seismisk analyse / dimensjonering av beholdere/tank · seismisk analyse / dimensjonering av...

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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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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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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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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Without anchors

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With anchors

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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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Envelope of minimum contact pressure (negative indicates risk ofuplift)

Without anchors

With anchors

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Envelope of maximum contact pressure

Without anchors

With anchors (higherpressure!)

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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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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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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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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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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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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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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

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