A 1D equivalent medium method for wave propagation across parallel jointed rock mass

J. C. Li, H. B. Li, W -G Ma, J. Zhao

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The one-dimensional equivalent medium method proposed in the present paper is an extension of the study by Li et al. (J.C. Li, G.W.Ma and J. Zhao. An equivalent viscoelastic model for rock mass with parallel joints. Journal of Geophysical Research, 115(B03), 2010). By analyzing the normal and shear equivalent property of a parallel jointed rock mass, the improved method is mainly to investigate P- and S-wave propagation normally across a rock mass with a set of parallel joints. For P-or S-wave, the method includes two portions: a viscoelastic medium model and a concept of "Virtual Wave Source (VWS)". The viscoelastic medium model is to describe the normal and shear property of the Representative Volume Element (RVE) for a rock mass. The VWS is proposed to take into account the wave reflections between the joints. Parameters in the viscoelastic medium model are derived analytically according to the basic solutions for P- or S-wave propagation across a RVE.The proposed method is then verified by applying identical incident waves to the discontinuous rock mass and the corresponding equivalent medium at one side to compare the output waves at the other side. The results from the Equivalent Medium Method (EMM) are very similar to those determined from the Displacement Discontinuity Method (DDM). The proposed method can be effectively applied to analyze P- or S-wave propagation normally across discontinuous rock mass with a set of parallel joints. By analysis, it is found that the P- or S-wave propagation normally across an equivalent medium is related to the VWS number and the ratio of the VWS spacing to an incident wave length. For a given VWS number, if the wave length of the incident wave is sufficiently long compared to the joint spacing, the effect of the VWS on wave propagation across rock mass is prominent. Finally, frequency dependence and joint spacing effect on the wave propagation across parallel jointed rock mass are discussed.

Original languageEnglish
Title of host publicationHarmonising Rock Engineering and the Environment - Proceedings of the 12th ISRM International Congress on Rock Mechanics
PublisherCRC Press
Number of pages6
ISBN (Print)9780415804448
Publication statusPublished - 2012
Externally publishedYes
EventInternational Society of Rock Mechanics Series of Symposia and Conferences 2011 - China National Convention Center (CNCC), Beijing, China
Duration: 18 Oct 201121 Oct 2011
Conference number: 12th


ConferenceInternational Society of Rock Mechanics Series of Symposia and Conferences 2011
Abbreviated titleISRM 2011
OtherInternational Congress on Rock Mechanics of the International Society for Rock Mechanics 2011

Proceedings title = Harmonising Rock Engineering and the Environment
Internet address


  • Dynamic equivalent method
  • Rock joints
  • Rock mass
  • Viscoelastic model
  • Wave propagation

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