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Applications in Mining

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Topics in Boundary Element Research

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Abstract

Mining is the term used for the extraction of mineral from the earth’s crust. The problems of analysis which arise are thus almost exclusively concerned with the excavation of ore from the “host material” and the stresses and displacements induced by the consequent mining excavations. The determination of these stresses and displacements then allows predictions to be made about the stability of the mine working and may affect the design of the mine layout.

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References

  1. Salamon, M. D. G., Elastic analysis of displacements and stresses induced by the Mining of seam or reef deposits. Part I Jnl. of S. Afr. Inst. Min and Metall, 64 (4), pp. 129–149, 1963

    Google Scholar 

  2. Salamon, M. D. G., Elastic analysis of displacements and stresses induced by the mining of seam or reef deposits. Part II, Jnl. S. Afr. Inst. Min and Metall, 64 (6), pp. 197–218, 1964

    Google Scholar 

  3. Salamon, M. D. G., Elastic analysis of displacements and stresses induced by the mining of seam or reef deposits. Part III, Jnl. S. Afr. Inst. Min and Metall, 64 (10), pp. 468–500, 1964

    Google Scholar 

  4. Salamon, M. D. G., Analysis of displacements and stresses induced by the mining of seam of reef deposits. Part IV, Jnl. S. Afr. Inst. Min and Metall, 65 (5), pp. 319–338, 1964

    Google Scholar 

  5. Starfield, A. M., Crouch, S. L., Elastic analysis of single seam extraction. In: New Horizons in Rock Mechanics. (Eds. Hardy, H. R., Jr. and Stefhanko, R.) ASCE, N.Y., pp. 421–439, 1973

    Google Scholar 

  6. Crouch, S. L., Solution of plane elasticity problems by the displacement discontinuity method. Int. J. Numer. Meth. in Eng.,10, pp. 301–343, 1976

    Google Scholar 

  7. Crouch, S. L., Computer simulation of mining in faulted ground. Jnl. S. Afr. Inst. Min and Metall, 79 (6), pp. 159–173, 1979

    MathSciNet  Google Scholar 

  8. Diering, T. A. C., Simulation of mining in non-homogeneous ground using the displacement discontinuity method. JnL S. Afr. Inst. Min and Metall, 80, No. 7, pp. 169–173, 1980

    Google Scholar 

  9. Wiles, T. D., Curran, J. H., A general 3-D displacement discontinuity method. Proc. 4th Int. Conf. on Numerical Methods in Geomechanics, ed. Eisenstein, A. A. Blakema, Rotterdam, 1, pp. 103–109, 1982

    Google Scholar 

  10. Crawford, A. M., Curran, T. H., Higher order functional variation displacement discontinuity method. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 19, pp. 143–148, 1982

    Google Scholar 

  11. Deist, F. H. et al., A new digital method for three dimensional stress analysis in elastic media. Rock Mechanics 5, 189–202, 1973

    Article  Google Scholar 

  12. Deist, F. H., Georgiadis, E., A computer system for three-dimensional elastic analysis using a boundary element approach. Chamber of Mines of South Africa, Research Report No. 43/76, Project No. GS 1510

    Google Scholar 

  13. Rizzo, F. T., An integral equation approach to boundary value problems of classical elastostatics. Q. Appl. Math. 25, 83–95, 1967

    MATH  Google Scholar 

  14. Cruse, T. A., Application of the boundary integral equation method to three-dimensional stress analysis. Computer & Structures, 3, pp. 509–527, 1973

    Article  Google Scholar 

  15. Lachat, J. C., A further development of the boundary integral technique for elastostatics. Ph.D. Thesis,University of Southampton, U.K.

    Google Scholar 

  16. Lachat, J. C., Watson, J. O., Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics. Int. Jnl. for Num. Meth. in Eng. 10, pp. 991–1005, 1976

    Google Scholar 

  17. Bannerjee, P. K., Butterfield, R., Boundary element method in Geomechanics. In: Finite Elements in Geomechanics. Ed. Gudekus, G., Chichester, Wiley 1977

    Google Scholar 

  18. Brady, B. H. G., Bray, J. W., The boundary element method for elastic analysis of tabular orebody extraction, assuming complete plane strain. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 15, pp. 29–37, 1978

    Article  Google Scholar 

  19. Brady, B. H. G., A boundary element method for three-dimensional elastic analysis of tabular orebody extraction. Proc. 19th Rock Mech. Symp., pp. 431–438, 1978

    Google Scholar 

  20. Cruse, T. A., Formulation of boundary integral equations for three-dimensional elastoplastic flow. Int. J. Solids & Structures, 7

    Google Scholar 

  21. Hocking, G., Stress analysis of underground excavations incorporating slip and separation along discontinuities. In: Recent Advances in Boundary Element Methods. (Ed. Brebbia, C. A.) Pentech Press, Plymouth, pp. 195–214, 1978

    Google Scholar 

  22. Wardle, L. J., Crotty, J. M., Two Dimensional boundary integral equation analysis for non-homogeneous mining applications. In: Recent Advances in Boundary Element Methods. Ed. Brebbia, C. A., Pentech Press, Plymouth, pp. 233–251, 1978

    Google Scholar 

  23. Telles, J. C. F., Brebbia, C. A., Plasticity. In: Progress in Boundary Element Methods. Ed. Brebbia, C. A., Pentech Press, London 1981

    Google Scholar 

  24. Beer, G. et al., Efficient analysis in geomechanics. 4th Int. Conf. on Numerical Methods in Geomech. Ed. Eisenstein, A. A. Blakema, Rotterdam, 1, pp. 5–13, 1982

    Google Scholar 

  25. Beer, G., Meek, J. L., Coupled Finite Element — Boundary Element analysis of infinite domain problems. Int. Conf. on Num. Meth. for Coupled Problems, ed. Bettess et al., Pineridge Press, Swansea, U.K., 1981

    Google Scholar 

  26. Sinha, K. P., Displacement discontinuity technique for analysis stresses and displacements due to mining in seam deposits. Ph.D. dissertation, University of Minnesota, 1979

    Google Scholar 

  27. Diering, T. A. C., An improved method for the determination by a MINSIM type of analysis of stresses and displacements around tabular excavations. Inl. S. Afr. Inst. Min Metall, 80, No. 12, pp. 225–228, 1980

    Google Scholar 

  28. Wilson, R. B., Cruse, T. A., Efficient implementation of anisotropic three-dimensional boundary integral equation stress analysis. Int. J. Num. Meth. in Engng., 12, 1383–1397

    Google Scholar 

  29. Banerjee, P. K, Integral equation methods for analysis of piecewise non-homogeneous three-dimensional elastic solids of arbitrary shape. Int. J. Mechanical Science, 18, pp. 293–303, 1976

    Google Scholar 

  30. Brady, B. H. G., Bray, J. W., The boundary element method for determining stresses and displacements around long openings in a triaxial stress field. Int. J. Rock Mech. & Min. Sci., 15 (1), pp. 21–28, 1978

    Article  Google Scholar 

  31. Hoek, E., Brown, E. T., Underground excavations in rock. Int. of Min. and Met., 44 Portland Place, London W 1N 4BR, England

    Google Scholar 

  32. Massonet, C. E., Numerical use of integral procedures. Chapter 10 in Stress Analysis. Ed. Zienkiewicz, John Wiley, London 1965

    Google Scholar 

  33. Oliviera, E. R. A., Plane stress analysis by a general integral method. J. ASCE, 94, No. EMI, PP. 79–101, 1968

    Google Scholar 

  34. Watson, J. O., Advanced implementation of the boundary element method for two and three dimensional elastostatics. Chapter 3 in Developments in Boundary Element methods —1. Ed. Banerjee, Applied Science Publ., 1979

    Google Scholar 

  35. Diering, T. A. C., Further developments of the boundary element method with applications in mining. MSc. thesis, University of the Witwatersrand, Johannisburg, South Africa, 1981

    Google Scholar 

  36. Riccardella, P. C., An improved implementation of the boundary integral techniques for two-dimensional elasticity problems. Carnegie Inst. of Tech., Dept. Mech. Eng., Pittsburgh, Report No. SM-72–76, 1972

    Google Scholar 

  37. Riccardella, P. C., An implementation of the boundary integral technique for planar problems of elasticity and elasto-plasticity. Carnegie Inst. of Tech., Dept. Mech. Engng., Pittsburgh, Report No. SM-73–10, 1973

    Google Scholar 

  38. Crotty, J. M., Wardle, L. J., Program BITEM user’s manual. Institute of earth resources, CSIRO Division of Applied Geomechanics, P.O. Box 54, Mount Waverley, Victoria, Australia, 1980

    Google Scholar 

  39. Wardle, L. J., Three dimensional boundary element program for mining applications: MIN3D2, Technical Report No. 116, CSIRO Div. of Applied Geomech., Australia, 1980

    Google Scholar 

  40. Watson, J. O., The solution of boundary integral equations of three-dimensional elastostatics for infinite regions. Proc. First Int. Seminar on Recent Advances in Boundary Element Methods, Univ. of Southampton, 1979

    Google Scholar 

  41. Lachat, J. C., Watson, J. O., Progress in the use of boundary integral equations, illustrated by examples. Computer Methods in Applied Mechanics and Engineering, 10 (3), pp. 273–289, 1977

    Article  MathSciNet  MATH  Google Scholar 

  42. Watson, J. O., Hermitian cubic boundary elements for plane problems of fracture mechanics, Res. Mechanica, 1981

    Google Scholar 

  43. Zienkiewicz, O. C., The Finite Element Method — Third Edition, McGraw-Hill 1977

    Google Scholar 

  44. Crotty, J. M., A block equation solver for large unsymmetric matrices arising in the Boundary Integral Equation Method. Int. J. Numer. Meth. in Engng., 18, pp. 997–1017, 1982

    Google Scholar 

  45. Hocking, G., Stress analysis of the 1100 orebody at Mount Isa. Proc. 19th U.S. Symposium on Rock Mechanics, Stateline, Nevada, 1978

    Google Scholar 

  46. Crotty, J. M., Wardle, L. T., Integral equation analysis of piecewise homogeneous media with structural discontinuities. In preparation. C.S.I.R.O., Div. of Applied Geomechanics, Australia, 1982

    Google Scholar 

  47. Bolteus, L., Tullberg, O., BEMSTAT — A new type of boundary element program for two-dimensional elasticity problems. 3rd Int. Sem. on Recent Advances in Boundary Element Methods, Irvine, USA, 1981

    Google Scholar 

  48. Zienkiewicz, O. C., Pande, G. N., Time dependent multi-laminate model of rocks — A numerical study of deformation and failure of rock masses. Int. Jnl. Num. Anal. Meth. Geomech., 1, pp. 219— 247, 1977

    Google Scholar 

  49. Venturini, U. S., Brebbia, C. A., Boundary Element formulation for non-linear applications in geomechanics. 4th Int. Conf. on Recent Advances in Boundary Element Methods, ed. Brebbia, Southampton, England, 1982

    Google Scholar 

  50. Venturini, U., Brebbia, C. A., The Boundary Element Method for the solution of no-tension materials in Boundary Element Methods. Ed. Brebbia, C. A., Springer Verlag, Berlin, New York 1981

    Google Scholar 

  51. Zienkiewicz, O. C., Kelly, D. W., Bettess, P., The coupling of the finite element method and boundary solution methods. Int. J. Numer. Meth. Eng., 11 (2), pp. 355–375

    Google Scholar 

  52. Mustoe, G. G. W., Symmetric variational boundary integral and finite element procedures in continuum mechanics. Ph.D. dissertation, Dept. of Civil Eng., Univ. of Wales, Swanesa, U.K., 1980

    Google Scholar 

  53. Beer, G., Finite element, boundary element and coupled analysis of unbounded problems in elastostatics. Int. J. Numer. Meth. Engng., in press

    Google Scholar 

  54. Brady, B. H. G., Wassyng, A., A coupled finite element — boundary element method of stress analysis. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, pp. 475–485, 1981

    Article  Google Scholar 

  55. Beer, G., BEFE — Users manual. Dept. of Civil Eng., University of Queensland, St. Lucia, Australia, 1982

    Google Scholar 

  56. Beer, G. et al., Prediction of the behaviour of shale hanging walls in deep underground excavations. 5th ISRM congress, Melbourne, Australia, 1983

    Google Scholar 

  57. Bettes, J. A., Economical solution technique for Boundary Integral matrices. Report C/R/399/81, Dept. of Civil Eng., University College of Swansea, U.K.

    Google Scholar 

  58. Brebbia, C. A., Walker, S., Boundary Element techniques in engineering. Newness-Butterworths, 1980

    Google Scholar 

  59. Mindlin, P. D., Force at a point in the interior of a semi-infinite solid. Physics, 7, pp. 195— 202, 1936

    Google Scholar 

  60. Telles, J. C. F., Brebbia, C. A., Boundary element solution for half-plane problems. Int. J. Solids Structures, 17, No. 12, pp. 1149–1158, 1981

    Article  MATH  Google Scholar 

  61. Wardle, L. J., Three-dimensional solutions for displacement discontinuities in cross-anisotropic media. CSIRO, Div. of Appl. Geomech., Technical paper No. 34, 1980

    Google Scholar 

  62. Wardle, L. J., Fundamental solutions and boundary integral formulation for tabular excavations in a non-homogeneous rock mass. CSIRO, Div. of Appl. Geomech., Techn. report No. 133, 1982

    Google Scholar 

  63. Wardle, L. J., Boundary element methods for solution of stress analysis problems in mining. CSIRO, Div. of Appl. Geomech., Techn. Report No. 102, 1980

    Google Scholar 

  64. Meek, J. L., Matrix Structural Analysis. McGraw-Hill Co, New York 1971

    MATH  Google Scholar 

  65. Hebblewhite, B. K., The use of modelling techniques for mine design. Australian Journal of Coal Mining Technology and Research, No. 1, 1982

    Google Scholar 

  66. Brebbia, C. A., Georgiou, P., Combination of boundary and finite elements in elastostatics. Appl. Math. Modelling, 3, pp. 212–220, 1979

    Article  MATH  Google Scholar 

  67. Banerjee, P. K, Butterfield, Boundary Element Methods in Engineering Science. McGraw-Hill, London 1981

    Google Scholar 

  68. Bywater, S., Cowling, R., Black, B. N., Stress Measurement and Analysis for Mine Planning. 5th ISRM Congress, Melbourne, Australia, 1983

    Google Scholar 

  69. Beer, G., BEFE — a combined oundary element finite element computer program. Adv. Eng. Software, Vol. 6, No. 2

    Google Scholar 

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Authors
  1. G. Beer
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  2. J. L. Meek
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Editors and Affiliations

  1. Department of Civil Engineering, The University, SO9 5NH, Southampton, England

    Carlos A. Brebbia

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© 1984 Springer-Verlag Berlin Heidelberg

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Beer, G., Meek, J.L. (1984). Applications in Mining. In: Brebbia, C.A. (eds) Topics in Boundary Element Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2877-1_9

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  • DOI: https://doi.org/10.1007/978-1-4899-2877-1_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-13097-2

  • Online ISBN: 978-1-4899-2877-1

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