The computational analysis of shallow depth tabular mining problems

Journal of the Southern African Institute of Mining and Metallurgy

Volumn 107, Issue 11, 2007, Pages 725-742

  Napier, J A L ^a,b   Malan, D F ^c  

^a CSIR ^*

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^c Groundwork Consulting (Pty) Ltd   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

REEF PILLARS; SHAPED PLANAR CRACKS; TABULAR MINING PROBLEMS;

BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; PLATINUM; PROBLEM SOLVING;

MINING;

EID: 37649009017     PISSN: 22256253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. BRUMMER, R.K. Modelling the Non-linear Behaviour of Fractured Seams in Deep Gold Mines, APCOM 87. Proceedings of the Twentieth International Symposium on the Applications of Computers and Mathematics in the Mineral Industries, vol. 1: Mining. Johannesburg, SAIMM, 1987. pp. 21-32.
2. BRADY, B.H.G. and 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., vol. 15, 1978. pp. 29-37.
3. CROUCH, S.L. Two-dimensional analysis of near-surface, single-seam extraction. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., vol. 10, 1973. pp. 85-96.
4. CROUCH, S.L. and STARFIELD, A.M. Boundary Element Methods in Solid Mechanics. George Allen & Unwin, 1983.
5. DEIST, F.H., GEORGIADIS, E., and MORIS, J.P.E. Computer applications in rock mechanics. Application of Computer Methods in the Mineral Industry, 10th International Symposium, Johannesburg, 1972.
6. JASWON, M.A. and SYMM, G.T. Integral equation methods in potential theory and elastostatics. Academic Press, London, 1977.
7. JOHNSON, K.L. Contact Mechanics. Cambridge University Press, 1985.
8. LANDAU, L.D. and LIFSHITZ, E.M. Theory of Elasticity, Third Edition, Pergamon Press, 1986.
9. MALAN, D.F. and NAPIER, J.A.L. Practical application of the TEXAN code to solve pillar design problems in tabular excavations. South African National Institute of Rock Engineering Symposium, 2006, Rustenburg, 2006. pp. 55-74.
10. MORIS, J.P.E. and ORAVECZ, K.I. Theoretical background to the development of a computer code for the modelling of seam-like deposits. Proceedings of the 26th US Symposium on Rock Mechanics, Rapid City, South Dakota, 1985. pp. 927-936.
11. NAPIER, J.A.L. and HILDYARD, M.W. Simulation of fracture growth around openings in highly stressed, brittle rock. J. S. Afr. Inst. Min. Metall., vol. 92, 1992. pp. 159-168.
12. NAPIER, J.A.L. Crack edge collocation for the direct computation of stress intensity factors using the displacement discontinuity method. South African Journal of Science, vol. 98, 2002. pp. 481-485.
13. NAPIER, J.A.L. and STEPHANSEN, S.J. Analysis of Deep-level Mine Design Problems Using the MINSIM-D Boundary Element Program, APCOM 87. Proceedings of the Twentieth International Symposium on the Applications qf Computers and Mathematics in the Mineral Industries, vol. 1: Mining. Johannesburg, SAIMM, 1987. pp. 3-19.
14. PEIRCE, A.P., SPOTTISWOODE, S.M., and NAPIER, J.A.L. The spectral boundary element method: a new window on boundary elements In rock Mechanics. Int. J. Rock Mech. Min. Sci. Sci. Geomech. Abstr., vol. 29, 1992. pp. 379-400.
15. PEIRCE, A.P. and NAPIER, J.A.L. A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics. Int. j. numer. methods eng., vol. 38, 1995. pp. 4009-4034.
16. PFALZNER, S. and GIBBON, P. Many-body tree methods in physics. Cambridge University Press, 1996.
17. PLEWMAN, R.P., DEIST, F.H., and ORTLEPP, W.D. The development and application of a digital computer method for the solution of strata control problems. J. S. Afr. Inst. Min. Metall., vol. 70, 1969. pp. 33-44.
18. RYDER, J.A. and OFFICER, N.C. An elastic analysis of strata movement observed in the vicinity of inclined excavations. J. S. Afr. Inst. Min. Metall., vol.64, 1964, pp. 219-244.
19. RYDER, J.A. and NAPIER, J.A.L. Error analysis and design of a large-scale tabular mining stress analyser. 5th Int. Conf on Num Methods in Geomech., Nagoya, Japan, 1985. pp. 1549-1555.
20. SALAMON, M.D.G. Elastic analysis of displacements and stresses induced by the mining of seam or reef deposits - Part I: Fundamental principles and basic solutions as derived from idealised models. J. S. Afr. Inst. Min. Metall., vol. 63, 1963. pp. 128-149.
21. Part II: Practical methods of determining displacement, strain and stress components from a given mining geometry, J. S. Afr. Inst. Min. Metall., vol. 64, 1964. pp. 197-218.
22. Part III: An application of the elastic theory: Protection of surface installations by underground pillars. J. S. Afr. Inst. Min. Metall, vol. 64, 1964. pp. 468-500.
23. Part IV: Inclined reef. J. S. Afr. Inst. Min. Metall., vol. 65, 1965. pp. 319-338.
24. SALAMON, M.D.G., BADR, S., MENDOZA, R., and OZBAY, M.U. Pillar Failure in Deep Coal Seams: Numerical Simulation. Proceedings of the 10th Congress of the International Society for Rock Mechanics, The South African Institute for Mining and Metallurgy, Johannesburg, 2003. pp. 1011-1018.
25. SNEDDON, I.N. Fourier Transforms. McGraw-Hill, 1951.
26. SPOTTISWOODE, S.M. Keynote address: Synthetic seismicity mimics observed seismicity in deep tabular mines. 5th International Symposium on Rockbursts and Seismicity in Mines Van Aswegen, G., Durrheim, R.J. and Ortlepp, W.D. (eds), S. Afr. Inst. Min. Metall., 2004. pp. 371-378.
27. STUART, A.D. An application of the fast Fourier transform in numerical elasticity. M.Sc. Thesis, University of the Witwatersrand, Johannesburg, 1979.
28. VAN DER MERWE, J.N. Beyond Coalbrook: what did we really learn? J. S. Afr. Inst. Min. Metall., vol. 106, 2006. pp. 857-868.
29. VIJAYAKUMAR, S., YACOUB, T.E., and CURRAN, J.H. A node centric indirect boundary element method: Three-dimensional discontinuities. Int. J Computers & Structures, vol. 76, 2000. pp. 687-703.
30. WATSON, B.P., ROBERTS, M.K.C., NKWANA, M.M., KUIJPERS, J., and VAN ASWEGEN, L. The stress-strain behaviour of in-stope pillars in the Bushveld Platinum deposits in South Africa. J. S. Afr. Inst. Min. Metall, vol. 107, 2007. pp. 187-194.
31. WILES, T.D. Reliability of numerical modelling predictions. Int. J. Rock Mech. Min. Sci. vol. 43, 2006. pp. 454-472.
32. YACOUB, T.E. and CURRAN, J.H. Analysis of post-peak pillar behaviour using the enhanced displacement discontinuity method. Proceedings of the 37th U.S. Rock Mechanics Symposium, Balkema, 1999. pp. 169-176.
33. ZIPF, R.K. MULSIM-NL Theoretical and Programmer's Manual. BuMines IC 9322, 1992.