Abstract
The overall dynamic mechanical behavior of a double-scale discontinuous rock mass with a nonlinear deformational macrojoint was investigated. A method of combining the split three characteristic lines with the piecewise linear displacement discontinuity model (DDM) was proposed. The method was applied to investigate the transmission coefficient of P-wave propagation normally through a double-scale discontinuous rock mass with a nonlinear deformational macrojoint. The results were verified by comparison with the results of P-wave propagation normally through a double-scale discontinuous rock mass with a linear deformational macrojoint. The results showed that for a small amplitude stress wave, the nonlinear deformational macrojoint can be simplified as a linear deformational form to study the stress wave propagation, whereas for a large amplitude stress wave, the effects of the nonlinear deformational behavior of the macrojoint must be considered. The difference of the effects of nonlinear and linear deformational macrojoints on large amplitude stress wave propagation can be overlooked in the low-frequency or high-frequency regions. In addition, when the incident stress wave amplitude and initial macrojoint stiffness are sufficiently large, the effects of the nonlinear deformational macrojoint on stress wave propagation can be overlooked, and the effects of microdefects must be considered. The influence degree of microdefects on the stress wave propagation increases with the increase of incident stress wave frequency.
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References
Bandis SC, Lumsden AC, Barton NR (1983) Fundamentals of rock joint deformation. Int J Rock Mech Min Sci Geomech Abstr 20(6):249–268
Barton N, Bandis S, Bakhtar K (1985) Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Min Sci Geomech Abstr 22(3):121–140
Cai JG, Zhao J (2000) Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses. Int J Rock Mech Min Sci 37(4):661–682
Cook NGW (1992) Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress. Int J Rock Mech Min Sci Geomech Abstr 29(3):198–223
Deng XF, Zhu JB, Chen SG, Zhao J (2012) Some fundamental issues and verification of 3DEC in modeling wave propagation in jointed rock masses. Rock Mech Rock Eng 45(5):943–951
Deng XF, Zhu JB, Chen SG, Zhao ZY, Zhou YX, Zhao J (2014) Numerical study on tunnel damage subject to blast-induced shock wave in jointed rock masses. Tunn Undergr Space Technol 43:88–100
Fakhimi AA, Fairhurst C (1994) A model for the time-dependent behavior of rock. Int J Rock Mech Min Sci Geomech Abstr 31(2):117–126
Fan LF, Yi XW, Ma GW (2013) Numerical manifold method (NMM) simulation of stress wave propagation through fractured rock. Int J Appl Mech 5(2):1350022
Fan LF, Gao JW, Du XL, Wu ZJ (2020a) Spatial gradient distributions of thermal shock-induced damage to granite. J Rock Mech Geotech Eng 12(5):917–926
Fan LF, Wang M, Wu ZJ (2020b) A split three-characteristics method for stress wave propagation through rock mass with double-scale discontinuities. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-020-02233-w
Hudson JA, Pointer T, Liu E (2001) Effective-medium theories for fluid-saturated materials with aligned cracks. Geophys Prospect 49(5):509–522
Ichikawa Y, Kawamura K, Uesugi K, Seo YS, Fujii N (2011) Micro- and macrobehavior of granitic rock: observations and viscoelastic homogenization analysis. Comput Methods Appl Mech Eng 191(1):47–72
Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics, 4th edn. Wiley-Blackwell, Malden
Ju Y, Sudak L, Xie H (2007) Study on stress wave propagation in fractured rocks with fractal joint surfaces. Int J Solids Struct 44(13):4256–4271
Kolsky H (1953) Stress waves in solids. Clarendon Press, Oxford
Kulhawy FH (1975) Stress deformation properties of rock and rock discontinuities. Eng Geol 9(4):327–350
Li JC (2013) Wave propagation across non-linear rock joints based on time-domain recursive method. Geophys J Int 193(2):970–985
Li JC, Ma GW, Zhao J (2010) An equivalent viscoelastic model for rock mass with parallel joints. J Geophys Res 115(B3):B03305
Li JC, Wu W, Li HB, Zhu JB, Zhao J (2013) A thin-layer interface model for wave propagation through filled rock joints. J Appl Geophys 91(4):31–38
Li JC, Li HB, Jiao YY, Liu YQ, Xia X, Yu C (2014) Analysis for oblique wave propagation across filled joints based on thin-layer interface model. J Appl Geophys 102:39–46
Li JC, Liu TT, Li HB, Liu YQ, Liu B, Xia X (2015) Shear wave propagation across filled joints with the effect of interfacial shear strength. Rock Mech Rock Eng 48(4):1547–1557
Li HB, Liu TT, Liu YQ, Li JC, Xia X, Bo L (2015) Numerical modeling of wave transmission across rock masses with nonlinear joints. Rock Mech Rock Eng 49(3):1–7
Li JC, Li NN, Li HB, Zhao J (2017) An SHPB test study on wave propagation across rock masses with different contact area ratios of joint. Int J of Impact Eng 105:109–116
Li XF, Li HB, Li JC, Li ZW (2018) Research on transient wave propagation across nonlinear joints filled with granular materials. Rock Mech Rock Eng 51(8):2373–2393
Li XF, Li HB, Li JC, Zhao J (2018) Effect of joint thickness on seismic response across a rock fracture filled with dry granular materials. Géotech Lett 8(3):1–19
Ma GW, Li JC, Zhao J (2011) Three-phase medium model for filled rock joint and interaction with stress waves. Int J Numer Anal Methods Geomech 35(1):97–110
Ma GW, Fan LF, Li JC (2013) Evaluation of equivalent medium methods for stress wave propagation in jointed rock mass. Int J Numer Anal Methods Geomech 37(7):701–715
Markov M, Levine V, Mousatov A, Kazatchenko E (2005) Elastic properties of double-porosity rocks using the differential effective medium model. Geophys Prospect 53(5):733–754
Niu LL, Zhu WC, Li SH, Guan K (2018) Determining the viscosity coefficient for viscoelastic wave propagation in rock bars. Rock Mech Rock Eng 51(5):1347–1359
Pyrak-Nolte LJ (1996) The seismic response of fractures and the interrelations among fracture properties. Int J Rock Mech Min Sci Geomech Abstr 33(8):787–802
Schoenberg M (1980) Elastic wave behavior across linear slip interfaces. J Acoust Soc Am 68(5):1516–1521
Wang LL, Labibes K, Azari Z, Pluvinage G (1994) Generalization of split hopkinson bar technique to use viscoelastic bars. Int J Impact Eng 15(5):669–686
Wei W, Shao ZS, Zhang YY, Qiao RJ, Gao JP (2019) Fundamentals and applications of microwave energy in rock and concrete processing—a review. Appl Therm Eng 157(5):113751
Wu K, Shao ZS (2019) Study on the effect of flexible layer on support structures of tunnel excavated in viscoelastic rocks. J Eng Mech ASCE 145(10):04019077
Yi W, Nihei KT, Rector JW, Nakagawa S, Myer LR, Cook NGW (1997) Frequency-dependent seismic anisotropy in fractured rock. Int J Rock Mech Min Sci 34(3–4):3490–2147483647
Zhao J, Cai JG (2001) Transmission of elastic p-waves across single fractures with a nonlinear normal deformational behavior. Rock Mech Rock Eng 34(1):3–22
Zhao J, Zhao XB, Cai JG (2006) A further study of P-wave attenuation across parallel fractures with linear deformational behavior. Int J Rock Mech Min Sci 43(5):776–788
Zhao XB, Zhao J, Cai JG, Hefny AM (2008) UDEC modelling on wave propagation across fractured rock masses. Comput Geotech 35(1):97–104
Zhao XB, Zhao J, Cai JG (2010) P-wave transmission across fractures with nonlinear deformational behaviour. Int J Numer Anal Methods Geomech 30(11):1097–1112
Zhu J, Hu SS, Wang LL (2009) An analysis of stress uniformity for concrete-like specimens during SHPB tests. Int J Impact Eng 36(1):61–72
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This research was funded by Beijing Natural Science Foundation [JQ20039] and National Natural Science Foundation of China, Grant number [51778021].
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Fan, L.F., Wang, M. & Wu, Z.J. Effect of Nonlinear Deformational Macrojoint on Stress Wave Propagation Through a Double-Scale Discontinuous Rock Mass. Rock Mech Rock Eng 54, 1077–1090 (2021). https://doi.org/10.1007/s00603-020-02308-8
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DOI: https://doi.org/10.1007/s00603-020-02308-8