Failure Analysis of RC Structures using Volume Control ... · PDF fileConcrete Materials,...

Concrete Materials, Mechanics and Engineering Lab. YONSEI UNIVERSITY

Failure Analysis of RC Structures using Failure Analysis of RC Structures using Volume Control TechniqueVolume Control Technique

--COE Intensive CourseCOE Intensive Course--

Feb. 3, 2005Feb. 3, 2005

Hokkaido University, Sapporo, JapanHokkaido University, Sapporo, Japan

HaHa--Won SongWon Song

School of Civil and Environmental EngineeringSchool of Civil and Environmental Engineering

CMME Lab. Yonsei Univ.

OutlineOutline

IntroductionIntroduction◆ Characteristic of failure in concrete structures

◆◆ Homogenized crack modelHomogenized crack model

◆◆ Volume control methodVolume control method

Modeling for cracked RC and ECCModeling for cracked RC and ECC◆◆ Constitutive equations of RC/ Layered shell elementConstitutive equations of RC/ Layered shell element

◆ Modeling of ECC as re-strengthening material

Analysis results and comparisonAnalysis results and comparison◆ RCCV subjected to internal pressure

◆ RC tank , RC slab, and RC box culvert subjected to various loading

◆ RC hollow column subjected to lateral loading

◆ Verification with PCCV

Conclusion and future workConclusion and future work


Performance of deteriorated/repaired RC structures ?Performance of deteriorated/repaired RC structures ?

0=−+∂∂

iii QdivJtθα

Pore pressureComputation

Governingequations

Size, shape, mix proportions, initial and boundary conditions

START

Temperature,Hydration level ofEach component

ConservationLaws satisfied?

no

yes

Incr

emen

t ti

me,

co

nti

nue

Du

rabi

lity

An

alys

isD

ura

bilit

y A

nal

ysis

Corrosion rate, crack,tension stiffening factorOutput

Ser

vice

abili

ty/S

afet

y A

nal

ysis

Ser

vice

abili

ty/S

afet

y A

nal

ysis

Deformation Compatibility,MomentumConservation

ContinuumMechanics

at each time step

re-strengtheningwith overlay

Nextiteration Hydration

computation

Bi-model porosityDistribution,Interlayer porosity

Microstructurecomputation

Pore pressures,RH and moisturedistribution

ChlorideTransport and

equilibrium

Dissolved andBound chlorideconcentration

Corrosion rate,Amount of O2

consumption

Corrosion model

Dissolved OxygenTransport andequilibrium

Ion equilibriummodel

Gas and dissolvedCO2 concentration

Carbon dioxideTransport and

equilibrium

Tension stiffening factor :α

tε

tt f/σ

Tension stiffening model

Max.Load

time

Service-lifedecrease

Structural analysis (FEM etc.)

Due to deterioration

α

εεσ )(t

tutt f=

4.0=α0.1=α

Due to re-strengthening

Performancedegradation/upgrade


Characteristics of concrete fracture and analysisCharacteristics of concrete fracture and analysis

Material instability

Micro cracksMicro cracks Major macro cracksMajor macro crackslocalize

Softening behaviorDecreased load resistant capacity after peakLocalized strain

Softening behaviorDecreased load resistant capacity after peakLocalized strain

Numerical problem in concrete fracture analysis :

Loss of ellipticity of governing equationIll-posed boundary value problem

Numerical problem in concrete fracture analysis :

Loss of ellipticity of governing equationIll-posed boundary value problem

Numerical drawback(Mesh sensitivity)

Numerical drawback(Mesh sensitivity)


Structural instability

Sources of NonSources of Non--linearity ; Material, Geometrical, Boundary and Contactlinearity ; Material, Geometrical, Boundary and Contact

Rt3 Rt2 Rt1 R

u

R

ut1 u t2 u t3 u t4 u

Load controlLoad control Displacement controlDisplacement control

λ

u

A

∆λ0

r

r

Circular path

Final solution

Tangential solution from point A

ArcArc--length control methodlength control method


Effort to solve material instability in progressive fracture analysis of concrete using FEM

Embedded discontinuities approximations (in 1990’s)Embedded discontinuities approximations (in 1990’s)

Homogenized crack modelHomogenized crack model

• Strain-stress relationship• Discontinuity : strain localization zone

Continuum approximation

• Displacement jump-traction• Discontinuity : crack

Discrete approximation

• Strain localization band width is finite (k ≫ 0)

Weak discontinuities

• Strain localization band width is very small (k → 0)

Strong discontinuities

Discrete crack model and smeared crack model (in 1980’s)Discrete crack model and smeared crack model (in 1980’s)


Effort to solve structural instability in progressive failure of concrete shell structures using FEM

Failure analysis of RC shell structures subjected to various loaFailure analysis of RC shell structures subjected to various loadingsdings

Load Control MethodLoad Control Method : difficulty to obtain post: difficulty to obtain post--peakpeakultimate behavior of RC structuresultimate behavior of RC structures

Displacement Control MethodDisplacement Control Method : difficulty to select a : difficulty to select a representative point for displacement representative point for displacement control in 3D control in 3D

Remove the drawback of load control method

overcome the limitation for displacement control method

Volume Control Volume Control MethodMethod

Layered shell utilizing in-plane constitutive

models of RC


Volume Control Method with Pressure NodeVolume Control Method with Pressure Node

Pressure Node : the uniform change of applied pressure on the Pressure Node : the uniform change of applied pressure on the shell shell

element element ((∆∆pp) () (Song and Song and TassoulasTassoulas, IJNME, 1993 ), IJNME, 1993 )


Path dependant pseudoPath dependant pseudo--volume control techniquevolume control technique

Pseudo Volume Pseudo Volume ( Song et. al, J. ( Song et. al, J. StrStr. Eng. 2002 ). Eng. 2002 )

PathPath--dependent Volume dependent Volume ( Song et. al, Nuclear Eng. and Design, 2003 )( Song et. al, Nuclear Eng. and Design, 2003 )


A

Loading condition checking

∂P∂Vnext

> 0Loading ; Vnext → P1next

Reloading ; Vnext → P3next

∂P∂Vnext

< 0 Unloading ; Vnext → P2next

i+1K

Ki= β is updated according to Loading history

Reloading

Vm = v + ΔVmext

ㅣ(UE)kㅣ

ㅣ(UA)kㅣ< ㅣtoleranceㅣ

(dA) is modified according to comparison experiment displ.

with analysis displ.

P(load)

0 Displacement, UStep i Step i+1

i+1∂P∂U

i+1K =

i∂P∂U

iK =

iK

i+1K

P(load)

0Displacement, U

Experiment

Analysis

(UE)k (UA)k

P(load)

deformed volume, VmVnext

Loading

Unloading

0

Initial volume, V

P1next

P3next

P2next

(dA) is updated according to Loading history

Using tangent Stiffness Matrix Checking (UE)k and (UA)k at each loading steps

Volume increment ΔVmext is controlled according to β

Algorithm for path dependant volume control technique Algorithm for path dependant volume control technique

(ΔVmext)next → ΔVm

ext


Pressure Node ← External modified pseudo volume increment ΔVmext

Compute volume change ΔViint using displacement increment Δuk

i

Using Stiffness matrix added Volume-Pressure relation term

Residual volume ΔViR = Δvm

ext - ΔViint

Out of balanced

Element stiffness and nodal vector ; Kei ＆ Fe

i

Assemble and compute RHS vector ; Ki ＆ Fi

Compute residual pressure using residual volume

[Δui, Δpi]T = [Ki]-1[pi, ΔVRI]T

Δpi +1 = Δpi + δpi +1

Δui +1 = Δui + δui +1

Checking convergence

δpi +1 < ㅣtoleranceㅣ

ΔViR < ㅣtoleranceㅣ

At every Gauss point

Calculate strain increment

Δεi = BΔuki

obtain unit vector, n

x’ = x + Δuki

Δuki ← considering loading condition

Using RC constitutive model orthogonal two-way fixed crack model

Calculate stress increment, Di, Δσi

(ΔVmext)next → ΔVm

ext

Structure type

Cylindrical ＆spherical shell structure Plate-like shell structure

Calculate ΔVmext

No

Yes

ASolution Solution

procedure procedure pathpath--dependant dependant volume control volume control

methodmethod


Layered shell elementLayered shell element

Degenerated, isoparametric, serendipity, quadratic shell element with drilling degree of freedom

Geometrical nonlinearity is considered by adopting total Lagrangian formulation

In plane constitutive laws applied to each layer of element consists of RC layers and PL layers


Constitutive law for each layerConstitutive law for each layer

Layered RC element

RC layer

Concrete layer

Concrete stress Steel stress

ㅡㅡ Concrete under compression : Concrete under compression : ElastoElasto--plastic fracture model (Maekawa et. al) plastic fracture model (Maekawa et. al) ㅡㅡ Cracked concrete : Smeared fixed crack model Cracked concrete : Smeared fixed crack model ㅡㅡ Concrete under shear : Crack density model (Maekawa and Li) Concrete under shear : Crack density model (Maekawa and Li)

Shear locking + Membrane lockingShear locking + Membrane locking

Reduced integration ( 2 Reduced integration ( 2 ΧΧ 2 Gaussian 2 Gaussian quadraturequadrature ))


In-plane constitutive models of cracked concrete

local strain of concrete

shear slip along crack

shea

r stre

ss

trans

ferre

d

aver

age

tens

ile

stre

ss

average tensile strain

mean shear strain

shea

r stre

ss

trans

ferre

dco

mp.

stre

ss

comp. strain

damage zone

crack location

mean stress

crack width

com

p. s

treng

th

redu

ctio

n 1.0

cracked concrete

Tension Stiffening

Shear Transferalong Cracks

Compression Softening

MEAN RESPONSELOCAL RESPONSEMULTI-SYSTEM

mean normal strain

com

p. s

treng

th

redu

ctio

n 1.0


Cracking criteria of concrete

Cracking is affected by past loading history.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.5 0.6 0.7 0.8 0.9 1.0

F rac tu re pa rame te r (K 0 )

Ra

tio

of

ten

sil

e s

tre

ng

th (

f tt/

f t)

Monotonic loading (Kupfer)

Monotonic loading

Reloading

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Norma l i z e d c ompre s s i v e s t r e ngth σ 2 /f ' c

No

rma

liz

ed

te

ns

ile

str

en

gth

Authors'

Niwa

Monotonic loading (Kupfer)

Monotonic loading (Maekawa)

Reloading (Maekawa)

σ1/ ft

< Failure envelope in tension-compression domain > < Normalized tensile strength and fracture parameter >

By taking account influence of continuum fracture in past compression, cracking criterion can be defined in the space of biaxial principal stresses

Compression-tension domain Where, σ1, σ2 : principal stress (σ1 > σ2)

ft : uniaxial tensile strength

Rf : tensile strength reduction factorTension-tension domain


Tension stiffening model

Concrete model under tensile stress is unrelated to spacing of cracks, direction of reinforcing bars and reinforcement ration.

Tension stiffening effect is known to increase overall stiffness of RC in tension compared with that of single reinforcing bar.

< Tension stiffening model for deformed bars (c=0.4) and welded meshes (c=0.2) >

Where, σt : average tensile stress, ε : average tensile strain

ft : uniaxial tensile strength, εtu : cracking strain

c : stiffening parameter


Steel model

Reinforcing bar model is based on the assumed cosine distribution of bar stress and concrete tension stiffening.

Where, fyt(-fyt) : Bare bar yield strength

fyt1 : Yield strength of bar in concrete

Es : Initial bar stiffness (before yielding)

Eb : Bauchinger’s effect stiffness

Eb = EB (ε0 > 0)

= 1 / (εp / fc+ 1/ Es)

ε0 = εp + fc (1/ Es - 1/ EB)

EB = - Es log10(10 εp)/6


MultiMulti--directional smeared crack approachdirectional smeared crack approach

OneOne--way active crack governs the overall nonlinearity as for inway active crack governs the overall nonlinearity as for in--plane cyclic shearplane cyclic shear


TwoTwo--way active cracks may control the overall nonlinearity way active cracks may control the overall nonlinearity as for out of plane cyclic actionas for out of plane cyclic action


Orthogonal two-way fixed crack model

Reinforced concrete

Already crack occurred?

Calculation of unun--cracked concretecracked concrete stress according to loading conditions

No

Concrete Reinforcement

Calculation of

strain

according to

reinforcement axis

Y

X

Ys

XsΘs

Calculation of x, y directional

reinforcement stress using

reinforcement modelreinforcement model

History renewal of concrete ＆ reinforcement

Combination of concrete stress ＆ reinforcement stress

Stress of reinforced concreteTransform stress into global coordinate

crack occurred?

Y

X

Yc Xc

Θc

Calculation of

stress

in coordinates

about cracks

Calculation of cracked concretecracked concrete stress using

constitutiveconstitutive models models

Compression model parallel to crack directionCompression model parallel to crack direction

Tension model normal to crack directionTension model normal to crack direction

-- tension stiffening model for concrete in RCtension stiffening model for concrete in RC

-- tension softening model for plain concretetension softening model for plain concrete

-- modeling of unloadingmodeling of unloading--reloading pathreloading path

ReRe--contact modelcontact model

Coupled compressionCoupled compression--tension modeltension modelShear transfer modelShear transfer model

No


ECC as durable overlays and repair layers

Engineered Cementitious Composites (ECC)V.C. Li et al. 1992~V.C. Li et al. 1992~

cementitious matrix + short random fibersconscious micromechanics-based design of material composition … Performance Driven Design Approach

high performance with low fiber content (~2%)


High performance cementitious composites

cementitious matrix + fibers

multiple cracking

high overall ductility intension and shear

with ease of processing and variability of shaping

0

1

2

3

4

5

0 2 4 6 8Strain (%)

Stre

ss (M

Pa)

multiple cracking

fracture localization

damage tolerance, durability, ...

3/28


Characteristic of ECC behavior

Strain hardening

Multiple cracking

0

1

2

3

4

5

0 2 4 6 8Strain (%)

Stre

ss (M

Pa)

multiple cracking

fracture localizationmechanical properties:

- high tensile strain capacity (~5%)- small crack width O(10~100 µm)

Localized failure


33--d homogenized crack modeld homogenized crack model

3-D formulation of homogenized crack model

• Mixture rule (R.E.V)j

ji

i µµ σσσ += jj

ii µµ εεε +=

1=+ ji µµ

jxy

ixyxy τττ ==

jyz

iyzyz τττ ==

jxx

ixxxx εεε ==

jzz

izzzz εεε ==

jzx

izxzx γγγ ==

jyy

iyyyy σσσ ==

Tzxy ggg },,{=g gKσδ j ][][ =

=

010000001000000010

][δ

=

333231

232221

131211

][KKKKKKKKK

K

==

2

1

000000

][][

S

S

Ne

KK

KKK

• Equilibrium & compatibility

• Velocity discontinuity at crack surface

crackwithconcrete

crackconcrete

jj

ii

:,

:,:,

εσ

εσεσ

Y

XZ

y

z x

B

H

W

t

Representative elementary volume(REV)


If t ≪ H ,

1HBW

t)-BW(H≅=iµ

Ht

HBWBWt

≅=jµ

jεδg ][t1

=

averaged crack strain

H1:µ =

Then, can be written asji εεε ji µµ +=Let μ be the ratio of the crack area and REV., i.e. ( )

ji εδεδεδ ][][][ ji µµ +=

gεδ

gεδ

i

i

µ+=

⋅+⋅=

][t1

Ht][1


• Structural relationshipii εDσ ][=

gεδεδ i µ+≈ ][][

jj

ii µµ σσσ +=

gBεAεδ i ][][][ +=

−−−−−−

−−−−−−

−−−−−−

=

3

56

3

33

3

54

3

53

3

52

3

51

2

46

2

45

2

22

2

43

2

42

2

41

1

26

1

25

1

24

1

23

1

11

1

21

][

CD

CK

CD

CD

CD

CD

CD

CD

CK

CD

CD

CD

CD

CD

CD

CD

CK

CD

µ

µ

µ

A

++

++

++

=

0

0

0

][

3

5432

3

5231

2

4523

2

4221

1

2513

1

2412

CDK

CDK

CDK

CDK

CDK

CDK

µµ

µµ

µµ

B

µ11

221KDC +=

µ22

442KDC +=

µ33

553KDC +=


• Structural relationship of (tensile) crack

gεδεδ i µ+= ][][

εSε 1i ][= εSεδ i ][][ =or

gεSεδ µ+= ][][i.e ,

εSδg )][][( −=∴ µ

ε)][]([1 Sδg −=µ

)][]([1][ SδS2 −=µ

Let

εSg 2 ][=then


• Total strain relationship

εSεδ i ][][ =

)][][1][()][1][(][ 1 δBABISµµ

++= −

εSε i ][ 1=

=

100000

000100

000001

][

363534333231

262524232221

161514131211

1

SSSSSSSSSSSS

SSSSSS

S


• Homogenized constitutive equationjσσσ i

ii µµ +=iσ≈

εSD ][][ 1=εDσ eq ][= ][][][ 1SDDeq =

RemarkCrack width, t, is removed in the final constitutive equation only expressed with μ . This is a solution for the mesh sensitivity problem without the introduction of additional length scale such as a characteristic length.→ Regularization of the continuum model


Constitutive equation for crack

Compression

x

p(x,y,z)

yθ

φ

• Bifurcation analysis for crack initiation

)(det)( lijkleq

i nDnF =n

=epS

epS

epN

KK

K

2

1

000000

][K

TcrS

crS

crn ttt },,{

21=t

jyzτj

xyτjyyσ

gKσδ j ][][ ==


Failure criteria and softening curve (compression)Failure criteria and softening curve (compression)

Drucker-Prager type0),(21 =−+= pkJIF εσα

Hardening and softening function1) Song and Na (1997)

peeek epp ασσσσσ β

23]1)[(),( 00 −−−++= −

∞

2) Song et al (2003), Farahat et al.(1995) 2])[(

0)( ξβ γ −−=PWp ekWk

3) Barcelona model

k(εp) (J. Lubliner, 1996))]2exp()exp()1[()( 0

pNN

pNNN

p babafk εεε −−−+=

k(Wp) (Modified Barcelona Model, MBM)

)]2exp()exp()1[()( 0p

NNp

NNNp WbaWbafWk −−−+=


Failure criteria and softening function (tension)Failure criteria and softening function (tension)

Failure criterial (Gopalaratnam and Shah, 1985))(1 ⋅−= kF σ

Hardening and softening function1) Gopalaratnam and Shah (1985)

)()(λκt

t eftk −=

2) Song et al. (2003)

)()( )( ληκ pyg

tpy efgk −=

3) Barcelona model(J. Lubliner, 1996))( pk ε

)]2exp()exp()1[()( 0p

ttp

tttp babafk εεε −−−+=

(MBM))( pygk

)]2exp()exp()1[()( ''0

pytt

pyttt

py gbagbafgk −−−+=


유한유한 요소요소 해석해석 흐름도흐름도Start

INPUTInput data-geometry, boundry

condition, material properties, etc

Load3DEvaluates equivalent nodal forces

INCREMIncrements applied loads

STIF3DCalculate element stiffness for

elastic and elasto-plastic behavior

REACTCalculate displacement and reactions

RESID3BCompute residual stress,

backward Euler integration scheme

CONVERCheck if solution has converged

OUTERSPrint results for this load increment

End

LO

AD

IN

CREM

EN

T L

OO

P

ITERATIO

N L

OO

P

NO

YES

INVAREvaluates invariant stress

YLD3D and FLOWPTDetermine flow vector, a,d, etc

연화함수 변경

손상함수 도입


Hardening and softening curve for concrete and ECC (tension)Hardening and softening curve for concrete and ECC (tension)

J. Lubliner (1996))]2exp()exp()1[()( ''

0pytt

pyttt

py gbagbafgk −−−+=

1>ta1<ta Concrete ①

ECC ②

0

0.5

1

1.5

2a°ªÀÇ º¯È-

1.8

0.012

a5 g( )

a4 g( )

a3 g( )

a2 g( )

a1 g( )

a05 g( )

a01 g( )

1.50 g

(0.1~5 )

①

②


Result for 2% polyetylane fiber contained ECC

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.02 0.04 0.06 0.08 0.1 0.12

Strain

Stress (

MPa)

experiment (Li, V. C., 1994)

ECC analysis (a5 b20)

concrete analysis (a0.1 b20)

①

②

⇒ at = 0.1 : Concrete①

⇒ at = 5 : ECC②


polyetylane fiber : 0.75% , 1% , 1.25%Experimental result ((TetsushiTetsushi Kanda, 1998)Kanda, 1998)

0

0.5

1

1.5

2

2.5

3

0 0.02 0.04 0.06 0.08 0.1 0.12Strain

Stress

(M

Pa)

experiment (vf 0.75)

experiment (vf 1.0)

experiment (vf 1.25)

Increased at

Decreased bt


0.75% ECC

0

0.5

1

1.5

2

2.5

3

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Strain

Stress (

MPa)

experiment (Tetsushi Kanda, 1998)

analysis (a4 b50)


1% ECC

0

0.5

1

1.5

2

2.5

3

0 0.02 0.04 0.06 0.08 0.1 0.12

Strain

Stress (

MPa)

experiment (Tetsushi Kanda, 1998)

analysis (a4 b25)


1.25% ECC

0

0.5

1

1.5

2

2.5

3

0 0.02 0.04 0.06 0.08 0.1

Strain

Stress (

MPa)

experiment (Tetsushi Kanda,1998)analysis (a5 b25)


Mesh sensitivity check on softening behavior

250

200

150

100

50

0

Axi

al S

tress

(kg/

cm2 )

0 .070.060.050.040.030.020.010.00

Disp lacement (mm)

Element 144 Element 300 Element 468


Comparison with experimental result

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.01 0.02 0.03 0.04

Displacement (mm)

Stress

(MPa)

experiment (Gopalaratnam &Shah, 1985)

analysis (HCM,2003)

analysis (HCM+MBM)


Mesh sensitivity check for tension

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Axi

al S

tress

(MPa

)

0.0400.0350.0300.0250.0200.0150.0100.0050.000

Prescribed Displacement (mm)

540 Elements 456 Elements 330 Elements


Tension failure with damage

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Displacement (mm)

Stress (

MPa)

no damage

damage


2 . 5 dd/

6

d

P

b

Flexural failure

• 528 elements

• 2977 nodes

0.2 2,680190.5×76.2×38

Specimen (mm)

2.97 1,68028.066.5×12.7

Notch (mm) cν)(GPaEc)(MPaft )/( mGPaKN )/( mGPaKS


Results

0

50

100

150

200

250

300

0 0.002 0.004 0.006 0.008 0.01

experiment (Bazant, etal., 1992)

analysis1 (FEM, 1998)

analysis2 (EDM, 2001)

analysis3 (HCM, 2003)

analysis (HCM+MBM)


RC panel of simulating RCCV wall subjected to biaxial tensionRC panel of simulating RCCV wall subjected to biaxial tension

Modeling as shell elementModeling as shell element

Specification < HICT and KAERI, 2001 >Compressive strength of concrete (σc) : 41.9MPa

Tensile strength of concrete (σt) : 2.87MPa

Modulus of elasticity of concrete (Ec) : 23828MPa

Yield strength of reinforcement (σy) : 410MPa

Modulus of elasticity of reinforcement (Es) : 205744MPaLayered shell elementLayered shell element


FEM MESH and Boundary conditionFEM MESH and Boundary condition

RC panel is discretized

as 10 x 10 mesh


StressStress--strain curve of strain curve of rebarsrebars

Hoop direction

Meridional direction

Bottom of RC panelTop of RC panel


Crack patterns of RC panelCrack patterns of RC panel

Top of RC panel by experiment Top of RC panel by volume control analysis

Bottom of RC panel by experiment Bottom of RC panel by volume control analysis


Deformed shape of RC panelDeformed shape of RC panel

Hoop dir. displacement. at 1Hoop dir. displacement. at 1stst crack occurrencecrack occurrence MeridionalMeridional dir. displacement at 1dir. displacement at 1stst crack occurrencecrack occurrence

Hoop dir. displacement. at rebar yieldingHoop dir. displacement. at rebar yielding MeridionalMeridional dir. displacement at rebar yieldingdir. displacement at rebar yielding


RCCV subjected to internal pressureRCCV subjected to internal pressure

Specification < SNL, 2001 >

Modeling with or without considering foundationModeling with or without considering foundation

Compressive strength of concrete (σc) : 46.0MPa


Modulus of elasticity of concrete (Ec) : 33,100MPa

Poisson’s ratio of concrete (νc) : 0.20

Yield strength of reinforcement (σy) : 450.0MPa

Modulus of elasticity of reinforcement (Es) : 214,000MPa

Poisson’s ratio of reinforcement (νs) : 0.30



Global behaviorsGlobal behaviors

Radial displacement Radial displacement –– Pressure relationship at midPressure relationship at mid--heightheight

Vertical displacement Vertical displacement –– Pressure relationship at springPressure relationship at spring--lineline


Crack patterns of RCCV Crack patterns of RCCV

1.0Pd (0.31MPa)

2.0Pd (0.62MPa)

3.0Pd (0.93MPa)


Deformed shape of RCCVDeformed shape of RCCV

1.0Pd (0.31MPa) 2.0Pd (0.62MPa)

Ultimate pressure3.0Pd (0.93MPa)


RC tank subjected to reversed cyclic loadingRC tank subjected to reversed cyclic loading

< Harada et al., 2001 >Compressive strength of concrete (σc) : 28.0MPa


Modulus of elasticity of concrete (Ec) : 22,600MPa



Specification

Layered shell elementLayered shell elementModeling as shell elementModeling as shell element


Relative horizontal displacement Relative horizontal displacement -- load curveload curve

Comparison experiment result with Comparison experiment result with pathpath--dependant volume control resultdependant volume control result

Comparison pathComparison path--dependant volume dependant volume control result with precontrol result with pre--test analysis resulttest analysis result


Crack status of RC tankCrack status of RC tank

Multi-directional cracks occurrence due to reversed cyclic loading

Crack status of RC tank by experimentCrack status of RC tank by experiment

Crack status of RC tank by volume control analysisCrack status of RC tank by volume control analysis


Deformed shape of RC tankDeformed shape of RC tank

Horizontal load = 3,037 Horizontal load = 3,037 kNkN

Horizontal load = Horizontal load = --2,200 2,200 kNkN


RC slab subjected to outRC slab subjected to out--of plane cyclic loadingof plane cyclic loading

Specification < Irawan, 2001 >Compressive strength of concrete (σc) : 37.0MPa





Central displacement Central displacement -- load curveload curve

Comparison existing volume control result Comparison existing volume control result with pathwith path--dependant volume control result dependant volume control result (IS1)(IS1)

Comparison existing volume control result Comparison existing volume control result with pathwith path--dependant volume control result dependant volume control result (IS2)(IS2)


Analysis result according to number of layered shell elementAnalysis result according to number of layered shell element

Analysis result according to number of layered shell elementAnalysis result according to number of layered shell element


Crack status of RC slabCrack status of RC slab

Specimen IS1 : vertical load = 193 Specimen IS1 : vertical load = 193 kNkN



Deformed shape of RC slabDeformed shape of RC slab


Isotropic reinforcement arrangement Isotropic reinforcement arrangement

Stiffness of IS1 > Stiffness of IS2Stiffness of IS1 > Stiffness of IS2Due to reinforcement arrangement

Specimen IS2 : vertical load = 144 Specimen IS2 : vertical load = 144 kNkNDue to reinforcement arrangement

Anisotropic reinforcement arrangement Anisotropic reinforcement arrangement


RC box culvert subjected to cyclic loadingRC box culvert subjected to cyclic loading

Specification < Irawan, 1995 >Compressive strength of concrete (σc) : 50.0MPa


Modeling with and without considering haunchModeling with and without considering haunch



LoadLoad--deflection curve of RC box culvertdeflection curve of RC box culvert

Static failure load : 48 Static failure load : 48 tonftonf Model of considering without considering haunchModel of considering without considering haunch

Model of considering with haunch Model of considering with haunch is reinforced concrete layeris reinforced concrete layer

Model of considering with haunch Model of considering with haunch is plain concrete layeris plain concrete layer


Crack status of RC box culvertCrack status of RC box culvert

Wall of RC box culvertWall of RC box culvert

Top slab and wall of RC box culvertTop slab and wall of RC box culvert


Deformed shape of RC box culvertDeformed shape of RC box culvert

Model of considering without haunchModel of considering without haunch

Model of considering with haunch Model of considering with haunch is plain concrete layer

Model of considering with haunch Model of considering with haunch is reinforced concrete layer is plain concrete layeris reinforced concrete layer


RC hollow column under lateral loading

Concrete Reinforcement

fcEc

ν

ft

76.5 MPa

31.4 GPa

2.63 MPa

0.21

fy

Es

fu

350 MPa

200 MPa

421 MPa


P

Stress-strain curve of concrete and reinforcing steel

(Masukawa et al., 1997)

Modeling as shell element

(a) Steel

(b) Concrete


Load-displacement curve

-300

-200

-100

0

100

200

300

-200 -150 -100 -50 0 50 100 150 200

Displacement (mm)

Loa

d (

kN

)

Volume Control Method

Masukawa et al., 1997

Experiment (Masukawa et al., 1997)

Masukawa et al., “Development of RC column members in use of high strength reinforcement”, Proceedings of JCI, Vol. 19, No. 2, pp. 557-564, 1997


ContourContour

(a) At final compression (a) At final tension


Crack patternsCrack patterns

A B

C D


Analysis of 1/4 prestressed concrete containment vessel(PCCV)

Sandia National Laboratories, Albuquerque, New Mexico,2000


Tendon layout Unbonded tendon


Characteristics of Model Test and AnalysisCharacteristics of Model Test and Analysis

The first model test to satisfy material and design details of design code (ASME Sec. III, Div.2)

• limit state test (LST) and structural failure mechanism test (SFMT)

◆ Large scale model including openings and steel liners

3D finite element modeling including tendons, rebars and openings using DIANA

◆ Pre-test analysis ◆ Post-test analysis

Introduction of volume control technique

1/4 Scale PCCVPCCV model


Model Tests (Failure Test due to Internal Pressure)Model Tests (Failure Test due to Internal Pressure)

Limit state test (LST)Limit state test (LST) Structural failure mechanism test (SFMT)Structural failure mechanism test (SFMT)

Pressurized by nitrogen gas

Structural soundness test & leakage test

1.5Pd, 2.0Pd, 2.5Pd and 3.3Pd

(Pd = 0.39 MPa )

Functional failure due to leakage was occurred at 3.3Pd due to tearing of liner

Pressurized by waterStructural failure at 3.6Pd


Structural Failure Mechanism Test (SFMT)


LST test result LST test result

-Hoop directional deformations govern PCCV behaviors


Test result and comparison with the analytical resultsTest result and comparison with the analytical results

Deformation profile at 135˚ section (magnified ×100)Deformation profile at 135˚ section (magnified ×100)

For higher pressure, analysis generally predicts larger deformations than those by the test

The analysis comparably well predicts the global behavior

LST

Analysis

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 2000 4000 6000 8000 10000

0.000 MPa

0.389 MPa

0.585 MPa

0.783 MPa

0.978 MPa

1.162 MPa

1.295 MPa

0.000 MPa

0.389 MPa

0.585 MPa

0.783 MPa

0.978 MPa

1.162 MPa

1.295 MPa


LST resultsLST results

900Final

3.3

1003.1

difficult to increase pressure3.0

liner strain: 2%evidence of liner tear

1.62.5

no evidence of distress2.0

no leakage0.51.5

ObservationLeakage Rate*Pressure/Pd

* volume change (%) per day (V/Day)**Permissible leakage rate for design pressure:

(pressurized water reactor with steel liner) 0.1% V/Day


ComparisonComparison

DeformationsDeformations

Experiment(SNL) Load control


Radial displ. at midheight Vertical displ. at dome apex

More stable solution is possible with volume control techniqueMore stable solution is possible with volume control technique


Rebar stains Rebar stains

Experiment(SNL)

Load control


Outer rebar hoop strain at dome 45˚Outer rebar hoop strain at midheight


Conclusions and future workConclusions and future work

For the failure analysis of RC shell structures using FEM, both

material and structural instability problems can be solved

effectively by the homogenized crack model and the volume

control technique.

In-plane constitutive laws of cracked concrete and modified

Barcelona model can be useful for the modeling of the layered

RC shell element and ECC repaired layers.

Failure analysis or performance evaluation of the deteriorated

RC shell structures repaired with the ECC layers is now under

carried out.


Thank you for Thank you for your kind attention!your kind attention!

song@[email protected]

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