Problems

The list of problems will be updated as problems are submitted and further information about the present problems and additional problems becomes available. Please keep watching these pages. À×ËÙÌåÓý_À×ËÙÌåÓýÖ±²¥ five problems will be selected depending on the expertise and interests of the participants.

1. Problem: Mine support mechanisms using a limit equilibrium analysis
   Industry: Mining industry
   Industry representative: Professor John Napier
   Moderator:
   Description: Some interesting problems arise in the analysis and design of support systems for mining excavations. These include the installation of liner materials such as sprayed concrete, wire meshing and anchored strands of steel cable to contain the movement of broken rock near the surfaces of active excavations. The failed rock cannot be assumed to behave elastically. An approximation that can be made is to represent the fractured rock as a pseudo-continuum in which the constitutive properties are assumed to be in a state of ?limit equilibrium?. In this case a fixed constraint exists between the local stress components at each point of the material. A simple example of such a constraint is the imposition of the Mohr-Coulomb failure criterion. (See also Jaeger and Cook, Chapter 9).
   
   The proposed problem of interest is to determine the detailed stress distribution and ?plastic flow? movements in a specified region of interest that is bounded by a support lining material and to determine the effect of the lining material properties in controlling these movements. A suggested geometrical configuration, and an elementary limit equilibrium analysis, is included in the supplementary document.
   
   References
   Jaeger, J.C. and Cook, N.G.W. 1979. ?Fundamentals of Rock Mechanics?, 3rd Edition, Chapman and Hall, London.
   Hill, R. 1950. ?The mathematical theory of plasticity?, Oxford, Clarendon Press.
   equilibriumderivation.doc.
   
   
2. Problem: Minimising the effects of rockbursts?
   Industry: Mining industry
   Industry representative: Professor Richard Stacey
   Moderator:
   Description:
   Rockbursts in mines are very violent events. Violent ejection of rock from the surfaces of underground openings is usually observed, and the velocities of such ejection can be of the order of 1 to 10 m/sec. After a rockburst event in 2005, it was noticed that, in one localized area, concrete in the floor had been subjected to heave (as a result of some ejection), but that an immediately adjacent mud-filled area was unaffected. This is illustrated in the photograph on the right. The violent loading of the steel arch by the concrete can also be observed in the photograph, but the adjacent arches were clearly not similarly loaded.
   
   In other tunnels similar observations were made ? where there had been water or mud on the floor, there was no observable rockburst damage. It is expected that this behaviour could be the effect of compressive wave reflection at the free surface (concrete, mud or water) and the mud or water has effectively served as a tensile wave trap. The behaviour raises the following questions:
   • Could the effects of rockbursts be mitigated in some cases by means of a soft coating or ?gel? covering on the rock surface?
   • If there is such a benefit, would it be wave frequency dependent?
   • Would the thickness of the ?soft? layer have any effect on the beneficial behaviour?
   • What about the effects of other waves, and interactions of waves?
     
     
3. Problem: Effect of thermal gradients on the random diffusion of a light solute, C, in a heavier solvent, Fe or Co
   Case 1 In zero gravity
   Case 2 In one g vertical
   Case 3 In an extreme pressure gradient
   Industry: Element Six Technologies
   Industry representative: Dr Joh Hansen
   Moderator:
   Description: A metal solvent such as iron or a similar alloy is maintained at just above its melting point. Powdered carbon is present at the hotter end of the solvent volume, typically the top, and a controlled migration of carbon atoms towards the colder end is desired. It is suspected that the rate of carbon transport is in some way governed by the temperature difference.

   The carbon atom is much lighter than any of the metal atoms used in the solvents. This suggests that buoyancy forces should oppose the movement of carbon.

   The central question is: does the presence in a liquid phase of a temperature gradient encourage the diffusion of the lighter species up or down the temperature gradient? Would this be true in zero gravity? How does the presence of a pressure gradient affect the result?

   Further refinements could include:
   a vertical gravitational field where upwards motion is subject to conservation of total energy;
   an extreme pressure field where mean free path decreases in the direction of higher pressure.

   References:
   1. Smith R W, Yang B J and Huang W D. The measurement of solute diffusion coefficients in dilute liquid alloys: the influence of unit gravity and G-Jitter on buoyancy convection. Annals of the New York Academy of Sciences, 1027 (2004), 110-128.
   2. Serga M A and Shevchuk S N. Simulation of temperature fields in a cell for growing diamond single crystals with stimulated nucleation. Journal of Superhard Materials, 27 (2005), 67-72.

4. Problem: Pre-split blasting technique in surface mines
   Industry: Mining industry
   Industry representative: Alan Naismith
   Moderator:
   Description:
   A method of protecting permanent faces from blasting damage in surface mines is to use the pre-split blasting technique. A series of closely spaced vertical and parallel holes is drilled in the rock and a fracture surface is created by a simultaneous and equal energy input into each hole. This technique appears to be successful in both brittle rock types such as sandstones and basalts and in softer materials such as kimberlite. However, there have been situations recently in which the pre-split technique is effective for about 80% of its height and then it appears to go away. Photograph 1 is attached which shows the general effect.

   The problem is to explore analytically and numerically the development of a fracture surface in the pre-split blasting technique. The outcomes that would be sought include:

   • Development of a relationship between energy input and fracture development for different rock brittleness.
   • Establishing the maximum hole spacing at which fracture propagation will occur.
   • Establishing a cause for the apparently anomalous fracture behaviour at the unconfined end of the hole.
   • Investigating the method of fracture propagation within a hole, in particular, determining the conditions under which ?multi-nodal? fracture initiation may occur as shown in Photograph 2.
   • Development of methods to control the direction and extent of fracture development, particularly in the upper part of the hole and where other fractures intersect the hole.
     
     
     
     
5. Problem: An optimal supply chain management for illuminating paraffin distribution in Southern Africa.
   Industry: Paraffin Safety Association in South Africa
   Industry representative: Dr Shehz d Kauchali
   Moderator: Professor Montaz Ali
   Description:
   The simplest supply chain addressed by optimization is the distribution network. This type of network is characterized by a flow of products between origins and destinations. Origins are facilities that originate freight, typically factory warehouses or distribution centers. Destinations are facilities that receive freight, mainly customer locations. The network could, however, represent an origin of supplier facilities or manufacturing plants and a destination of distribution centers.
   However, the network considered in this problem is of advanced type where a broader logistics environment is evolved. Optimization for this type of network may involve simultaneously determining the number, location and mission of production facilities, supplier locations, as well as the previously described distribution network. There are therefore a number of decision variables, the cost function and constraints involved
   in the optimization model that need to be developed. The major logistical issue that needs to be addressed in the model is the siting and selection of the packaging operations.
   Thus the optimization tool would select the most economically favorable sites for increased production. However, the optimization framework that needs to developed must permit a user to select the optimal distribution network to varying degrees of complexity.
   The primary aim of the study is to define a framework, within which it is possible to design the optimal distribution network, for the delivery of paraffin into a range of end-user environments.
   
   
6. Problem: Multi-stage manufacturing sequence management
   Industry: Nissan
   Industry representative: Dr Pekka Pihlajas ri
   Moderator: Colin Myburgh
   Description:
   Automotive manufacturers are committed to producing many vehicle models on
   shared equipment ? both to reduce investment in capital equipment, and to allow rapid shifts in volumes to better react to market demand. These facilities are configured in multi-stage networks of conveyors with both merges and splits.
   Manpower is scheduled and facilities are configured to satisfy this demand subject to constraints imposed by different stages. Typical constraints include high switching costs between models, vehicles of the same colour must be grouped and combinations of options require different amounts of labour to fit.
   The vehicle production sequence needs to be chosen to best match capacity to demand while avoid the violation of facility and manpower constraints.
   For further information multi-stage-manufacturing-sequence.doc.
   
   
7. Problem: Distribution and Inventory Cost Optimization
   Industry: Super Group Supply Chain Partners
   Industry representatives: Dr Tomasz Jekot and Mr Stephen Povey
   Moderator:
   Description:
   There is a vending machine selling one item. A single distributor is responsible for the delivery of stock to replenish the machine. The distributor has several modes of transport with known tariffs. The tariffs are calculated according to the delivery date and the amount transported (i.e. the longer the delivery time and the more units ordered the lower cost per unit). When a level of l units is reached an order for a delivery of x units within a delivery time of t hours is placed with the distributor.
   Find l, x and t to maximise the profits (P) of the vending machine.

   Reference: WL Winston, Operations Research 3rd Edition 1993
   For further information inventory_cost_optimisation.doc

8. Problem: The effect of the yield stress on the laminar/turbulent transition
   Industry: Mining Industry
   Industry representative: Professor Paul Slatter
   Moderator: Professor Tim Myers
   Description:
   The laminar/turbulent transition is important for pipe system design as the behaviour of the fluid changes fundamentally at the transition point. For non-Newtonian fluids there are many different approaches but no guidelines as to which approach is more accurate. The topic has become more important recently, with the effect of the yield stress dominating the pipe flow behaviour of mining trailings in large pipes (diameter >1m). The problem is to derive a mathematically rigorous formulation for the constant C(n) in the relation between the mean fluid velocity and the yield stress. The value of C(n) is required for practical pipeline design.

   Reference
   Slatter, PT ?The role of the yield stress on the laminar/turbulent transition?. 9th International Conference on Transport and Sedimentation of Solid Particles, Cracow: 2-5 September, 1997. pp 547-561.

   The constant C(n) occurs in Equation (19) of this reference.

   To access the reference slatter.pdf