1. Tony Leach (Itasca Africa)
Use of numerical modelling to estimate shotcrete requirements using a Ground Reaction Curve approach
Kevin Le Bron (Golder)
Tony Leach (Itasca Africa)
William Joughin (SRK)

2. Introduction Simrac Project SIM 040204
Numerical modelling to investigate:
Shotcrete/rockmass interaction
Load/deformation performance requirements of shotcrete under a range of geotechnical conditions

3. Modelling requirements
Modelled rock mass needs to fragment
Effect of discontinuities on lining – local loading
Identify deformations under various geotechnical conditions – rock type, GSI, field stress

4. Model design – ‘laboratories’
Realistic tunnel in bedded strata
Generic tunnel (voronoi tesselation)
Wedge Ejection
Various experiments to examine shotcrete loading due to discontinuities using UDEC

5. Objectives
Derive magnitude of rock movements under a range of geotechnical conditions in SA mines
Interpret movements applied to shotcrete
Derive Ground reaction curves
Assess effect of stress change on movement
Assess effect of excavation size on movement
Assess effect of bolting, shotcrete bond strength, etc.

6. Generic Tunnel Model 2D model using UDEC
Discontinuous rock mass created using a voronoi tesselation (0.2m block size)
Simple properties based on UCS, GSI derived using Rocscience’s Rocklab program.
3.5 x 3.5 tunnel

12. Limitations of including support
Need hundreds of models to cover support permutations!
Generally in deep mines, support can supply sufficient pressure to prevent unravelling, but not to prevent failure or limit deformation prior to final unravelling
Key factor is the deformation that shotcrete will undergo
Adopt a Ground Reaction Curve approach

13. What is a Ground Reaction Curve?
Support Pressure
Elastic response
Rock failure initiated
Unravelling
Tunnel wall deformation

14. GRC model methodology
Model tunnel excavated and initially internal rock is replaced with a high support pressure
Pressure is incrementally reduced to zero
Measure modelled wall deformation
GRC is graph of pressure versus deformation

15. Example of modelled GRC

16. Range in rock mass cases

17. Effect of excavation size

18. Effect of support pressure on failure envelope
Excavation Size
Depth of sidewall instability (% of width of excavation)
Support Pressure
1 kPa
10 kPa
100 kPa
3.5 m wide excavation
37%
5 m wide excavation
32%
7 m wide excavation
22%

19. Effect of stress change
Stress change is the main inducer of deformation in mining
How to account for stress change with GRC graphs?
GRC graphs developed for static stress cases
Is it reasonable to jump from one graph to the next?

20. Effect of stress change

21. GRC models versus explicit support

22. Deformation in 2D and 3D
How to relate GRCs from 2D models to point of installation of support relative to face?
UDEC versus FLAC3D
Simple tunnel model

23. 3D deformations (mm)

24. 3D deformations (%)

25. Conclusions Deformation applied to support is key
GRC methodology adopted as best means to assess deformation applied to shotcrete
Limited tendency for shotcrete to bulge between bolts
Layer deflection smoothly distributed over tunnel height (except where slabs punch through)
Consider bolt spacing as design slab size in assessing performance
Consider total wall deflection/number of bolts as shotcrete panel deflection
Permits design using yield line theory