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A simple physical modelling technique for the demonstration of interaction between underground openings
Vol. 16, pp. 217 to 219 © PergamonPress Ltd 1979.Printed in Great Britain
0020-7624/79/0601-0217502.00/0
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
Technical Note A Simple Physical Modelling Technique for the Demonstration of Interaction between Underground Openings B. STIMPSON*
INTRODUCTION For students of rock engineering the testing of intact rock and the theory of elasticity provide a useful basis for design for some classes of rock mechanics problems, but this approach should be complemented by laboratory and classroom exercises aimed at giving the student an understanding of the behaviour of jointed, inhomogeneous, non-elastic rock masses. For obvious reasons the teaching and demonstration of rock mass behaviour in the classroom or laboratory is more difficult than the study of intact rock properties. Case histories are certainly indispensable in bridging the gap between idealized rock mass behaviour and reality but well documented, photographed and instrumented case histories are few. Numerical modelling is capable of including non-linear (both geometric and material) properties of rock masses but the facilities and/or budgets are not always available for this approach to be used as a regular classroom tool. Inexpensive, simple physical models represent a third approach which may be of value, not only to college educators, but also to industrial training programs. For example, simple physical models may be used to demonstrate to mining machine operators the importance of not cutting too wide a span in room-and-pillar operations. Probably the most widely known simple physical modelling technique is the base friction method which can provide very interesting and illustrative models of rock mass behaviour [1]. The method is restricted to kinematic modelling and has a number of deficiencies including the incorrect simulation of situations where parts of the rock mass attain significant horizontal momentum and then either impact another surface or lose contact with adjacent surfaces I-2]. However, in many situations this effect is not significant and quite convincing demonstrations can be set up. A second disadvantage of the base friction method is the low stresses induced in the model material. It is difficult to demonstrate compressive rock fracture and crushing. If a very weak model material is used the material can * Department of Mineral Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2El.
fail by means of a shallow "thrust fault" passing from the base of the friction model to the surface and the model is invalid. The base friction method is, therefore, most suited to illustrating the kinematics of rock masses with continuous joint systems dissecting hard intact rock. An alternative approach is to construct vertical model frames in which gravity is used directly and in which higher stresses can be generated. This Technical Note describes a simple technique for demonstrating interaction between underground mine openings using this method. As with base friction modelling, it does not claim to be a quantitative approach and is intended for classroom or laboratory demonstrations.
VERTICAL FRAME MODEL The plane strain frame may be of any size though for practical and economic reasons one measuring 0.9 m (3 ft) in width and 1.2 m (4 ft) in height is suitable. One side of the frame comprises a 10 mm (0.38 in) thick glass plate through which the model can be observed. Stiffeners or a thicker plate will be required to reduce bending for larger frames. The other side of the frame is formed from a 7.6 cm (3 in) thick slab of 'rigid' polyurethane foam which is supported by cross beams to limit bending. The glass plate and polyurethane slab enclose a 2.54 cm (1 in) space for the model material. The model material should be capable of being cut with a blade so that discontinuities can be introduced into the material. Mixtures of flour, vegetable oil, fine sand and silt-size glass shot make an inexpensive, easily handled material. A typical mix consists of 55% flour, 20% vegetable oil, 7% sand, 18% glass shot (by weight). The glass shot increases the compactability of the material but also reduces the angle of internal friction. More recently derived materials include flour and methanol and various granular materials mixed with Shellac [3]. The construction and testing of a model proceeds as follows: (a) Outline the system of mine openings on the polyurethane slab with a marker and cut out each
217
218
Technical Note
Fig. 1. Caving of hanging wall in steeply dipping bedded sequence being 'mined' up-dip.
opening so that a plug of polyurethane can be removed. Pin each plug in its original position with pins or tape. (b) Erect frame in vertical position and place model material. Provide some means of gently tamping or vibrating material to help achieve uniform compaction. (c) Lay frame in horizontal position and remove glass plate. (d) With thin metal blade introduce system of discontinuities required into model material. (e) Lightly spray surface with lacquer using different colors to identify different strata. The lacquer produces a thin, brittle skin which accentuates cracking and the system of discontinuities. (f) Reclamp glass plate on frame and bring frame into vertical position. (g) Remove first pre-cut plug of polyurethane foam and excavate model material. A small vacuum probe makes an ideal 'excavator'. (h) At completion of excavation re-insert plug of TABLE 1. Mine depth represented by 1 m (3.28 ft) high model m ft 50 100 200 400 800 1000
164 328 656 1312 2624 3280
Joint spacing that is simulated by 1 mm (0.04in) model joint spacing m ft 0.05 0.10 0.20 0.40 0.80 1.00
0.16 0.33 0.66 1.31 2.62 3.28
Typical mine depths and joint spacings that can be simulated by using flour, vegetable oil, fine sand, glass shot model materials with model discontinuities at 1 mm (0.04 in) spacing.
polyurethane and proceed to mine subsequent openings in correct sequence. The sequence of events viewed through the glass plate may be filmed for permanent record. Since gravity is being used directly caving processes occur more rapidly than in a base friction model and a high speed camera is therefore desirable. Figure 1 shows one frame from a sequence of events involving the caving of a hanging wall in bedded strata as mining proceeded up-dip in two separate stopes. Additional refinements could, of course, be added to the model frame so that horizontal loads could be simulated. This would add to the versatility of the frame for teaching purposes. Since the model materials of flour, vegetable oil, sand and glass shot are extremely weak a relatively small model frame can be used to simulate considerable depths of overburden. Table 1 shows the mine depth represented by a 1 m (3.24 ft) model and the simulated joint spacing assuming joints could be cut as closely as 1 mm (0.04 in) in the model. In some cases where it is not necessary to model the entire overburden lead shot could be used to load the upper surface of the material and simulate overburden load. This technique would permit closer joint spacings to be simulated (see Table 1"). The facility described above can assist in the student's understanding of rock mass behaviour and is relatively inexpensive to construct and operate.
Received 22 November 1978
Technical Note
REFERENCES 1. Goodman R. E. Methods of Geological Engineering in Discontinuous Rocks, pp. 280-287, West, New York (1976).
219
2. Spang R. M. Possibilities and limitations of the base friction model. Rock Mechanics 12, 185-198 (1977). 3. Stimpson B. A new approach to simulating rock joints in physical models. Int. J. Rock Mech. Min Sci. 16, 215-216 (1979).
0020-7624/79/0601-0217502.00/0
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
Technical Note A Simple Physical Modelling Technique for the Demonstration of Interaction between Underground Openings B. STIMPSON*
INTRODUCTION For students of rock engineering the testing of intact rock and the theory of elasticity provide a useful basis for design for some classes of rock mechanics problems, but this approach should be complemented by laboratory and classroom exercises aimed at giving the student an understanding of the behaviour of jointed, inhomogeneous, non-elastic rock masses. For obvious reasons the teaching and demonstration of rock mass behaviour in the classroom or laboratory is more difficult than the study of intact rock properties. Case histories are certainly indispensable in bridging the gap between idealized rock mass behaviour and reality but well documented, photographed and instrumented case histories are few. Numerical modelling is capable of including non-linear (both geometric and material) properties of rock masses but the facilities and/or budgets are not always available for this approach to be used as a regular classroom tool. Inexpensive, simple physical models represent a third approach which may be of value, not only to college educators, but also to industrial training programs. For example, simple physical models may be used to demonstrate to mining machine operators the importance of not cutting too wide a span in room-and-pillar operations. Probably the most widely known simple physical modelling technique is the base friction method which can provide very interesting and illustrative models of rock mass behaviour [1]. The method is restricted to kinematic modelling and has a number of deficiencies including the incorrect simulation of situations where parts of the rock mass attain significant horizontal momentum and then either impact another surface or lose contact with adjacent surfaces I-2]. However, in many situations this effect is not significant and quite convincing demonstrations can be set up. A second disadvantage of the base friction method is the low stresses induced in the model material. It is difficult to demonstrate compressive rock fracture and crushing. If a very weak model material is used the material can * Department of Mineral Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2El.
fail by means of a shallow "thrust fault" passing from the base of the friction model to the surface and the model is invalid. The base friction method is, therefore, most suited to illustrating the kinematics of rock masses with continuous joint systems dissecting hard intact rock. An alternative approach is to construct vertical model frames in which gravity is used directly and in which higher stresses can be generated. This Technical Note describes a simple technique for demonstrating interaction between underground mine openings using this method. As with base friction modelling, it does not claim to be a quantitative approach and is intended for classroom or laboratory demonstrations.
VERTICAL FRAME MODEL The plane strain frame may be of any size though for practical and economic reasons one measuring 0.9 m (3 ft) in width and 1.2 m (4 ft) in height is suitable. One side of the frame comprises a 10 mm (0.38 in) thick glass plate through which the model can be observed. Stiffeners or a thicker plate will be required to reduce bending for larger frames. The other side of the frame is formed from a 7.6 cm (3 in) thick slab of 'rigid' polyurethane foam which is supported by cross beams to limit bending. The glass plate and polyurethane slab enclose a 2.54 cm (1 in) space for the model material. The model material should be capable of being cut with a blade so that discontinuities can be introduced into the material. Mixtures of flour, vegetable oil, fine sand and silt-size glass shot make an inexpensive, easily handled material. A typical mix consists of 55% flour, 20% vegetable oil, 7% sand, 18% glass shot (by weight). The glass shot increases the compactability of the material but also reduces the angle of internal friction. More recently derived materials include flour and methanol and various granular materials mixed with Shellac [3]. The construction and testing of a model proceeds as follows: (a) Outline the system of mine openings on the polyurethane slab with a marker and cut out each
217
218
Technical Note
Fig. 1. Caving of hanging wall in steeply dipping bedded sequence being 'mined' up-dip.
opening so that a plug of polyurethane can be removed. Pin each plug in its original position with pins or tape. (b) Erect frame in vertical position and place model material. Provide some means of gently tamping or vibrating material to help achieve uniform compaction. (c) Lay frame in horizontal position and remove glass plate. (d) With thin metal blade introduce system of discontinuities required into model material. (e) Lightly spray surface with lacquer using different colors to identify different strata. The lacquer produces a thin, brittle skin which accentuates cracking and the system of discontinuities. (f) Reclamp glass plate on frame and bring frame into vertical position. (g) Remove first pre-cut plug of polyurethane foam and excavate model material. A small vacuum probe makes an ideal 'excavator'. (h) At completion of excavation re-insert plug of TABLE 1. Mine depth represented by 1 m (3.28 ft) high model m ft 50 100 200 400 800 1000
164 328 656 1312 2624 3280
Joint spacing that is simulated by 1 mm (0.04in) model joint spacing m ft 0.05 0.10 0.20 0.40 0.80 1.00
0.16 0.33 0.66 1.31 2.62 3.28
Typical mine depths and joint spacings that can be simulated by using flour, vegetable oil, fine sand, glass shot model materials with model discontinuities at 1 mm (0.04 in) spacing.
polyurethane and proceed to mine subsequent openings in correct sequence. The sequence of events viewed through the glass plate may be filmed for permanent record. Since gravity is being used directly caving processes occur more rapidly than in a base friction model and a high speed camera is therefore desirable. Figure 1 shows one frame from a sequence of events involving the caving of a hanging wall in bedded strata as mining proceeded up-dip in two separate stopes. Additional refinements could, of course, be added to the model frame so that horizontal loads could be simulated. This would add to the versatility of the frame for teaching purposes. Since the model materials of flour, vegetable oil, sand and glass shot are extremely weak a relatively small model frame can be used to simulate considerable depths of overburden. Table 1 shows the mine depth represented by a 1 m (3.24 ft) model and the simulated joint spacing assuming joints could be cut as closely as 1 mm (0.04 in) in the model. In some cases where it is not necessary to model the entire overburden lead shot could be used to load the upper surface of the material and simulate overburden load. This technique would permit closer joint spacings to be simulated (see Table 1"). The facility described above can assist in the student's understanding of rock mass behaviour and is relatively inexpensive to construct and operate.
Received 22 November 1978
Technical Note
REFERENCES 1. Goodman R. E. Methods of Geological Engineering in Discontinuous Rocks, pp. 280-287, West, New York (1976).
219
2. Spang R. M. Possibilities and limitations of the base friction model. Rock Mechanics 12, 185-198 (1977). 3. Stimpson B. A new approach to simulating rock joints in physical models. Int. J. Rock Mech. Min Sci. 16, 215-216 (1979).