Nonlinear Analysis of Reinforced Concrete Structures in ... · CERVENKA CONSULTING PRAGUE, CZECH...

CERVENKA CONSULTING

PRAGUE, CZECH REPUBLIC

WWW.CERVENKA.CZ

October 2008

1

Nonlinear Analysis

of Reinforced Concrete Structures

in Design and Structural Assessment

Jan Cervenka

Červenka Consulting, Prague, Czech Republic

Outline:

Červenka Consulting - Computer simulation (virtual testing) of concrete structures

Finite element system ATENA – theoretical background, structure, practical applications

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Contents

1. What is simulation?

1. Numerical models for the simulation of reinforced concrete:

1. Nonlinear finite element analysis

2. Material models, fracture-plastic, microplane

3. Special FE for reinforced concrete modeling

• Validation:

• Tension stiffening

• Round robin predictions

• Full scale structural tests

• Applications:

• Bridges

• Tunnels

• Nuclear containment

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Why nonlinear simulation of structures?

Supports expert engineering knowledge

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E 2 E 3 E 10 E 15 E 18 E 27

low strength

high strength

Nonlinear simulation of reinforced concrete structures obrazy trhlin při provozním zatížení

bez oslabení

kulaté otvory

plné vyztužení

kulaté otvory

pouze třmínky

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ATENA:

reinforcement modeling

realistic crack display

run-time visualization

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Nonlinear Finite Element Analysis

ATENA analysis

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Nonlinear constitutive models in ATENA

variety of nonlinear material models:

for concrete

plain

reinforced

pre-stressed

fibre reinforced

other quasi-brittle materials

masonry

rock

soil

metals

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Material Models for Concrete

Uniaxial law Bi-axial criterion 3D failure surface

Menetrey Willam, ACI 1995 Kupfer 1969

Plasticity

Damage mechanics

Microplane models

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Program ATENA

Crack band method – correct energy dissipation during the fracturing process

concrete in tension

tensile cracks

post-peak behavior

fracture energy

crack band method

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Demonstration Examples – mesh objectivity

Importance of Fracture mechanics x Stress-strain laws

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Exponential Model

0,00E+00

2,00E-04

4,00E-04

6,00E-04

8,00E-04

1,00E-03

1,20E-03

1,40E-03

1,60E-03

0,00E+00 1,00E-04 2,00E-04 3,00E-04 4,00E-04 5,00E-04 6,00E-04 7,00E-04 8,00E-04

Deformation [m]

Su

pp

ort

Re

actio

n [M

N]

Coarse Mesh (80x16.7mm)

Fine Mesh (26.7x16.7mm)

Finest Mesh (15.4x16.7mm)

Theory of Elasticity

Experiment

Local Strain Model

0,00E+00

2,00E-04

4,00E-04

6,00E-04

8,00E-04

1,00E-03

1,20E-03

1,40E-03

1,60E-03

0,00E+00 1,00E-04 2,00E-04 3,00E-04 4,00E-04 5,00E-04 6,00E-04 7,00E-04 8,00E-04

Deformation [m]

Support

Reactio

n [M

N]

Coarse Mesh (80x16.7mm)

Fine Mesh (26.7x16.7mm)

Finest Mesh (15.4x16.7mm)

Theory of Elasticity

Experiment

Fracture mech.:

Local model:

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Program ATENA

Numerical core - nonlinear material models

concrete in tension

tensile cracks

post-peak behavior

crack band method

fracture energy

fixed or rotated cracks

crack localization

deterministic size-effect

is captured

Crack band size: L

e = w

L

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Special elements for reinforced concrete analysis

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Reinforcement bond model

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VALIDATION: Simulation of laboratory experiments

Reality

Simulation

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Validation and Reliability

Blind Predictions

Toronto Panel (Collins, Melhorn) 1986

competition results (Panel C).

a) Variations in predicted shear

strength

b) Variations in predicted

load-deformation

response

winner Vladimir Cervenka

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Validation: Round Robin Competition, Marti 2005

ATENA predictions

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Validation: Field Test – Örnsköldsvik, Sweden

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Validation: Field Test

Örnsköldsvik, Sweden

Final failure Step 40, Cracks: in elements, <5.000E-03; ...), openning: <-4.092E-04;4.226E-02>[m], Sigma_n: <-1.912E+01;2.009E+00>[MPa], Sigma_T: <-2.535E+00;2.151E+00>[MPa]

ATENA analysis Field test

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0

2

4

6

8

10

12

14

0 20 40 60 80 100 120 140

Deflection [mm]

Lo

ad

[M

N]

Exper. side 1 Exper. side 2

Initial ATENA w/o CFRP Initial ATENA w. CFRP

Eurocode 2 ATENA final

Analysis with stirrups

Örnsköldsvik Bridge – shear strength

comparison, experiment, ATENA calculation

Stirrups not modelled in the initial analyses

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0 20 40 60 80 10010 30 50 70 90

Displacement [mm]

0

2

4

6

8

10

12

0.5

1

1.5

2.5

3

3.5

4.5

5

5.5

6.5

7

7.5

8.5

9

9.5

10.5

11

11.5

Loa

d [M

N]

West beam mid-span displacement

East beam mid-span displacement

ATENA

3D analysis by LTU

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Foundation slab – cracks due to underground water pressure

forensic investigation

crack

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ATENA numerical simulation

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Foundation slab

Measured cracks

FE analysis

Results due

to water

pressure

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Foundation slab

Measured cracks

FE analysis

Results due

to shrinkage

Constant shrinkage

based on EC2

Conclusion:

Cracks not due to shrinkage

but due to water pressure

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Measured

deflections

Analyzed

deflections

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Construction 514, bridge crossing river Berounky

near Prague, Czech Rep., design Novák & Partner, Ing. M. Šístek

Global verification

of safety during

construcion stages

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Double console

Pier n. 39

112 m

50 m 50 m

35 m

1,4 m

R = 750 m

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Prestressing cables

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Special continuum 3D layered

shell elements, concrete C35/45

výztuž

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Loading Cases

ZS16 vertical wind pressures

ZS17 concreting vehicle

ZS18 longitudinal wind

ZS19 cross-wind

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0

20

40

60

80

100

120

140

160

180

-1.00-0.80-0.60-0.40-0.200.000.20

Maximal deflection [m]

Rela

tive lo

ad

[%

]

Structural capacity

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Optimization of precast structures

precast prestressed hollow core slabs without shear reinforcement

shear failure test in laboratory … and in nonlinear computer simulation

(crack widths)

0.000866

0.000812

0.000758

0.000704

0.00065

0.000596

0.000541

0.000487

0.000433

0.000379

0.000325

0.000271

0.000217

0.000162

0.000108

0.0000541

-3.02E-12

V1

L1

Output Set: Load Step ID 40

Contour: C:COD CRACK_ATTRIBUTES

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ATENA applications

plain concrete lining

railway tunnel in Prague

typical cross section

outer diameter 6 m

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New Railway Connection in Prague

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New Railway Connection in Prague – tunnels under the Vítkov Hill

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Nonlinear analysis of the tunnel profile

finite element model

5000 elements

1 m longitudinal section

plane stress state

supported by nonlinear springs

reflect soil properties

variants:

various upper vault thickness

plain or reinforced

with or without bottom vault

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Nonlinear analysis of the tunnel profile

finite element model

1 m longitudinal section

plane stress state

supported by nonlinear springs

reflect soil properties

Drucker-Prager ground

variants:

various upper vault thickness

plain or reinforced

with or without bottom vault

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Step 26, NSf-UZL - nevyztuzene osteni 300, MSU, zima, liniove pruzne ulozeni Scalars:iso-areas, Basic material, in nodes, Principal Stress, Max., <-5.027E-01;9.964E-01>[MPa]

-5.027E-01

-4.500E-01

-3.000E-01

-1.500E-01

0.000E+00

1.500E-01

3.000E-01

4.500E-01

6.000E-01

7.500E-01

9.000E-01

9.964E-01

Results from NLA

Iso-areas of

principal stress

maximal (tensile)

unreinforced

ultimate limit state

dead load

creep

shrinkage

temperature in winter

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Results from NLA

normal forces

bending moments

unreinforced


dead load

creep

shrinkage


Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E-16;5.182E-01>[MPa]

-5

.03

7E

-04

1

.78

4E

-02

8.0

76E

-03

8.516E-03

-2.745E-02

-1.0

06E-03 -

8.3

30

E-0

3 5.324E

-03

-2.763E-02

1.7

52E

-02

-5

.09

9E

-04

1

.25

2E

-04

-1.248E-01

-4.2

36E

-02

-4.7

66

E-0

2

-4.4

27E

-02

-6.749E-02

-6.697E-02

-1.258E-01 1

.08

1E

-04

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Results from NLA

Crack pattern

unreinforced


dead load

creep

shrinkage


Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E-16;5.182E-01>[MPa]

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Results from NLA

Main crack

description

of crack width

max. 1.6 mm

unreinforced


dead load

creep

shrinkage


Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, <2.000E-04; ...), openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E-16;5.182E-01>[MPa]

7.4

23E

-04

9.7

72

E-0

4

1.2

69E

-03

1.5

92E

-03

4.4

93E

-04

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BARC, Indie, Containment Pressure Test

Model 1:4

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3D model

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ATENA

3D shell element

geometry

layers

reinforcement

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3D Analysis – 3.00 design pressure, P = 0.4239 MPa

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0

0.5

1

1.5

2

2.5

3

3.5

4

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Radial Displacement [m]

Inte

rna

l P

ressu

re [

MP

a]

Axi-symmetric

3D old

3D new

2D - 3D Analysis – Comparison

Design Pressure 0.1413 MPa

3.2 – 3.5 Pd

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New 3D Model based on BARCOM 2009 workshop – corrected cover of openings

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Safety formats for non-linear analysis - 4 methods

Example:

• bending

• shear - deep beam

• bridge pier – geometric nonlin.

• railway tunnel

Comparative study of different safety formats

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Safety Formats for Nonlinear Analysis

xd

R

RE

Rx - is the structural resistance

obtained by nonlinear analysis

gR - is the global safety factor of the

structural resistance

Ed - is the factorized load effect as in

the case of partial safety factor method

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Safety Format (1), PSF Method

Partial safety factors , ,( ) ( )d G i dd jE R

Use design value of material

parameter to calculate Rd:

design val.= characteristic val.

partial safety factor

30

120

.5

ckcd

c

ff MPa

Action Resistance

Med < Mrd

fyd

fcd

1.0

dd

RE

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Safety Format (2), EN1992-2

,( ) /d G i m RE R

Adjusted “mean” values of material parameters:

0.85cm ckf f 1.1ym ykf f

1.27R All failure modes:

Global safety factor

1.1 x 1.15/1.5

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Safety Format (3), ECOV

Estimate of Coefficient of Variation

Coefficient of variation, assuming lognormal distribution of resistance

Global resistance factor

1ln

1.65

mR

k

RV

R

exp( )m

R R RV 4.7 0.8R

Reliability index Resistance sensitivity

exp( )d m R RR R V

exp( 1.65 )k m RR R V we need

2 analyses

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Safety Format (4), Probabilistic Analysis

Reliability index:

( )P E R

Probability of failure:

( )Z

( 0)P Z

Z E R (1) (2)

EN 1990: Basis of structural design, 2002

~ 4.7

~ 10-6

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Safety and Reliability Factors

Safety factors

scatter – not considered

Probabilistic approach

scatter - considered

Z

Z

m

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Results – probabilistic, SARA+ATENA 120 samples

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Bending Beam

300 6000 (t=1000 mm) 300

300 5f14

77.9 93Ed RdM kNm M kNm

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Example: Deep beam

Tested by: Melvin Asin, Delft University, 1999

Nonlinear, probabilistic analysis by: ATENA, 2006

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Deep beam

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Reinforced Concrete Bridge Pier

Horizontal deflection [mm]

Lo

ad facto

r

Interaction diagram

PSF

Mean

EN 1992-2

Characteristic

w/o geom. nonlin.

PSF

Mean

Charact.

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Safety Formats Comparison

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Types of Nonlinear Analysis

Ultimate Limit State – max load

(ULS)

Service Limit State – deflection

(SLS) crack width

Seismic Assessment

(SA) pushover

accelerogram

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-100 0 100 200 300 400 500 600

Radial Displacement [mm]

Inte

rnal P

ress

ure

[M

Pa]

Radial displ @ z=23 m

Radial displ @ z=10 m

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Types of Nonlinear Analysis

Structural details

reinforcement detailing

special details

problems with

boundary conditions

Overall structural behaviour

redistribution due to cracking

ULS, SLS, SA

bending OK

shear or other local effects

not modelled??

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Modelling Issues

for nonlinear analyses of RC

Columns

bending failure

expected

Use beam

elements with

fibres

Shear + bending

failure

Use solid

elements

Bending

failure

expected

Use shell

elements

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Conclusions

Simulation by nonlinear analysis is used as a standard tool in design practice or for the evaluation of existing structures

• Removes inconsistency in standard design process between linear analysis and non-linear cross-section check

• Provides insight into the structural behavior

• Helps to discover critical locations and failure modes

• May discover additional load-carrying capacity

• Ideal tool for checking reinforcement detailing in complicated D-regions

State of art:

• “Complexity” -> old myth from the 20th century

• Available in many commercial finite element codes

• Computationally more demanding than linear analysis

• Supplement standard design based on linear analysis and section design

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Thank you for your attention

Nonlinear Analysis of Reinforced Concrete Structures in ... · CERVENKA CONSULTING PRAGUE, CZECH...

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