Stability Analysis
Fill Stresses
The vertical and horizontal stresses are calculated using multiple analytical methods. The stresses at the base of the stope are reported in the table and the chart shows the variation in stress by fill depth.
- Martson Cohesionless Model. Marston, A., 1930. The theory of external loads on closed conduits in the light of the latest experiments. In Highway research board proceedings (Vol. 9).
- Modified Martson's Cohesionless Model. Aubertin, M., Li, L.S.T.B.M., Arnoldi, S., Belem, T., Bussière, B., Benzaazoua, M. and Simon, R., 2003. Interaction between backfill and rock mass in narrow stopes. Soil and rock America, 1(2), pp.1157-1164.
- Terzaghi's Cohesive Model. Terzaghi, K., 1943. Theoretical soil mechanics. johnwiley & sons. New York, pp.11-15.
- Van Horn's 3D Model. Van Horn, D.A., 1964, September. A study of loads on underground structures. In Proceedings of the Symposium on Soil-Structure Interaction (No. Conf Paper).
Vertical Exposure
The required UCS for vertical exposure is calculated using multiple analytical methods. Most methods only apply to a single vertical exposure. One approach looks at multiple vertical exposures. The arching effect is related to the perimeter of the stope not yet exposed. The order of exposure can be adjusted by editing the exposure priority.
- Narrow Face. Askew, J., McCarthy, P.L. and Fitzgerald, D.J., 1978. Backfill research for pillar extraction at ZC/NBHC. Mining with backfill, 12, pp.100-110.
- Frictional Sliding Block. Mitchell, R.J., Olsen, R.S. and Smith, J.D., 1982. Model studies on cemented tailings used in mine backfill. Canadian Geotechnical Journal, 19(1), pp.14-28.
- Frictionless Sliding Block. Mitchell, R.J., 1983. Earth mechanics in earth structures engineering. In Earth Structures Engineering (pp. 38-86). Springer, Dordrecht.
- Modified Mitchell. Li, L. and Aubertin, M., 2012. A modified solution to assess the required strength of exposed backfill in mine stopes. Canadian Geotechnical Journal, 49(8), pp.994-1002.
- Block and Wedge. Li, L., 2014. Generalized solution for mining backfill design. International Journal of Geomechanics, 14(3), p.04014006
- Multiple Exposures. Bloss, M.L., 1992. Prediction of cemented rock fill stability: design procedures and modelling techniques. University of Queensland. Winch, C., 1999. Geotechnical characteristics and stability of paste backfill at BHP Cannington mine. BE Hons Thesis, James Cook University, Townsville, Australia.
Horizontal Exposure
The required UCS for horizontal exposure is calculated using multiple analytical methods. The analysis is for a 2D beam. This might be the first "plug" run. There is optional beam loading to represent additional fill mass above the beam. The beam loading can be estimated from the vertical stress.
The sill pillar analysis is based on Mitchell and Roettger (1989) that considers a number of failure modes:
- Crushing Failure (convergence of the stope)
- Rotational Failure
- Flexural Failure
- Caving Failure
- Sliding Failure
Mitchell, R.J. and Roettger, J.J., 1989. Analysis and modelling of sill pillars. Innovations in mining backfill technology, pp.53-61.
The voussoir beam analysis is based on the original work of Evans (1941) and later Beer and Meek (1982) that considers the strength of a compressive arch within the rectangular beam. The analysis looks at crushing and sliding failure. The procedure was also described in Diederichs and Kaiser (1998).
Evans, W., 1941. The strength of undermined strata. Trans. Inst. Min. Metall, 50, pp.475-500.
Beer, G. and Meck, J.L., 1982. Design curves for roofs and hanging-walls in bedded rock based on'voussoir'beam and plate solutions. Trans.-Inst. Min. Metall., Sect. A;(United Kingdom), 91.