Analytical solution for determining the required strength of a side-exposed mine backfill containing a plug

Backfilling is well known in the mining industry. A basic issue associated with mine backfill design is the determination of the strength of the backfill required to maintain the stability of the backfill body upon removal of a side wall when an adjacent secondary stope is excavated. This task is usually accomplished using a solution proposed by Mitchell et al. in the early 1980s. Recently, this solution has been reviewed and a modified solution has been proposed. These existing solutions, however, were developed for a uniform backfill. In practice, mine stopes are usually divided into primary and secondary stopes. Primary stopes are often backfilled in two stages: a plug pour and a final pour. In many cases, the cement content of the plug pour is higher than that of the final pour. The positive effect of the stronger plug is neglected in both the original and the modified Mitchell et al. solutions. Here, a new analytical solution is developed for estimating the required strength of a laterally exposed backfill by taking the plug into account. The proposed solution reduces to the modified Mitchell et al. solution if the plug pour and final pour have the same cement content. If the plug pour has a cement content higher than that of the final pour, the required backfill strength calculated with the proposed solution is lower than the values estimated with the modified Mitchell et al. solution; the same conclusion can be drawn to the comparison between the proposed solution and the original Mitchell et al. solution when the bond cohesion along the side walls is close to the cohesion of the backfill. Furthermore, the proposed solution indicates that an optimal cohesion ratio between the plug and final pours exists: there is no benefit in using excessively high cement content in the plug pour. It is noted that the proposed solution is valid only for high, narrow backfilled stopes, solutions for low and wide backfilled stopes are under development.