RELIABILITY OF REINFORCED CONCRETE BRIDGE DECKS WITH...

Defence of DOCTORAL DISSERTATIONOstrava, December 12, 2007

RELIABILITY OF REINFORCED CONCRETE BRIDGE DECKS WITH RESPECT TO INGRESS OF CHLORIDES

Ing. Petr Konečný

TO INGRESS OF CHLORIDES

POSUZOVÁNÍ SPOLEHLIVOSTI ŽELEZOBETONOVÉ MOSTOVKYS OHLEDEM K PŮSOBENÍ CHLORIDŮ

Supervisor: Prof. Ing. Pavel MAREK, DrSc.

Faculty of Civil Engineering

VŠB-Technical University of Ostrava

Czech Republic.

Outline� Introduction� Objectives of the thesis

� Chloride diffusion - 2D FEM model


Petr KONEČNÝ

� SBRA in ANSYS FEM system

� Example

� Results of parametric study

� Brief summary and conclusions

Introduction� A lot of bridges from reinforced concrete needs early

reconstructions due to early degradation.

� Durability of RC bridge decks are reduced especially

due to corrosion of reinforcement followed by cover


Petr KONEČNÝ

due to corrosion of reinforcement followed by cover

degradation and loss of carrying capacity.

� Deterioration models can help in the identification of

significant parameters in order to build more durable

structures.

� Nature of deterioration problems involves stochastic � Nature of deterioration problems involves stochastic

parameters. It is a field for application of probabilistic

method such as Simulated-Based Reliability

Assessment (SBRA)

Introduction – Protection against Deicers


Petr KONEČNÝ

� Selected bridge deck has reinforcement

protected by cover and epoxy-coating

� Typical protection in Northeastern USA

RC Slab Epoxy-coated Rebars

Asphalt OverlayWaterproof MembraneRC Slab Non-protected Rebars

� Typical protection in Northeastern USA

Epoxy-coated Rebars

e.g. Northeastern USA Europe

Introduction – Crack vs. Holidays

� Reinforcing steel corrosion initiationis accelerated by interaction of:� Cracks in RC bridge deck


Petr KONEČNÝ

� Flaws in epoxi-coating of reinforcing steel (mashed and bare areas, holidays)


Petr KONEČNÝObjectives of the thesis

� Probabilistic durability assessment of concrete bridges� Probabilistic durability assessment of concrete bridgesaffected by deicing agents applied to melt snow.

� Study of the potential of SBRA method with respect to chloride ingress induced corrosion of bridge decksthat have steel reinforcement protected with epoxy-coating.

� Development of the:

Page 6

� Development of the:� 2-D FEM diffusion model that can address

the crack effect.

� Software tool for integration of the SBRA method and commercial FEM package.

Diffusion Coefficient

0 25*10-12 m2/s


0 25*10-12 m2/s


Petr KONEČNÝEstimation of Corrosion Initiation Likelihood

• 2D – FEM chloride

ingress model

2D – FEM chloride

ingress model

• SBRA module for

ANSYS PDS

environment


0 25*10-12 m2/s


0 25*10-12 m2/s

Page 7

environment

• Example


Petr KONEČNÝIntroduction – Bridge Deck

Bridge Structure

Page 8



Transverse cross-section

Page 9



Analyzed element

Page 10



Analyzed element

Page 11



Crack

Page 12



Element cross-section

Page 13



Efect of transverse crack on chloride ion ingresson chloride ion ingress

Page 14

Longitudinal rebar

Holidays on rebarepoxy-coating

2D – FEM chloride ingress model

� Chloride ingress is modelled by diffusion using 2.ND Ficks law

� 2D – Numerical solution with FEM utilization� Acceptable for chloride ingress modelling with regards to


Petr KONEČNÝ

� Acceptable for chloride ingress modelling with regards to bridge deck crack vs. damaged epoxy-coated rebar system interaction.

� ANSYS Program system

• Heat transfer / diffusion process analogy

• Transient analysis

� Stochastic parameters

� Apparent diffusion coefficient,

� Rebar depth,

� Crack depth,

� Epoxy-coated rebar damage, etc.


Petr KONEČNÝ2D – FEM chloride ingress model

Mesh and boundary conditions

Chlorides “loading” 0.6%

0.25

m

Chloride concentration after 10 years


≈3500 Elements (Plane55)

Page 16

Model of bridge deck in ANSYS





0.25

m

Concentration of soluble chlorides – 10 years



Page 17






0.25

m

Rebar




Page 18






Holiday

0.25

m

Rebar



≈3500 Elements

Page 19


2D – FEM chloride ingress model

FEM macro scheme


Petr KONEČNÝ

2-D FEM model (time-dependant chloride ion concentration computation)

Input

Reliability Analysis(corrosion initialisation)

ANSYS APDL macro language.




ingress model

2D – FEM chloride

ingress model

• SBRA module for

ANSYS PDS

environment


0 25*10-12 m2/s


0 25*10-12 m2/s

Page 21

environment

• Example


Petr KONEČNÝIntroduction – Reliability Assessment

� Simulation-Based Reliability Assessment SBRA

� Safety, Serviceability� Safety, Serviceability

� Performance-Based Design� Durability, Corrosion, Fatigue, Degradation of Materials

� Reliability is expressed by probability of corrosion initiation Pf

( ) ( )00 <RFP=<SRP=Pf −

Page 22

( ) ( )00 <RFP=<SRP=Pf −

Stochastic Idea of Deterioration Problem

Chl

orid

e C

once

ntra

tion


Petr KONEČNÝ

Durability with Regards to Chloride Ion Ingress

Threshold for Corrosion Initiation: Cth

C

Chl

orid

e C

once

ntra

tion

Cth

RF(t)=Cth-Cx,t

Corrosion Propagation

Chl

orid

e C

once

ntra

tion

Life SpanCorrosion Initiation Period

Cx,t

( ) ( )00,, <RFP=<CCP=P ttxthtf −

SBRA in ANSYS FEM system

� Probabilistic reliability analysis usingSBRA module for ANSYS:


Petr KONEČNÝ

� Probabilistic analysis of systems using universal FEM software.

� Variables described by both nonparametric distributions (histograms) and parametric.

� Direct Monte Carlo simulation.

SBRA module for ANSYS

Random variable-----------SBRA Module

ANSYS


Petr KONEČNÝ

eg. 10k cycles

Random variable-----------(RV) description---------

SBRA Module

Monte Carlo Simulation

•RV generation

•FEM macro – diffusion model

•Input & Output log

Macro language APDLCrack Depth

0

Interactive evaluation-----------------of results

ANSYSPDS

•Input & Output log




ingress model

2D – FEM chloride

ingress model

• SBRA module for

ANSYS PDS

environment


0 25*10-12 m2/s


0 25*10-12 m2/s

Page 26

environment

• Example

Example

� Response to the considered “loading” by chlorides is computed using Fick’s second Law of diffusion.

Reliability is expressed using probability of


Petr KONEČNÝ

� Reliability is expressed using probability of

corosion initiation that is time-dependent.

� Pf,t =P ( RFt ≤ 0 ) [m-2]

� Reliability function: RF = Cth - Cx,y,t

� C - chloride ion concentration in the � Cx,y,t- chloride ion concentration in the most exposed loaction of the reinforcement

� Cth – chloride threshold[% by mass of total cementitious materials]


Petr KONEČNÝExample – Input Parameters

� Random variables are described based on field � Random variables are described based on field

date and engineering judgement using histograms

and parametric distributions.

Diffusion CoefficientDiffusion CoefficientRebar Depth

NominalRebar DepthRebar Depth

Nominal

� Histograms - field date

Page 28


0 25*10-12 m2/s


0 25*10-12 m2/s 0.04 0.11 m

Nominal

0.0750.04 0.11 m0.04 0.11 m

Nominal

0.075

240 cores taken from 77 bridge spans: (SOHANGHPURWALA et al., 1998)

�Apparent coefficient of diffusion �Depth of reinforcement

Example – Input Parameters�Parametric distributions - Aproximation


Petr KONEČNÝ

Chloride Threshold

ACI CEB

Frequency of Holidays

(SOHANGHPURWALA et al., 1998)

�Relative position of first holiday – Uniform <0,1>

Crack Depth

0 Deck Depth

0.2 0.4 %

Crack Spacing

0.25m

1.15 mµ=0.7

0 100 m-1

(SOHANGHPURWALA et al., 1998)

�Relative position of first holiday – Uniform <0,1>

� Relative position of first crack – Uniform <0,1>

�Deterministic parameters�Surface Soluble Chloride Concentration - 0.6 [%]

�Depth of Slab – 0.23 [m]

m


Petr KONEČNÝExample – FEM Macro

� FEM model is used with Monte Carlo � FEM model is used with Monte Carlo

simulation within the SBRA module

framework in ANSYS environment.

� FEM model is repeated 10 000 times with

variable input parameters.

Page 30

variable input parameters.


Petr KONEČNÝExample - Chloride Concentration

Crack influence

Fre

quen

cy

Exposure 10 years

20

30

10

Page 31Cxy10 [%]

0.0 0.6Chloride Concentration - Cx,10 [%]

Fre

quen

cy

Exposure [years]

50

100C th,ACI =0.2%


Petr KONEČNÝExample – Corrosion Initiation

Corrosion started

Page 32

Age[years]


Petr KONEČNÝExample - Sensitivity Analysis

0.4


Chloride Threshold

Rebar Depth

Crack Depth

0.0

0.4

Page 33

Chloride Threshold

Holiday Frequency

-0.7

RFxy10 [%]


Petr KONEČNÝ

Probability of Corrrosion Initiation - P ft [%.m-1]

100

Example - Probability of Corrosion Initiation

54

65

7379

8488 90

51

62

7076

82

53

63

7278

8387

90 92

42

93

85

50

75

100

e.g. Pd=50%

Page 34

11

3940

28

31

25

20

25

10 20 30 40 50 60 70 80 90 100Expozition [years]

Cxyt

Black bar

1D Reference

Pd - Tikalsky

d

28 Age [years]


Petr KONEČNÝParametric Study – Effect of Holidays

Probability of Corrosion Initiation - P ft [%.m -1]ft

com19-dc1-cd0.2-m100-cs1

61

6975

8083

42

7883

8790 92

51

62

7076

8185

51

44

72

63

52

4050

75

100Cxyt-m-100

Cxyt-m-10

Cxyt-m-1

Black bar

Reference 10 times reduced holiday frequency

Page 35

2732

3640 42

11

25

39

25

39

11

44

27

1421

40

0

25

10 20 30 40 50 60 70 80 90 100Age [years]

100 times reduced

Holiday frequency


Petr KONEČNÝParametric Study – Effect of Diffusion Coefficient

Probability of Corrosion Initiation - P ft [%.m -1]com16-dc1-cd0.2-m10-cs1com16-dc1-cd0.2-m10-cs1

51

61

6975

8083

7278

8387 90

51

62

7076

85

92

63

52

81

50

75

100Cxyt-dc-1

Cxyt-dc-0.1

Black bar-dc-1

Black bar-dc-0.1

Reference-dc-1

Reference-dc-0.1 10 times reduced

Diffusion coefficient

Page 36

25

39

7 8 9 1023 24 25 25 26 27

11

25

51

11 114 5 63

4028

2822

21

39

20

25

10 20 30 40 50 60 70 80 90 100Age [years]

Diffusion coefficient


Petr KONEČNÝSummary

� Probabilistic approach for estimation of the corrosioninitiation of bridge deck reinforcing steel with by method SBRA using 2-D FEM model in ANSYS is method SBRA using 2-D FEM model in ANSYS is presented.

� SBRA module for ANSYS is used for application of

random variables described by bounded histograms

in Monte Carlo.

� Chloride ingress is modelled by 2.ND Fick’s Law for

Page 37

� Chloride ingress is modelled by 2.ND Fick’s Law for diffusion using 2D FEM application with regards to stochastic interaction of bridge deck crack vs. damaged epoxy-coated rebar system.

� The probability of corrosion initiation is used in order to qualitatively compare various scenarios with respect to durability.


Petr KONEČNÝConclusions

� Probabilistic approach can be used to study effect of crack and holiday interaction with regards to bridge crack and holiday interaction with regards to bridge deck durability.

� The most important variable is diffusion coefficient(mix design).

� The effect of epoxy-coated reinforcement improves durability under proper handling and construction practices.

Page 38

practices.� The research in the area of reliability of RC bridge

deck is valuable and deserves further attention.

Thank you

RELIABILITY OF REINFORCED CONCRETE BRIDGE DECKS WIT H RESPECT TO INGRESS OF CHLORIDES

by

Ing. Petr Konečný


Petr KONEČNÝQuestions

� Complex chloride transport model� Propagation phase. How do you solve that?� Propagation phase. How do you solve that?� Could you estimate how significant would be

difference between apparent coefficient and real diffusion coefficient?

� Which mechanical properties of the bridge deck and dynamic load affect the degradation of the reinforced concrete deck?

Page 40

concrete deck?� How can these damages be investigated in the real

bridge? How can one calculate these uncertainties?


Petr KONEČNÝ

More Complex Chloride Transport Model

� Simple diffusion model.

x2CC ∂∂ (Eq. 4) (Eq. 5)

−

t

xerfC=C

ctx, 4D

10

1D – model with respect to advection and bound chlorides

2

2

x

CD=

t

Cc ∂

∂∂∂

Cf - Concentration of free κ - Moisture diffusivity

� Diffusion – advection model (Bear and Bachmat)

(Eq. 4) (Eq. 5)

( )t

C

x

wC

xx

CwD

x=

t

wCb

fff

∂∂−

∂∂

∂∂+

∂∂

∂∂

∂∂

κ

Page 41

Cf - Concentration of free chlorides

Cb - Concentration of bound salts

w - Volumetric moisture content

Pavlík Z et al., Water and salt transport and storage properties of Mšené sandstone, Constr. Build. Mater (2007), doi:10.1016/j.conbuildmat.2007.05.010

κ - Moisture diffusivityD - Salt dispersion

coefficientt - Timex - Depth


Petr KONEČNÝMore Complex Chloride Transport Model

� Numerical sollution� The 2D FEM macro can be adjusted in order to � The 2D FEM macro can be adjusted in order to

allow for more complex model.� Change of „surface“ chloride concentration.� Advection (moisture transport) model

requires the time-dependent diffusion constant.

� The simple model form (Eq. 4) can be used for 2CC ∂∂

Page 42

� The simple model form (Eq. 4) can be used for qualitative comparison very efficiently.

ROVNANÍKOVÁ, P., PAVLÍK, Z., ČERNÝ, R. (2002). “Měření současného přenosu vody a chloridů jako podklad pro predikci koroze výztuže v betonu. In Beton TKS, 2002, vol. 6, pp. 46-49, (in Czech)

2

2

x

CD=

t

Cc ∂

∂∂∂


Petr KONEČNÝPropagation phase

� The integration with propagation phase would be useful in order to evaluate the reliability of the useful in order to evaluate the reliability of the structure in terms of carrying capacity.

� Selection of suitable mathematical model for localized corrosion of steel

� Compute the resistance of the RC crossection based on the loss of steel bar area.

� Incorporate it into stochastic analysis and compute

Page 43

� Incorporate it into stochastic analysis and compute the Pf

Pf = P (S – Rt) < Pd (safety)


Petr KONEČNÝ

� Mathematical model for localized corrosion of steel – e.g.

Propagation phase

(Gonzalez et. al.)(Gonzalez et. al.)

pt - depth of the pitψ - uncertainty factort - timeti - time to corrosion initiationicorr – corrosion currentRcorr – 4-8 when localized corrosion

(pitting) occursA

pt

D

Page 44

Ar,t - net cross sectional area of a corroded rebar (Val &Melchers)Gonzales, J.A., Andrade, C., Alonso, C. And Feliu, S. (1995) Comparison of rates of

general corrosion and maximum pitting penetration on concrete embedded steel reinforcement, Cement and Concrete Research, 25(2), p.257-264

Val, D. & Melchers, R.E. (1998) Reliability analysis of deteriorating reinforced concrete frame structures, Structural Safety and Reliability, Balkema, Rotterdam, 105-112

FReET-D PROGRAM DOCUMENTATION , Červenka consulting


Petr KONEČNÝ

Apparent Coefficient vs. Real Diffusion Coefficient

� Aparent diffusion constant can be used for � Aparent diffusion constant can be used for

comparison of different material and

construction scenarios.

� It gives qualitative answer which scenario is

better – which structure would last longer.

Page 45

� It does not adress the question of the change

of Dc over time and depth of slab with respect

to chloride concentration.


Petr KONEČNÝDegradation, Mechanical Properties and Dynamic Loading

� Which mechanical properties of the bridge deck and dynamic load

affect the degradation of the reinforced concrete deck?affect the degradation of the reinforced concrete deck?

� Cracking depends on the

� Strength (w/c relationship)

� Modulus of elasticity – lower ME – lower stresses

� Shrinkage

� Thermal strain (heat of hydration)

� Structural loading (static and dynamic)

Page 46

� Structural loading (static and dynamic)

� Cracking growth enhanced by traffic induced vibration

� Vibration severity and lenght of span enhance the crack growth more

(Camisa, S.J. et. al., Field Evaluations of Early Age Bridge Deck Behavior, 2003)


Petr KONEČNÝEpoxy-coating Damage Investigation

� New Structure� New Structure� Reinforcement visual survey before casting

� Existing Structure� Taking core

� Extruding reinforcement

� Visual inspection of the reinforcement with recording of the mashed areas, bare areas etc.

Page 47

mashed areas, bare areas etc.

� Holiday detection can be performed in accordance with ASTM62Method that uses an electrical current flow through a epoxy-coating to indicate the presence of a holiday.


Petr KONEČNÝOther Questions

Page 48


Petr KONEČNÝTime-consumption

� 10000 simulations � 10000 simulations

� 60 hours - 100 years of chloride exposure with performance analysis in interval of 5 years.

� 24 hours - 50 years with 10 year intervals are studied, then the analysis takes about.

� One dual core processor of SUN workstation,

Page 49

� One dual core processor of SUN workstation,

12 GB memory and 2.4 Ghz frequency. The

computer has a Linux operating system


Petr KONEČNÝNumber of Simulation

Pf

Page 50

0 2500 10000

Binary and Ternary Blends�The diffusion coefficient is reduced to reflect the

HPC properties (binary and ternary blends). Other input values remain the same.

NINTH CANMET/ACI INTERNATIONAL CONFERENCE Warsaw, May 20-25, 2007


0 25*10-12 m2/s


0 25*10-12 m2/s0.49 m 2 / s

mean

0 25*10-12 m2/s0 25*10-12 m2/s2.5*10-12 m2/s0.49 m 2 / s


Petr KONEČNÝFrequency of holidays

Frequency of Holidays

1616 m-1

(SOHANGHPURWALA et al., 1998), cca. 240 cores from 77 bridge spans

� Number of holidays* per bar in core:

132 m-10

mean

Page 52

� Number of holidays* per bar in core:� Mean = 12.2

� Max = 169

� Mean bar length = 93 mm (3.7 in)

* Holidays including blisters, bare and mashed areas


Petr KONEČNÝDiffusion / heat Analogy

• Thermal conductivity – KXX = Dc• Thermal conductivity – KXX = Dc

• Mass density - DENS = 1

• Thermal capacity – C = 1

Page 53

Introduction

� The thesis is focused on a stochastic

reinforced concrete bridge deck 2-D chloride

ingress model.


Petr KONEČNÝ

ingress model.

� The model combines a finite element model

and a Monte Carlo simulation technique for

application with chloride ingress in concrete

with cracks.

Introduction - Chloride Ion Diffusion

� Chloride ingress is modelled by diffusion using 2.ND Ficks law


Petr KONEČNÝ

2CD=

C ∂∂Dc - Effective diffusion

coefficientt - Time

� 1D –Solution does not allow for chloride ingressmodelling with regards to bridge deck crack vs. damaged epoxy-coated rebar system interaction.

2x

CD=

t

Cc ∂

∂∂∂ t - Time

x - DepthC - Chloride ion

concentration

damaged epoxy-coated rebar system interaction.

−

t

xerfC=C

ctx, 4D

10

C0 - Surface Chloride ion concentration

Cx,t - Chloride ion concentration at depth xin time t.


Petr KONEČNÝReliability Function vs. Crack Depth

Page 56


Petr KONEČNÝReliability Function vs. Diffusion Coefficient

Dc[m

2 /s×

10-1

2 ]40

Corrosion Initiated

Page 57

RFxy10[%]

0-0.4 0.40


Petr KONEČNÝReliability Function vs. Holidays in Epoxy-coating

Mash

N[m

-1]

100Corrosion Initiated

Page 58

RFxy10[%]

Sensitivity to Holiday Frequency

0

10

-0.4 0.40


Petr KONEČNÝReliability Function vs. Rebar Depth

x[m

]0.12

Corrosion Initiated

Page 59

RFxy10[%]

0.04-0.4 0.40


Petr KONEČNÝReliability Function vs. Chloride Threshold

Cth

[%]

0.4

Corrosion Initiated

Page 60

RFxy10[%]

0.2-0.4 0.40


Petr KONEČNÝReliability Function vs. Crack Spacing

Crc

ks[m

]1-D Model

1.2

1.0

Page 61

Crc

k

2-D Model0.2

-0.4 0.40RFxy10[%]

Corrosion Initiated


Petr KONEČNÝComparison of 2-D and 1-D Solution

Page 62

Epoxy-coating and Crack Effect (left) 1-D Analytical Solution (right),

T=100 years



Crack Influence

Epoxy-coating Blackbar

Crack Influence

No Holidays

Corrosion InitiatedPf=92%



Page 63T=100 years

RFxy100[%] RFblackbar100[%] RFanalytic100[%]-0.4 -0.40.38 0.29 -0.33 -0.310 00

1-D Analytical Solution

(right),

Crack Effect (left)



1-D

Analytical

Solution

Page 64

Epoxy-coating and Crack Effect

T=100 years


Petr KONEČNÝConclusions - more

� Enhancing the model with:� Propagation phase of corrosion.� Early age bridge deck behaviour - crack propagation.� Better characterization of input parameters.� Time-dependent diffusion coefficient and surface.

concentration.

� Programming a stand alone program would bring a model closer to engineers and speed up the

Page 65

model closer to engineers and speed up the simulations.

Date post:	19-Apr-2020
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

RELIABILITY OF REINFORCED CONCRETE BRIDGE DECKS WITH...

Documents