Effects on risk for degradation of rendered autoclaved aerated concrete

1233 Pages·2005·64.97 MB·English

10DBMC International Conférence On Durability of Building Materials and Components
LYON [France] 17-20 April 2005

Modelling of Corrosion induced Failure
of Reinforced Concrete Structures

F. Buyle-Bodin, A.L. Thang, M. Dekoster, O. Blanpain,
O. Maurel
USTL,
Cité Scientifique, F-59655 Villeneuve d’Ascq, France
[email protected]

TT1-31

ABSTRACT

Many reinforced concrete (RC) structures are suffering from corrosion related problems much earlier
than their expected service life.
Steel reinforcement is subjected to corrosion due to carbonation and chloride attack. Carbonation
ordinarily induces uniform corrosion. Chloride attack induces generally localised corrosion at cracks
level. The consequences of the corrosion at local scale are a decrease of sound steel active cross
section, a development of cracking in concrete cover, and a loss of steel-concrete bond.
To carry out structural assessment of corroded structure elements needs to evaluate the consequences
of the corrosion at global scale. These consequences depend on the sort of corrosion, the corrosion
rate, the localisation and the extension of corroded areas, and the crack density.
A Finite Element model has been developed to simulate the flexural behaviour of corroded RC
elements. The FE model was calibrated with different experimental studies. For the computation,
special elements were used to model the interface between steel and concrete. They are called rust
elements. Their size is fixed and their characteristics infer from measurable parameters as corrosion
localisation or rate. Their efficiency to compute flexural behaviour of corroded RC elements has been
highlighted.
The FE model has been used to simulate different types of corrosion instance, varying nature,
localisation, extension, rate, and cracking. For each case the ultimate load, the ultimate deflection, and
the stiffness were computed. The final objective is to provide an efficient tool of evaluation of
structural assessment and of failure prediction from deterioration assessment.

KEYWORDS

Reinforced Concrete, Degradation, Corrosion, Finite Elements, Failure

1 INTRODUCTION
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

Many structures are suffering from corrosion related problems much earlier than their
expected service life. Reinforcing steel bars are subjected to corrosion due to carbonation and
chloride attack. Carbonation ordinarily induces general corrosion whereas chloride attack
induces localised corrosion at cracks level. The consequences of corrosion at local scale are a
decrease of sound steel active cross section, a development of cracking in concrete cover, and
a loss of steel-concrete bond. To carry out structural assessment of corroded structure
elements needs to evaluate the consequences of the corrosion at global scale. These
consequences depend on the type of corrosion, the degree of corrosion, the localisation and
the extension of corroded areas, and the crack density.

A Finite Element study has been developed to simulate the flexural behaviour of corroded RC
elements [Dekoster 2003]. The FE calculation was calibrated from different experimental
studies [Dekoster et al. 2003, Castel et al. 2000, Lee et al. 1998]. For the computation special
elements were used to represent the interface between steel and concrete. They are called
“rust” elements. Their size was fixed and their characteristics were inferred from measured
parameters representing the degradation of materials as degree and extension of corrosion.
Their efficiency to compute flexural behaviour of corroded RC elements has been
highlighted.

The “rust” elements were used to simulate various instances of corrosion, varying nature,
localisation, extension, and degree. For each case the load, the deflection, and the stiffness
were computed. The final objective is to provide an efficient tool of evaluation of global
structural assessment from local deterioration assessment.

2 COMPUTATIONAL PROCEDURE

2.1 Reinforced concrete model

A damage elastic plastic model and volume elements are used to model the concrete. An
elastic plastic model and bar elements are used to model the steel bars. The reduction of the
steel cross section with the corrosion degree is supposed to be linear:
A = A*(1−η) (1)
c
where A is the corroded steel cross section, A the original steel cross-section, and η the
c
corrosion degree.
The computation is performed following the smeared crack approach. This choice induces
that the model cannot take into account the longitudinal secondary cracking pattern generated
by corrosion, and looses its accuracy near the bearings where the shear effects become
predominant.

2.2 Rust element

The rust production x is considered to be a function of the corrosion penetration x, assuming
r
that the increase of volume is two times the initial section (Equation 2). A parametric study
[Dekoster 2003] had shown that the choice of this factor of expansion is not very relevant.
Equation 3 gives the relationship between the rust production x, the original radius of
r
reinforcement r , and the corrosion degree η (between 0 and 1).
0
x = 2x (2)
r
x = 2r (1− 1−η) (3)
r 0
TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

In their model, [Molina et al. 1993] had simulated the corrosion simply with a linear variation
of the materials properties from those of steel to those of rust. In our study [Dekoster 2003,
Dekoster et al. 2003], rust and steel are considered as distinct materials and simply their
section is changing. For the steel, the use of bar elements allows easily the decrease of the
reinforcement section. To model the rust, volume elements (three nodes triangular) are used.
The mechanical characteristics of the rust are assumed to be closed to these of water [Molina
et al. 1993]. The real section of rust must be represented by fictitious layers of rust (Fig. 1).

VIRGIN STEEL
Concrete splitting
Rust
r
0
x
rc xr CONCRETE

y y
e
section: S section: s
r r
modulus: E modulus: E
r eqr
z z

Figure 1. Real and reconstructed steel and rust section

As the corrosion is not homogeneously distributed along the reinforcement, the size of the
rust element is defined with regard to the part of the beam with the lowest corrosion degree
n . To fit the real conditions of corrosion and the needs of the modelling, an equivalent
min
modulus E is used and is presented in equation 4. The real section of rust is presented in
eqr
equation 5, the reconstructed section of rust in equation 6 and finally equation 7 give the
relation between those parameters and the material and geometrical properties:
S
E = E r (4)
eqr r s
r
S (η) = 2π[(r +x)2 −(r −x)2]=8πr2(1− 1−η) (5)
r 0 0 0
s (η)= 2ex = 2r e(1− 1−η ) (6)
r 0 min
4πr
E (η)=E 0 (7)
eqr r e
TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

This use of a volume element rather than un-dimensional interface elements following stress-relative
displacement laws is the main original aspect of this model. Only the knowledge of the corrosion
degree needs to be correctly fitted.

2.3 Simulation parameters

The geometrical and mechanical parameters, which can be modified for simulation work, are
presented in Fig. 2. For the present study, the same values as [Castel et al. 2000] are used and
presented in Table 1.
Concrete Steel

l a e d h E f f φ E f
b c t s y

mm mm mm mm mm GPa MPa MPa mm GPa MPa

2800 1400 150 258 280 36 65.3 6.8 12 250 500

Table 1. Geometrical and mechanical parameters
The corrosion instances are simulated by varying the location, the size, the degree of
corrosion of the corroded zone, and the location of the loading point (Table 2 and Fig. 3).

Parameters Values

Size of the corroded zone (p )
1 100 300 500
(mm)

Location of the loading point
0 -400 -800

from the centre (p ) (mm)
2
Location of the mid of the
0 -200 -400 -600 -800
corroded zone from the centre (p )
3
Corrosion (%) 10 20
Table 2.
Parameters used for the simulation

a
e
d
h
l

Figure 2. Beam dimensions

p2
p1
p3
p1: size of the corroded zone
p2: loading point
p3: position of the corroded zone

Figure 3. Presentation of the parameters used for the simulation
TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

3 STUDY OF CORROSION INFLUENCE ON BEAM FLEXURAL BEHAVIOUR AT
SERVICEABILITY CONDITIONS

For the selected geometric and mechanical values (Table 1,[ Castel et al. 2000]), the service
load given by the French code BAEL 91 is equal to 19.2 kN. In first, the beam presumed new
is loaded until the service load F . The service deflection (u ) is plotted at this point. Then,
ser ser
to take into account the various delayed deformations as shrinkage, swelling, fatigue, the
beam is unloaded, corrosion is introduced by considering the degraded characteristics of
materials and again the beam is loaded until service load [Dekoster et al. 2003-2].
Load decrease ratio Deflection increase ratio
p = 0 p = 0
2 2
p p
3 3
p η -800 -600 -400 -200 0 p η -800 -600 -400 -200 0
1 1
0.1 0.09 0.09 0.10 0.11 0.08 0.1 0.10 0.10 0.11 0.12 0.09
100 100
0.2 0.11 0.10 0.11 0.12 0.11 0.2 0.12 0.11 0.12 0.14 0.12
0.1 0.13 0.12 0.13 0.12 0.11 0.1 0.15 0.14 0.15 0.14 0.13
300 300
0.2 0.14 0.14 0.14 0.15 0.16 0.2 0.16 0.17 0.17 0.17 0.19
0.1 0.13 0.14 0.14 0.15 0.15 0.1 0.15 0.17 0.17 0.17 0.17
500 500
0.2 0.15 0.19 0.19 0.19 0.20 0.2 0.18 0.23 0.23 0.24 0.25
p = -400 p = -400
2 2
0.1 0.10 0.11 0.10 0.11 0.10 0.1 0.11 0.12 0.11 0.12 0.11
100 100
0.2 0.11 0.12 0.11 0.12 0.11 0.2 0.12 0.13 0.12 0.14 0.12
0.1 0.14 0.14 0.12 0.13 0.12 0.1 0.16 0.16 0.14 0.15 0.13
300 300
0.2 0.16 0.16 0.15 0.16 0.15 0.2 0.20 0.19 0.18 0.18 0.18
0.1 0.17 0.15 0.15 0.13 0.13 0.1 0.21 0.17 0.18 0.16 0.14
500 500
0.2 0.23 0.20 0.20 0.19 0.18 0.2 0.29 0.25 0.25 0.23 0.23
p = -800 p = -800
2 2
0.1 0.03 0.04 0.08 0.04 0.02 0.1 0.03 0.04 0.09 0.05 0.02
100 100
0.2 0.04 0.05 0.10 0.08 0.02 0.2 0.05 0.05 0.11 0.08 0.03
0.1 0.10 0.10 0.15 0.14 0.05 0.1 0.11 0.10 0.18 0.16 0.06
300 300
0.2 0.14 0.15 0.18 0.17 0.06 0.2 0.16 0.18 0.23 0.20 0.08
0.1 0.12 0.10 0.20 0.19 0.14 0.1 0.14 0.11 0.25 0.24 0.16
500 500
0.2 0.21 0.18 0.24 0.24 0.18 0.2 0.27 0.22 0.31 0.31 0.22

Table 3. Load decrease and Deflection increase ratios
The new deflection (u ) corresponding to the service load and the load (F )
ser-c ser-c
corresponding to the previous service deflection are plotted. The results are presented as
ratios by report to the sound beam values.
F −F
Load decrease ratio= ser ser−c (8)
F
ser
u −u
Deflection increase ratio= ser−c ser (9)
u
ser
The load decrease ratio is representing the loss of mechanical capacity of the structure, and at
serviceability conditions is corresponding to the decrease of load for a given deflection linked
to a critical opening of cracks. This decrease is related to the decrease of stiffness of the
corroded structure. The deflection increase ratio is representing the consequence of the
corrosion process in terms of deformation. The results presented in Table 3 show a similar
evolution for load decrease and deflection increase but for a same simulation, the deflection
increases higher than the load decreases.

TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

The increase of the ratios is well related to the increase of the size of the corroded zone . But
the maximal ratios are not systematically observed at the level of the application of the load,
except at mid-span. For the point of application located at 400 mm, the maximal ratios are
observed at the end of the corroded zone near the bearing. For the point of application located
at 800 mm, the maximal ratios are observed at the middle between the point of application of
the load and the mid-span.

4. STUDY OF CORROSION INFLUENCE ON BEAMS AT FLEXURE ULTIMATE STATE

In this case, the new beam is loaded until the service load (F ). Then, after the unloading of
ser
the beam, and the introduction of corroded characteristics, the beam is loaded until the
ultimate state, plotting the ultimate deflection (u ) and the ultimate load (F ) of the corroded
uc uc
simulation. A loading of the sound beam at ultimate state has been simulated as a preliminary
in order to determinate the ultimate deflection of the sound beam (u ) and its ultimate load
ut
(F ).The results are presented as ratio by report to the sound beam values.
ut

F −F
Ultimate load decrease ratio= ut uc (10)
F
ut
u −u
Ultimate deflection decrease ratio = ut uc (11)
u
ut

The load decrease ratio is representing the loss of strength capacity of the corroded structure compared
with the sound structure, and at ultimate conditions is corresponding to a decrease of safety factor.
This decrease is mainly related to the reduction of the reinforcement steel cross section induced by
corrosion. The deflection decrease ratio is representing the consequence of the corrosion process in
terms of ductility. This decrease is related to a combination of the reduction of the steel cross section
and the reduction of the stiffness of the corroded structure induced by the decrease of bond.

For the serviceability conditions, the ratios corresponding to a degree of corrosion of 0.2 are
just a little higher than these corresponding to a degree of corrosion of 0.1. For the ultimate
conditions, the difference is notably higher, sometimes of two or three times.

It can be observed in Table 4 that the evolutions of the deflection and load ratios are different
from these corresponding to the serviceability conditions. First, for the simulation with 100
mm size of corroded zone, the ultimate deflection is strongly more reduced than the ultimate
load. For the other sizes (300 and 500 mm), the reductions are quantitatively the same than
for 100 mm size, but deflection reduction is located at the ends of the corroded zone, while
load reduction remains located at the loading point [Dekoster 2003].

For the ultimate load and for all the sizes of corroded zone, the minimal ratio is observed at
the loading point. The difference with the variation of the loading point is not very high.

For the ultimate deflection, the ratio decreases when the size of the corroded zone increases.

Those results confirm that deflection and load are not influenced in the same way by the loss
of bond and the loss of steel cross section. It is principally the loss of steel cross section that
affects the load reduction, while it is the loss of bond that affects the deflection reduction.

TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

Table 4. Ultimate load and Ultimate deflection ratios
Ultimate load decrease ratio Ultimate deflection decrease ratio
p = 0 p = 0
2 2
p p
3 3
p η -800 -600 -400 -200 0 p η -800 -600 -400 -200 0
1 1
0.1 0.00 0.00 0.02 0.06 0.11 0.1 0.00 0.00 0.09 0.18 0.55
100 100
0.2 0.01 0.04 0.08 0.12 0.19 0.2 0.00 0.15 0.24 0.55 0.59
0.1 0.00 0.03 0.03 0.07 0.08 0.1 0.00 0.20 0.22 0.37 0.24
300 300
0.2 0.01 0.05 0.05 0.18 0.19 0.2 0.00 0.23 0.24 0.58 0.30
0.1 0.02 0.02 0.03 0.11 0.10 0.1 0.04 0.04 0.21 0.35 0.11
500 500
0.2 0.03 0.04 0.12 0.18 0.19 0.2 0.23 0.25 0.48 0.58 0.20
p = -400 p = -400
2 2
0.1 0.01 0.04 0.09 0.05 0.01 0.1 0.00 0.22 0.46 0.24 0.00
100 100
0.2 0.03 0.11 0.22 0.13 0.06 0.2 0.02 0.46 0.60 0.53 0.18
0.1 0.03 0.07 0.10 0.08 0.03 0.1 0.03 0.41 0.14 0.40 0.06
300 300
0.2 0.02 0.16 0.19 0.17 0.08 0.2 0.00 0.54 0.30 0.50 0.26
0.1 0.02 0.10 0.12 0.10 0.06 0.1 0.11 0.36 0.11 0.25 0.23
500 500
0.2 0.05 0.18 0.19 0.17 0.13 0.2 0.35 0.44 0.19 0.50 0.43
p = -800 p = -800
2 2
0.1 0.08 0.03 0.00 0.00 0.00 0.1 0.38 0.13 0.00 0.00 0.00
100 100
0.2 0.08 0.13 0.03 0.00 0.00 0.2 0.57 0.45 0.09 0.00 0.00
0.1 0.09 0.07 0.03 0.00 0.00 0.1 0.21 0.17 0.00 0.00 0.00
300 300
0.2 0.17 0.16 0.13 0.00 0.00 0.2 0.29 0.31 0.13 0.00 0.00
0.1 0.08 0.08 0.03 0.00 0.00 0.1 0.14 0.02 0.13 0.00 0.00
500 500
0.2 0.18 0.17 0.13 0.00 0.00 0.2 0.32 0.05 0.32 0.00 0.00

5 CONCLUSIONS

The developed tool of simulation presented in this study enables the prediction of the
mechanical behaviour of corroded RC structures. It is possible to take into account the
location, the expanse and the degree of corrosion of the corroded zone to simulate the
behaviour at serviceability and ultimate conditions.

At serviceability conditions, the increase of the size and of the degree of corrosion of the
corroded zone induces the decrease of the load ratio and the increase of the deflection ratio.
The reduction of the bond between steel and concrete is the main factor of mechanical
degradation for these conditions.

At ultimate conditions, the both load and deflection are reduced. It is principally the loss of
steel cross section that affects the ultimate load decrease, and the loss of bond that affects the
ultimate deflection decrease. This is confirmed by the fact that the main deflection decreases
are observed at the end of the corroded zone.

The model presents a set of limitations:
- the corrosion is graduated by the degree of corrosion, which cannot be measured directly in
situ;
- the use of the smeared crack approach gives greater place to the bending cracking at the
expense of shear and secondary cracking;
- the model is fitted to global scale analysis and is not suited to local scale analysis;
- the model is not very accurate near the bearings where the shear effect becomes
predominant.
TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence on Durability of Building Materials and Components
LYON [France] 17-20 April 2005

But the model allows taking into account the degradation of the bond with the corrosion by
using only one parameter, unlike other models as analytical ones, which need three or more
parameters to characterise the bond or the tension-stiffening degradation [Buyle-Bodin &
Rezaie 2000, Castel et al. 2002].

The model will be used soon in a French large benchmark leaning on the study of 40 years old
control beams of French sea water dam “Barrage de la Rance” near Saint Malo. It will be in
competition with analytical and FE models.

6 REFERENCES

Buyle-Bodin, F. & Rezaie, F. 2000, ‘Modelling at global scale of mechanical effects of the corrosion
of the steel reinforcement of RC beams’, Life prediction and aging management of concrete
structures, D.J. Naus ed., RILEM Proceedings 16, 43-52.
Castel, A., François, R. & Arliguie, G. 2000, ‘Mechanical Behaviour of Corroded Reinforced Concrete
Beams – Part 1: Experimental Study of Corroded Beams’, Materials and Structures, 33, 539-
544.
Castel, A., François, R. & Arliguie, G. 2002, ‘Mechanical modelling of reinforced concrete damaged
by steel corrosion’, Comptes rendus de l’Académie des Sciences, serie IIb/mechanics, 330, 45-
50.
Dekoster, M. 2003, ‘Etude du comportement mécanique des structures en béton armé dégradé par la
corrosion’, Thèse de Doctorat, Université de Lille 1.
Dekoster, M., Buyle Bodin, F., Maurel, O. & Delmas ,Y. 2003, ‘Modelling of the flexural behaviour
of RC beams subjected to localised and uniform corrosion’, Engineering Structures, 25[10],
1333-1341.
Dekoster, M., Buyle Bodin, F. & Maurel, O. 2003-2, ‘Structural assessment of reinforced concrete
elements subjected to localised and general corrosion’, Life prediction and aging management
of concrete structures, D.J. Naus ed., RILEM Proceedings 29, 115-126.
Lee, H.S., Tomosawa, F. & Noguchi, T. 1998, ‘Fundamental Study on Evaluation of Structural
Performance of Reinforced Concrete Beam Damaged by Corrosion of Longitudinal Tensile
Main Rebar by Finite Element Method’, Journal of Structural and Construction Engineering,,
AIJ[506], 43-50.
Molina, F.J., Alonso, C. & Andrade C. 1993, ‘Cover cracking as a function of rebar corrosion : Part 2
Numerical model’, Materials and Structures, 26, 532-548.

TT 1-31, Modelling of Corrosion induced failure of RC structures, Buyle-Bodin et al.
10DBMC International Conférence On Durability of Building Materials and Components
LYON [France] 17-20 April 2005

A prediction model for concrete carbonation based on coupled
CO -H O-ions transfers and chemical reactions
2 2

M. Thiery, P. Dangla, G. Villain, G. Platret
Laboratoire Central des Ponts et Chaussées
58 boulevard Lefebvre, 75732, Paris Cedex 15, France
[email protected]

TT1-58

ABSTRACT

It is a recognized fact that steel corrosion reduces the serviceability and safety performance of
reinforced concrete. Usually high alkaline conditions in concrete lead to the formation of a passive
layer at the steel surface. However the natural diffusion of the atmospheric carbon dioxide (CO ) into
2
the concrete induces a decrease of the pore water pH value after reactions with hydrates such as
portlandite Ca(OH) and calcium silicate hydrates C-S-H. Under low-pH conditions, the passive layer
2
breaks down allowing the corrosion to start. Because the carbonation products (calcium carbonates
CaCO ) have higher molar volumes than the hydrates, there is a significant decrease of porosity during
3
carbonation. Moreover, the carbonation releases water previously combined to the hydrates. In this
research, a model accounting for CO -H O-ions transfers, carbonation reactions, pH fall, porosity
2 2
reduction and water mass supply is developed.

The authors measure by mercury intrusion the drop of porosity after carbonation of Portland cement
pastes with water-cement W/C ratios ranging from 0.35 to 0.6. By using thermal analysis, they
correlate these results to the quantity of carbonated hydrates. Analytical expressions used in modelling
are proposed to link the decrease of porosity due to carbonation with the amounts of consumed
hydrates.

To simulate carbonation phenomena in concrete, dissolution-dissociation of CO in pore water,
2
dissolution of Ca(OH) and precipitation of CaCO are formulated in the framework of chemical
2 3
equilibrium and kinetic laws. A macroscopic kinetic of C-S-H carbonation is proposed following a
topotactic transformation. These chemical reactions are introduced in the mass balance equations as
source or sink terms. The constitutive laws of transfer are diffusion of CO , electro-diffusion of
2
species in solution and convection of liquid water. The capillary pressure is directly linked to the
liquid phase (due to the low value of the gaseous phase pressure with respect to the liquid phase one)
and the moisture transport is assumed to be controlled by the sole liquid phase, the contribution of the
vapour transfer being neglected. We consider that carbonation leads to variations of porosity, as well
as of water content, and consequently to modifications of transfer properties. 1D boundary value
problems are worked out by a finite volume method. Unknown parameters of chemical kinetics are
calibrated with experimental results of accelerated carbonation of a cement paste. Then, the model is
validated with results of accelerated carbonation of a concrete. The model is thus able to reasonably
predict the carbonation phenomena and pH profiles in concrete for accelerated conditions.

KEYWORDS

Carbonation - Cement based materials - Durability - Mass transport - Modelling