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Abbreviations
- \( \varepsilon_{j} \) :
-
Measured strain wave at the position of the gauge j (j = a, b)
- \( \varepsilon^{p} ,\varepsilon^{n} \) :
-
Positive and negative strain waves, respectively
- \( \varepsilon_{j}^{p} ,\varepsilon_{j}^{n} \) :
-
Positive and negative strain waves at the position of the gauge j (j = a, b), respectively
- \( \varepsilon_{i} ,\varepsilon_{r} ,\varepsilon_{t} \) :
-
Incident, reflected and transmitted strain waves, respectively
- \( \varepsilon^{p - } ,\varepsilon^{p + } \) :
-
Positive strain waves at the front and back sides of rock joints, respectively
- \( \varepsilon^{n - } ,\varepsilon^{n + } \) :
-
Negative strain waves at the front and back sides of rock joints, respectively
- \( \varepsilon^{ - } ,\varepsilon^{ + } \) :
-
Strains at the front and back sides of rock joints, respectively
- \( \dot{\varepsilon }_{f} \) :
-
Strain rate of filled joints
- \( \Updelta \varepsilon_{n} \) :
-
Normalized closure of non-filled contact joints
- \( \Updelta \varepsilon_{f} \) :
-
Normalized closure of filled joints
- \( \Updelta t \) :
-
Time interval for positive or negative strain wave propagation between the points a and b
- \( \sigma^{ - } ,\sigma^{ + } \) :
-
Stresses on the front and back sides of rock joints, respectively
- \( \sigma_{n} \) :
-
Stress of non-filled contact joints
- \( \sigma_{f} \) :
-
Stress of filled joints
- \( c \) :
-
Longitudinal wave propagation velocity
- \( E \) :
-
Young’s modulus of the rock bar
- \( l \) :
-
Length of the rock bar
- \( l_{s} \) :
-
Thickness of the filled joint
- \( T \) :
-
Transmission coefficient
- \( t_{j}^{p} \) :
-
Time interval for positive strain wave propagation between the points O and j (j = a, b)
- \( t_{j}^{n} \) :
-
Time interval for negative strain wave propagation between the points Y and j (j = a, b)
- \( v^{ - } ,v^{ + } \) :
-
Particle velocities at the front and back sides of rock joints, respectively
- \( x_{j} \) :
-
Distance between the points O and j (j = a, b)
References
Brown ET (1981) Rock characterization testing and monitoring: ISRM suggested methods. Pergamon, Oxford
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 37:661–682
Doan ML, Gary G (2009) Rock pulverization at high strain rate near the San Andreas fault. Nature Geosci 2:709–712
Felice CW, Gaffney ES, Brown JA, Olsen JM (1987) Dynamic high stress experiments on soil. Geotech Test J 10:192–202
Kolsky H (1953) Stress waves in solids. Oxford University Press, London
Leucci G, Giorgi LD (2006) Experimental studies on the effects of fracture on the P and S wave velocity propagation in sedimentary rock (“Calcarenite del Salento”). Eng Geol 84:130–142
Li JC, Ma GW, Zhao J (2010a) An equivalent viscoelastic model for rock mass with parallel joints. J Geophys Res 115:B00305
Li JC, Ma GW, Huang X (2010b) Analysis of wave propagation through a filled rock joint. Rock Mech Rock Eng 43:789–798
Li JC, Ma GW, Zhao J (2011) Analysis of stochastic seismic wave interaction with a slippery rock joint. Rock Mech Rock Eng 44:85–92
Ma GW, Li JC, Zhao J (2011) Three-phase medium model for filled rock joint and interaction with stress waves. Int J Numer Anal Geomech 35:97–110
Meng H, Li QM (2003) An SHPB set-up with reduced time-shift and pressure bar length. Int J Impact Eng 28:677–696
Pyrak-Nolte LJ, Myer LR, Cook NGW (1990) Transmission of seismic waves across single natural fractures. J Geophys Res 95:8617–8638
Vales F, Moravka S, Brepta R, Cerv J (1996) Wave propagation in a thick cylindrical bar due to longitudinal impact. JSME Int J Ser A 39:60–70
Zhao J (2000) Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to dynamic strength of brittle rock materials. Int J Rock Mech Min Sci 37:1115–1121
Zhao H, Gary G (1997) A new method for the separation of waves: application to the SHPB technique for an unlimited duration of measurement. J Mech Phys Solid 45:1185–1202
Zhao J, Li HB, Wu MB, Li TJ (1999) Dynamic uniaxial compression tests on a granite. Int J Rock Mech Min Sci 36:273–277
Zhao J, Cai JG, Zhao XB, Li HB (2006) Experimental study of ultrasonic wave attenuation across parallel fractures. Geomech Geoeng An Int J 1:87–103
Zhao J, Cai JG, Zhao XB, Li HB (2008) Dynamic model of fracture normal behavior and application to prediction of stress wave attenuation across fractures. Rock Mech Min Sci 41:671–693
Zhu JB, Perino A, Zhao GF, Barla G, Li JC, Ma GW, Zhao J (2011) Seismic response of a single and a set of filled joints of viscoelastic deformational behavior. Geophys J Int 186:1315–1330
Acknowledgments
This work is sponsored by the Swiss National Science Foundation (200021_124846). The equipment is partially supported by Swiss National Science Foundation (200021_116536). The authors also would like to thank Mr. J.-F. Mathier, Mr. L. Gastaldo and Mr. L.F. Morier of EPFL-LMR, for their assistance in equipment setup and test preparation.
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Wu, W., Li, J.C. & Zhao, J. Loading Rate Dependency of Dynamic Responses of Rock Joints at Low Loading Rate. Rock Mech Rock Eng 45, 421–426 (2012). https://doi.org/10.1007/s00603-011-0212-z
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DOI: https://doi.org/10.1007/s00603-011-0212-z