RESPONSE OF ORE MASSES TO STOPE SEQUENCE VARIATIONS
*N. Saeidi, D. Millar
LaurentianUniversity
935 Ramsey Lake Road
Sudbury, Canada P3E 2C6
(*Corresponding author: nsaeidi@laurentian.ca)
ABSTRACT
For a mine section comprising 100 different stoping activities, there are ~10 158 different possible stoping
sequences to explore in the mine schedule optimization search and this figure is indicative of the challenge
posed in maximising profitability through mine schedule optimization.Any viable excavation timetable
must satisfy all conditions that will constrain feasible sequences. In general, consideration of additional
constraint will tend to reduce profitability. Geomechanical constraints on mine schedules, introduced with
the aim of avoiding excavation instabilities, can be established for underground mine schedule
optimization processes but, currently, this is done only rather crudely; precedence relations between
excavation activities (stoping or development) are encoded to produce particular stope sequence patterns
(e.g. chevron or pyramidal sequences) that ‘override’ basic access precedence.
The work reported aimed to investigate automated processes for formulation of such geomechanical
constraints. The timetable optimization approach to the problem precipitated a fresh look at time dependent,
and excavation sequence dependent, deformation. Abundant evidence emerged that supported the notion
that any methodology developed that failed to account for such time and sequence dependencies was itself
bound to failure. Yet, it was also recognised that any deviation at all from an assumption of linear elasticity
for geomechanical numerical modeling, adopted to inform geomechanical constraint formulation, would
rapidly lead to impractical levels of computational effort.
Thus the approach presented here represents a compromise: the elastic stress fields induced by individual
mining activities are computed for each activity, independently considered within a computational domain
identical to that of all other activities. These are stored in a database. Instability risk for a specific sequence
of mine activities can be assessed through superimposition of stress fields drawn from the pre-computed
database. Time stamps allocated to events corresponding to the excavation processes permit the conversion
of the sequence of elastic stress fields into a time table of stress fields. For specific locations within the
computational domain, the aggregate effect of the sequence of mine activities leads to stress-time histories
having a castellated appearance, a result of the near instantaneous response of an elastic medium to the
excavation perturbations. Time dependent deformation responses are crudely allowed for through the reprofiling these castellated histories through graphical construction of curved responses, where the curve
gradients are related to a viscous parameter. Such curves form the basis for a geomechanical constraint
formulation adopted mine schedule optimization.
Figure 1 – Typical time-dependent stope closure of the Ventersdorp Contact Reef at Western Deep Levels
Mine[1]. Dashed lines are added to emphasize differences between expected elastic and visco-elastic
deformation responses.
KEYWORDS
Mine schedule optimization, time-dependent deformability, excavation sequencing
[1] Malan, D. F., 1999. Time-dependent Behaviour of Deep Level Tabular Excavations in Hard Rock. Rock Mechanics
and Rock Engineering, Springer-Verlag , 32(2), pp. 123-155.