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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. Introduction.
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Finite element modelling of load shed and non-linear buckling solutions of confined steel tunnel liners10th Australia New Zealand Conference on Geomechanics, Brisbane Australia, October, 2007 Doug Jenkins - Interactive Design Services Anmol Bedi – Mott MacDonald
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
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
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
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
Geotechnical Analysis –Bending Moment transfer to Steel Liner
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.
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.
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.
