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Numerical determination of the chloride Numerical determination of the chloride diffusion coefficient in cracks and cracked diffusion coefficient in cracks and cracked
0 10 20 30 40 50 600.0
0.2
0.4
0.6
0.8
1.0
D=0.5 cm2/day
C(x,t)/Cs
Depth (mm)
Time=100 days
Time=300 days
Time=800 days
L. C. WANG
20112011--22--2323 11
diffusion coefficient in cracks and cracked diffusion coefficient in cracks and cracked concreteconcrete
Licheng WANG Dr.
Dalian University of Technology, Dalian China
Contents
�� 1.1. Research backgroundResearch background
�� 2. Basic models2. Basic models
2.1 Mesocopic structure of concrete2.1 Mesocopic structure of concrete
L. C. WANG
20112011--22--2323 22
2.2 Truss network model2.2 Truss network model
�� 3. Method to determine the diffusion coefficient in 3. Method to determine the diffusion coefficient in
crackscracks
�� 4. 4. Chloride ions diffusion in cracked concreteChloride ions diffusion in cracked concrete
�� 5. Coclusions5. Coclusions
1. Research background
L. C. WANG
� Cracks can increase the penetration of chlorides in concrete.
� The effect of cracking depends on the crack width.
20112011--22--2323 33
Mechanical action Frost attack
1. Research background
L. C. WANG
�Many works have been done to investigate the transport
properties of cracked concrete and the penetration speed of
chloride ions in an individual crack.
20112011--22--2323 44
Kato, E., Kato, Y. and Uomoto, T. J. Adv.
Concr. Tech., 2005, 3(1): 85-94.Takewaka, K., Yamaguchi, T. J. Adv.
Concr. Tech., 2003, 1(2): 139-146.
Olga G.R. and Doug Hooton, R., ACI Mater. J, 2003, 100(2): 120-126.
L. C. WANG
20112011--22--2323 55
Chloride solution
Ismail M., Toumi A., Francois R., Cem. Concr. Res., 2004, 34(4): 711-716
2. Basic models
Macro scale Meso scale
Real stru
cture
Analytic
al m
odel
Three-phase composite
2.1 Mesoscopic structure of concrete
L. C. WANG
20112011--22--2323 66
Homogeneous
material
Heterogeneous
material
Real stru
cture
Analytic
al m
odel
= Mortar + Coarse Aggregate
+Interface
2.2 Truss network model
Two types of truss element for
chloride ions transportation:
Truss element inside Voronoi
element
Truss element on boundary
Voronoi
element
L. C. WANG
20112011--22--2323 77Formation of the truss network
Truss element on boundary
For chloride transport through the area A
can be represented by a 1-D line element.
ACl-
2
L
C2
∂∂
=∂ C
DC
Fick’s second law:
2.2 Truss network model
Governing equation
L. C. WANG
20112011--22--2323 88
C1
1
∂∂
=∂ x
Dxt
=
−
−+
∂∂
∂∂
+
−
−
0
0
21
12
6
1
11
11
22
11
2
1
2
1
CC
CCA
tC
tCAL
C
C
L
AD
ψ
Dispersed with the Gallerkin
method as
Before cracking
Role of cracks on the diffusion of chloride ions and its realization
L. C. WANG
The objective of our
study is to determine
20112011--22--2323 99
After cracking
cracks
study is to determine
the penetration rate of
chlorides in a single
crack.
3. Method of determination of Dcr
L. C. WANG
3.1 Cracks induced by mechanical loading
Chloride solution
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Ismail M., Toumi A., Francois R. and Gagne R., ‘Effect of crack opening on the local diffusion of chloride in inert materials’, Cem. Concr. Res., 2004, 34(4):
711-716
L. C. WANG
Chloride solution
Diffusion coefficient of the crack Dcr is 2.032×10-9m2/s .
20112011--22--2323 1111
Perpendicular to the crack
surface
Determination of Dcr at different crack widths
wcr=128µµµµm wcr=60µµµµm wcr=53µµµµm
L. C. WANG
20112011--22--2323 1212
wcr=34µµµµm wcr=21µµµµm
Dcr=10000mm2/h
when wcr≥≥≥≥ 60µµµµm and
Dcr=3000mm2/h
when wcr < 60µµµµm.
Exposed surfaceExposed surface
L. C. WANG
4. Chloride ions diffusion in cracked concrete
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a) Photo scan of the test specimen b) Numerical analysis results
c) Profile from exposed surface
L. C. WANG
40mm
Chloride penetration in cracked samples
20112011--22--2323 1414
Olga G.R. and Doug Hooton, R., ACI Mater. J, 2003, 100(2): 120-126.
50mm
Test sampleNumerical model
Crack width wcr=90 µµµµm
3. Chloride ions diffusion in cracked concrete
L. C. WANG
20112011--22--2323 1515
Profiles vertical to the exposed
surface and lateral to the crack wall
Exposed surface
Exposed surface
L. C. WANG
Comparison between test findings and analytical results
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Photo scan of the test specimen, dark
curves meaning the diffusion depthThis study
Ishida, et al. Cem. Concr. Res., 2009,
39(10): 913-923.
50mm
Tapered crack on chloride diffusion
L. C. WANG
20112011--22--2323 1717
Exposed surfacewcr=0.2mm
50mm
1. A mesoscopic simulation method, the truss network model, is
successively applied to the chloride transport analysis on cracked
concrete;
5. Conclusions
L. C. WANG
20112011--22--2323 1818
2. The diffusion coefficient of chlorides in cracks with different sizes is
determined.
