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, 2007Doug Jenkins - Interactive Design ServicesAnmol Bedi Mott MacDonald

Introduction Port Hedland Under Harbour TunnelLined with 250 m thick gasketed precast concrete segments now corrodingProposal to reline with steel backgrouted linerGeotechnical and structural finite element analysesComparison with analytical solution

TopicsThe proposed remedial workConfined liner bucklingJacobsen Closed Form Buckling SolutionLinear buckling FEAApplication to the projectCurrent stress state in tunnel linerFuture Installation of Steel LinerGeotechnical FEA resultsConclusions

Port Hedland Under Harbour Tunnel

Material Properties

Closed Form SolutionsUnrestrained solution similar to Euler column bucklingRigid confinement restrains initial bucklingGap between pipe and surrounding material allows single or multi lobe buckling to occurBuckling frequently forms a single lobe parallel to the tunnel

Single Lobe Buckling

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

Jacobsen Equations

Jacobsen Equations

Jacobsen Equations

Parametric Study

Unrestrained Buckling Model

Unrestrained Buckling

Unrestrained Buckling

Unrestrained Buckling

FE Model for Restrained Buckling

FE Model Detail

FE Model Detail

Restrained Buckling - deflection

Restrained Buckling - deflection

Restrained Buckling - gap

Effect of contact friction and restraint stiffness

Effect of surcharge pressure

Geotechnical Analysis Current Stress State

Geotechnical Analysis Elastic Modulus v Bending Moment

Geotechnical Analysis Bending Moment transfer to Steel Liner

Geotechnical Analysis Axial Load Distribution in Steel

Summary Parametric StudyFE 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 AnalysisThe 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.

ConclusionsFor 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 loadingDeterioration of the concrete liner was found not to increase the bending moments in the steel liner significantlyIn 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.