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Feb. 2010, Volume 4, No.2 (Serial No. 27)

Journal of Civil Engineering and Architecture, ISSN 1934-7359, USA

Probabilistic Assessment of Pitting Corrosion Effect on

Flexural Strength of Partial Prestressed Concrete

Structures in a Chloride Environment

Muhammad Sigit Darmawan

Department of Civil Engineering, Institut Teknologi Sepuluh Nopember (ITS), Surabaya 60111, Indonesia

Abstract: Like reinforced concrete (RC) structure, Prestressed concrete (PC) structures cannot escape from corrosion related problems,

especially when they are subjected to very aggressive environment, such as chloride environment. The corrosion of PC and RC

structures can take place if the concrete quality is not adequate, the concrete cover is less than that specified in the design, poor detailing

during design and construction. For RC structures, corrosion in the reinforcing steel generally leads to serviceability problems (staining,

cracking and spalling of concrete). By contrast, for PC structures, corrosion of prestressing strands may initiate structural collapse due

to higher stress levels in the steel and smaller diameter of the prestressing steel. Research on corrosion effect on concrete structure has

mainly considered the effect of corrosion have on reinforced and full prestressed concrete structure. In this study, a structural

framework will be developed to predict the flexural strength of partial prestressed concrete structures in a chloride environment. The

corrosion model previously developed for reinforced and prestressed concrete structures will be combined to predict the effect of

corrosion has on partial prestressed concrete structures. Note that in partial prestressed concrete structures, both non prestressing steel

(passive) and prestressing (active) reinforcement are utilized to carry the load. The framework developed will be combined with

probability analysis to take into account the variability of parameters influencing the corrosion process. This approach allows more

accurate prediction of service life of partial prestressed concrete structures in a chloride environment.

Key words: Corrosion, partial prestressed concrete structure, chloride, probability.

1. Introduction

Corrosion of reinforcing and prestressing steel due to

chloride contamination can result in considerable

reduction in service life of concrete structures. In

general, corrosion is of most concern because of the

associated reduction in steel cross-sectional area,

cracking, spalling and loss of bond, which over time will

lead to reductions of strength and serviceability of structures. For prestressed concrete (PC) structures, the

corrosion of prestressing strands may initiate structural

collapse due to higher stress levels in the steel and

smaller diameter of prestressing steel. A post-mortem

analysis of the collapsed bridge showed that the 40 year

Muhammad Sigit Darmawan, PhD, research field: stochasticmodeling of deteriorating of concrete in aggressive

environments. E-mail: [email protected].

old post-tensioned bridge failed as a result of pitting

corrosion near the box girder joint [1].

Chloride contamination is considered to be the major

causes of corrosion of reinforced concrete (RC) and PC

structures. This is caused by either from the application

of deicing salts in cold regions or exposure to sea-spray

in chloride environments. The deterioration of

reinforced concrete structures due to chloride attack

comprises of two stages. The first stage involves themovement of chlorides through concrete cover until

they reach the threshold chloride concentration at the

steel to initiate active corrosion (Fig. 1). The second

stage is called corrosion propagation, where

reinforcing steel corrodes causing loss of steel area

(metal loss) and therefore reduces structural capacity.

Different methods have been made to model

chloride penetration in concrete (i.e., corrosion

initiation). The different methods proposed clearly



Probabilistic Assessment of Pitting Corrosion Effect on Flexural Strength of Partial PrestressedConcrete Structures in a Chloride Environment

26

underline that the actual chloride penetration process

is very complicated, and may involve a combination

of processes contributing towards the overall ingress

of chlorides [2]. Of all the available models, it is

generally accepted that the model based on diffusion

theory represents the chloride ingress in concrete.

Hence, in this paper only corrosion propagation will

be discussed.

Corrosion propagation is mainly modeled by

assuming a relatively uniform loss of material thickness

[3], see Fig. 2. However, this approach is not accurate

for concrete structures subjected to chloride attack,

which usually experiences pitting corrosion, see Fig. 3

[4]. Pitting corrosion model for PC structures subjectedto chloride attack can be found in the literature [5]. This

model was developed from accelerated corrosion test

using four slabs, each of dimensions 1500 mm × 1000

mm × 250 mm with wires/strands. Using a similar

approach, pitting corrosion model for RC structures

subjected to chloride attack was developed [6]. From

these tests, it was found that the distribution of

Fig. 1 Deterioration model.

Fig. 2 General corrosion.

Fig. 3 Pit-configuration [4].

Fig. 4 Inverse CDF (CDF-1) plots for maximum pit-depths

in prestressing wires[5].

Fig. 5 Inverse CDF (CDF-1) plots for maximum pit-depths

in a reinforcing bar [6].

maximum pit-depths for prestressing wires and

reinforcing bar is best represented by the Gumbel

(EV-Type I), see Figs. 4 and 5.

2. Corrosion Model for Partial PC Structures

Research on corrosion effect on concrete structure

has so far considered only the effect of corrosion haveon reinforced and full prestressed concrete structure. In

this study, a structural framework will be developed to

predict the flexural strength of partial prestressed

concrete structures in a chloride environment. Note that

in partial prestressed concrete structures, both non

prestressing steel (passive) and prestressing (active)

reinforcement are utilized to carry the load. The

corrosion model previously developed for reinforced




27

and prestressed concrete structures will be combined to

determine the effect of corrosion has on partial

prestressed concrete structures. The framework

developed will be combined with probability analysis

to take into account the variability of parameters

influencing the corrosion process. This approach

allows more accurate prediction of service life of

partial prestressed concrete structures in a chloride

environment.

The following assumptions are made in developing a

more general probabilistic model for pitting corrosion:

(1) homogeneous environment along the wire/rebar

under consideration (corrosion rate assumed constant

along wire/rebar);(2) after an initial period of corrosion, the number of

pits formed is assumed constant, length of pit is held

constant and pit depth continues to increase; and

(3) at any cross-section of the wire/rebar only one pit

can form.

The predicted Gumbel distribution of maximum pit

depth (a in mm) at any time T (years), corrosion rate

icorr (1) in μA/cm2

at start of corrosion propagation and

wire/rebar length L (mm) is thus:

i

e

a

54.0corr aTT ee)L,i,T(f

54.0

a

54.0

>λα

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ μ−

λα

−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ μ−

λα−

(1)

where

( )[ ]

[ ]⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛

⎭⎬⎫

⎩⎨⎧

−+θκ

+−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛

⎭⎬⎫

⎩⎨⎧

−−+θκ

+−−

=λ+θ

+θ

2

1

ocorr o

2

o

2

1

icorr o

2

o

1T1

1(1)0.0232iDD

1TT1

1(1)0.0232iDD

(2)

To= exp

1

θ+1( )ln

θ +1( ) icorr −expTo−exp( )+ κ −θ−1( ) icorr (1)( )κicorr (1)

⎛

⎝ ⎜⎜

⎞

⎠⎟⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥ (3)

μ =μo−exp +1

αo−expln

L

Lo−exp

⎝ ⎜⎜ ⎠⎟⎟ α = αo−exp

(4)

year 1TT )TT()1(i)TT(i iicorr icorr ≥−−κ×=− θ(5)

obtained from statistical analysis of maximum pit

depths recorded from the accelerated corrosion tests

(see Tables 1 and 2), Do is the initial diameter of the

wire/rebar (mm), and κ and θ are corrosion rate

empirical factors. If corrosion rate reduces with time

then κ = 0.85 and θ = -0.29 [3]. Otherwise, if

corrosion rate is constant with time (time-invariant)

Table 1 Statistical parameters for the maximum pit-depths

of prestressing strand.

a (mm)To-exp

(years)

icorr-exp

(µA/cm2)

Length

Lo(mm)µo-exp αo-exp

mean COV

0.03836 186 650 0.84 8.10 0.91 0.17

μο-exp,αο-exp are Gumbel parameters

Table 2 Statistical parameters for the maximum pit-depths

of reinforcing bar.

a (mm)To-exp

(years)icorr-exp

(µA/cm2)LengthLo(mm)

µo-exp αo-exp

mean COV

0.076712 150 325 1.68 2.99 1.87 0.23

then κ = 1 and θ = 0. The geometric model is then

used to predict the loss of cross-sectional area for a pit

size of depth a, see Fig. 3 [4].

3. Statistical Parameters of Maximum

Pit-depths Distribution

The maximum pit-depth of corroded prestressing or

reinforcing steel is an important parameter as it is the

likely place of critical (minimum) section of the steel.

Therefore, it is also the likely place where failure of the

steel occurs. Statistical parameter of maximum pit-depth distribution used in this study is given in

Tables 1 and 2 for prestressing strands [5] and

reinforcing bars [6], respectively. These statistical

parameters were obtained from accelerated corrosion

tests using concrete slabs, each of dimensions 1500

mm × 1000 mm × 250 mm with strands/rebar. The

accelerated corrosion process was introduced to the

rebar using an electric current which was induced from

a power supply through a current regulator. At the

completion of each corrosion test the specimen was

broken up and the steel then cleaned, dried and

weighed using the method as specified by Standard

Practice for Preparing, Cleaning, and Evaluating

Corrosion Test Specimens [7]. The pit-depth in the

corroded steel was then measured using a micrometer

gauge.

The pitting corrosion statistical parameters µo-exp

and αo-exp are indicative only and increased confidence






29

reinforcing steel area at time T, and f p and f s are the

stress in the prestressing steel and reinforcing steel,

respectively. As the time since corrosion (T) increases,

the corrosion will decrease the steel area and therefore

reduce the flexural strength of partial prestressed

concrete beam.

6. Illustrative Example

For illustrative purpose, the corrosion model

developed will be used to determine the effect of

corrosion has on partial PC beam shown in Fig. 7[15].

The prestressing steels (Ap) comprise two cables, each

consisting of 18 supergrade 7-wire strands of 12.5 mm

diameter, whereas passive reinforcement (As)

comprise of 10 reinforcing bar of 32 mm diameter. The

beam is exposed in a near-coastal area. Four different

scenarios of corrosion are considered

(1) No corrosion,

(2) Only reinforcing bars corrode,

(3) Only prestressing steels corrode,

(4) Both reinforcing bar and prestressing steel

corrode.

The corrosion rate used in the analysis is 1 μA/cm

2

(0.012 mm/year), which can be classified as low to

moderate corrosion rate [17].

For no corrosion case, the histogram of flexural

strength of PC beam (Mn) obtained from Monte Carlo

simulation is shown in Fig. 8. The Monte Carlo

simulation is performed by generating randomly all

variables influencing the ultimate flexural strength Mn

Fig. 7 Prestressed concrete T-beam (All units are in mm).

(equation 6) and then determine the ultimate flexural

strength Mn. This process is repeated many times as

required (i.e., 1000000 simulations). The generation

of these variables is based on statistical parameters a

shown in Table 3. The detail of Monte Carlo

simulation can be found elsewhere [18].

Fig. 8 shows that for the case without corrosion, the

flexural strength has a mean value of 666.8 ton-m,

with coefficient of variation of 4.44%. For the second

case (only rebars corrode), the histogram of flexural

strength of PC beam (Mn) after 40 years since

corrosion initiation is shown in Fig. 9. Fig. 9 shows

that the mean flexural strength has decreased from

666.8 ton-m to 560.6 ton-m (15% reduction) whencompared with the case without corrosion.

Fig. 8 Ultimate flexural strength for no corrosion case.

Fig. 9 Ultimate flexural strength for corrosion at

reinforcing bars.

1500

815675900

250

Ap

As




30


prestressing steel.


reinforcing and prestressing steel.

Fig. 12 Distribution of ultimate flexural strength with time.

For the third case (only prestressing steel corrode),

the histogram of flexural strength of PC beam (Mn)

after 40 years since corrosion initiation is shown in

Fig. 10. Fig. 10 shows the mean flexural strength has

decreased from 666.8 ton-m to 494.5 ton-m (26%

reduction) when compared with the case without

corrosion.

For the last case (both passive and active

reinforcement corrode), the histogram of flexural

strength of PC beam (Mn) after 40 years since

corrosion initiation is shown in Fig. 11. Fig. 11 shows

the mean flexural strength has decreased from 666.8

ton-m to 486.5 ton-m (28% reduction) when

compared with the case without corrosion.Fig. 12 demonstrates the effect of corrosion has on

flexural strength of PC beam, by assuming that both

prestressing steel and reinforcing bar is corroding.

This figure shows that with time the flexural strength

of the beam decreases considerably. For example after

40 years since corrosion initiation, the probability of

flexural strength less than 500 ton-m is around 50%.

For the case without corrosion, the probability of

flexural strength less than 500 ton-m is zero. This

figure clearly indicates that corrosion has significant

effect on flexural strength of PC beam.

For corroded high strength steel, such as

prestressing steel, there is high possibility to have

different mode of failure than yielding. It is known

Fig. 13 Effect of different mode of failure of corroded

prestressing steel on ultimate flexural strength.






32

(2) Sensitivity analysis found that pitting model

parameters for prestressing steel, corrosion rate, yield

strength of prestressing steel, model error for flexure,

and cover thickness as the most important parameters

influencing the flexural strength of partial prestressed

concrete beam.

References

[1] E. Proverbio and G. Ricciardi, Failure of a 40 year old

post-tensioned bridge near seaside, Proc. Int. Conf.

Eurocorr, London, 10-14 September, 2000.

[2] V. G. Papadakis, A. P. Roumeliotis, M. N. Fardis and C.

G. Vagenas, Mathematical modeling of chloride effect on

concrete durability and protection measures, in: R. K. Dhir

and M. R. Jones (Eds.), Concrete Repair, Rehabilitation

and Protection, E & FN Spon, London, 1996, pp. 165-174.

[3] K. A. T. Vu and M. G. Stewart, Structural reliability of

concrete bridges including improved chloride-induced

corrosion models, Structural Safety 22 (2000) 313-333.

[4] D. V. Val and R. E. Melchers, Reliability of deteriorating

reinforced concrete slab bridges, Journal of Structural

Engineering 123 (1997) 1638-1644.

[5] M. S. Darmawan and M. G. Stewart, Effect of spatially

variable pitting corrosion on structural reliability of

prestressed concrete bridge girders, Australian Journal of

Structural Engineering 6 (2006) 147-158.

[6] M. S. Darmawan, Pitting corrosion model for reinforced

concrete structures in a chloride environment, The Future

Development in Civil Engineering Based on Research and

Practical Experience (International Conference),

University Pelita Harapan and University Stuttgart

Germany, Lippo Karawaci, Jakarta, Indonesia, CD-ROM,

26-27 September, 2007.

[7] ASTM G1-03, Standard practice for preparing, cleaning,

and evaluating corrosion test specimens, American

Standard Testing Materials (ASTM), West Conshohocken,

Pennsylvania, USA, 1999.

[8] M. S. Darmawan and M. G. Stewart, Spatial

time-dependent reliability analysis of corroding

pretensioned prestressed concrete bridge girders,

Structural Safety 29 (2007) 16-31.

[9] M. G. Stewart, Workmanship and its influence on

probabilistic models of concrete compressive strength,

ACI Materials Journal 92 (1995) 361-372.

[10] S. A. Mirza, D. K. Kikuchi and J. G. MacGregor, Flexural

strength reduction factor for bonded prestressed concrete

beams, ACI Journal 77 (1980) 237-246.

[11] S. A. Mirza and J. G. MacGregor, Variability of

mechanical properties of reinforcing bars, Journal of the

Structural Division 105 (1979 a) 921-937.

[12] S. A. Mirza and J. G. MacGregor, Variations in

dimensions of reinforced concrete members, Journal of the

Structural Division 105 (1979b) 751-766.

[13] B. Ellingwood, T. V. Galambos, J. G. MacGregor and C.

A. Cornell, Development of a Probability Based Load

Criterion for American National Standard A58, National

Bureau of Standards Special Publication 577, US

Government Printing Office, Washington DC, 1980.

[14] K. A. T. Vu and M. G. Stewart, Structural reliability of

concrete bridges including improved chloride-induced

corrosion models, Structural Safety 22 (2000) 313-333.

[15] R. F. Warner, B. V. Rangan, A. S. Hall and K. A. Faulkes,

Concrete Structures, Longman Press, Melbourne, 1998.

[16] AS 3600, Concrete Structures, Standards Association of

Australia, Homebush, New South Wales, Australia, 2001.

[17] BRITE/EURAM, The residual service life of reinforced

concrete structures, Final Technical Report, Report No.

BRUE-CT92-0591, 1995.

[18] A. S. Nowak and K. R. Collins, Reliability of Structures,

McGraw-Hill Higher Education, New York, 2000.

[19] D. A. Jones, Principles and Prevention of Corrosion,

Macmillan Publishing Co, New York, 1996.

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