Skip to main content
SpringerLink
Log in

Formulations of the three-dimensional discontinuous deformation analysis method

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper extends the original 2D discontinuous deformation analysis (DDA) method proposed by Shi to 3D cases, and presents the formulations of the 3D DDA. The formulations maintain the characteristics of the original 2D DDA approach. Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact, such as of vertex-to-vertex, vertex-to-edge and edge-to-edge types, can be handled easily based on the C-P method. The matrices of equilibrium equations have been given in detail for programming purposes. TheC program codes for the 3D DDA are developed. The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples. The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes. Finally, implications and future extensions are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Goodman RE, Taylor RL, Brekke TL. A model for the mechanics of jointed rock.Journal of the soil mechanics and foundations division, ASCE, 1968, 94(SM3): 637–659

    Google Scholar 

  2. Crouch SL, Starfield AM. Boundary Element Method in Solid Mechanics. Allen and Unwin, 1983.

  3. Shi GH, Goodman RE, Discontinuous deformation analysis. In: Dowding CH, Singh MM, eds. Proceedings of the 25th US Symposium on Rock Mechanics, New York: Society of Mining Engineers of AIME, 1984. 269–277

    Google Scholar 

  4. Shi GH, Goodman RE. Two-dimensional discontinuous deformation analysis.International Journal for Numerical and Analytical Methods in Geomechanics, 1985, 9: 541–556

    Article  MATH  Google Scholar 

  5. Shi GH. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of block systems. [PhD Thesis], Berkeley: University of California, 1988

    Google Scholar 

  6. Shi GH, Goodman RE. Generalization of two-dimensional discontinuous deformation analysis for forward modeling.International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13(4): 359–380

    Article  MATH  Google Scholar 

  7. Shi GH. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures.Engineering Computations. 1992, 9(2): 157–168

    Google Scholar 

  8. Cai YE, Liang GP, Shi GH, et al. Studying an impact problem by using LDDA method. In: Salami R, Banks D, eds. Proceedings of the 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Albuquerque: TSI Press, 1996. 288–294

    Google Scholar 

  9. Lin CT, Amadei B, Jung J, et al. Extensions of discontinous deformation analysis for jointed rock masses.International Journal of Rock Mechanics and Mining Science, 1996, 33(7): 671–694

    Article  Google Scholar 

  10. Lin JS, Lee DH. Manifold method using polynomial basis function of any order. In: Salami R, Banks D, eds. Proceedings of the 1st International Forum on Discontinous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Albuquerque: TSI Press, 1996. 365–372

    Google Scholar 

  11. Koo CY, Chern JC. The development of DDA with third order displacement function. In: Salami R, Banks D, eds. Proceedings of the 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Albuquerque: TSI Press, 1996. 342–349

    Google Scholar 

  12. Shyu KK. Nodal based discontinuous deformation analysis. [PhD Thesis]. Berkeley: University of California, 1993

    Google Scholar 

  13. Chang CT. Nonlinear dynamic discontinuous deformation analysis with finite element meshed block system. [PhD Thesis]. Berkeley: University of California, 1994

    Google Scholar 

  14. Al-Zahrani RM. A coupled displacement deformation analysis and boundary element method for twodimensional elastostatic problems. [PhD Thesis]. University of Pittsburgh, 2000

  15. Kim YI, Amadei B, Pan E. Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis.International Journal of Rock Mechanics and Mining Science, 1999, 36(7): 949–970

    Article  Google Scholar 

  16. Yeung MR. Application of Shi's discontinuous deformation analysis to the study of rock behavior. [PhD Thesis]. Berkeley: University of California, 1991

    Google Scholar 

  17. Ke TC, Bray JD. Modeling of particulate media using discontinuous deformation analysis.Journal of Engineering Mechanics, 1995, 121(11): 1234–1243

    Article  Google Scholar 

  18. Thomas PA, Bray JD, Ke TC. Discontinuous deformation analysis for soil mechanics. In: Salami R, Banks D, eds. Proceedings of the 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Albuquerque: TSI Press, 1996. 454–461

    Google Scholar 

  19. Thomas PA, Bray JD. Capturing nonspherical shape of granular media with disk clusters.Journal of Geotechnical and Geoenvironmental Engoneering, 1999, 125(3): 169–178

    Article  Google Scholar 

  20. Maclaughlin MM. Discontinuous deformation analysis to the kinematics of landslides. [PhD Thesis]. Berkeley: University of California, 1997

    Google Scholar 

  21. Koo CY, Chern JC. Modification of the DDA method for rigid block problems.International Journal of Rock Mechanics and Mining Science, 1998, 35(6): 683–693

    Article  Google Scholar 

  22. Shi GH. Three dimensional discontinuous deformation analysis. In: Elsworth D, Tinucci JP, Heasley KA, eds. Proceedings of the 38th US Rock Mechanics Symposium, Washington, DC, 2001. 1421–1428

  23. Yeung MR, Jiang QH, Sun N. Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods.International Journal of Rock Mechanics & Mining Sciences, 2003, 40(2): 265–275

    Article  Google Scholar 

  24. Jang HI, Lee CI. Development of a three-dimensional discontinuous deformation analysis technique and its application to toppling failure. In: Hatzor YH, ed. Proceedings of the 5th International Conference on Analysis of Discontinuous Deformation. Abingdon, Balkema, 2002. 225–229

    Google Scholar 

  25. Shi GH. Simplex integration for manifold method. In: Salami R, Banks D, eds. Proceedings of the 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Albuquerque: TSI Press, 1996. 205–262

    Google Scholar 

  26. Cundall PA. Formulations of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in s system composed of many polyhedral blocks.International Journal of Rock Mechanics and Mining Science, 1988, 25(3): 107–116

    Article  Google Scholar 

  27. Taniguchi T. Non-linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion.Earthquake Engineering and Structural Dynamics, 2002, 31(8): 1481–1500

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil and Hydraulic Engineering, Dalian University of Technology, 116024, Dalian, China

    Liu Jun, Kong Xianjing & Lin Gao

Authors
  1. Liu Jun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kong Xianjing
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by the National Natural Science Foundation of China (50139010)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jun, L., Xianjing, K. & Gao, L. Formulations of the three-dimensional discontinuous deformation analysis method. Acta Mech Sinica 20, 270–282 (2004). https://doi.org/10.1007/BF02486719

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02486719

Key words

Search

Navigation