Tom tat luan an tieng anh: Nghiên cứu độ bền thấm nước và thấm ion clo clorua của bê tông cốt liệu nhẹ ứng dụng trong dự đoán tuổi thọ kết cấu cầu.

Ministry of Education and Training
University of Transport and Communications
__________________________

LE QUANG VU

DURABILITY OF LIGHTWEIGHT CONCRETE DUE TO
WATER AND ION ABSORPTION AND
ITS APPLICATION IN FORECASTING THE LIFESPAN
OF BRIDGE STRUCTURE
Discipline: Transport Construction Engineering
Code: 9580205
Major: Bridge and Underground Infrastructure
Engineering

TECHNICAL DOCTORAL THESIS SUMMARY

Hanoi - 2022


Work Completion Location:
University of Transport and Communications

Supervisor:
1. Assoc Prof. Dr. Tran The Truyen
University of Transport and Communications
2.

Assoc Prof. Dr. Do Anh Tu
University of Transport and Communications

Critical lecturer 1:
Critical lecturer 2:
Critical lecturer 3:

The thesis will be defended in front of the members of the thesis
committeee at the University of Transport and Communications
Date: …/…/2022

Thesis can be found in:
- National Library of Vietnam
- Library of University of Transport and Communications

2


Introduction
1. The urgency of the Topic
The application of lightweight concrete (Lightweight Concrete – LWC) in the construction
in countries around the world shows prominent advantages such as: Reducing the self-weight of the
bridge structure, thereby improving the exploitation capacity of the live load; Reduced costs of
hoisting, mounting, and transporting prefabricated components due to reduced structural weight.
This is convenient for span by span erection method and reduces construction costs; Increases
structural durability due to good adhesion between aggregate and cement; Reduces the effect of
stress concentration normally created around the aggregate particles for ordinary concrete; Reduces
micro-cracks caused by shrinkage and creep; Increased durability of concrete by reducing microcracks; Improved resistance to penetration of chlorine ions. Evidence of Cl- ion content after 23
years of exploitation by US researchers shows that: As the thickness of the concrete layer increases,
the Cl- ion content decreases compared to normal concrete.
Currently in Vietnam, the application of LWC in the construction of buildings has been
relatively much done; Initially, there were applied studies in transport construction, especially the
construction of bridge structural components. Some typical projects such as Fortuna Hanoi Hotel, Long

Bien Sports Center or Hanoi Club are implemented by Thien Giang Lightweight Concrete Production
Joint Stock Company; Building with 7 floors at No. 132 Khuat Duy Tien; 6-storey house at 130 Giang
Vo street; 11-storey hotel on Hang Thung street; 200 m2 floor of Xanh Plat restaurant at No. 10 Pham
Ngoc Thach… by CICO Investment Constructıon Consultancy Joınt Stock Company (CiCo)). The
results obtained are very positive and highly appreciated by the Ministry of Construction. However, in
the traffic construction industry in general, and in the construction of bridge structures in particular, this
is still an issue that needs to be studied and applied.
The mix composition of LWC and the experiment to determine the mechanical and physical
characteristics of this concrete have been mentioned by many researchs. The results have shown
the similarities and differences of LWC compared to normal concrete (NC) at the same compressive
strength grade. However, the long-term durability of lightweight and reinforced concrete structures
using LWC is still a question that needs to be answered, especially with LWC, and structures using
this concrete type exploited in climatic conditions in Vietnam.
Evaluation of the durability of LWC and structures using it has been conducted by several
studies around the world. In principle, the measurement methods for assessing the water
permeability, and chlorination of LWC as well as predicting the lifespan of reinforced concrete
structures using LWC are carried out in the same way as for normal concrete. However, the
results obtained show large dispersion. The main reason is due to different aggregate
compositions, different concrete ages, different sample forms, and test methods.
Evaluation of water permeability and chloride ion permeability of LWC and structures
using LWC is a very new issue in Vietnam; especially considering the influence of the load
factor. Thus for, no research has been conducted on this issue. It is necessary to have studies
evaluating the long-term durability of LWC structures to supplement the database for the design
of LWC structures used in civil and traffic construction. From the experimental results to
evaluate the water permeability and chloride ion permeability of lightweight concrete, it is
possible to build models to predict the lifespan of reinforced concrete structures using
lightweight concrete according to the reinforcement corrosion criteria.
From the urgent requirements and important implications in proposing a model to
evaluate the influence of loads on the permeability of lightweight aggregate concrete and its
application in predicting the lifespan of reinforced concrete buildings in general and bridge

works in particular, especially in line with the probabilistic bridge design philosophy of Vietnam
bridge design standards, the research topic "Evaluation of water and chloride ion permeability
1


of lightweight concrete and application in predicting the lifespan of bridge structure using
probability theory" was selected as the thesis topic.
The thesis content consists of 4 chapters:
 Introduction
 Chapter 1: Overview of Lightweight Concrete, Researchs relate to the durability of LWC
and structures using this concrete type.
 Chapter 2: Analyses of water and chloride ion permeability of Lightweight Concrete.
 Chapter 3: Building model to predict the lifespan of Lightweight Concrete Structures.
 Chapter 4: Calculation and prediction of lifespan of lightweight reinforced concrete structures
considering the simultaneous influence of load effects and environmental impacts.
 Conclusions
 Recommendations
2. Target of the Thesis
The targets of the thesis are:
 Determining the water and chloride ion permeability features of lightweight concrete;
 Building calculating model to forecast the lifespan of structures using lightweight concrete;
 Evaluating the mining lifetime of structures using lightweight concrete.
3. Research Object and Scope
3.1. Research Object
The research object is concrete using lightweight aggregate keramzit and structures using
this concrete.
The durability of lightweight concrete due to water and ion absorption and the lifespan of LWC structure.
3.2. Scope of Research
 The thesis only focuses on the effect of chloride ions on steel corrosion, not on concrete corrosion of sulphate.
 Research on the durability properties of lightweight concrete produced in Vietnam

conditions: water repellency, chlorine ion permeability under the conditions of
temperature, humidity and time as specified by the test standards..
 Predicting the lifespan of reinforced concrete structures using LWC.
4. Research method
 Analysis, Synthesis, and Comparison.
 The main research method is a combination of theoretical and experimental research methods.
Using advanced theories of concrete durability to determine empirical correlations and conduct
experimental research with lightweight concrete materials and structures to verify.
 Modeling to predict the lifespan of concrete bridge using lightweight concrete.
5. The thesis's new contributions
 The thesis has conducted experimental studies, analysis of water permeability and chloride ion
penetration through C30 lightweight concrete under the impact of loads.
 Research results show that when increasing the compressive load, the water permeability of concrete
increases significantly; especially after inside concete initiate changing the void structure due to the impact
of pre-compressive load or direct compression. A water penetration test model that considers direct
compressive loads has been designed, manufactured and tested based on recent world research results; This
experimental equipment has been improved to make the measurement process more convenient,
especially the process of controlling the load and recording data completely automatically.
 Research results show a significant effect of compressive load on chloride ion permeability of
lightweight concrete. A chlorine ion permeation test model that considers direct compressive loads
has been designed, manufactured and tested based on recent world research results; This test
equipment has been improved to make the measurement process more convenient, especially the
process of controlling the compressive load in lightweight concrete.
2


 The thesis has proposed the relationship between the chloride ion diffusion and the water
permeability factor of lightweight concrete. Determine the Ck coefficient to calculate the chloride
ion diffusion coefficient from the water permeability coefficient of the same lightweight concrete.
Therefrom, a formula for calculating the relationship between water permeability and chloride ion

diffusion coefficient of lightweight concrete is proposed, taking into account the effect of stress in
concrete for the type of lightweight concrete under consideration.
 The thesis builds a calculating model to predict the service life of lightweight concrete structures in
Vietnam conditions, taking into account the influence of permanent loads and operational loads.
CHAPTER 1: OVERVIEW OF LIGHTWEIGHT CONCRETE, RESEARCHS RELATE
TO THE DURABILITY OF LWC AND STRUCTURES USING THIS CONCRETE TYPE
Lightweight Concrete and its applications
According to European standard EN 206-1:2000 [43], lightweight concrete has a density
less than 2,000kg/m3 and compressive strength ranges from 8 - 80MPa (pier sample).
Light-weight concrete according to ACI 213R-03 [25] is concrete with a density of 1,120 - 1,920
kg/m3 and a minimum compressive strength at 28-day of 17 MPa. Consequently, when the
density of normal concrete is reduced from 2,400kg/m3 to 1,900kg/m3 for lightweight concrete,
it is possible to reduce the self-weight of the structure significantly, helping to reduce the weight
of the structure. saving rebar and prestressed reinforcement, reducing construction costs.
The use of light aggregates is a fundamental factor in achieving a small density. In addition to the density
of aggregates, the concrete density also depends on the aggregate grade, aggregate moisture content, gas content,
cement content, water/binder ratio (w/b), chemical and mineral admixtures, etc. Beside the materials, the concrete's
density also depends on the compaction method, the curing conditions, etc.
The density of LWC withstood a variable load of 1200 - 2000 kg/m3 compared to
2300 - 2400 kg/m3 of heavy concrete. Most of the properties of LWC are related to the density,
especially the compressive strength.
Research of water permeability of lightweight concrete
Water permeability is defined as the ability that allows fluids to pass through a porous
medium due to a difference in potential energy. The permeability of lightweight concrete or a
hollow material is highly dependent on the parameters of the concrete environment such as
porosity, and pore structure. According to Scrivener (2001), when the porosity and inter-pore
communication in concrete increase, the waterproofing durability of concrete is reduced; and
the straighter the pores, the faster the seepage flow rate. Under the mechanical impact or high
enough amount of temperature, the destruction in concrete accompanied by cracks increases the
preceding parameters, therefore, the permeability of concrete will also increase rapidly [61].

Figure 1.1 - Impact of porosity, shape - size of voids and the connectivity of pores on the
permeability of concrete (Scrivener (2001))
3


The studies of Abbas (2000) on the influence of void gap on the strength and permeability of LWC
showed that the concrete strength depends on the void ratio of the material; however, the permeability
depends mainly on the connectivity between the pores. Once the concrete has a high hollow connection due
to cracks appearing for many reasons (shrinkage, creep, mechanical impact, high temperature, corrosion...)
during the exploitation process, the permeability of concrete increases rapidly.
The differences in humidity, hydrostatic pressure, stress, temperature, and chemical concentrations
disturb the equilibrium of fluids in the porous material; Therefore, the movement of the fluid occurs to
reestablish a new balance. The migration process of this fluid is usually described in terms of adsorption,
diffusion, absorption, and permeation. In concrete, both the physical structure of the concrete and the state
of the water in the pores affect these processes.
Dang Thuy Chi (2018) [3] studied determining the waterproofness of lightweight concrete. Each
concrete grade was tested on a sample set of 6 cylinders with a diameter of 150 mm and height of 150 mm.
The results show that the LWC LC40 type is penetrated by water when the water pressure reaches 12 atm,
achieving waterproofing grade B10. While the two types of LWC LC50 and LC60 have a water pressure
of more than 12 atm, the sample has not been penetrated by water, achieving the maximum waterproof
grade B12. This result is similar to that of normal heavy concrete.
Research of chlorine ion permeability of lightweight concrete
According to the research results of Youm et al. [70] on LWC using silica fume, silica fume improves
the microstructure of cement mortar, thereby improving the chloride ion permeability of LWC. Futhermore,
LWC using silica fume has chlorine ion permeability test results less affected by the type of aggregate. On
the other hand, Liu et al. [51] commented that the chloride ion permeability of LWC increased with
increasing lighweight material content in concrete. In addition, Liu et al. also concluded that concrete using
lightweight material and sand usually has the same permeability, chloride ion permeability compared to
normal concrete with the same w/b ratio.

Basheer, & Long, 2005, Lo et al., 2008 [52] showed that as the percentage of lightweight aggregate
increases, the strength of LWC decreases. The reason is explained by the increased area of cement paste and
aggregate, which increases the penetration ability of water and chlorine ions, although most chlorine ions do
not penetrate through lightweight aggregates (Chia & Zhang, 2002 [36]).
Dang Thuy Chi (2018) conducted tests to measure the permeability of lightweight concrete
with 3 target strength grades of 30, 50, and 60 MPa. The results of the chloride ion permeability
test showed that the permeability gradually increased from 166 Columb to 193 Columb when
the average compressive strength decreased from 69 to 50 MPa. The permeability is very low,
equivalent to the average value measured on heavy concrete with compressive strength of 80
MPa [33]. Consequently, the experimental results seem to be suitable with Liu's comments [51]
that LWC has a higher chloride ion permeability than heavy concrete with the same compressive
strength at 28-day (but with a higher w/b ratio).
Researchs on corrosion initiation time and corrosion propagation time, service lifespan
In 1980, at the international conference on concrete in the marine environment organized by the
American Concrete Institute (ACI), Tuuti [16] suggested that reinforced concrete structures working in the
marine environment would be diffused into the concrete by chloride ion and accumulates on the surface of
the reinforcement. When the chloride ion concentration at the reinforcement surface reaches the critical
concentration threshold, it will begin to corrode the reinforcement. Corrosion of reinforcement will lead to
two consequences. The first is that it reduces the cross-sectional area of the reinforcement leading to a
decrease the resistance. Second, corroded reinforcement will produce corrosion products, volume expansion
corrosion products cause tensile stress in the protective concrete layer and cause cracking, splitting, and
breaking of concrete.
Modeling predicting service lifespan of reinforced concrete structures due to chloride ion
diffusion should show the processes leading to corrosion of steel in concrete caused by chloride
ions. These processes are basically described as follows:
4


- Chloride ions in the environment accumulate on the concrete surface.
- Chloride ions are diffused into the concrete through a number of mechanisms, mainly

diffusion.
- Chloride ion concentration is accumulated over time at the surface of the reinforcement.
- When the chloride ion concentration at the reinforcement surface reaches the critical
threshold level, the passive film on the reinforcement surface is broken and the corrosion
process begins.
- Products of corrosion have a larger volume than the corroded reinforcement, causing
tensile stress in the protective concrete layer.
- Concrete has poor tensile strength, so cracks will appear either perpendicular or
horizontally that forming layer separation between the reinforcements.
- Cracks forming cracks or breaking cause the structure to deteriorate such as function is
no longer guaranteed or unsafe. This can be seen as a time when a repair is required.
- Corrosion causes loss of steel cross-sectional area, leading to an unsatisfied bearing limit
state.
Tuutti, K. gave a two-stage model of the service life of reinforced concrete structures as
shown in Figure 1.2. Accordingly, the service life consists of two successive stages: the
corrosion initiation stage and the corrosion propagation stage according to Equation 1.1.
(1.1)
t = t1 + t 2 ;
Where:
- t: The lifespan has already been used;
- t1: The corrosion initiation stage;
- t2: The corrosion propagation stage.

Figure 1.2 - Service lifespan of reinforced concrete structures:
Tuuti's two-stage model (1980)
Conclusion of Chapter 1
Through many studies on the water permeability of LWC, it has been shown that the
permeability of concrete is influenced by two main factors: One is the porosity characteristics
such as size, structure, and the connection between the pores; The second is the micro-cracks in
the concrete, especially at the interface between the aggregate and the binder. In which, the

effect of stress due to external influences on concrete permeability is still not clear.
Meanwhile, for construction works in the marine environment, an important damage phenomenon that
needs to be taken into account is the process of corrosion of reinforcement in concrete due to chloride ions. There
have been many researchs that have proposed, the relationship between chloride ion diffusion coefficient of
concrete, water/cement ratio, time, Coulombs quantity. In addition, studies evaluating the effect of pre-stress state
in concrete have also been carried out. The ion diffusion experiments through concrete include steady state diffusion
experiment, unstable state diffusion experiment, electric field migration experiment. In general, performing chloride
ion penetration tests is complicated (especially when considering stress states in concrete). Therefore, the indirect
determination of chloride ion diffusion coefficient through simpler tests such as water penetration test is of great
significance in assessing the durability and predicting the service lifespan of LWC structures.
5


CHAPTER 2: ANALYSES OF WATER AND CHLORIDE ION PERMEABILITY OF
LIGHTWEIGHT CONCRETE
2.1. Problem
The experiments in this chapter evaluate the water permeability of some typical lightweight
concrete commonly used in bridge constructions in Vietnam. LWC with a strength of 30 MPa
(mark C30) was used in these tests. The experimental process includes the following
experiments:
- Testing to determine the compressive strength of concrete.
- Testing to determine the water permeability and chlorination of pre-stressed concrete.
- Testing to determine the water permeability and chlorination of post-tensioned concrete
To design the grade for concrete with compressive strength fc' = 30 MPa (C30), the PhD
student used Bim Son cement - PC 40 (meeting the requirements of TCVN 2682:2009).
 Small Grain - Size (Sand - S)
Sand used for concrete is natural sand with grain size from 0.14 to 5mm - according to TCVN
7570-2008; from 0.075 to 4.75 mm - according to the Unified Soil Classification System
(USCS) and from 0.08 to 5mm according to French standards.
Sand used in this study is from Da River.

 Large Grain - Size (Crushed stone)
Using Crushed stone from Hoa Binh.
Stone materials for making concrete must have suitable strength and loss. Crushed stone has
good roughness, closely bonded with cement mortar, so the flexural strength of concrete made
from it is higher than that of concrete made from gravel.
 Water (W)
Using domestic water for concrete production and curing. Water used must be clean water
according to TCVN 4056: 2012: Water for concrete and mortar - Technical requirements.
2.2. Results of water permeability test with pre-stressed concrete samples
Based on the results of the experiments, we build a diagram of the waterproofness of C30
concrete when considering the pre-compressive stress as follows (Figure 2.1):

Figure 2.1 - Increase of water permeability (k) according to relatively stress

max

When max > 0.5 and the water pressure is larger than 10 atm, the water permeability increase rapidly. This
shows that the effect of pre-compressive stress is large enough to increase the water permeability of LWC, it is these
residual mechanical effects that facilitate water penetration easier through the concrete specimen, especially when
max > 0.5, the occurrence of concrete damage caused the water permeability to increase faster. Especially in the
experiment, we found that max equal to 0.8 showed a huge difference in water permeability in LWC.
6


Figure 2.2 - Plot of permeability coefficient (K) changing over time
with stress class max = 0.6.

Figure 2.3 - Plot of permeability coefficient (K) changing over time
with stress class max = 0.7.
The water permeability of concrete is almost unchanged or changes slowly when the relative stress value

max < 0.5; After this threshold, the permeability coefficient starts to increase rapidly. When the relative stress
max ≥ 0.6, the water permeability increases very quickly; This can be explained by the fact that the microstructure
of concrete is destroyed after this stress threshold - which is the threshold for the appearance of dispersed failure
zones (according to the approach of concrete failure mechanics) - causing increase the water permeability of
concrete. The law of increasing the water permeability of concrete after 28 days in this experiment is similar to the
law of increasing the water permeability of early-age concrete published by Banthia & al (2005) when mechanical
failure has not yet appeared in concrete.
Charge (Coulombs)

1500
MẪU 1
MẪU 2
MẪU 3
MẪU 4
MẪU 5
MẪU 6

1000

500

0
0

(max) 0.2

0.4

0.6

0.8

1

Figure 2.4 - Chloride ion permeability of LWC with strength of 30 Mpa according to
compressive prestressed in concrete
7


When the pre-compressive stress in concrete: max ≤ 0.5, the chloride ion permeability increases
linearly and fairly evenly; After this threshold, the chlorine permeability increases sharply.
Chlorine ion permeability value of concrete grade 30Mpa at loads of 30% and 50% of f'c is from 200 300(C) - at medium grade, when load is 80% of f'c, the charge through the sample increases rapidly to
1300(C) - high.

Figure 2.5 - The increase law of chloride ion diffusion coefficient according to precompression stress of lightweight concrete C30 sample.
According to the chart in Figure 2.5, when the compressive stress is lower than 50% of max, the
permeability change is not significant, but when the pre-compressive stress reaches 70% of max, the
permeability coefficient increases about 2.7 times compared to the permeability of unloaded concrete.
The law of increasing the chloride ion permeability coefficient according to the precompression stress of C30 LWC is expressed by the following formula:
Exponential Regression: D/Do = 9.1226(max)2 – 3.4256(max) + 1.0816
(2.12)

Figure 2.6 - Experiment for determining the chloride ion permeability of lightweight concrete
under direct compression
The relationship of the chloride ion permeability (C) of concrete C30 according to the rapid
permeability test corresponding to the stress values when compressing the concrete specimen at the same
time is shown in Figure 2.7. The experimental results show that the chloride ion permeability changes much
when there is the presence of simultaneously acting loads. However, before and after loading, the chloride
ion permeability is within the "average" grade according to TCVN 9337-2012 standard. When increasing
the load corresponding to the stress  to 30% and 50% compared to the stress max, the permeability of

concrete increases by 24.50% and 39.48%, respectively. When increasing the stress to 80% of max, the
permeability of concrete has a large increase. In the case of reduced chloride ion permeability, it will lead to
8


a longer time of chloride ion penetration through the protective concrete layer to cause corrosion of
reinforcement in reinforced concrete construction. From this result, it is shown that in prestressed concrete
structure, when compressive stress in concrete is within the appropriate limit, it can prolong the penetration
time and increase the service life due to chloride ion penetration.

Figure 2.7 - Relationship of chloride ion permeability through concrete with lightweight
concrete compressive stress.
The law of increasing the chloride ion permeability coefficient according to the direct
compressive stress of LWC C30 is expressed by the following formula:
Exponential Regression: D/Do = 4.4975(max)2 – 1.9529(max) + 0.9543

(2.13)

Banthia & al (2008) suggested that the relationship between water permeability coefficient
K and chloride ion diffusion coefficient D of fiber reinforced concrete as follows:
K=𝐶𝐾 𝑥𝐹 0.5 𝑥𝑆 0.5 𝑥𝐷
Where:
- S is a factor that takes into account the effect of compressive stress in concrete, which is
expressed as the ratio between the water permeability coefficient of the loaded concrete and the
unloaded concrete: S =

𝐾𝑙𝑜𝑎𝑑𝑒𝑑
𝐾𝑢𝑛𝑙𝑜𝑎𝑑𝑒𝑑

- F is the factor taking into account the effect of fiber reinforcement content in concrete; The

coefficient F is expressed as the ratio between the water permeability coefficient of fiberreinforced concrete and the water permeability coefficient of concrete without fiber.
When only considering ordinary concrete: (F = 1): F =

𝐾ℎ𝑎𝑣𝑖𝑛𝑔 𝑓𝑖𝑏𝑒𝑟
𝐾𝑛𝑜 𝑓𝑖𝑏𝑒𝑟

- Ck is the coefficient considering the relationship between water permeability and chloride ion
𝐾
diffusion coefficient of unloaded concrete: 𝐶𝑘 =
𝐷𝑜

The chloride ion diffusion coefficient of concrete is calculated from the results of the rapid
chloride ion penetration test according to Berke and Hicks (1993) as follows:
D = 1,03x10-2xQ0,84 x10-12(m2/s)

Ck coefficient for concrete C30 considering the correlation between water permeability
coefficient and chloride ion diffusion coefficient of unloaded concrete calculated from the
results of water permeability and chloride ion permeability test is:

𝐶𝑘 =

3.5𝑥10−11
1.205𝑥10−12

= 29.05
9


Figure 2.8 - The diagram of the chlorine ion diffusion coefficient relationship based on
Banthia theory and experimental results of C30 lightweight concrete

Through Figure 2.8, it can be seen that the calculation results of the theoretical chlorine ion
diffusion coefficient, and the chlorine ion permeability test results are quite close.
Experimental results show that, when the stress level in concrete max ≤ 0.3, the chloride ion
diffusion coefficient decreases, when this stress level increases, the diffusion coefficient increases
gradually and sharply when the stress level in concrete exceeds the threshold max ≥ 0.6.
The calculation results allow to propose the formula for calculating the chloride ion
diffusion coefficient from the water permeability coefficient as follows:
For Concrete C30: Kw = 29.05 S0.5 D
With this formula, we can easily calculate the chloride ion diffusion coefficient from the
water permeability coefficient of some commonly used concrete types.
2.3. Conclusions of Chapter 2
Experimental results to determine the waterproofness of lightweight concrete C30 subjected to
pre-compression stress showed that, at the threshold max max > 0.5, marking a rapid increase of
water permeability when the water pressure is greater than 10atm , this proves that the influence of
pre-compression stress is large enough to increase the water permeability of lightweight concrete,
it is these residual mechanical effects that facilitate water penetration through the concrete
specimen, especially when max max > 0.5, the occurrence of concrete destruction caused the
increase in water permeability to increase faster. Especially in the experiment, when the threshold
max = 0.8, it showed a huge difference in water permeability in lightweight concrete.
The test results of water permeability measurement of LWC C30 subjected to direct compressive stress
show that the water permeability of concrete is almost unchanged or changes slowly when the relative stress
value max < 0.5; After this threshold, the permeability coefficient starts to increase rapidly. When the
relative stress max ≥ 0.6, the water permeability increases very quickly; This can be explained because
the microstructure of concrete is destroyed after this stress threshold - which is the threshold for the
appearance of dispersed failure zones (according to the approach of concrete failure mechanics) - causes
increase the water permeability of concrete. The law of increasing the water permeability of concrete after
28 days in this experiment is similar to the law of increasing the permeability of young concrete published
by Banthia & al (2005) when mechanical failure has not yet been appeared in concrete.
The results of chloride ion permeability test with concrete samples subjected to pre-compression stress show that,
when the pre-compressive stress in concrete max ≤ 0.8, the chloride ion permeability increases linearly and fairly

evenly; After this threshold, the chloride ion permeability increases sharply.
The results of the chloride ion permeability test with concrete samples subjected to direct loads show
that the chloride ion permeability changes much when there is the presence of simultaneously acting loads.
However, before and after loading, the chloride ion permeability is within the "average" level according
to TCVN 9337-2012 standard. The decline in permeability at a stress of 30% of max is explained by the
stress causing micro deformation and because the stress is still within the elastic limit, no cracks have
-

10


arisen, but on the contrary, the density increases and the voids of the concrete decreses thus reduce the
permeability. The rate of chloride ion penetration through concrete decreased when the stress was at 30%
of max and increased at 50% of max and 70% of max.
Finally, the author proposes the relationship between water permeability coefficient and
chloride ion diffusion coefficient of concrete.
For concrete C30: Kw = 29.05 S0.5 D
CHAPTER 3: BUILDING A STRUCTURAL LIFESPAN PREDICTION MODEL
USING LIGHTWEIGHT CONCRETE
3.1. Introduction
The purpose of this chapter is to build a model to predict the influence of loads and environment on the service
life of bridge structures using lightweight reinforced concrete according to the criteria of initiation of reinforcement
corrosion in concrete. The experimental results in Chapter 2 will be used as the basis for establishing models to predict
the lifespan of the building. These models will be applied in forecasting the life of a specific bridge.
This chapter is structured into two main parts. The first part of the chapter is the part to build a predictive
model that considers the effects of loads and environmental conditions simultaneously. The second part is
the lifespan prediction calculations for a specific bridge structure taking into account the change of protective
concrete layer thickness, surface chlorine ion concentration, pre-stress and direct compression in concrete.
3.2. Scope of Research
In the scope of research of this thesis, only referring to the service life according to the penetration of

chlorine ions into the concrete bridge structure causing corrosion of reinforcement.
The service life of reinforced concrete bridges due to chloride ion intrusion is the time from the
beginning of exposure to the environment with chlorine ions to the time when chlorine ions cause corrosion
of reinforcement leading to cracking of protective concrete or until corrosion causes a loss of reinforcement
cross-sectional area, reducing the resistance to a level that endangers the bearing limit state. The service life
of reinforced concrete bridges calculated according to chloride ion penetration will be calculated in years
and is the sum of two successive stages: the corrosion initiation stage and the corrosion propagation stage.
Within the scope of this thesis, regarding the long-term damage of the structure due to corrosion, it only
considers the evaluation of the service life of a reinforced concrete transport structure as the time when the
corrosion begins in reinforcement due to the diffusion of chloride ions into the concrete or more precisely
the time that the concentration of chlorine ions (C) at the surface of the reinforcement reaches the critical
value (Ccr). The change in the lifespan of the building according to this corrosion criterion is expressed
according to the changes in the thickness of the protective concrete layer and the permeability of the concrete
related to the diffusion coefficient of chloride ions into the concrete with consideration to the stress factor.
3.3. Building a model to predict the service life of lightweight reinforced concrete
structures according to the criteria of reinforcement corrosion taking into account the
stress state of the concrete.
The input parameters in the problem are important. This thesis will be based on the input
parameters from the experiments in chapter 2 along with the results of domestic and foreign
authors. Those parameters will be recommended to be used for the model to be built.
3.3.1. Building a model to predict the service life of reinforced concrete bridges according to
the criteria of reinforcement corrosion initiation
In 1975, Crank proposed a mathematical model for the diffusion process based on Fick II's
law. In case the diffusion coefficient is constant, the chloride ion concentration on the
reinforcement surface in formula 3.1 with the boundary condition C0 = C (0, t) (the surface
chloride ion content is constant) and the initial conditions C = 0, x > 0 and t = 0, are determined by:
x
(3.1)
)) ;
Cx = Cs (1 − erf (

2√Dt
11


Where:
- Cx is chloride ion concentration at depth x ;
- erf is the error function ;
- Cs is the chloride ion concentration at the concrete surface of the structure ;
- t is the corresponding time ;
- x is the depth from the concrete surface of the structure to the determining point ;
- D is the chloride ion diffusion coefficient.
The process of corrosion of reinforcement begins when Cx = Ccr; then x = h (thickness of the
protective concrete layer) we have:
h
(3.2)
))
Ccr = Cs (1 − erf (
2√Dt
In fact, the service life of buildings in general and traffic constructions in particular according to corrosion
criteria is significantly higher than the results calculated by the above formula because of chloride diffusion
and surface chloride concentration are time dependent factors.
To consider the time factor in the expression of chloride diffusivity values of normally intact
concrete, Mangat & Molloy (1994) proposed the law of change of Kc with time of the following form:
t0 m
(3.3)
D = D28 ( ) ;
t
Where:
- D28: is the chloride ion diffusion coefficient at the age of 28 days;
- t0 : concrete age (t0 = 28 days);

- m: is the empirical coefficient taken as follows: (according to A.Costa and J.Appleton
(1998))
 Area affected by sea waves: m = 0.245 ;
 The tidal range: m = 0.2 ;
 Coastal climate zone: m = 0.29.
To consider the time factor in representing the surface chloride concentration value of Cs in this thesis,
the author took or changed the suggestion of A. Costa & J. Appeleton (1998) as follows:
(3.4)
Cs = Cso . t n ;
where: Cso is the concentration of surface chloride after 1 year; n is the experimental coefficient.
According to different environmental conditions the values of Cso (as % by mass of concrete) and n for
typical ordinary concrete are taken as follows (A. Costa & J. Appeleton (1999)):
- Area affected by sea waves: Cso = 0.24; n = 0.47;
- Tidal area range: Cso = 0.38; n = 0.37;
- Coastal climate zone: Cso = 0.12; n = 0.54.
Thus, considering the time change of chloride diffusion coefficient and surface chloride
concentration, (3.2) is rewritten as follows:
x
)
Cx = Cso t n (1 − erf (
(3.5)
2√D28 𝑡0𝑚 t1−m
The minimum thickness of the protective concrete layer h needed to prevent corrosion of
reinforcement in concrete is calculated as follows:
Ccr
(3.6)
)
h = 2√3D28 𝑡0𝑚 t1−m × erf −1 (
Cso t n
3.3.2. Building a model to predict the service life of reinforced concrete bridges according to

the criteria of reinforcement corrosion taking into account the stress state of concrete
Different from the state when not bearing the load, the concrete structure is intact, when subjected to a large enough
load, the concrete structure is destroyed leading to a very rapid increase in the permeability of the concrete, which will
12


create favorable conditions for the faster the chloride diffusion into the concrete increases, the higher the concentration of
chloride ions at the surface of the reinforcement and consequently the earlier corrosion of the reinforcement. To explain
this, when the stress in the concrete exceeds the crack limit, it will cause the concrete to crack and facilitate the rapid
increase in water permeability and chloride ion diffusion.
To consider the effect of the stress state on the diffusion of chloride ions into the concrete, the formula
determines the relationship between the increase in chloride ion diffusion coefficient with time and the preor direct compression state. The next chapter will be used in the calculations.
Therefore, from formulas 3.5 and 3.6, we can establish a formula to determine the life of reinforced
concrete constructions according to the criteria of starting corrosion of reinforcement in concrete.
a) The case of the pre-compressive stress state

b) The case of direct compressive stress states

3.4. Model to predict lifespan of lightweight reinforced concrete structures with consideration
of probability theory
3.4.1. Probability theory of failure and long-term age
The simplest computational model to describe the failure case of one load variable S and
one resistance variable R. In principle, the variables R and S can be multiple loads and be
represented in multiple units. The only requirement is that they have proportions.
If R and S are independent of time, the failure case can be understood as follows (Kraker,
de Tichler and Vrouwenvelder, 1982):
{Failure} = {R < S}
(3.7)
In other words, failure occurs when the resistance is less than the load acting on the structure.
The failure probability Pf is now defined as the failure probability.

Pf = P (R < S)
(3.8)
Resistance R or load S or both can be time dependent loads. Therefore, the failure probability can also be
a time-dependent load. Considering that R(г) and S(г) are instantaneous natural-law values of resistance and
load at time the probability of failure in a lifetime г can be defined by:
Pf(г) = P{R(г)< S(г)} with every г < t
(3.9)
Determining the function Pf(г) according to the above equation is very difficult mathematically.
Normally, resistance and load cannot be treated as instantaneous natural values. That is why R and S
are considered as random loads with time dependent distributions or constant density distributions.
Consquently, the failure probability usually defines:
Pf(t) = P {R(t)< S(t)}
(3.10)
According to the above definition, the probability of failure increases continuously over time
as shown in the chart below.

Figure 3.1 - The probability of failure increases continuously over time
At time t = 0, the density distributions of the loads are very far apart and the probability of
initial failure is small. With the moment the distributions approach each other, the resulting
13


overlapping area increases. The overlap area illustrates the failure probability area. The function
Pf(t) is characterized as a distribution function. If the long-term life is so defined, then the case
tL < t is the same as the failure case with the long-term life t, the long-term life distribution
function is defined as:
FL = P (tL < t) = Pf(t)
(3.11)
Where FL is the cumulative distribution of the long-term lifetime.
The probability density function is defined as the origin of the distribution function:

f L (t ) 

d
FL (t )
dt

(3.12)

At random point, the probability of failure can be determined by the sum of the products of two
probabilities: (1) the probability that R < S at S = s and (2) the probability that S = s, open wide for
all sequences of S:
Pf   P{R  S / S  s}.P{S  s}
(3.13)
s

To consider continuous distributions, the failure probability Pf at random point in time can
be determined using convolutional integration:


Pf 

 F (s). f (s)ds
R

(3.14)

s



Where:
FR(s) is the distribution function of R.
fs(s) is the probability density function of S
s is the common load or deviation of R and S
The general method for solving this integration problem with the time-dependent distributions of R and S
can be very complex. Direct resolution of these integrals is only available in some cases, for example the
distribution of R and S is normal. However, integrals can be solved by approximation. The distribution of the
long-term life can be found by calculating the failure probability values at different times such as t = 10, 20, 30...
3.4.2. Probabilistic design method
With the probabilistic durable design method, the distributions of the load, the characteristic curve and the longterm life are also taken into account. The condition is understood as the probability that the design formula is incorrect.
The design formulation can be established according to the working principle or the long-term life principle being
essentially the same as in the defined design. According to the working principle, the following requirement must be
satisfied: The probability of the structural resistance that is less than the load during service time must be less than a
certain allowable failure probability:
Mathematically the request is understood as:
P{Failure}tg = P{R – S < 0}tg < Pfmax
(3.15)
Where P{failure}tg is the probability of failure of the structure in the desired long-term life tg.
Pfmax is the maximum allowable failure probability.
The problem can be solved if the distributions of load and resistance are found.
When the long-term life rule is used, the requirement is established as follows: The probability that the
long-term life of the structure is shorter than the desired life is less than some allowable failure probability.
P{Failure}tg = P{tL < tg} < Pfmax
(3.16)
The problem can be solved if the distribution of the long-term life is determined. If the
pattern of the distribution is not known, it must be inferred against some known distribution.
One solution to the distributions of the long-run lifetimes is assumed to be lognormal.
3.4.3. Design according to the working principle in the case where R and S have a normal
distribution
The case that the working principle is used in the durable design, and the loads and resistances are

normally distributed loads, the probability of failure is determined using the test index β:
14


 ( R, t )   ( S , t )
(3.17)
( [R, t ]   2 [S , t ])1/2
μ is the mean, σ is the standard deviation.
The test index β is normally distributed (0, 1). The failure probability corresponding to β is
available in tables or in updated functions in spreadsheet applications. In structural design, the
test index β is considered as the factor of safety or the reliability index. Usually, R or S is
constant. The above relationship is shortened as follows:
r  [S , t ]
 (t ) 
(3.18)
 [S , t ]
[R, t ]  s
 (t ) 
(3.19)
 [R, t ]
Where r and s are constants.
In the case where r is a constant and s is a function of time and is approximated by an
attenuation model, the problem is called a performance problem.
Since the mean and standard deviations are time dependent, the β index is also time
dependent. To find the distribution of long-term life, the failure probabilities must be solved
with some value of t (t = 0, 10, 20, etc. annually).
3.4.4. Building a model to predict the service life of reinforced concrete structures using
lightweight concrete taking into account the uncertainty of the input parameters
The service life of reinforced concrete structures using lightweight aggregate concrete is
calculated as the time from the time the construction is put into operation to the time when the

reinforcement in the concrete begins to corrode. The service life depends on 4 factors: chloride
diffusion coefficient D, equilibrium chloride concentration at the concrete surface Cs, limit
chloride concentration and concrete coating Ccr, and protective concrete layer thickness h.
In recent studies, the limiting chloride concentration Ccr was considered to be normally
distributed with mean and coefficient of variation (COV) of 0.027 - 0.045% and 0.05 - 0.296
(Enright and Frangopol 1998a; Stewart 2009); Stewart and Rosowsky 1998; Yanaka 2004. The
surface chloride concentrations (CS) were modeled using a logarithmic normal distribution with
mean and COV ranges of 0.10 - 0.40% and 0.05 - 0.50, respectively (Vu and Stewart 2000). The
thickness of the protective concrete layer is influenced by the quality of construction, which is
modeled according to a normal distribution or a normal logarithmic probability distribution (Enright
and Frangopol 1999a).
The chloride diffusion coefficient in this study is described according to the normal
distribution law with the mean value and the COV range of 0.32-2.58 cm2/year and 0.05-1.6
respectively (the normal distribution model proposed by many authors as Yanaka (2004)).
Conditions for the reinforcement in lightweight concrete structures to corrode are:
C (x, t) ≥ Ccr or f = C(x, t) – Ccr ≥ 0
The probability that a corrosion event will occur is shown as follows:
Pf = P[C(x, t) – CCr ≥ 0]
Using the Monte-Carlo simulation it is possible to easily calculate the probability of a
corrosion failure occurring. The probability of corrosion occurring is calculated by the formula:
1
Pf = ∑𝑁
𝐼(𝑓(𝑥, 𝑡))
𝑁 1
Where I is the instruction function:
I = 0 if f (x, t) < 0
I = 1 if f (x, t) ≥ 0.
Applying the above formulas with the parameters from research and experimental
experiments, it is possible to calculate the probability of the occurrence of reinforcement
corrosion incidents. The expected design lifespan of the building is 100 years.

 (t ) 

2

15


3.5. Conclusions of Chapter 3
In order to propose a model to predict the service life according to chloride ion permeability, at
the beginning of chapter III, the author presented the basic concepts, characteristics and differences
in the service life and durability of a structure. Direct deterioration and indirect deterioration are
considered to be the two main mechanisms leading to the deterioration of reinforced concrete bridge
structures, in which, within the scope of this research, the author only mentions to the service life
according to the penetration of chloride ions into the concrete bridge structure causing corrosion of
reinforcement. The model to predict the life of reinforced concrete structures is built based on
Tuutti.K's model and consists of two stages according to the penetration of chlorine ions into the
concrete bridge structure causing corrosion of reinforcement. And in this study, regarding the longterm damage of the structure due to corrosion, the author only considers the assessment of the
service life of a reinforced concrete traffic structure as the time when the corrosion begins.
Corrosion of reinforcements in concrete due to diffusion of chloride ions into concrete or more
precisely time that concentration of chlorine ions (C) at the surface of reinforcement reaches the
critical value (Ccr). The equation for calculating the concentration of chlorine ions at the
reinforcement surface is taken according to Fick's 2nd law (RILEM 14 (2005) - A. Sara & E.
Vesikari).
At the end of the chapter, the author provides a model for predicting life according to
probability theory when considering the process of chloride penetration causing corrosion of
reinforcement. And the design according to the working principle in the case of R and S with
normal distribution is selected in this study.

CHAPTER 4: CALCULATION OF FORECASTING THE LIFESPAN OF
LIGHTWEIGHT REFORCED CONCRETE STRUCTURES CONCERNING

EFFECTS OF LOAD EFFECTS AND IMPACTS OF ENVIRONMENT
4.1. Calculation and prediction of service life of lightweight concrete used in slab structure
of railway bridge deck with defined model.
The proposed model and experimental values presented in chapter 3 are applied in this
calculation.

Figure 4.1 - Relationship between the thickness of the protective concrete layer and the life of
the building according to the pre-compressive stress
In Figure 4.1, with the case of pre-compressive load, the rule of changing the life of the
building according to the thickness of the protective concrete layer is quite similar; an increase
in pre-compressive stress will require a thicker protective concrete layer thickness.
In Figure 4.2 we see, with the case of direct compressive load; the rule of changing the life
of the structure according to the thickness of the protective concrete layer depends on the state
of pre-compressive stress in different stages. When max = 0.3, the thickness of the concrete
layer decreases, but when max = 0.5, the thickness of the concrete layer increases and
increases significantly when max = 0.7.
16


Figure 4.2 - Relationship between the thickness of the protective concrete layer and the
lifespan of the building under direct compressive stress
4.2. Calculation and prediction of service life of lightweight concrete used in slab
structure of railway bridge deck with probability model
Table 4.1 - Input parameter
Standard

Coefficient of

deviation

variation

𝝈

(%)

38,00

5,70

15

0,06

0,009

15

0,24

0,03

15

Factor, n

0,47

0,0705

15

Thickness of protective concrete layer, h

60

9

15

Experimental coefficient, m

0,245

3,675

15

Input Parameter
Initial chloride ion diffusion coefficient
(mm2/năm)
Threshold corrosive concentration
Surface chlorine ion concentration after 1
year:

The

average

value 𝝁

Cv

In this study, the parameters D, m, C s , Ccr , and m are considered as random variables of
the normal distribution form N (µ, σ) where µ is the mean and σ is the standard deviation.
Others are treated as constants. The reference coefficient of variation C v is 15% and don’t
change (with a standard deviation of 15% of the mean) for all parameters in Table 4.1.
D = 38.00 (mm2/year) (D = 1.205x10-12 (m2/s)) with lightweight concrete according to the
corrosion initiation criteria; with water/cement ratio (w/c) = 0.27; hmin = 60mm for coastal
concrete structure. Choosing herein h = 60mm; Δh = 0 (mm) with marine atmosphere; the design
service life is 100 years; m = 0.245 for lightweight concrete, CCr = 0.06% (by weight of
concrete), kcu = 1.0 with 7-day concretre structure curing and ken = 0.68 for marine atmospheres.
4.2.2.1. Effect of chloride ion diffusion coefficient D
The effect of the diffusion coefficient D on the probability of corrosion incident Pf is shown
in Figure 4.10. We see that over a certain period of time, keeping other parameters constant, an
increase in D leads to an increase in Pf, this is because the higher the diffusivity represents the
higher transport of chloride ions into the concrete. The D0 factor depends on the quality of the
concrete mainly the w/c ratio and the type of binder. Assuming Pmt = 0.1 (β = 1.3), Figure 4.3
shows that the time to start corrosion of concrete structure is about 28, 20 and 19 years
respectively with diffusion coefficient D = 47.50 ; 38.00 and 57.01 (mm2/year).
17


The probability of corrosion Pf

1

D=57,01
0.8

D=38,00

0.6
0.4

 =1,3

D=47,50

0.2
0
0

10

20

30

40

50

60

70

80

90

100

Time(year)

Figure 4.3 - Effect of diffusion coefficient D on the probability of corrosion failure
4.2.2.2. Effect of the thickness of the protective concrete layer, h
The effect of h on Pf is shown in Figure 4.4. When h increases, Pf decreases, or in other words,
if Pf is the same, the time to start corrosion of reinforcement increases. In order to initiate corrosion,
the external chloride ions must be transported from the concrete surface through the protective layer
and to the reinforcement, so the greater the thickness of the protective concrete layer, the longer the
chloride concentration will reach the reinforcement at the critical level and the longer the service
life of the reinforced concrete. Thus, the thickness of the protective concrete layer is one of the most
important parameters affecting the service life of the reinforced concrete. If we take Pmt = 0.1 (β =
1.3), the corrosion start time of the reinforced concrete is about 29, 41 and 57 years, respectively,
with the thickness of the protective concrete layer h = 60, 75 and 90mm, respectively.
The probability of corrosion Pf

1
0.8

h=75mm

0.6

h=60mm
0.4

h=90mm

 =1,3

0.2
0
0

10

20

30

40

50

60

70

80

90

100

Time (year)

Figure 4.4 - Effect of protective concrete layer thickness h on the probability of corrosion incident
4.2.2.3. Effect of critical chloride concentration Ccr

Figure 4.5 shows that the effect of C Cr on Pf is similar to the thickness of the protective
concrete layer, which means if CCr increases, Pf will decrease. It is clear that as the C Cr
increases, the time it takes for chloride ions from outside to penetrate the concrete to reach the
level of CCr increases and thus Pf decreases. The concentration of C Cr depends on the quality
of the concrete (w/c ratio, binder grade) and the type of steel used. If we take P mt = 10-1 (β =
1.3), the corrosion time of concrete structure is about 29, 38 and 46 years, respectively, with
CCr = 0.06, 0.075 and 0.09%, respectively.
18


The probability of corrosion Pf

1
0.8

CCr = 0,075%

0.6

CCr = 0,06%
0.4

CCr = 0,09%
0.2

 =1,3

0
0

10

20

30

40

50

60

70

80

90

100

Time (year)

Figure 4.5 - The effect of the critical chloride concentration Ccr on the probability of
corrosion incident
4.2.2.4. Effect of chloride concentration on concrete surface CS
The effect of CS on Pf is shown in Figure 4.6, increasing CS causes Pf to increase. Since the
higher the CS, the greater the difference in chloride concentration between the surface and the
interior of the concrete that led to the chloride transport faster into the concrete, resulting in the
faster the chloride reaching the CCr concentration. CS concentration depends on time, quality of
concrete (w/c ratio, binder type) and type of contact environment. Corrosion start time of

concrete is about 25, 39 and 42 years, respectively, with CS = 0.36; 0.3 and 0.24%.
The probability of corrosion Pf

1
0.8

CS = 0,36%
CS = 0,3%

0.6
0.4

CS = 0,24%
0.2

 =1,3

0
0

10

20

30

40

50

60

70

80

90

100

Time (year)

Figure 4.6 - Effect of concrete surface chloride concentration CS on the probability of corrosion incident
4.2.2.5. Effect of age factor, n
The effect of n on P f is shown in Figure 4.7. The larger n represents, the greater
resistance of concrete to chloride penetration from the environment over time (the lower
the chloride ion diffusion coefficient of concrete over time). They lead to a decrease in P f
(increasing the life of the concrete structure). The dependent coefficient n depends mainly
on the type of binder and the environmental exposure conditions. Corrosion start time of
concrete is about 32, 42 and 56 years, respectively, with the coefficient n = 0.47; 0.5875
and 0.705.

19


The probability of corrosion Pf

1
0.8

n = 0,47
n = 0,5875

0.6
0.4

n = 0,705
0.2

 =1,3

0
0

20

40

60

80

100

Time (year)

Figure 4.7 - Effect of age factor n on the probability of corrosion failure
4.4. Conclusions of Chapter 4
Applying the calculation to predict the lifespan of the railway bridge deck structure using lightweight
reinforced concrete with parameters from the experiment and taken according to the recommendations of

some typical standards in the world, the results show that the service life of the bridge deck structure using the
lightweight reinforced concrete according to the corrosion initiation criterion is significantly reduced when the
pre-compressive stress increases. The change of protective concrete layer thickness has a great influence on
the lifespan of reinforced concrete structures.
- In the case of pre-compressed load; the law of changing the lifespan of the construction according to the
thickness of the protective concrete layer is quite similar; An increase in pre-compressive stress will require a
thicker protective concrete layer thickness.
- In case of direct compressive load; the rule of changing the lifespan of the structure according to the
thickness of the protective concrete layer depends on the state of pre-compressive stress in different stages.
When max = 0.3, the thickness of the protective concrete layer decreases, but when max = 0.5, the
thickness of the protective concrete layer increases and increases significantly when max = 0.7.
Through the application of probability theory when considering the process of chloride intrusion causing
corrosion of reinforcement to predict the lifespan of reinforced concrete structures using lightweight materials.
The life prediction model is designed based on the working principle in case the normal distribution of
resistance R and load S are selected in this study. Combining Monte - Carlo simulation with 4 input parameters:
chloride diffusion coefficient (D), equilibrium chloride concentration at the concrete surface (Cs), limiting
chloride concentration (Ccr) and protective concrete layer thickness (h) inferred the relationship between the
probability of corrosion incidents and concrete-related factors. From the research results, some conclusions are
drawn as follows:
- The thickness of the concrete protection layer (h) has the greatest influence on the probability of corrosion
incident (Pf), followed by the parameters n, Ccr, Cs and D.
- Under the penetration of chloride ions, in order to increase the quality of the concrete structure or increase
the life of the concrete structure, it is necessary to increase the values of the parameters n, Ccr and at the same
time reduce the parameters D and Cs to reduce the probability of corrosion incident Pf.
- The thickness of the protective concrete layer has an extremely important role under the
impact of the environment on reinforced concrete structures. Therefore, the thickness of the
protective concrete layer must be selected as reasonably as possible.

20

CONCLUSION AND RECOMMENDATION
1. Conclusion
The thesis has carried out the research contents related to the analysis of water permeability
and chloride ion permeability of some types of lightweight concrete used in construction with
consideration of compressive stress effects in concrete. The new contributions of the thesis are
summarized as follows:
1/ Experimental studies, analysis of water permeability through lightweight concrete under
the influence of loads for concrete C30. Research results show that when increasing the
compressive load, the water permeability of concrete increases significantly; especially after
in concrete there is a change in the void structure due to the action of pre-compression or
direct compression.
A water penetration test model that considers direct compressive load has been designed,
manufactured and tested based on recent world research results; This experimental equipment
has been improved to make the measurement process more convenient, especially the process
of controlling the load and recording data completely automatically.
The test results of water permeability measurement under the influence of pre-compression
load show that, when max > 0.5, marking a rapid increase of water permeability when water
pressure is greater than 10atm, this proves the influence of pre-compression stress is large
enough to increase water permeability of lightweight concrete, it is these residual mechanical
effects that facilitate water penetration thr
ough the concrete specimen, especially when max > 0.5 , the occurrence of concrete
destruction caused the increase in water permeability to increase more rapidly. Especially in the
experiment, we found that when max = 0.8 showed a huge difference in water permeability
in lightweight concrete.
The test results of water permeability measurement under the influence of direct compressive
load show that the water permeability of concrete is almost unchanged or changes slowly when
the relative stress value max < 0.5; After this threshold, the permeability coefficient starts to
increase rapidly. When the relative stress max ≥ 0.6, the water permeability increases very
quickly; This can be explained because the microstructure of concrete is destroyed after this

stress threshold - which is the threshold for the appearance of dispersed failure zones (according
to the approach of concrete failure mechanics) - causing increase the water permeability of
concrete. The law of increasing the water permeability of concrete after 28 days in this
experiment is similar to the law of increasing the water permeability of young concrete
published by Banthia & al (2005) when mechanical failure has not yet been appeared in
concrete.
2/ Experimental studies analyzing chloride ion permeability through lightweight concrete
under the influence of load for concrete C30, the research results show a significant influence
of compressive load on chloride ion permeability of lightweight concrete.
A chloride ion permeation test model considering direct compressive load has been designed,
fabricated and tested based on recent world research results; This test equipment has been
improved to make the measurement process more convenient, especially the process of
controlling the compressive load in concrete.
The results of chloride ion penetration test with lightweight concrete samples subjected to
pre-compression load show that, Chlorine ion permeability at load levels when /max = 0;
0.3; 0.5 of lightweight concrete C30 is low level and has a litter change than that of normal
concrete C30. The large change at grade 0.8P marks a rapid increase in the chloride ion
permeability of lightweight concrete C30 compared to normal concrete C30. This change has
a big difference because the compressive stress approaches the destructive value, the
21


structures in the concrete are broken into, allowing chloride ions to penetrate. This is in full
agreement with the rating scale of coercivity according to ASTM C1202 [24]. The reason for
lightweight concrete has an aggregate shell that may contain water or chlorine ions.
When compressed with a load of 0.8P, the clay particles are broken, losing their ability to
block chlorine ions, so that chlorine ions can quickly penetrate through the concrete. The clay
particles of lightweight concrete are filled with water to a state of water saturation in the
concrete, when the sample is saturated with water, seepage begins to occur. In contrast to normal
concrete, seepage occurs earlier because the aggregate is gravel, so it is impervious to water. In

addition, when adding fine mineral admixtures to the composition for lightweight concrete, the
effectiveness of chlorine ion waterproofing increases sharply.
The law of increasing the chloride ion permeability coefficient according to the precompression stress of lightweight concrete C30 is expressed by the following formula:
Exponential Regression: D/Do = 9.1226(/max)2 – 3.4256(/max) + 1.0816
The results of chloride ion permeability test with lightweight concrete samples subjected
to direct compressive loads show that the chloride ion permeability changes strongly when
there is the presence of simultaneous acting loads. However, before and after loading, the
chloride ion permeability is within the "average" level according to TCVN 9337-2012. When
the stress is increased to 30% and 50% of max, the permeability of concrete increases by
24.50% and 39.48%, respectively. When increasing the stress to 80% of max, the
permeability of concrete has a large increase. In the case of reduced chloride ion
permeability, it will lead to a longer time of chloride ion penetration through the protective
concrete layer to cause corrosion of reinforcement in reinforced concrete constructions.
From this result, it is shown that in prestressed concrete structure, when compressive stress
in concrete is within the appropriate limit, it can prolong the penetration time and increase
the service life due to chloride ion penetration.
The law of increasing the chloride ion permeability coefficient according to the precompression stress of lightweight concrete C30 is expressed by the following formula:
Exponential Regression: D/Do = 4.4975(max)2 – 1.9529(max) + 0.9543
3/ Determine the coefficient C to calculate the chloride ion diffusion coefficient from the
water permeability coefficient of the same type of concrete. From there, a formula for
calculating the relationship between water permeability coefficient and chloride diffusion
coefficient of concrete is proposed, taking into account the influence of stress in concrete C30
as follows:
Kw = 29.05 S0.5 D.
4/ The thesis has used the proposed model to calculate and predict the service life of
reinforced concrete structures using lightweight concrete in Vietnam conditions, taking into
account the influence of permanent load and operational load.
- The case of the pre-compressive stress state (operational load)
h=

2√D0 t1−m t m
0

σ 2
σ
Ccr
(9.1226 (
) − 3.4256 (
) + 1.0816) × erf −1 (
)
σmax
σmax
Cso t n

- The case of direct compressive stress states (permanent load)
h=

2√D0 t1−m t m
0

(4.4975 (

σ

2

σ
Ccr
) − 1.9529 (
) + 0.9543) × erf −1 (

)
σmax
σmax
Cso t n

In the case of pre-compressed load; the law of changing the lifespan of the construction
according to the thickness of the protective concrete layer is quite similar; an increase in precompressive stress will require a thicker protective concrete layer thickness.
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In the case of direct compression loads; the rule of changing the life of the structure
according to the thickness of the protective concrete layer depends on the state of pre compressive stress in different stages. When /max = 0.3, the thickness of the protective
concrete layer decreases, but when /max = 0.5, the thickness of the protective concrete
layer increases and increases significantly when /max = 0.7
In the model of predicting the life of reinforced concrete structures using lightweight
materials, the uncertainty of input parameters and Monter-Carlo simulation were taken into
account to calculate the probability of a corrosion occurring.
5/ Carrying out the calculation and prediction of the service life of the railway bridge deck
structure using lightweight reinforced concrete with parameters from the experiment and
taken according to the recommendations of some typical standards in the world, the results
showed that the service life of the bridge deck structure using the lightweight reinforced
concrete according to the corrosion initiation criterion was significantly reduced when the
pre-compressive stress increased. The change of protective concrete layer thickness has a
great influence on the lifespan of reinforced concrete structures.
6/ Applying the calculation to predict the service life of the lightweight aggregate concrete
slab structure of the railway bridge deck with the probabilistic model gives some conclusions:
- The thickness of the concrete protection layer (h) has the greatest influence on the
probability of corrosion incident Pf, followed by the parameters n, Ccr, Cs and D.
- Under the penetration of chloride ions, in order to increase the quality of the concrete
structure or increase the life of the concrete structure, it is necessary to increase the values of

the parameters n, Ccr and at the same time reduce the parameters D and Cs to reduce the
probability of corrosion incident Pf.
- The thickness of the protective concrete layer has an extremely important role under the
impact of the environment on reinforced concrete structures. Therefore, the thickness of the
protective concrete layer must be selected as reasonably as possible.
2. Recommendations for future research
Future research directions are expected as follows:
- Studying the accumulation of chloride ions on the lightweight concrete surface of
different types of concrete for different regions of Vietnam.
- Studied random characteristics of diffusion and corrosion processes.
- Studying the simultaneous effects of many factors such as: mechanical, physical,
chemical, and thermal.
- Study of water permeability and chloride permeability for lightweight concrete structures
subjected to flexion and tension simultaneously.

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