Seismisk analyse / dimensjonering av beholdere/tank
Anton GjørvenThanh Ngan Nguyen
NEED2012
Background
The purpose with this presentation is to demonstrate different calculation methods and design principles for
seismic response of "full containment" (stand-alone steel inner tank, separated from outer concrete cylinder) LNG (liquefied natural gas) tanks
to show how an earthquake can impact the design of the steel inner tank. The basic principles of anchoring/no anchoring of the steel inner tank is a significant factor of the costs of an LNG tank.
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Background
Relevant projects Risavika: H = 20 m (Ht = 21 m), R = 22.5 m, H/R = 0.89
Lysekil: H = 37.5 m (Ht = 38.2 m), R = 16 m, H/R = 2.34
Lysekil: High H/R-ratio is a challenge when considering safe shutdownearthquake (SSE - return period 4975 years. Operating basis earthquake(OBE) - return period 475 years)
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Background
Response calculations and design are normally based on hand calculations using standards
Analyses, both explicit and implicit, have been executed to compare and validate the hand calculations
Parameters of interest: Base shear and overturning moment (foundation, stresses in bottom
insulation layers)
Compressive stress in tank wall ("elephant foot" buckling, EC8-4 A.10)
Uplift and anchorage of tank
Typical "elephant foot buckling"
Foto: Prof. J.M. Rotter, The University of Edinburgh
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Basic design assumptions
General: Eurocode 2 (Concrete) and Eurocode 3 (Steel) Tanks: Eurocode 1, Part 4 (Action on tanks) and Eurocode 3, Part 4-2
(Design of steel tanks) Eurocode 8 (Earthquake), Part 1 (General)
Chapter 3: Ground conditions and seismic excitation
Ref.: NS-EN 1998-1:2004/NA:2008 Figure NA.3(903) Ref.: NS-EN 1998-1:2004/NA:200Figure NA.3(901)
Eurocode 8, Part 4 (Silos, tanks and pipelines) Chapter 2: General
Chapter 4: Specific rules for tanks
Annex A: Seismic analysis procedures for tanks
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Basic design assumptions
EN 1473 (Installation and equipment for LNG) Structural parts vital for the plant safety shall remain operational after both
operating basis earthquake (OBE) and safe shutdown earthquake (SSE)
EN 14620 (Design and manifacture of steel tanks for storage of LNG) Part 1 (General)
• 7.1.4 Earthquake design: "For … full containment tanks, the primary liquid container shall be designed to contain the liquid during an OBE and SSE action."
• 7.3.2.2.13: OBE earthquake
• 7.3.3.3: SSE earthquake
• Annex C: Seismic analysis
Part 2 (Metallic components)• 5.1.2.2: Requirements to allowable tensile stress in tank anchorage for OBE and SSE (NB:
Allowable stress theory, not limit state theory)
• 5.8.1: Other requirements to tank anchorage
Part 3 (Concrete components)
Part 4 (Insulation components)• 6.3.2.2.1: Overall safety factor for brittle materials (insulation) for OBE and SSE (NB: Allowable
stress theory)
• Annex C: Tank bottom insulation - Limit state theory
Part 5 (Testing, drying, purging and cool-down)
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Design of LNG tanks
Foto: Norconsult. An LNG tank is a complex structure. Here is the outer concretewall from one of our projects - picture is taken from below and upwards.
Foto: Norconsult. Steel roofunder construction.
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Design of LNG tanks
The steel inner tank is the part where the seismic conditions can have a significant influence to basic design, for example the anchoring of theinner tank.
The "slenderness" of the tank or the ratio H/R combined with theground condition govern the anchoring system to be used.
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Explicit analysis - Abaqus
In an explicit analysis, the earthquake excitation is defined with a time history
The model consists of the container – a cylinder (open top) made by steel filled with LNG
Two cases are studied –without and with anchors (“smeared” representation)
For each case, one earthquake definition based on Norwegian Standards has been used
The FE model does not consider the outer concrete cylinder since the obtained results (max. displacement during earthquake) indicate that the interaction forces will be negligible
Model definition: Steel tank: Shell elements
LNG: Continuum elements. Material defined by wave speed and dynamic viscosity (Equation of state (EOS) material model - only available in Abaqus/Explicit)
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Explicit analysis - Abaqus
FE model, interactions: Steel tank and LNG
Steel tank and bottom layers(Foamglas, sand)
Bottom layers and ”rock” (analytical rigid surface)
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Explicit analysis - Abaqus
Gravity load (LNG) is initially in equilibrium with a hydrostatic pressure The initial stress state is obtained with a dynamic (explicit) approach
using time integration This is done by increasing the gravity load with a smooth amplitude
curve in 10 seconds, thereafter continued 10 seconds further without any load change in order to decrease oscillations of the unbalanced solution
Stress state in LNG and tank wall is checked
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Explicit analysis - Abaqus
The earthquake excitation is applied at the reference node for the “rock” as prescribed acceleration in the 1- and 3-directions
The base acceleration has been multiplied by factors 1 respectively 0.3 for these directions and the earthquake is analyzed during 10 seconds
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Explicit analysis - Abaqus
Without anchors
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Explicit analysis - Abaqus
With anchors
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Explicit analysis - Abaqus
Vertical section force lower part of wall (positive indicates risk of uplift)
without anchors
with anchors (higherstress oncompression side, reduced risk of uplifton tension side)
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Explicit analysis - Abaqus
Envelope of minimum contact pressure (negative indicates risk ofuplift)
Without anchors
With anchors
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Explicit analysis - Abaqus
Envelope of maximum contact pressure
Without anchors
With anchors (higherpressure!)
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Explicit analysis - Abaqus
History plot of uplift at the corner of the tank
Vertical section force in anchors
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EC8-4 A.9: Effect of uplift on stress in the wall (unachored)
EN 1998-4:2006 (E) Figure A.11:
EN 1998-4:2006 (E) A.9.2:
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Explicit analysis - Abaqus
Rigid (dashed line) vs. elastic (solid line) bed, history plot of verticalsection force
Without anchors(small differences)
With anchors (elasticbed gives generallyhigher compressionforces than rigid bed)
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Explicit analysis - Abaqus
SUMMARY AND CONCLUSIONS
Material model for LNG EOS material is used
Elastic material is also possible - gives more balanced initial state
Elastic material shows less damping during seismic excitation
Results when using anchors are very similar to the case withoutanchors
Max. vertical displacement for the case without anchors is slightlyhigher than with anchors
However, the uplift seems to have a rather small impact on the verticalstresses in the tank wall
The case with anchors has actually increased section force compared to the case without anchors
An explicit analysis is probably a very good approach to study thedynamic behaviour for an LNG tank excited by seismic action
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Simplified calcuation of overturing moment
⋅ 0.8 ⋅ ⋅ ⋅2.5
1.0 ⋅ 0.8 ⋅ 0.5 ⋅ 1.0 ⋅2.51.5
0.667
⋅ ⋅ ⋅ 1.5 ⋅ 30000 ⋅ 490 ⋅ 0.667 ⋅ 18.75 276
OBE (475 years):
SSE (4 975 years):
1.0, 3.0 → 276 ⋅3.01.5
552
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Hand calculations - Malhotra
EC8-4 A.3.2.2 Simplified method for fixed base tanks
The response is splitted into impulsive and convective part, impulsive is dominating for high tanks
EN 1998-4:2006 (E) Table A.2:
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Hand calculations - Malhotra
Acceleration from elastic response spectrum, EC8-1 Return period other than TNCR = 475 years is taken into account with the
importance factor γI (evaluated from EC8-1 2.1(4) Note)
Impulsive damping ξ = 2 %, convective damping ξ = 0.5 %
Impulsive and convective period → EC8-4 Eq. (A.35) and (A.36)
Base shear and moment → EC8-4 Eq. (A.37) and (A.38)
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Hand calculations - Malhotra
Compressive stress
Tension force ⋅
Number of anchors 2 ⋅
Uplift? Unachored → EC8-4 A.9: Effect of uplift on stress in the wall
Ref.: EN 1998-4:2006 (E) Figure A.11
SSEOBE
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Response spectra for hand calculations
Simplified calculations:1.55%
Max. value of spectrum
Malhotra/EC8-4:" 1.0" (elastic response spectrum)
2%Period 0.4 ?
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Partial factors for LNG tank design
Limit state Loadfactor
Material factor q
OBE (475 yrs) Ordinary ULS Yes Yes No (1.0)
SSE (4975 yrs) Accidental ULS No (1.0) No (1.0) Yes?
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Implicit analysis - Abaqus
EC8-4 A.2
Ref.: EN 1998-4:2006 (E) Figure A.1
Why not implicit analysis with response spectrum step? Material model for the fluid?
Interaction between the fluid and the flexible steel wall?
Hydrodynamic pressure: Motion of the fluid due to seismic excitation is preserved as "snapshot" of max. pressure ("pushover" analysis)
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Implicit analysis - Abaqus
The rigid impulsive (hydrodynamic) pressure is applied on the tank wall for theacceleration from the elasticresponse spectrum
The LNG fluid is also applied as a hydrostatic pressure
A contact algorithm is appliedbetween the tank bottom and an analytical rigid surface, allowingfor separation
Base shear and moment corresponds well with Malhotra's
simplified method
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Implicit analysis - Abaqus
Stresses in tank wall and anchors, in addition to uplift may be studied
Results obtained from implicit analysis are in good agreement withhand calculations SSE: Uplift and stress in wall OK with anchors, not OK without. Unanchored
case: Highly increased stresses due to extensive deformations
OBE: OK with and without anchors. Unanchored case: Increasedcompressive stress is moderate
An implicit analysis is more conservative than an explicit analysis. It is in good agreement with hand calculations and may not give any newinformation of the behaviour that can be found by simplified methods.
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Summary
Several types of calculations/analyses - benefits and limitations Simplified hand calculations
Simplified procedure - Malhotra
Implicit analysis
Explicit analysis
Which results are trustworthy? Unachored tanks: Increased compressive stress when uplifted
(Eurocode, implicit model (moderate!)) Anchored tanks: Increased compressive stress due to tension in
anchors (explicit model)
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Summary (continued)
0 500 1000
Compression in tank wall (with anchors)
[MPa ∙10]
Tension in anchoring[kN]
Base shear [MN∙10]
Overturning moment[MNm]
Hand calculations(Malhotra)
Abaqus implicit
Abaqus explicit
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Conclusions
Calculation method may govern the decisions regarding the necessityof anchoring the tank
Advanced FE methods (explicit analyses) tend to give reduced values ofthe governing parameters (hand calculations are more conservative)
The complexity of explicit analyses is very high and need a lot ofengineering time