Skip to main content
Log in

A Numerical Study on Wave Transmission Across Multiple Intersecting Joint Sets in Rock Masses with UDEC

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

This paper presents a numerical study on wave transmission across jointed rock masses with UDEC, where multiple intersecting joint sets exist. The capability of UDEC of studying wave transmission across rock joints is validated through comparison with analytical solutions and experimental data. Through parametric studies on wave transmission across jointed rock masses, it is found that joint mechanical and spatial parameters including joint normal and shear stiffnesses, nondimensional joint spacing, joint spacing ratio, joint intersecting angle, incident angle, and number of joint sets together determine the wave transmission. And for P wave incidence, compared with other parameters, joint normal stiffness, nondimensional joint spacing, and joint intersecting angle have more significant effects on wave transmission. The physical reasons lying behind those phenomena are explained in detail. Engineering applications and indications of the modeling results are also mentioned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  • Bakhtar K, Jenus JJ (1994) Characterization of geologic and engineered systems at KLOTZ tunnel explosion site Älvdalen, Sweden. United States Air Force: Aeronautical Systems Center, ASC–TR–94–7014, Air Force Material Commands, Eglin Air Force Base

  • Barla G, Monacis G, Perino A, Hatzor YH (2010) Distinct element modelling in static and dynamic conditions with application to an underground archaeological site. Rock Mech Rock Eng 43:877–890

    Article  Google Scholar 

  • Beer G (1986) Implementation of combined boundary element-finite element analysis with applications in geomechanics. In: Banerjee PK, Watson JO (eds) Developments in boundary element methods. Applied Science, London, pp 191–226

    Google Scholar 

  • Bergab (2000) Feasibility study: rock conditions Geological investigations. Test–site G 3655. Swedish Defense Research Agency

  • Berglund R (2001) Large scale tests in Älvdalen: Test no. 4a and 4b. Weapons and Protection SE-147 25 Tumba, Swedish Defense Research Agency

  • Brady BH, Hsiung SH, Chowdhury AH, Philip J (1990) Verification studies on the UDEC computational model of jointed rock. In: Mechanics of jointed and faulted rock, Balkema, Rotterdam, pp 551–558

  • Cai JG, Zhao J (2000) Effects of multiple parallel fractures on apparent wave attenuation in rock masses. Int J Rock Mech Min Sci 37:661–682

    Article  Google Scholar 

  • Chen SG (1999) Discrete element modelling of jointed rock mass under dynamic loading. Dissertation, Nanyang Technological University

  • Chen SG, Zhao J (1998) A study of UDEC modelling for blast wave transmission in jointed rock masses. Int J Rock Mech Min Sci 35:93–99

    Article  Google Scholar 

  • Crotty JM, Wardle LJ (1985) Boundary integral analysis of piecewise homogeneous media with structural discontinuities. Int J Rock Mech Min Sci Geomech Abstr 22:419–427

    Article  Google Scholar 

  • Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of the International Symposium on Rock Mechanics, Nancy, France, pp 11–18

  • Daehnke A, Rossmanith HP (1997) Reflection and refraction of plane stress waves at dissipative interfaces. In: Rossmanith HP (ed) Damage and failure of interfaces. Balkema, Rotterdam, pp 315–320

    Google Scholar 

  • Deng XF, Chen SG, Zhu JB, Zhou YX, Zhao ZY, Zhao J (2012) UDEC-AUTODYN hybrid modeling of a large-scale underground explosion test. Submitted to Rock Mech Rock Eng

  • Dowding CH (1985) Blasting vibration monitoring and control. Prentice-Hall, Saddle River

    Google Scholar 

  • Fan SC, Jiao YY (2004) On modelling of incident boundary for wave transmission in jointed rock masses using discrete element method. Comput Geotech 31:57–66

    Article  Google Scholar 

  • Ghaboussi J, Wilson EL, Isenberg J (1973) Finite elements for rock joints and interfaces. J Soil Mech Found Div 99:833–848

    Google Scholar 

  • Goodman RE, Taylor RL, Brekke T (1968) A model for the mechanics of jointed rock. J Soil Mech Found Div 94:637–659

    Google Scholar 

  • Hansson H, Forsén R (1997) Mitigation effects of water on ground shock: Large scale testing in Älvdalen, FOA–R–97–00510–311–SE. FOA, Tumba

    Google Scholar 

  • Hao H, Wu YK, Ma GW, Zhou YX (2001) Characteristics of surface ground motions induced by blasts in jointed rock mass. Soil Dyn Earthquake Eng 21:85–98

    Article  Google Scholar 

  • Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics, 4th edn. Blackwell Publishing, Malden

    Google Scholar 

  • King MS, Myer LR, Rezowalli JJ (1986) Experimental studies of elastic-wave transmission in a columnar-jointed rock mass. Geophys Prospect 34:1185–1199

    Article  Google Scholar 

  • Lemos JV (1987) A distinct element model for dynamic analysis of jointed rock with application to dam foundation and fault motion. Dissertation, University of Minnesota

  • Li JC, Ma GW, Huang X (2009) Analysis of wave transmission through a filled rock joint. Rock Mech Rock Eng 43:789–798

    Article  Google Scholar 

  • Li YX, Zhu ZM, Li BX, Deng JH, Xie HP (2011) Study on the transmission and reflection of stress waves across joints. Int J Rock Mech Min Sci 48:364–371

    Article  Google Scholar 

  • Lyser J, Kuhlemeyer G (1969) Finite dynamic model for infinite media. J Eng Mech Div 4:859–876

    Google Scholar 

  • Morland LW (1977) Plane wave propagation in anisotropic jointed media. Q J Mech Appl Math 30:1–21

    Article  Google Scholar 

  • Nolte DD, Pyrak-Nolte LJ, Beachy J, Ziegler C (2000) Transition from the displacement discontinuity limit to the resonant scattering regime for fracture interface waves. Inter J Rock Mech Min Sci 37:219–230

    Article  Google Scholar 

  • Perino A, Orta R, Barla G (2012) Wave propagation in discontinuous media by the scattering matrix method. Rock Mech Rock Eng 45:901–918

    Google Scholar 

  • Pyrak-Nolte LJ, Myer LR, Cook NGW (1990a) Transmission of seismic waves across single natural fractures. J Geophys Res 95:8617–8638

    Article  Google Scholar 

  • Pyrak-Nolte LJ, Myer LR, Cook NGW (1990b) Anisotropy in seismic velocities and amplitudes from multiple parallel fractures. J Geophys Res 95:11345–11358

    Article  Google Scholar 

  • Rossmanith HP, Knasmillner RE, Daehnke A, Mishnaevsky L (1996) Wave propagation, damage evolution, and dynamic fracture extension. Part II. Blasting. Mater Sci 32:403–410

    Article  Google Scholar 

  • Schoenberg M (1980) Elastic wave behavior across linear slip interfaces. J Acoust Soc Am 68:1516–1521

    Article  Google Scholar 

  • Schwer LE, Lindberg HE (1992) Application brief: a finite element slideline approach for calculating tunnel response in jointed rock. Int J Num Anal Meth Geomech 16:529–540

    Article  Google Scholar 

  • Vorobiev O (2010) Discrete and continuum methods for numerical simulations of non-linear wave propagation in discontinuous media. Int J Numer Meth Eng 83:482–507

    Google Scholar 

  • Vorobiev O, Antoun T (2011) Equivalent continuum modeling for non-linear wave propagation in jointed media. Int J Numer Meth Eng 86:1101–1124

    Article  Google Scholar 

  • Watanabe T, Sassa K (1995) Velocity and amplitude of P-waves transmitted through fractured zones composed of multiple thin low-velocity layers. Int J Rock Mech Min Sci 32:313–324

    Google Scholar 

  • Zhao J, Cai JG, Zhao XB, Li HB (2006a) Experimental study of wave attenuation across parallel fractures. Geomech Geoeng 1:87–103

    Article  Google Scholar 

  • Zhao XB, Zhao J, Cai JG (2006b) P-wave attenuation across fractures with nonlinear deformational behavior. Int J Numer Anal Meth Geomech 30:1097–1112

    Article  Google Scholar 

  • Zhao XB, Zhao J, Cai JG, Hefny AM (2008) UDEC modelling on wave transmission across fractured rock masses. Comput Geotech 35:97–104

    Article  Google Scholar 

  • Zhao XB, Zhu JB, Zhao J, Cai JG (2012) Studies of wave attenuation across parallel fractures using propagator matrix method. Int J Numer Anal Meth Geomech 36:1264–1279

    Article  Google Scholar 

  • Zhu JB, Zhao J (2013) Obliquely incident wave propagation across one joint set with virtual wave source method. J Appl Geophys 88:23–30

    Article  Google Scholar 

  • Zhu JB, Zhao XB, Li JC, Zhao GF, Zhao J (2011a) Normally incident wave transmission across one joint set with virtual wave source method. J Appl Geophys 73:283–288

    Article  Google Scholar 

  • Zhu JB, Zhao GF, Zhao XB, Zhao J (2011b) Validation study of the distinct lattice spring model (DLSM) on P-wave transmission across multiple parallel joints. Comput Geotech 38:298–304

    Article  Google Scholar 

  • Zhu JB, Perino A, Zhao GF, Barla G, Li JC, Ma GW, Zhao J (2011c) Seismic response of a single and a set of filled joints of viscoelastic deformational behavior. Geophys J Int 186:1315–1330

    Article  Google Scholar 

  • Zhu JB, Zhao XB, Wu W, Zhao J (2012) Wave propagation across rock joints filled with viscoelastic medium using modified recursive method. J Appl Geophys 86:82–87

    Article  Google Scholar 

Download references

Acknowledgments

We would like to acknowledge the two anonymous reviewers and the Editor, Professor Giovanni Barla, for their constructive comments. Dr. Yingxin Zhou is acknowledged for the sharing of field measured data. This research is financially supported by the Swiss National Science Foundation (200021-116536) and National Natural Science Foundation of China (40702046).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. B. Zhu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, J.B., Deng, X.F., Zhao, X.B. et al. A Numerical Study on Wave Transmission Across Multiple Intersecting Joint Sets in Rock Masses with UDEC. Rock Mech Rock Eng 46, 1429–1442 (2013). https://doi.org/10.1007/s00603-012-0352-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-012-0352-9

Keywords

Navigation