Mine schedule optimization with geotechnical constraints

Abstract

If a mining project consists of n stoping activities these can be scheduled in n! ways according to the duration between the activities and their precedence. Mine schedule optimization manipulates the precedence relationships and the duration of the mining activities in order to maximize the Net Present Value (NPV). However, unexpected instabilities may impede or disrupt the schedule and thus reduce the profitability and so geotechnical aspects of the operation need to be taken into account. The mine schedule optimization software considered in this work is the so-called Schedule Optimization Tool (SOT). This thesis reports the work for development of new geomechanical constraints for any mine scheduling tool to find the safest and the most profitable schedule, exemplified within the SOT framework. The core hypothesis of this research is that there is a time-dependent aspect of the rock behaviour that leads to instability, a consequence of dependence of geotechnical instability upon the sequence and duration between stoping activities. There is evidence presented in this work that supports this hypothesis. An automated procedure for timely and computationally efficient calculations of the instability metrics is presented. This can be applied to evaluate the geomechanical stability of any of the n! schedules for excavating n stopes or applied to evaluate geomechanical stability of schedules arising in the schedule optimization process. However, in practice, the number of feasible schedules is much less than n! due to the precedence constraints. The approach starts with computing n elastic stress fields induced after excavating each individual stope independently within an identical computational domain using Compute3D. The stress-time series of each iv and/or every sequence of stoping are generated through superimposition of these pre-computed stress fields, and the time stamps of blasting for excavation are allocated corresponding to the stoping timetable. Different blasts are allowed to be timetabled at the same time. By means of Hooke’s law and the 3D Kelvin-Voigt creep model the elastic strain time series and the viscoelastic strain time series are produced for the stress-time series. Based on the Mohr- Coulomb Failure criterion three (in)stability indicators are defined: i. ‘Strength Factor’ to evaluate state of stress at each stage of each schedule as a proportion of is strength ii. ‘Strainth Factor’ to evaluate state of elastic strain at each stage of each schedule as a proportion of a limiting ‘rupture’ strain iii. ‘Viscoelastic-strainth Factor’ to evaluate state of viscoelastic strain at each stage of each schedule as a proportion of a limiting ‘rupture’ strain. To provide a perspective of the (in)stability condition in the computational domain for all the feasible sequences of stoping, 12 (in)stability metrics were defined and the results of each are illustrated in the form of ‘(in)stability indicator diagrams’. The overall methodology is applied to an example of excavating 6 open stopes. Additionally, a methodology is theorized to evaluate the stability condition in the rock mass surrounding the stopes for a series of stoping and backfilling schedules. The methodology is based on pre-computing one additional stress field element for each stope, which represents the effect of the fill loading on the rock mass. The calculations for this approach are consistent with the time and computational efficiency of the original methodology. The computational effort v increases to ‘2n’ pre-computed stress fields rather than ‘n’: as problem sizes double, computational time doubles, rather than increases in polynomial or exponential time.