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

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

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

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

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

<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

∂
= − − +
∂ ∂
(2.4)
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

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

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
 
= ≤ = = + +
 ÷
 
[ ] [ ]

 
 
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)

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

( , ) ( , )
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

=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

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:

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

( )
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

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
− −

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 .

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
≤ =
∑

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
−
= −

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

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

(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

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

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.

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

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

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

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:

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