-term stability of underground structures [C], 2013, Wroclaw, Poland, ISRM: 807812

[5] OkuboS, HashibaK, FukuiK. Loading rate dependency of the strengths of some Japanese rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 58: 180-185

[6] XieS, LinH, ChenY, et al. . A new nonlinear empirical strength criterion for rocks under conventional triaxial compression [J]. Journal of Central South University, 2021, 28(5): 1448-1458

[7] JinF. Comparison of tensile and compressive behaviours of rock [J]. Chinese Journal of Geotechnical Engineering, 1998, 20(2): 31-33(in Chinese)

[8] ZhangY, ElN M H, WuW, et al. . Dynamic torsional impedance of large-diameter pipe pile for offshore engineering: 3D analytical solution [J]. Applied Mathematical Modelling, 2022, 111: 664-680

[9] WuW, LiuH, YangX, et al. . New method to calculate apparent phase velocity of open-ended pipe pile [J]. Canadian Geotechnical Journal, 2020, 57(1): 127-138

[10] GuanW, WuW, JiangG, et al. . Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect [J]. Journal of Central South University, 2020, 27(12): 3839-3851

[11] YuJ, ZhuY, YaoW, et al. . Stress relaxation behaviour of marble under cyclic weak disturbance and confining pressures [J]. Measurement, 2021, 182: 109777

[12] JeongH S, KangS S, ObaraY. Influence of surrounding environments and strain rates on the strength of rocks subjected to uniaxial compression [J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(3): 321-331

[13] YuJ, RenC, CaiY, et al. . Analytical approach for evaluating the dynamic self-bearing capacity of tunnels [J]. International Journal of Geomechanics, 2021, 21(8): 1-15

[14] TangY, OkuboS, XuJ, et al. . Loading-rate dependence of rocks in postfailure region under triaxial compression [J]. Advances in Materials Science and Engineering, 2018, 20181496127

[15] OkuboS, FukuiK, QiQ. Uniaxial compression and tension tests of anthracite and loading rate dependence of peak strength [J]. International Journal of Coal Geology, 2006, 68(3–4): 196-204

[16] WangC, CaoC, LiC, et al. . Experimental investigation on synergetic prediction of granite rockburst using rock failure time and acoustic emission energy [J]. Journal of Central South University, 2022, 29(4): 1262-1273

[17] LiD, LiX, CharlieL. Experimental studies of mechanical properties of two rocks under direct compression and tension [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(3): 624-632(in Chinese)

[18] YuX, WangQ, LiX, et al. . Experimental research on deformation of rocks indirect tension and compression [J]. Rock and Soil Mechanics, 2008, 29(1): 18-22(in Chinese)

[19] KaramanK, CihangirF, ErcikdiB, et al. . Utilization of the Brazilian test for estimating the uniaxial compressive strength and shear strength parameters [J]. Journal of the Southern African Institute of Mining and Metallurgy, 2015, 115(3): 185-192

[20] LiP, CaiM. Energy evolution mechanism and failure criteria of jointed surrounding rock under uniaxial compression [J]. Journal of Central South University, 2021, 28(6): 1857-1874

[21] BieniawskiZ TEngineering rock mass classifications [M], 1989, New York, Wiley-Interscience

[22] WawersikW R, FairhurstC. A study of brittle rock fracture in laboratory compression experiments [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1970, 7(5): 561-575

[23] HORIBE T. Japanese Industrial Standard Method of test for compressive strength of rock [EB/OL]. [1975-12-01]. https://kikakurui.com/m/M0302-2000-01.html.

[24] HashibaK, OkuboS, FukuiK. A new testing method for investigating the loading rate dependency of peak and residual rock strength [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 894-904

[25] AbbasM, BohloliB, MondolN H, et al. Brazilian tensile strength test-post-failure behavior of Jurassic and Cretaceous shales from Svalbard [C], 2015, Madrid, Spain, EAGE Publications BV: 1-5

[26] TaniguchiW, HasegawaH, IwasaK, et al. Fundamental properties of geo environment for design study of repository [R], 1999, Tokyo, Japan Nuclear Cycle Development Institute(in Japanese)

[27] SugitaY, YuiMData set of the relationship between unconfined compressive strength and tensile strength of rock mass [R], 2002, Tokyo, Japan Nuclear Cycle Development Institute(in Japanese)

[28] OkuboS, OtaA, AkiyamaM. Abrasivity of rock and bit wear in drilling [J]. Journal of Mining and Materials Processing Institute of Japan, 1997, 113(5): 325-332(in Japanese)

[29] OkuboS, FukuiK, NishimatsuY. Estimating abrasivity of rock by laboratory and in situ tests [J]. Rock Mechanics and Rock Engineering, 2011, 44(2): 231-244

[30] FukuiK, OkuboS, NishimasuY. Generalized relaxation behaviour of rock under uniaxial compression [J]. Journal of Mining and Materials Processing Institute of Japan, 1992, 108(7): 543-548(in Japanese)

[31] OkuboS, FukuiK. An analytical investigation of a variable-compliance-type constitutive equation [J]. Rock Mechanics and Rock Engineering, 2006, 39(3): 233-253

[32] XuX, KarakusM, GaoF, et al. . Thermal damage constitutive model for rock considering damage threshold and residual strength [J]. Journal of Central South University, 2018, 25(10): 2523-2536

[33] AltindagR, GuneyA. Predicting the relationships between brittleness and mechanical properties (UCS, TS and SH) of rocks [J]. Scientific Research and Essays, 2010, 5(16): 35-39

[34] KalamarasG S, BieniawskiZ TA rock mass strength concept for coal seams incorporating the effect of time [C], 1995, Tokyo, Japan, ISRM: 295302