The rock pillar stress analysis in order to obtain an effective dimensioning and guarantee the mining void stability

Document Type : Article


1 University of Tabriz

2 Department of Environment , Land and Infrastructure Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, Turin 10129 , Italy

3 Department of Civil and Environmental Engineering, Amirkabir University of Technology, ‎ ‎ Tehran, Iran


In the room and pillar mining method is of fundamental importance the dimensioning of the pillars. The area of influence method is typically used today for dimensioning of the pillars, but an overdimensioning or critical stability conditions can happen with this method.
A parametric analysis with tri-dimensional numerical modelling was carried out to study in the detail the stress conditions in the rock pillars. This made it possible to identify a critical point, where the minimum local safety factor is reached, at the corners of the pillar close to the roof of the mining room.
Through the estimation of the major principal stress at the critical point it was possible to evaluate the minimum local safety factor in function of the geometric and geomechanical parameters of the problem.
The dimensioning of the pillars through the local safety factor at the critical point makes it possible to avoid overdimensioning and static problems, which instead can occur when simplified calculation methods are used.
The use of proposed figures can allow a fast pre-dimensioning of the pillar, leaving the more detailed numerical modelling only to the found geometric configuration.


Main Subjects


1. Esterhuizen, G.S., Dolinar, D.R., and Ellenberger, J.L. Pillar strength in underground stone mines in the United States", International Journal of Rock Mechanics & Mining Sciences, 48(1), pp. 42-50 (2011).
2. Peduto, D., Arena, L., Ferlisi S., and Fornaro, G. Analysis of subsidence phenomena via DInSAR data at di erent scales", Proceedings of the 8th WSEAS International Conference on Environmental and Geological Science and Engineering EG '15, Salerno, Italy
3. Mortazavi, A., Hassani, F.P., and Shabani, M. A numerical
investigation of rock pillar failure mechanism
in underground openings", Computers and Geotechnics,
36(5), pp. 691-697 (2009).
4. Kaiser, P.K. and Tang, C.A. Numerical simulation of
damage accumulation and seismic energy release during
brittle rock failure", Part II: Rib Pillar Collapse.
International Journal of Rock Mechanics & Mining
Sciences, 35(2), pp. 123-134 (1998).
5. Jaeger, J.C. and Cook, N.G.W., Fundamentals of Rock
Mechanics, 4th Edn., p. 513, Blackwell Publishing,
London (2007).
6. Do, N.A., Dias, D., Oreste, P., and Djeran-Maigre
I. 2D numerical investigation of segmental tunnel
lining behaviour", Tunnelling and Underground Space
Technology, 37, pp. 115-127 (2013).
7. Do, N.A., Dias, D., Oreste, P., and Djeran-Maigre, I.
Three-dimensional numerical simulation for mechanized
tunnelling in soft ground: The in
uence of the
joint pattern", Acta Geotechnica, 9(4), pp. 673-694
8. Do, N.A., Dias, D., Oreste, P., and Djeran-Maigre, I.
Three-dimensional numerical simulation of a mechanized
twin tunnels in soft ground", Tunnelling and
Underground Space Technology, 42, pp. 40-51 (2014).
9. Ranjbarnia, M., Oreste, P., and Fahimifar, A.
Analytical-numerical solution for stress distribution
around tunnel reinforced by radial fully grouted rockbolts",
Int. J. Numer. Anal. Meth. Geomech, 40(10),
pp. 1844-1862 (2016).
10. Innaurato, N., Oreste, P., Peila, D., and Castiglia
C. First results of a parametric study through 3D
numerical modeling for the study of the behavior of
pillars of ornamental stones underground quarries"
[Primi risultati di uno studio parametrico attraverso
modellazione numerica 3D per lo studio del comportamento
dei pilastri di cave sotterranee di pietre
ornamentali], in Le cave di pietra ornamentali, Torino,
Italy, Ed. Geam, pp. 151-158 (2000).
11. Martin, C.D. and Maybee, W.G. The strength of
hard-rock pillars", International Journal of Rock Mechanics
& Mining Sciences, 37(8), pp. 1239-1246
12. Hoek, E. and Brown. E.T., Underground Excavations
in Rock, The Institute of Mining and Metallurgy,
London (1980).
13. Lunder, P. and Pakalnis, R. Determination of the
strength of hard-rock. mine pillars", Can. Inst. of Min.
and Met Bulletin, 90(1013), pp. 51-55 (1997).
556 M. Ranjbarnia et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 543{556
14. Maybee, W.G. Pillar design in hard brittle rocks",
Master's Thesis, School of Engineering, Laurentian
University, Sudbury, ON, Canada (1999).
15. Salamon, M.D.G. and Munro, A.H. A study of the
strength of coal pillars", J.S. Afr. Inst. Min. Metall.,
65, pp. 55-67 (1967).
16. Hardy, M.P. and Agapito, J.F.T. Pillar design in oil
shale mines", In Proc. 16th US Symp Rock Mech.,
ASCE, New York, USA, pp. 257-266 (1977).
17. Gonzalez-Nicieza, C., Alvarez-Fernandez, M.I.,
Menendez-Diaz, A., and Alvarez-Vigil, A.E. A
comparative analysis of pillar design methods and
its application to marble mines", Rock Mech. Rock
Engng., 39(5), pp. 421-444 (2006).
18. Potvin, Y., Hudyma, M.R., and Miller, H.D.S. Design
guidelines for open slope support", Bull. Can. Min.
Metall., 82, pp. 53-62 (1989).
19. Krauland, N. and Soder, P.E. Determining pillar
strength from pillar failure observations", Eng. Min.
J., 8, pp. 34-40 (1987).
20. Sheorey, P.R., Loui, J.P., Singh, K.B., and Singh,
S.K. Ground subsidence observations and a modi ed
uence function method for complete subsidence
prediction", Int. J. Rock Mech. Min. Sci., 37(5), pp.
801-818 (2000).
21. Itasca, FLAC 3D manual (2006). http://www.itascacg.
22. Guarascio, M. and Oreste, P. Evaluation of the stability
of underground rock pillars through a probabilistic
approach", American Journal of Applied Sciences,
9(8), pp. 1273-1282 (2012).
23. Oreste, P. Stability of rock pillars with singular
and persistent discontinuities", American Journal of
Applied Sciences, 9(9), pp. 1354-1372 (2012).
24. Lederer, M. and Khatibi, G. Finite element implementation
of a novel version of strain gradient elasticity",
Proceedings of the 6th WSEAS International Conference
on Theoretical and Applied Mechanics TAM
'15, Salerno, Italy (2015).
25. Hoek, E. and Brown, E.T. Practical estimates or
rock mass strength", Int. J. Rock Mech. Min.g Sci.
& Geomech. Abstr., 34(8), pp. 1165-1186 (1997).
26. Hoek, E., Carranza-Torres, C. and Corkum, B. Hoek-
Brown failure criterion-2002 edition", In: Proceedings
of the 5th North American Rock Mechanics Symp.,
Toronto, Canada, 1, pp. 267-73 (2002).
27. Hoek, E. A brief history of the development of the
Hoek-Brown failure criterion", Soils and Rocks, 30(2),
pp. 85-92 (2007).
28. Cai, M., Kaiser, P.K., Uno, H., Tasaka, Y., and
Minami, M. Estimation of rock mass deformation
modulus and strength of jointed hard rock masses
using the GSI system", International Journal of Rock
Mechanics & Mining Sciences, 41(1), pp. 3-19 (2004).
29. Marinos, P. and Hoek, E. GSI: a geologically friendly
tool for rock mass strength estimation", Proc. International
Conference on Geotechnical & Geological Engineering,
GeoEng 2000, Technomic Publ., Melbourne.
Australia, pp. 1422-1442 (2000).
30. Wei, R., Zhang, S., Karunasena, W., Sivakugan, N.,
and Zhang, H. Blast simulation in underground mines
using the combined nite-discrete element method",
Proceedings of the 7th WSEAS International Conference
on Simulation, Modelling and Optimization,
Beijing, China (2007).
31. Singh, M. and Rao, KS. Empirical methods to estimate
the strength of jointed rock masses", Engineering
Geology, 77(1-2), pp. 127-137 (2005).
32. Laubscher, D.H. Design aspects and e ectiveness of
support systems in di erent mining conditions", Trans