Prediction of service life due to the exposure of chlorides of reinforced concrete bridges near coastal areas in Vietnam = Dự báo tuổi thọ sử dụng của cầu bê tông cốt thép ven biển Việt Nam do xâm nhập clo (tóm tắt + toàn văn)

1
INTRODUCTION
1. Meaning of the topic performed in this thesis
Roadway network system in Vietnam has been much invested and rapidly
developed by Vietnamese government since recent decades. Demand of the
safety and the durability of old or new bridges is an important task that should
be ensured.
Among the bridges of the Vietnamese roadway network, there are many
ones running along or near coastal areas. The reinforced concrete structures in
general and reinforced concrete bridges in particular under the seawater
environment are gradually being impacted by invading chloride, as a result,
these structures are corroded and their durability as well as service life is
reduced.
The structures located on the lowest level of tide water and coastal
structures will be strongly affected by the reinforcement corrosion. Damage
form of these structures is that the reinforcement within concrete is
electrochemically corroded by the diffusion of chloride ions in environment
into concrete. When the chloride concentration at the reinforcement surface
reaches some threshold levels causing reinforcement corrosion, chloride will
break the passive film on the surface of reinforcing steel, the corrosion will
occur. When the corrosion occurs, its product is corrosive rust. Rust absorbs
water to expand its volume which causes the cover concrete layer cracked and
broken. Corrosion of steel reinforcement reduces the bond between
reinforcement and concrete and the cross-sectional area of steel reinforcement.
These lead to the reduction of resistance in bending, compression resistance
and shear strength.
The service life of a reinforced concrete structure under chloride impact is
determined from the time the structure constructed to the time it becomes
unsafe for using due to the damages caused by the corrosion. The time stage
includes two sub-stages: Initiation corrosion stage and propagation corrosion
stage. The first stage is the necessary time so that chloride ions penetrate and

concentrate on reinforcement surface with “concentration threshold causing
corrosion”, while the second stage is started from the end of the first stage to
the time the concrete cover layer is entirely cracked due corrosion or the cross-
section area of reinforcement is reduced to the disability of bearing capacity of
the structure.
With the purpose to predict the service life of reinforced concrete bridges
impacted by chloride penetration near coastal areas in Vietnam, the author
selects the thesis title “Prediction of service life due to the exposure of
chlorides of reinforced concrete bridges near coastal areas in Vietnam”.
2. Purposes of the thesis
The thesis aims at researching of the penetration and reinforcement
corrosion of chloride in reinforced concrete bridges so as to:
2
1) Determine parameters of chloride penetration process into concrete
such as: Chloride diffusion coefficient D; Chloride concentration on
concrete surface Cs; chloride threshold causing reinforcement
corrosion C
th
.
2) Establish a model to predict the service life of reinforced concrete
bridges impacted by chloride impact near coastal areas in Vietnam.
3) Propose the methods to increase the service life. To apply the model
for components of T-shaped bridges.
3. Content of the thesis
The thesis includes 4 chapters which are summarized as follows:
Chapter1 “Literature review of the studies on the service life of concrete
bridges which are impacted by chloride penetration”
Chapter 2 “Determination of chloride diffusion coefficients in concrete”.
Chapter 3 “Establishment of a service life prediction model of reinforced
concrete bridges which are impacted by chloride penetration near coastal areas

in Vienam”.
Chapter 4 “Methods to increase the service life and examples”.
Part “Conclusion and Recommendation” presents the conclusions,
recommendations and future research orientations.
CHAPTER 1. LITERATURE REVIEW OF THE STUDIES ON THE
SERVICE LIFE OF CONCRETE BRIDGES IMPACTED BY
CHLORIDE PENETRATION IN THE WORLD AND IN VIETNAM
1.1 Introduction
The reinforced concrete bridges in Vietnam are now being designed with
advanced standards and integration [1]. The design philosophy of the standards
is that bridges are designed for satisfying all limit states with the
considerations of the economics, aesthetics and durability. The problem of the
durability of concrete is also interested. In this regard, the reinforcement
corrosion is the biggest concern. Penetration of chloride and CO
2
is the main
cause of reinforcement corrosion damage, which reduces the durability and
shorten the service life. Measures to reduce the penetration of chloride ions
and CO
2
into concrete are expected to significantly enhance the durability and
service life of concrete bridges.
The causes of damages in concrete bridges were statistically presented by
professor Mutsuyoshi (2001). His study showed that the main cause was due to
the chloride penetration which occupied 66% of the damages, while the
carbonation only occupied 5%.
The service life of reinforced concrete bridges due to chloride penetration
is often defined as the time from the structures initially exposed to chloride
environment until the time the concrete cover layer is entirely cracked due
3

corrosion or the cross-section area of reinforcement is reduced to disability of
bearing capacity of the structures.
Currently, studies on the prediction of the service life have been being
attracted and conducted by material and civil engineering associates in over
the world.
1.2 Studies on durability and service life in the world
1.2.1 Studies on durability theory of concrete
1.2.2 Studies on chloride penetration mechanisms into concrete
1.2.2.1 Diffusion
The first Fick’s law
( )
1 1
C
J D .
x
∂
= −
∂
The second Fick’s law
( )
2
2
1 2
C C
D .
t x
∂ ∂
=
∂ ∂
1.2.2.2 Migration

1.2.3 Studies on reinforcement corrosion mechanisms
1.2.3.1 General
In galvanic corrosion, there are two reactions occurring at the interface of
metal and electrolyte: The electronics liberating reaction at the anode
(oxidation) and electronics consuming reaction at the cathode.
In the study of Nielsen A. (1985) [46], the volume of non-hydrated iron
oxide Fe
2
O
3
is twice than that of the steel replaced, but the volume of hydrated
one is 6.5 times greater than that of the steel replaced. This causes the cracks
and breaks the cover concrete layer.
1.2.4 Tests of chloride penetration resistance in concrete
Three test methods to determine diffusion coefficients D are classified
based test time consuming.
Table 1.2 Test methods of chloride penetration
Test method Time consuming
Long-term test Salt ponding test
AASHTO T259
90 days after 28 days of
maintenance
Bulk Diffusion Test
(Nord test)
40-120 day after maintenance
Short-term test Rapid chloride
permeability test -RCPT-
AASHTO T277 (ASTM
C1202)
6 hours after 28 days of

maintenance
Electrical Migration Depended on voltage and concrete
Rapid Migration Test 18 hours after 28 days of
maintenance (AASHTO TP64-03)
Resistivity 30 minutes
4
1.2.5 Studies on diffusion coefficients
Stanish (2000) [53] performed tests on determining the experiment
relationship between chloride diffusion coefficients in concrete at the age of 28
days and at 20
o
C and the ratio of water/cement.
Zhang and Gjorv [67] developed a simple approach to determine the
diffusion coefficients of chloride ions as shown in Eq.1.19:
( )
o
T LV dC
D 1.19
E C A dt
β
=
Berke et al. (1992) developed an experiment formula (1.20) used for the
relationship between diffusion coefficients and transferred charge date in tests.
( )
12 0,84 2
eff 0
D 0,0103 10 (Q ) (m / s) 1.20
−
= × ×
Omar S. Baghabra Al-Amoudi presented his experiment studies on the

magazine Cement & Concrete Composites, issue 31 in 2009 [47].
( )
( )
2
12
b
'
c
a m
D 10 1.21
s
f
−
 
= ×
 ÷
 
f’
c
compressive strength of concrete MPa; a, b are experiment constants.
1.2.6 Studies on initiation corrosion stage and propagation corrosion
stage, service life
Tuutti, K. (1980). “The service life of structures relating to
reinforcement corrosion”. The author proposed a two-stage model of the
service life of reinforced concrete structures, which considered D as a
constant of time.
Figure 1.14: Service life of reinforced concrete structures: Two-stage model
of Tuuti 1980
[
59

]
A study in Euro-DuraCrete (2000) [32]– Durability design based on
probability features of concrete structures.
A study in Finland (2003) includes a programming named as
LIFECON[57]- Life cycle management of concrete infrastructures to enhance
increase their durability. The approaching method is based on semi-
5
probability and full probability of chloride and CO
2
penetration to determine
the service life of the operation concrete structures.
A study of ACI Committee in America is named as “Life 365” (2012)
[22] – a model to predict the service life of concrete structures contacted to
chloride. In the study, the serviced life includes two stages: the initiation
corrosion stage and propagation corrosion stage. The study assumed that the
concrete is in saturated humidity state. The propagation corrosion stage is 6
year fixed for all types of structures.
1.3 Studies performed in Vietnam
Prof.Dr. Huu et al. 2008[7], “High-strength and high-quality concrete”
The authors mentioned the durability of concrete and components effecting to
the durability. In the study, a method to increase the durability is to use high-
quality concrete with low chloride diffusion coefficients.
"A study on the chloride deionized-electrochemical technology and
alkalinity recovery area around concrete" of the transport institute of science
and technology in 2007 [20]. Their purpose is to reduce the concentration of
chloride ion in concrete and to restore the alkalinity level around
reinforcement down below the corrosive chlorine thresholds. This work is very
difficult and expensive, not basic. Moreover, these studies are conducted on
existing structures.
Studies of the Institute of construction technology science “Corrosion

status of reinforced concrete structures in Vietnam sea areas and some
experiences of using the corrosion inhibitors Calcium Nitrite” in 2010 of Dr.
Khoan, Pham-Van and Dr. Trang, Nguyen-Nam [9].
1.4 Comment and research orientation of the thesis
The new problems arising from the above studies that are needed to be solved:
- To determine the diffusion coefficients in concrete from fast
chloride permeability test according to the Standard ASTM C1202.
- The service life due to chloride penetration of reinforced concrete
bridges with taking the effects of temperatures, humidity in both
stages of corrosion initiation and propagation.
- The corrosion propagation stage is needed to have a quantitative
prediction.
The thesis are going to deal with the problems mentioned above based on
calculation models. The methodology is based on a mathematical model of
diffusion process to determine the corrosion initiation stage as well as a
mathematical model of corrosion activation that causes by concrete cracking to
determine the corrosion propagation stage.
6
CHAPTER 2. DETERMINATION OF CHLORIDE DIFFUSION
COEFFICIENTS IN CONCRETE
2.1 General
Diffusion coefficient of chloride ion in concrete is an important parameter
to predict the corrosion initiation stage for concrete reinforcement. The
coefficient can be determined based on experiments or predicted based on the
concrete mixing method.
The chapter describes the fast permeability tests according to ASTM
C1202 based on 16 concrete samples to determine the diffusion coefficient D,
and to compare the results obtained with ones predicted.
Chloride diffusion coefficient in concrete
The coefficient is D which is used in Fick’s law. The unit of D in SI is

m
2
/s.
x
C
DJ
∂
∂
−=
RILEM-TC-178 proposes two types of diffusion coefficients as follows:
a) Effective diffusion coefficient D
eff
A coefficient in a stable state
b) Apparent diffusion coefficient
A unstable diffusion coefficient. The coefficient is obtained based on
immerging test or structure observation with the applying of the second Fick’s
law of diffusion.
Chloride diffusion coefficient D is a function of material, environment,
time and humidity.
2.2 Test and determination of chloride diffusion coefficient in concrete
2.2.1 Fast chloride permeability test ASTM C1202
Table 2.2. Chloride ion permeability level
Charge Passed (coulombs ) Chloride Ion Penetrability
> 4000 High
> 2000 ÷ 4000
Moderate
> 1000 ÷ 2000
Low
100 ÷ 1000
Very low

<100 Negligible
2.2.2 Results of fast chloride permeability test ASTM C1202
Table 2.3 Test results of C1202
No. Sample name W/C
Date of
sample
casted
Date of
test
Temp-
erature
o
C
∆T
o
C
Qc6h
r -6
hours
(C)
Q
0
- 6
hours
(C)
I=Q
0
/t
(mA)
1 C30-1 0.4 22/3/12 20/4/12 30 16 3264 2536 117.4

2 C30-2 0.4 22/3/12 20/4/12 30 16 3317 2577 119.3
3 C30-3 0.4 22/3/12 20/4/12 30 16 3298 2562 118.6
4 C35-1 0.375 22/3/12 21/4/12 33 16 3012 2340 108.3
7
5 C35-2 0.375 22/3/12 21/4/12 33 16 2892 2247 104.0
6 C35-3 0.375 22/3/12 21/4/12 33 16 2945 2288 105.9
7 C40-1 0.35 22/3/12 20/4/12 35 14 2477 1983 91.8
8 C40-2 0.35 22/3/12 20/4/12 35 14 2523 2020 93.5
9 C40-3 0.35 22/3/12 20/4/12 35 14 2464 1973 91.3
10 C50-1 0.33 29/3/12 27/4/12 39 12 2117 1747 80.9
11 C50-2 0.33 29/3/12 27/4/12 39 12 2195 1812 83.9
12 C50-3 0.33 29/3/12 27/4/12 39 12 2180 1799 83.3
13 C50-8%SF-1 0.3 29/3/12 27/4/12 45 4 337 316 14.6
14 C50+8%SF-2 0.3 29/3/12 27/4/12 45 4 322 301 14.0
15 C50+8%SF-3 0.3 29/3/12 27/4/12 45 4 365 342 15.8
16 C50+15%FA-1 0.35 22/3/12 19/4/12 40 14 2475 1981 91.7
17 C50+15%FA-2 0.35 22/3/12 19/4/12 40 14 2500 2001 92.7
18 C50+15%FA-3 0.35 22/3/12 19/4/12 40 14 2357 1887 87.4
2.2.3 Formulation of chloride diffusion efficient based on test results
C1202
In a steady state condition, total chloride ion flux includes three
components, they are diffusion, migration and convection as shown in Eq. 2.4
[23],
i
i i i i
C
zF E
J D D C C u
x RT x
∂

∂
= − − +
∂ ∂
(2.4)
When the electrical field is applied to the concrete sample, the pure
diffusion effect in concrete is small and can be neglected. As a result, Eq.2.4 is
turned to be 2.5 as.
x
E
CD
RT
zF
J
ii
∂
∂
−=
(2.5)
Based on C.Andrade (1993), the flux of a migrating type is proportional
to current intensity:
i
It
J
zF
=
(2.6)
Equation 2.6 is substituted into Eq.2.5 with taking ∂x=L; ∂E=E, C
i
=C
o

,
we obtain the formulation of the diffusion coefficient in steady state as
follows:
( )
i
2 2
o
It RTL
D 2.7
z F EC A
=
Fron the test ASTM C1202: Co=0,52mol/l; E=60V; A=7854mm
2
;
L=50mm; z=1;t
i
=1; R=8,314Jmol
-1
K
-1
; F=9,6485x10
4
Cmol
-1
are substituted in
to Eq.2.7 to give:
( )
2
16
C1202

m
D 1, 822 IT 10 ( ) 2.9
s
−
= × ×
2.2.4 Application of equation D
C1202
to determine chloride diffusion
coefficients based on test results C1202
Equation 2.9 is applied to determine the diffusion coefficients in
standard table 3.2 of chloride ion permeability level below.
8
Table 2.4. Results of D
C1202
obtained from tests
No. Name of sample Q
(C)
Q
0
(C)
I
mA
Migration
speed
(mol/l.s)
D
C1202

( m
2

/s)
1 C30-1 3264 2536 117.4 4.87E-06 6.83E-12
2 C30-2 3317 2577 119.3 4.95E-06 6.94E-12
3 C30-3 3298 2562 118.6 4.92E-06 6.90E-12
4 C35-1 3012 2340 108.3 4.49E-06 6.36E-12
5 C35-2 2892 2247 104.0 4.31E-06 6.11E-12
6 C35-3 2945 2288 105.9 4.39E-06 6.22E-12
7 C40-1 2477 1983 91.8 3.81E-06 5.39E-12
8 C40-2 2523 2020 93.5 3.88E-06 5.49E-12
9 C40-3 2464 1973 91.3 3.79E-06 5.36E-12
10 C50-1 2117 1747 80.9 3.35E-06 4.78E-12
11 C50-2 2195 1812 83.9 3.48E-06 4.95E-12
12 C50-3 2180 1799 83.3 3.45E-06 4.92E-12
13 C50+8%SF-1 337 316 14.6 6.06E-07 8.57E-13
14 C50+8%SF-2 322 301 14.0 5.79E-07 8.19E-13
15 C50+8%SF-3 365 342 15.8 6.56E-07 9.29E-13
16 C50+15%FA-1 2475 1981 91.7 3.8E-06 5.47E-12
17 C50+15%FA-2 2500 2001 92.7 3.84E-06 5.52E-12
18 C50+15%FA-3 2357 1887 87.4 3.62E-06 5.21E-12
2.3 Prediction of the apparent diffusion coefficient
2.3.1 Apparent diffusion coefficient
The thesis summarizes the studies of the apparent diffusion coefficient in
the world. The coefficient is predicted as follows:
[ ]
( )
28
w
. exp( 0,165 ) . ( ). ( ). ( ) 2.18
cr
app cr

cr
D D SF f t f T f H D
s
= − +
SF is percentage of silica fume which used to substitute cement amount
in concrete; f(t),f(T),f(H) are effective coefficients of concrete,
temperature, relative humidity to chloride diffusion coefficient in
concrete.
[ ]
( 12,06 2, 4 / )
2
28
( / ) 22
10
w c
D m s
− +
=
[ ] [ ]
28
( ) ( 25 ) 22 ; 0, 2 0,4( / 50 / 70) 22
m
t
f t f t year m FA SG
t
 
= ≤ = = + +
 ÷
 
[ ] [ ]

4
ef
1 1 1
( ) exp 22 ; ( ) 24
1
1
1
r
c
U
f T f H
R T T
H
H
 
 
= − =
 
 ÷
 
 
 
 
 
−
 
+
 ÷
−
 

 
 
2.3.2 Determination of the diffusion coefficient based on prediction and
experience
2.4 Comparison of results and discussion
2.4.1 Comparison of obtained diffusion coefficient D
Table 2.7 D
C1202
, D based on prediction and experience formulas
No. Name of sample W/C D
C1202
( m
2
/s)
D based on
Stanish
D based on
Zhang –
D based
on Berke
D based on
Omar S.
9
( m
2
/s) Gjor( m
2
/s) ( m
2
/s)

Baghabra
( m
2
/s)
1 C30-1 0.4 6.83E-12 7.94E-12 1.15E-11 7.45E-12 2.36E-11
2 C30-2 0.4 6.94E-12 7.94E-12 1.17E-11 7.55E-12 2.36E-11
3 C30-3 0.4 6.90E-12 7.94E-12 1.16E-11 7.52E-12 2.36E-11
4 C35-1 0.375 6.36E-12 6.92E-12 1.06E-11 6.97E-12 1.37E-11
5 C35-2 0.375 6.11E-12 6.92E-12 1.02E-11 6.73E-12 1.37E-11
6 C35-3 0.375 6.22E-12 6.92E-12 1.03E-11 6.84E-12 1.37E-11
7 C40-1 0.35 5.39E-12 6.03E-12 8.91E-12 6.06E-12 8.53E-12
8 C40-2 0.35 5.49E-12 6.03E-12 9.08E-12 6.16E-12 8.53E-12
9 C40-3 0.35 5.36E-12 6.03E-12 8.86E-12 6.03E-12 8.53E-12
10 C50-1 0.33 4.78E-12 5.40E-12 7.80E-12 5.45E-12 3.87E-12
11 C50-2 0.33 4.95E-12 5.40E-12 8.09E-12 5.62E-12 3.87E-12
12 C50-3 0.33 4.92E-12 5.40E-12 8.03E-12 5.59E-12 3.87E-12
13 C50+8%SF-1 0.3 8.57E-13 1.22E-12 1.37E-12 1.29E-12 1.06E-12
14 C50+8%SF-2 0.3 8.19E-13 1.22E-12 1.31E-12 1.25E-12 1.06E-12
15 C50+8%SF-3 0.3 9.29E-13 1.22E-12 1.49E-12 1.38E-12 1.06E-12
16 C50+15%FA-1 0.35 5.47E-12 6.03E-12 8.90E-12 6.06E-12 1.06E-12
17 C50+15%FA-2 0.35 5.52E-12 6.03E-12 8.99E-12 6.11E-12 1.06E-12
18 C50+15%FA-3 0.35 5.21E-12 6.03E-12 8.48E-12 5.81E-12 1.06E-12
2.4.2 Discussion of diffusion coefficients D obtained
Based on results obtained of D, a following comment raises: chloride
diffusion coefficient determined from the test based on C1202 as in Eq. 2.9 is
basically suitable to results of Stanish used in Life 365.
2.5 Conclusion of chapter 2
1. Experiment study of fast chloride permeability level according to
ASTM C1202 for typical concrete samples was conducted. The test
results have shown that concrete grades C30-C40-C50 with electricity

quantity transmitted from 2577 to 1799 (coulomb) belong to low and
average chloride ion permeability level.
2. A formulation to determine the chloride diffusion coefficient based on
charge transfer according to ASTM C1202 is proposed as follows:
2
16
C1202
m
D 1,822 IT 10 ( ) (2.9)
s
−
= × ×
3. The chloride diffusion coefficient of the samples ASTM C1202 is
determined as shown in Eq.2.9. After that, the comparison between the
present study and other predictions is performed to give a conclusion
that the chloride diffusion coefficient determined from the test based
on C1202 as in Eq. 2.9 is basically suitable to results of Stanish used
in Life 365 as well as those of Berke.
4. The thesis has synthesized studies of foreign authors and to propose a
predictive formulation of apparent chloride diffusion coefficient as
shown in Eq. 2.18.
10
CHAPTER 3. ESTABLISHMENT OF SERVICE LIFE PREDICTION
MODEL USED IN REINFORCED CONCRETE BRIDGES DUE TO
CHLORIDE PENETRATION AT COASTAL AREAS IN VIETNAM
1.5 General introduction
3.1.1 Definition of the service life
The service life of reinforced concrete bridges under chloride impact
is determined from the time the structure exposed to chloride ion environment
to the time the concrete cover layer is entirely cracked due corrosion or the

cross-section area of reinforcement is reduced to disability of bearing
capacity of the structure.
3.1.2 Service life based on the penetration of chloride in sea environment
To predict the service life of concrete structures, the end of the service
life needs to be determined.
In this thesis, the author is going to determine the service life for two
cases:
1. The end of the service life is considered as the time the concrete
cover layer is cracked due to corrosion.
2. The end of the service life is the time that corrosion caused the
damage to the structure in strength limit state.
There are many opinions of damage process of concrete
reinforcement. According to Tuuti (1980) [59], the process has two stages:
initiation stage and propagation stage as shown in Eq.3.1.
( )
1 2
3.1
t t t= +
In which: t
1
is the corrosion initiation stage; t
2
is the corrosion propagation
stage.
1.6 Construction of corrosion initiation stage prediction model
1.6.1 General
From the second law of Fick about diffusion:
( )
2
2

( , ) ( , )
3.2
C x t C x t
D
t x
∂ ∂
=
∂ ∂
In which: C(x,t) is the chloride concentration at the depth x and time t ; D is
the chloride diffusion coefficient ; x is the depth measured from the concrete
surface ; t is time.
1.6.2 Parameters of the model
3.2.2.1 Chloride diffusion coefficient (D)
3.2.2.2 Chloride concentration accumulation on concrete surface
( ) ( )
, ax
, ax
, ax
3.3
s m
s
s m
s m
C
kt whent
k
C t
C
C when t
k


≤


=


≥


11
Table 3.1 Build-up Rates and maximum concentration of surface chloride
Region Build-up Rate
(%/ year)
C
s,max
(%/)
Intertidal zone instantaneous 0.8
Marine spray zone 0.10 1.0
Within 800 m of the ocean 0.04 0.6
Within 1500 m of the ocean 0.02 0.6
The thesis selects the rule of surface chloride concentration accumulation
of Michael Thomas as shown in Eq.3.3, but the maximum surface chloride
concentration (C
s,max
) is different for different sea regions of Vietnam.
3.2.2.3 Chloride concentration threshold causing the corrosion for
concrete reinforcement
- For normal reinforced concrete C
th

=0.05%
- For pre-stressed concrete C
th
=0.012%
1.6.3 Construction of corrosion initiation stage prediction model
3.2.3.1 One-dimension problem: (1D diffusion)
When the chloride concentration C(x,t) at the cover concrete layer
depth reaches the corrosion concentration threshold C
th
, the reinforcement is
initially corroded.
1
( , )
c
th
x d
C x t C
t t
=
=
=
t
1
is corrosion initiation stage
3.2.3.2 Two-dimension problem: (2D diffusion)
( )
2 2
2 2
( , , ) ( , , ) ( , , )
3.7

C x y t C x y t C x y t
D
t x y
 
∂ ∂ ∂
= +
 
∂ ∂ ∂
 
3.2.3.3 The problem is solved based on finite difference method
Crank-Nicolson because D and C
s
are changeable.
1.6.4 Establishment of programming algorithm diagram in MATLAB
to determine the corrosion initiation stage.
Two examples to determine the corrosion initiation stage in MATLAB:
1D diffusion problem is used for a wall plate and inner reinforcements of
bridge piers. 2D diffusion problem is used for angular reinforcements of
bridge piers and beams.
The programming algorithm of both examples are presented in
Appendix 1.
1.7 Construction of corrosion propagation stage prediction model
1.7.1 General
1.7.2 Available applying models
1.7.3 Proposed model
1.7.3.1 Assumptions
To develop a new corrosion model, the following assumptions are
applied:
12
1) Uniform corrosion process around reinforcement leads to a

uniformly distributed pressure going through the center of
concrete-reinforcement interface. The concrete around
reinforcement is considered as thick-walled cylinder and the wall
thickness is assumed to be the thinnest concrete cover layer
thickness.
2) Stresses and strains in concrete appear due to the volume dilation
of corrosive products. Concrete cover is considered as a linearly
elastic material.
3) There are porous areas around concrete-reinforcement interface,
corrosive products will diffuse into the gaps.
4) During the development of cracking, a part of corrosive products
will be filled into the cracks.
Figure 3.6: Idealization of concrete cover layer as a thick-walled cylindrer:
(a) initial concrete sample; (b) concrete deformation, (c) deformation of
corrosive products (d) Rust filled into open cracks.
13
Figure 3.7 : Time stage from the iniatiation of reinforcement corrosion to
concrete cover completely cracked and the load capacity risk
In the crack propagation time, a small part of corrosive products will be
penetrated into through-center cracks. After that, required amount of corrosive
reinforcement to cause the completely cracked concrete cover can be
determined based on two components (Figure 3.7):
1.7.3.2 The relationship between reinforcement weight loss of
reinforcement and through-center pressure.
Where ρ is the symbol of percentage of the reinforcement weight loss
M
loss
per initial reinforcement weight M
s
over a unit length:

( )
os
100% 3.33
l s
s
M
M
ρ
= ×
( )
( )
2
'
2 2
0 0 0
2 2
ef 0 0
2 ( ) 2
1 1 1
( )
3.40
1
sp
c
c
c
f
L r L r
v
d E r L r d

n
δ
γ
ρ
 
 
+ +
+ + + + −
 
 
+ −
 
 
=
−
Equivalent redius loss is determined as:
1
1
2 2 2
∆ = − = − −
ρ
s n c
d d d
r r
( )
( )
1
1 1 3.41
2
s c

d
r
ρ
∆ = − −
1.7.3.3 The amount of corrosive products penetrating into cracks
( )
2 1
3.44
s s
L
r r
d
∆ = ∆
( )
2 1
3.45
s s
L
r k r
d
∆ = ∆
14
Reinforcement radius loss
∆
r
s2
corresponding to weight loss
percentage ρ
2
is:

( )
2
3.46
c
L
k
d
ρ ρ
=
From Eqs. (3.40) and (3.46), the total weight loss percentage is
determined as:
( )
( )
2
'
2 2
0 0 0
2 2
ef 0 0
2 ( ) 2
1 1 1
( )
(1 ) 3.47
1
sp
c
c
c
f
c r L r

v
d E r L r d
L
k
d n
δ
γ
ρ
 
 
+ +
+ + + + −
 
 
+ −
 
 
= +
−
1.7.3.4 Establishment of the prediction model according to
complete crack of concrete cover
By using Faraday’s law, reinforcement loss due to corrosion is
determined as:
( )
or
os
3.48
c r
l s
MI

M t
zF
=
In which M
loss
is the consumed reinforcement weight loss (g); M is
element mass of ion Fe, M = 56 g/mol; z is the valence of iron, F is the
Faraday’s constant, F = 96.500 C/mol and t is corrosion time determined in
seconds (s).
Corrosive current density i
corr
is defined as corrosive current per each
reinforcement surface unit. If the unit length L
0
= 1 cm and the diameter d is in
mm, a relationship between I
corr
(A) and i
corr
(µA/cm2) can be obtained as:
( )
6 7
or or or
1 10 10 3.49
10
c r c r c r
d
I i di
π π
− −

= × × =
Where ρ
s
=7.85g/cm3 and L
0
=1cm. Eq. (3.33) can be expressed as
( )
2
2
os
0.0616 3.50
4 10
l s s s
d
M M d
π
ρ ρ ρ ρ
 
= = =
 ÷
 
( )
2
os
7
or or or
2.5 96500 0.0616
234762 3.51
56 10 3600
l s

c r c r c r
zFM d d
t
MI di i
ρ ρ
π
−
× ×
= = =
× × ×
( )
( )
( )
( )
2
2
'
2
0 0
0
2
2
ef
0 0
2
or
2 2
. 1 1
26,799( ) 3.53
1 .

sp
c
c
c r
f
r L r
L
d E d
r L r
t d kL
n i
δ
ν
 
 
+ +
 
+ + + −
 
 
+ −
 
 
 
 
= + ×
−
Prediction of current density i
( )
4 0.215

or
3034
0.9259exp 7.98 0.771ln(1.69 ) 1.16 10 2.24 3.54
c r cl c
i C R t
T
− −
 
= + − − × +
 
 
[ ]
{ }
7.2548
90.537 1 exp 5 50(1 ( ) (3.55)
c
R H H
−
= + − − Ω
15
1.7.3.5 Establishment of prediction model according to the danger
due to corrosion
General equation of load limit state according to 22TCN 272-05[1] as
follows:
(3.58)
i i n r
Q R R
η γ φ
≤ =
∑

In pure bending beams, percentage of reinforcement cross-section loss
which is dangerous to flexural limit state can be determined as:
1 (3.59)
u
th
r
M
M
ρ
= −
In which: M
r
is factored flexural capacity; M
u
is the maximum moment
caused by factored design loads.
For compressing members, factored compressing capacity is symboled as
P
r
, axial compression load corresponding to strength limit state is P
u
.

(3.60)
r rc rs
P P P
= +
P
rc
is the capacity part created by concrete cross-section; P

rs
is the
capacity part cretated by reinforcement cross-section.
(3.61)
r rc rs rs
P P P P= + − ∆
The cross-section reaches a limit state when:

1 (3.64)
u rc
th
rs
P P
P
ρ
−
= −
Similarly, percentage of reinforcement cross-section loss
which is dangerous to the exural limit state of members
subjected to both compressing and bending:

1 (3.65)
u rc
th
rs
M M
M
ρ
−
= −

M
rc
is the capacity part created by concrete cross-section; M
rs
is the
capacity part cretated by reinforcement cross-section; M
u
is factored flexural
moment.
For stirrup under shear:

1 (3.66)
u rc
th
rs
V V
V
ρ
−
= −
Based on Eq. 3.51, corrosion propagation time (in years) which is
dangerous to bearing capacity limit states is determined as:
( )
2
or
26.8 3.67
th
c r
d
t

i
ρ
=
1.8 Programming diagram for determinination of the service life of
concrete bridges “LifeConBridge”
16
Figure 3.11: Programming algorithm for determining of the service life due to
chloride penetration corrosion.
1.9 Outputs and comments
1.9.1 Validation of outputs obtained based on the present study
Table 3.4 Output of corrosion initation time H=100%
Concrete cover (mm) w/c
D
28
10
-12
(m
2
/s)
T(
o
C) H(%) C
s
(%) C
th
(%)
t
1
(year)
based on

present study
t
1
(year)
based
on Life
365
20 0.35 6.026 20 100 0.6 0.05 4.40 4.60
30 0.35 6.026 20 100 0.6 0.05 6.60 6.80
40 0.35 6.026 20 100 0.6 0.05 9.10 9.30
50 0.35 6.026 20 100 0.6 0.05 12.0 10.80
60 0.35 6.026 20 100 0.6 0.05 15.3 15.10
70 0.35 6.026 20 100 0.6 0.05 18.9 17.50
80 0.35 6.026 20 100 0.6 0.05 23.1 22.8
17
90 0.35 6.026 20 100 0.6 0.05 27.8 26.00
100 0.35 6.026 20 100 0.6 0.05 33.20 32.90
(Output based on SF=0; FA=0; SG=0)
Table 3.5 Output of corrosion initation time H=75%
Concrete cover (mm) w/c
D
28
10
-12
(m
2
/s)
T(
o
C) H(%) C

s
(%) C
th
(%)
t
1
(year)
based on
present study
t
1
(year)
based on
Life 365
20 0.35
6.026
20 75 0.6 0.05 6.20
4.60
30 0.35
6.026
20 75 0.6 0.05 9.70
6.80
40 0.35
6.026
20 75 0.6 0.05 14.1
9.30
50 0.35
6.026
20 75 0.6 0.05 19.20
10.80

60 0.35
6.026
20 75 0.6 0.05 25.30
15.10
70 0.35
6.026
20 75 0.6 0.05 32.60
17.50
80 0.35
6.026
20 75 0.6 0.05 40.90
22.8
90 0.35
6.026
20 75 0.6 0.05 50.40
26.00
100 0.35
6.026
20 75 0.6 0.05 61.00
32.90
(Output based on SF=0; FA=0; SG=0)
Saturating humidity of “LifeConBridge” is less different to that of Life
365.
Table 3.6 Output of corrosion propagation time
d (mm) L (mm)
i
corr
(µA/cm2)
t
2

(year)
t
2
( year) based
on Liu’s test
16 47.50 2.35 1.45-1.93 1.84
16 69.60 1.80 2.85-3.80 3.54
16 27.18 3.77 0.57-0.74 0.72
12.7 52.07 1.81 2.29-3.04 2.38
(Output based on k=0.25, n=2.5-3.0)
The corrosion propagation time of the present study is suitable to that of
Liu’s test
1.9.2 Output of Examples
Table 3.7 Output of corrosion initation time according to some parameters
Concrete cover (mm) w/c SF(%) FA(%)
D
28
10
-12
(m
2
/s)
T(
o
C) H(%) C
s
(%) C
th
(%) t
1

(year)
70 0.35 0 6.26 20 75 0.6 0.05 32.1
60 0.35 0 6.26 20 75 0.6 0.05 24.88
70 0.4 0 7.94 20 75 0.6 0.05 25.62
70 0.35 0 6.26 22 75 0.6 0.05 29.63
70 0.35 0 6.26 20 85 0.6 0.05 20.42
70 0.35 0 6.26 20 75 0.6 0.045 30.58
70 0.35 5 3.48 20 75 0.6 0.05 66.66
70 0.35 8 2.12 20 75 0.6 0.05 105.88
70 0.35 0 5 6.26 20 75 0.6 0.05 38.64
18
70 0.35 0 8 6.26 20 75 0.6 0.05 43.47
Table 3.8 Output of corrosion propagation time based on some parameters
( Opinion 1:Cover concrete layer is completely cracked)
Concrete cover
(mm)
d (mm) f'
sp
(MPa) T(
o
C) H(%)
i
corr
(µA/cm
2
)
t
2
(year)
70 16 3.3 20 75 1.47 5.81

60 16 3.3 20 75 1.47 4.77
70 18 3.3 20 75 1.47 5.38
70 16 3.0 20 75 1.47 5.46
70 16 3.3 22 75 1.58 5.42
70 16 3.3 20 85 1.54 5.54
Table 3.8 Output of corrosion propagation time based on some parameters
(Opinion 2: corrosion causing a danger to the structure )
Concrete
cover (mm)
d (mm) f'
sp
(MPa) T(
o
C) H(%)
i
corr
(µA/cm
2
)
(year) at
ρ
th
=2.5%
70 16 3.3 20 75 1.47 9.94
60 16 3.3 20 75 1.47 9.94
70 18 3.3 20 75 1.47 11.19
70 16 3.0 20 75 1.47 9.94
70 16 3.3 22 75 1.58 9.28
70 16 3.3 20 85 1.54 9.48
1.10 Service life of reinforced concrete bridges at the coastal areas in

Vietnam
1.10.1 Climate characteristics at the coastal areas in Vietnam and
Climate change
3.6.1.1 Climate characteristics in Vietnam
3.6.1.2 Climate change in Vietnam in the future
Prediction of climate change and sea water rising in Vietnam published
by the Ministry of Natutal Resources and Enviroment is the base to evaluate
the influence of these causes and to establish a plan to cope with them.
3.6.1.3 General evaluation of the influence of climate change to the service
life
Tropical climate (hot and wet) in Vietnam is a cause to speed up the
diffusion process of chloride ion into concrete as well as corrosion process that
is dangerous to structures, especially concrete bridges.
The predicted sea water rising will be high (570-730mm), salt will
penetrate into Vietnamese rivers and it will affect on reinforced concrete
structures, especially concrete bridges.
1.10.2 Service life of reinforced concrete bridges at the coastal
areas in Vietnam
The service life of the reinforced concrete bridges which their spans
cannot be substituted will be considered as equaling to the minimum service
life of structural members (foundation, abutment, pier, and superstructure).
2
t
19
( ) ( )
min 3.68
i
T T
=
+ Substructures lying in the coastal areas

There are four zones of substructures lying in salt water: frequently
immerged zone, tidal zone, splashing zone and sea air zone (figure 3.15).
Figure 3.15: Four coastal zones of concrete piers
+ Superstructures in the coastal areas
Superstructures belong to the sea air zone.
Figure 3.16: Quantitation of the surface distribution of cloride concentration
1.11 Conclusion of chapter 3
1. A prediction model for service life of reinforced concrete bridges by
invading chlorine "LifeConBridge" at the coastal areas in Vietnam was
successfully constructed, in which the end of life is defined as the time at
which cover concrete layer is completely cracked or the time at which the
steel section loss due to corrosion endangers strength limit states.
2. The service life of reinforced concrete bridges according to
“LifeConBridge” program consists of two continuous stages: corrosion
initiation stage and corrosion propagation stage.
+ The corrosion initiation stage is determined based on the Fick’s second
diffusion law and is simulated based on the finite difference method. Three
20
parameters are considered to effect to the time period of this stage:
Material parameter which includes chloride diffusion coefficients in
concrete, chloride concentration threshold of reinforcement corrosion;
Environmental parameter includes surface chloride concentration,
temperature, humidity of the environment; and structural parameter which
is the thickness of covering concrete layer.
+ Corrosion propagation stage model is formulated for two cases: Case 1:
the end of service life is considered as the time at which cover concrete
layer is completely cracked; Case 2: the end of service life is considered
as the time at which the corrosion endangers strength limit states.
3. Output of the pattern “LifeConBridge” is suitable with results of other
models and experiments, thus it is basically believable.

CHAPTER 4. METHODS USED TO INCREASE THE SERVICE LIFE AND
EXAMPLES
4.1 Methods used to increase the service life
4.1.1For new structures
A method to increase the service life of such structures is to increase the
corrosion initiation stage.
4.1.1.1 Measures relating to structural engineering
Figure 4.1: The relationship between cover concrete layer and corrosion
initation stage
21
Hình 4.2: The relationship between cover concrete layer and time stage started from
corrosion initation to cracking
4.1.1.2 Measures relating to materials
1. Small ratio of water/cement used
Figure 4.3: The relationship between the ratio of w/c and corrosion iniation time
2. The additives Silica fume used
Figure 4.4: The relationship between the percentage of silica fume and corrosion
initation time (The cover concrete layer thickness C=75mm, temperature 25
o
C,
humidity H=75% corresponding to coastal areas)
3. Increasing of limit chloride threshold
Corrosion inhibitor (CNI: Calcium nitrite) can be used to increate the
chloride threshold C
th
.
4. Measures to increase accumulating time of chloride on concrete
surface
For coastal air zone, membrane or painting methods can be used.
4.1.1.3 Combination of measures

Table 4.1 Output of service life corresponding to combination of measures
Alternative
Concrete cover (mm) w/c
SF
(%)
FA
(%)
SG
(%)
CNI
(l/m
3
)
t
1
(year)
t
2
(year)
t
1+
t
2
(year)
1 75 0.4 2 5 5 0 46.9 5.78 52.68
2 75 0.4 2 5 5 10 101.1 2.46 103.56
22
3 75 0.375 2 5 0 10 98.9 2.46 101.36
4 75 0.375 2 0 0 10 80.0 2.46 82.46
5 75 0.375 2 0 5 10 93.0 2.46 95.46

6 75 0.35 2 2 0 10 99.1 2.46 101.56
7 75 0.35 4 0 0 0 57.7 5.78 63.48
8 75 0.325 2 0 0 10 103.7 2.46 106.16
9 75 0.325 2 0 0 0 48.6 5.78 54.38
10 75 0.30 2 0 0 10 118.2 2.46 120.66
11 75 0.30 4 0 0 0 74.4 5.78 80.18
(Performed under the temperature 23
o
C and humidity 75%, for
reinforcement d=16mm, f’c=40MPa)
To reach the service life 100 years, alternatives 2,3,6,8,10 can be used as
shown in table 4.1.
4.1.2For old structures
It is necessary to evaluate the status of the old structures before proposing
measures to increase their service life.
Two effective methods can be applied for corroded reinforcement
structures:
+ Electrochemical chloride removal.
+ Protection of cation.
4.2 Examples for a bridge
4.2.1 Parameters needed for predicting of the service life of the bridge
4.2.1.1 Parameters of structure and material
Table 4.2 Parameters of structure and material
Structural
Member
Type of
reinforcement
Diamete
r
(mm)

Concrete
cover
(mm)
Concrete Valu
e of
ρ
th
(%)
Grad
e
(MPa
)
w/c SF
(%)
Tower
Reinforcement 32 80 50 0,35 2,0 7,5
Stirrup 16 65 50 0,35 2,0 7,0
Approaching
bridge pier
Reinforcement
32
90 40
0,37
5
2,0 7,5
Stirrup
16
75 40
0,37
5

2,0 7,0
Approaching
bridge
beams
Reinforcement 22 55 50 0,35 2,0 2,5
Stirrup
16
40 50 0,35
2,0 5,0
4.2.2Parameter of environment
Table 4.3 Parameter of environment
Structural
Member
Zone max Cs
(%)
Accumulatin
g
rate Cs
(%/năm)
Annual
temperatur
e
(
o
C)
Annual
humidity
(%)
Tower tidal 0,60 Instance 25,9 80
23

Pier tidal 0,60 Instance
Approaching
bridge beam
Sea air 0,40 0,04
4.2.3Output of service life determination
Table 4.4 Output of service life determination, 1D problem
Structural
member
Type of
reinforcement
Output based on present
study
Output based on
Life 365
t
1
(year)
t
2
(year)
t
1
+t
2

(year)
t
1
(year)
t

1
+t
2

(year)
Tower
Reinforcement 20.40 4.97 25.37 17.80 23.80
Stirrup 12.20 5.74 17.94 9.90 15.90
Approaching
bridge pier
Reinforcement 23.00 5.73 28.73 19.20 25.20
Stirrup 14.60 6.93 21.53 13.10 19.10
Approaching
bridge beam
Reinforcement 18.30 3.90 22.20 16.00 22.00
Stirrup 13.50 3.70 17.20 10.70 16.70
24
Bảng 4.5 Output of service life determination, 2D problem
Structural
member
Type of
reinforcement
Output based on present
study
Output based on
Life 365
t
1
(year)
t

2
(year)
t
1
+t
2

(year)
t
1
(year)
t
1
+t
2

(year)
Tower Reinforcement 15.20 4.97 20.17 12.0 18.0
Approaching
bridge pier
Reinforcement 17.40 5.73 23.13 13.2 19.2
Approaching
bridge beam
Reinforcement 14.40 3.90 18.30 12.00 18.00
4.3 Conclusion of chapter 4
Based on applying the model “LifeConBridge” to some cases, the
corrosion initiation time can be lengthened based on following methods:
1 To use concrete types which possess a high resistance of chloride
penetration and a small D (high performance concrete). The concrete
ingredient should be:

+ Low ratio of water/cement=0.30-0.35
+ Additives: silica fumes 4-7%, fly ash, slag.
2 Enough thickness of the cover concrete layer is designed as warning of
Standard 22TCN 272-05: concrete within sea environment L ≥75mm,
concrete within tidal areas L≥100mm.
3 To use methods to increase the concentration threshold that causes the
reinforcement corrosion, such as:
+ Chemical corrosion inhibitor Ca(NO
2
)
2
+ Un-stained steel used.
4 To use methods to increase the accumulating time of chloride
concentration on surface C
s
such as:
+ Membrane
+ Painting
5 To use a combination of the above methods.
The methods to increase the corrosion propagation time: Painting of
reinforcement by using epoxy, coating or galvanizing.
CONCLUSIONS AND RECOMMENDATIONS
1/ Conclusion
1. Experiment study of fast chloride permeability level according to
ASTM C1202 for typical concrete samples was conducted. The test
results have shown that concrete grades C30-C40-C50 with electricity
quantity transmitted from 2577 to 1799 (coulomb) belong to low and
average chloride ion permeability level.
2. Chloride diffusion coefficients are formulated based on fast
permeability test ASTM C1202. These formulas are used to determine

chloride coefficients for 18 samples, then the outputs are well
compared to the results of prediction models of Stanish and Berke.
25
3. Studies of foreign authors has been synthesized and a predictive
formulation of apparent chloride diffusion coefficient is proposed
based on concrete mixing ingredients, temperature, humidity of
environment, age of concrete and crack level of concrete, as shown in
Eq. 2.18.
4. A new model “LifeConBridge” was successfully formulated to predict
the service life of reinforced concrete bridges at the coastal areas in
Vietnam due to chloride penetration based on MATLAB
programming. The service life includes two continuous stages:
corrosion initiation stage and corrosion propagation stage. The model
was applied for some examples and the outputs show that: the
corrosion initiation stage (t1) at humidity H=100% is consistent with
the output of “Life365”; the corrosion propagation stage is consistent
with the test result of Liu. Therefore, the proposed model is
believable.
5. The effect of some parameters to the service life of reinforced concrete
bridges in Vietnamese environment was considered for the proposed
model (the thickness of cover concrete layer, ratio of water/cement,
silica fume, chloride concentration threshold of reinforcement
corrosion).
2/ Recommendations
+ In the present condition in Vietnam, it is acceptable to use the
formulation of determination of chloride diffusion coefficients in concrete
according to the outputs of fast permeability tests ASTM C1202 as
performed in Chapter 2. The output of the coefficients can be used as
input of the prediction pattern.
+ Service life pattern of the present study can help designers to have a

reasonable designing method for concrete bridges at the coastal areas.
+ For studies on reinforced concrete structures in chloride environment,
the programming algorithm, formulations and conclusions present in this
thesis can be used as a useful reference.