1. Finite element modelling of load shed and non-linear buckling solutions of confined steel tunnel liners 10th Australia New Zealand Conference on Geomechanics, Brisbane Australia, October, 2007
Doug Jenkins - Interactive Design Services
Anmol Bedi – Mott MacDonald

2. Introduction Port Hedland Under Harbour Tunnel
Lined with 250 m thick gasketed precast concrete segments – now corroding
Proposal to reline with steel backgrouted liner
Geotechnical and structural finite element analyses
Comparison with analytical solution

3. Topics The proposed remedial work Confined liner buckling
Jacobsen Closed Form Buckling Solution
Linear buckling FEA
Application to the project
Current stress state in tunnel liner
Future Installation of Steel Liner
Geotechnical FEA results
Conclusions

4. Port Hedland Under Harbour Tunnel

5. Material Properties

6. Closed Form Solutions
Unrestrained solution similar to Euler column buckling
Rigid confinement restrains initial buckling
Gap between pipe and surrounding material allows single or multi lobe buckling to occur
Buckling frequently forms a single lobe parallel to the tunnel

7. Single Lobe Buckling

8. Comparison of buckling theories
Berti (1998) compared theories by Amstutz and Jacobsen
Amstutz approach was simpler, but assumed constants may be unconservative
Also found that rotary symmetric equations are unconservative compared with Jacobsen
Computerised analysis allows the more conservative Jacobsen method more general use

9. Jacobsen Equations

10. Jacobsen Equations

11. Jacobsen Equations

12. Parametric Study

13. Unrestrained Buckling Model

14. Unrestrained Buckling

15. Unrestrained Buckling

16. Unrestrained Buckling

17. FE Model for Restrained Buckling

18. FE Model Detail

19. FE Model Detail

20. Restrained Buckling - deflection

21. Restrained Buckling - deflection

22. Restrained Buckling - gap

23. Effect of contact friction and restraint stiffness

24. Effect of surcharge pressure

25. Geotechnical Analysis – Current Stress State

26. Geotechnical Analysis – Elastic Modulus v Bending Moment

27. Geotechnical Analysis –Bending Moment transfer to Steel Liner

28. Geotechnical Analysis – Axial Load Distribution in Steel

29. Summary – Parametric Study
FE buckling analysis results in good agreement with analytical predictions under uniform load for both unrestrained and restrained conditions.
Under hydrostatic loads the unrestrained critical pressure was greatly reduced, but there was very little change for the restrained case.
FE results in good agreement with Jacobsen for gaps up to 20 mm.
Varying restraint stiffness had a significant effect, with reduced restraint stiffness reducing the critical pressure.
A vertical surcharge pressure greatly increased the critical pressure, with the pipe failing in compression, rather than bending.
Variation of the pipe/rock interface friction had little effect.

30. Summary – Geotechnical Analysis
The coefficient of in-situ stress (K0) and the soil or rock elastic modulus both had an effect on the axial load in the steel liner.
Since plasticity had developed around the segmental liner further deterioration of the concrete segments resulted in only small further strains in the ground.
The arching action of the ground and the small increase in strain resulted in increased axial load in the concrete segments and steel liner, but negligible bending moment transferred to the steel liner.

31. Conclusions
For the case studied in this paper the Jacobsen theory was found to be suitable for the design of the steel liner since:
It gave a good estimate of the critical pressure under hydrostatic loading
Deterioration of the concrete liner was found not to increase the bending moments in the steel liner significantly
In situations with different constraint stiffness or loading conditions the Jacobsen results could be either conservative or un-conservative.
Further investigation of the critical pressure by means of a finite element analysis is therefore justified when the assumptions of the Jacobsen theory are not valid.