Finite element modelling of Finite element modelling of load shed and non-linear load shed and non-linear buckling solutions of confined buckling solutions of confined steel tunnel liners steel tunnel liners 10th Australia New Zealand Conference 10th Australia New Zealand Conference on Geomechanics, on Geomechanics, Brisbane Australia, October, 2007 Brisbane Australia, October, 2007 Doug Jenkins - Interactive Design Services Anmol Bedi – Mott MacDonald
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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,
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Finite element modelling of load shed Finite element modelling of load shed and non-linear buckling solutions of and non-linear buckling solutions of
Effect of surcharge pressureEffect of surcharge pressure
-300.0
-200.0
-100.0
0.0
100.0
200.0
300.0
0 500 1000 1500 2000 2500
Pressure, kPa
Str
es
s,
MP
a
0 kPa Top face 30 kPa 60 kPa 120 kPa
0 kPa bottom 30 kPa 60 kPa 120 kPa
Geotechnical Analysis – Current Stress Geotechnical Analysis – Current Stress StateState
Geotechnical Analysis – Elastic Modulus v Geotechnical Analysis – Elastic Modulus v Bending MomentBending Moment
Elastic Modulus v Bending Moment
0
0.5
1
1.5
2
2.5
3
0% 20% 40% 60% 80% 100% 120%
% of in-situ Elastic Modulus
Ben
din
g M
omen
t (kN
m)
K0 = 0.3
ko=3
Geotechnical Analysis –Bending Moment Geotechnical Analysis –Bending Moment transfer to Steel Linertransfer to Steel Liner
Geotechnical Analysis – Axial Load Geotechnical Analysis – Axial Load Distribution in SteelDistribution in Steel Axial Force (Ko=0.3)
450
500
550
600
650
700
0 2 4 6 8 10 12 14
Distance Around Liner [m]
Axi
al F
orc
e [k
N]
Summary – Parametric StudySummary – 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 AnalysisSummary – 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.
ConclusionsConclusions 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.