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)

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

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

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

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.

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

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

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

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

Example of modelled GRC

Range in rock mass cases

Effect of excavation size

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%

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?

Effect of stress change

GRC models versus explicit support

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

3D deformations (mm)

3D deformations (%)

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