ATENA Nonlinear Analysis in Design&Assessment

CERVENKA CONSULTING

PRAGUE, CZECH REPUBLIC

WWW.CERVENKA.CZ

December 2013

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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ATENA:

reinforcement modeling

realistic crack display

run-time visualization

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Nonlinear Finite Element Analysis

ATENA analysis

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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

ressure

[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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LOCAL

action in a section

of elastic structure

resistance of

SECTION

dS

d dS R

dR

GLOBAL

action on a structure

resistance of

STRUCTURE

Gd GdS R

GdS

GdR

Verification of limit states by global approach, fib model code 2010

Linear Non-linear

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Safety Formats for Nonlinear Analysis

fib Model Code 2010

xd

R

RE

Rx - is the structural resistance

obtained by nonlinear analysis

R - is the global safety factor of the

structural resistance

Ed - is the factorized load effect as in

the case of partial safety factor method

Methods in fib 2010:

(1) Full probabilistic, (2) EC 1992-2, (3) ECOV, (4) PSF

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SAFETY FORMATS OF

DESIGN RESISTANCE

Full probabilistic analysis

Global safety factor

Partial safety factors

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GLOBAL SAFETY FACTOR Eurocode 2-2

“mean” values of material parameters

design resistance

global resistance factor 1.27R

*( , )m cm smd

R

R f fR

* 0.8 .1,5 1cm ck sm skf f f f

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GLOBAL FACTOR EN 1992-2- Probabilistic concept

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Assuming lognormal function

PDF for resistance can be defined

by mean and characteristic values of resistance

1ln

1.65

mR

k

RV

R

METHOD ECOV

(Estimate of Coefficient of Variation of resistance)

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METHOD ECOV

(Estimate of Coefficient of Variation of resistance)

exp( )R R RV /d m RR R 1ln

1.65

mR

k

RV

R

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2014-01-14 Assessment for

Future Traffic

15

LARGE LIGHTLY REIFORCED BEAM

Experiments by Collins, Yoshida, University of Toronto 2000

LARGE LIGHTLY REINFORCED BEAMS

Experiments by Collins, Yoshida, Toronto 2000

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FE model Y2000/0

Compressive strength fc = 37 MPa

Steel yield stress fy = 470 MPa

FE model YB2000/4

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Failure animation:

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Experime

nt

Analysis

Crack pattern at failure

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Mesh size effect with parameter set A

0

100

200

300

400

500

600

0 2 4 6 8 10

Displacement [mm]

Lo

ad

[kN

]

Experiment Y0

M 200

M 100

M 50

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Probabilistic analysis – random sampling LHS

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Future Traffic

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Safety formats: Without shear reinforcement

YB2000/0

0

0.001

0.002

0.003

0.004

0.005

0.006

0 200 400 600 800

P[kN]

PD

F (P

)

safety

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Safety formats:With light shear reinforcement

YB2000/4

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 500 1000 1500 2000

P[kN]

PD

F (

P)

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CASE STUDY

simple RC beam

deep beam

bridge pier

railway bridge

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24

PSF ECOV EN 1992-2 Probabilistic

Example 1

Bending

1.04 1.04 0.99 1.0

Example 2

deep beam

1.02 1.04 1.0 1.0

Example 3

bridge pier

0.98 1.04 0.96 1.0

Example 4

bridge frame

0.99 0.96 0.92 1.0

Example 5

shear beam

Y0

1.03 0.98 1.02 1.0

Example 6

shear beam

Y4

0.81 1.04 0.82 1.0

average 0.98 1.01 0.95 1.0

Comparison of design resistances

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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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Special elements for reinforced concrete analysis

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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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LOAD-DISPLACEMENT RESPONSE

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

deflection [mm]

loa

d in

ten

sity

[kN

/m2

]full

circular opening strong

circular opening, ties

circular opening

service load 12 kN/m2

dead load 7.75 kN/m2

Verify design of reinforcement

detailing in critical members

Global

safety

factor

EN1992-2

DIN

1.3

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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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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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Pushover analysis of NPP control room building

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Control Room Building 3D FE Model

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Column Reinforcement Stresses for Loading in X+

X

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Pushover Curves for Median Response

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Pushover Curves – Comparison with Elastic Response Spectrum

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Objectives:

Verification of sustainability

Probabilistic seismic evaluation of fragility curves

Capacity modeled by pushover curves

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Offshore wind power plants – Baltic sea Germany

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High stress concentration

near the shear keys

Standard design

approaches based

on stress checks not

applicable

Global approach was

used for ULS and FLS

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Shrinkage cracks Cracks and plastic strains

at failure

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,max ,0.3c cd fatf

FLS check using the simplified fib model code approach

810N

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FLS check applied as reduced compressive strength

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0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10

Re

lati

ve

lo

ad

le

ve

r [-

]

Rel. maximal pile-pin displacement [mm]

FLS-min, Model F w/o Vert. Beads

FLS-min, Model G with Vert. Beads

Global verification using partial factor approach

from model code 2010

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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

ATENA Nonlinear Analysis in Design&Assessment

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