Corrosion Science 51 (2009) 2857–2862
Contents lists available at ScienceDirect
Corrosion Science
journal homepage: www.elsevier.com/locate/corsci
Influence of conductivity on cathodic protection of reinforced alkali-activated
slag mortar using the finite element method
R. Montoya a, W. Aperador b, D.M. Bastidas c,*
a
Mathematics Department, Chemistry Faculty, National Autonomous University of Mexico, UNAM, University City, 04510 Mexico, DF, Mexico
Composite Materials Group, Universidad del Valle, Cali, Colombia
c
CENIM-National Centre for Metallurgical Research, CSIC, Avda. Gregorio del Amo 8, 28040 Madrid, Spain
b
a r t i c l e
i n f o
Article history:
Received 27 May 2009
Accepted 1 August 2009
Available online 11 August 2009
Keywords:
A. Steel reinforced concrete
B. Modelling studies
C. Cathodic protection
a b s t r a c t
Cathodic protection (CP) is considered to be the only rehabilitation method for chloride-induced rebar
corrosion in reinforced concrete structures. The protection current distribution depends on several
parameters, such as the geometry and number of rebars and the concrete resistivity. In order to investigate the influence of concrete resistivity on the possibilities and limitations of rebar protection, this paper
presents a numerical approach based on the finite element method (FEM) in conjunction with laboratory
results to determine its impact on the CP of alkali-activated slag mortar. An ordinary Portland cement
was also tested for comparative purposes.
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Cathodic protection (CP) as a rehabilitation method has proven
to stop corrosion in salt-contaminated bridge decks, regardless of
whether or not the concrete contains chlorides [1]. CP extends
the service life of buried steel pipelines, oil and gas well casings,
offshore oil-drilling structures, seagoing ship hulls, marine piles,
water tanks and chemical equipment. The concept behind CP consists of shifting the electrode potential of a metal to a more negative value where the corrosion rate is sufficiently low to suppress
the anodic reaction [2]:
Fe ! Fe2þ þ 2e
ð1Þ
and the cathodic reaction is enhanced:
O2 þ 2H2 O þ 4e ! 4OH
ð2Þ
2Hþ þ 2e ! H2
ð3Þ
thus decreasing the overall corrosion current. Oxygen reduction (Eq.
(2)) is the main cathodic reaction in concrete, because concrete has
a high pH and oxygen is thermodynamically a far more powerful
electron acceptor than the hydrogen ion (Eq. (3)). The direct current
(DC) for CP systems can be supplied either via mains power in
impressed current CP systems (ICCP) or by a sacrificial anode CP
system (SACP). In a SACP device, single or multiple anodes
distribute the cathodic current to the protected structure. For buried structures the anodes are often inert graphite. For immersed
* Corresponding author. Tel.: +34 91 553 8900; fax: +34 91 534 7425.
E-mail address: david.bastidas@cenim.csic.es (D.M. Bastidas).
0010-938X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.corsci.2009.08.020
seawater structures they may be high-silicon cast iron or platinum-coated titanium. Magnesium, zinc, aluminium, and aluminium–zinc–indium alloy sacrificial anodes, welded to buried and
immersed structures, provide long-term CP.
The very high temperatures (1400–1500 °C) required to manufacture ordinary Portland cement (OPC) account for the high cost of
this process, which is responsible for 40% of all energy consumed.
Indeed, the cement industry is regarded to generate 6–7% of all
greenhouse gases emitted world-wide [3]. Thus, granulated blast
furnace slag (GBFS) may represent an option for emission mitigation. An alkali-activated cement is a system in which an alkaline
activator promotes the pozzolanic reactions on an inorganic solid
of natural or artificial origin to generate a material with cementitious characteristics. One such material is alkali-activated slag
(AAS) cement, which is the result of mixing GBFS and alkaline substances [4].
The aim of this paper is to assess the effectiveness of CP of reinforced AAS and OPC mortars with different conductivities using a
numerical approach based on the finite element method (FEM). A
two-dimensional simulation of the potential distribution was
developed and its accuracy was verified by laboratory results using
the criterion of measured polarized potential values between
0.85 and 1.0 V vs. a copper/copper sulphate electrode (Cu/
CuSO4) (CSE) [5].
2. Numerical method
Numerical methods, such as the finite difference method (FDM),
boundary element method (BEM) and FEM, have been used to
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R. Montoya et al. / Corrosion Science 51 (2009) 2857–2862
design CP and electrochemical systems [6]. These methods have
been adapted to calculate the current and potential distributions
in complex structures. FDM was one of the first methods developed
and presents the disadvantage of its instability in complex geometry systems. This limitation is partially solved using the FEM technique. Numerical methods require the discretization of a large
volume domain, generating a great number of equations, but
may be simply applied in the case of inhomogeneous domains.
They were also initially used to predict steel corrosion behaviour
addressing coplanar electrode configurations with varying degrees
of polarization effects, generally limited to a one-dimensional
approach.
In all of these numerical treatments the governing field equations are the Poisson and Laplace equations:
jD/ ¼ j
!
@2/ @2/ @2/
¼ f ðx; y; zÞ
þ
þ
@x2 @y2 @z2
ð4Þ
with the additional assumption that the electrolytic medium and
electrode materials possessed constant electrical properties, where,
in Eq. (4), f ðx; y; zÞ ¼ 0 for Laplace’s equation; f ðx; y; zÞ – 0 for
Poisson’s equation [7]; D is Laplace’s operator; j is conductivity;
and / is the electrical potential. The BEM and FEM techniques have
been used for numerical modelling of galvanic corrosion and CP
[8–14], and improved using the penalty function method (PFM)
and a multipeaked cost function (MCF), which was coupled with a
genetic algorithm method (GAM) combined with the conjugate
gradient method (CGM) [15]. Pipelines have also been CP modelled
by coupling the FEM and BEM techniques and including non-negligible ohmic voltage drops (IR) [16]. CP of coated pipelines with bare
metal surfaces has been modelled using the BEM technique coupled
with an iterative Newton–Raphson algorithm [17,18].
2.1. The two-dimensional boundary value problem
Considering the physical situation shown in Fig. 1a, a twodimensional square container with a reinforced cylindrical mortar
specimen and an AISI 304 stainless steel (SS) anode has been developed. The corresponding boundary value problem is:
jD/ ¼ f ðx; yÞ
ð5Þ
with (x, y) coordinates in the X domain, which is the union of X1
and X2 domains (see Fig. 1a), i.e. the steel/mortar system within
one domain (X1) and the electrolyte (NaCl) within the other domain
(X2), where j and / have been defined above; and f ðx; yÞ is the
ICCP externally applied to the steel rebar/mortar system through
the AISI 304 SS anode.
The boundary conditions are: j @/
¼ 0 in C1 (container) and
@n
¼
hð/Þ
in
C
(rebar)
(see
Fig.
1a),
where
n is the external vecj @/
2
@n
tor normal to the boundary; and hð/Þ is the function that represents the polarization curve of the steel rebar immersed in 3.5%
NaCl electrolyte. Its variational formulation was carried out in
the same way as in Ref. [13], but in the present study the polarization curve was used directly, instead of the Butler–Volmer equation, in C2 (rebar) (see Fig. 1a). The X domain was discretized
into 925 elements and the Gauss–Seidel method was employed
to solve the system thus established. The mathematical function
used to approximate the AISI 304 SS anode was:
n
o
f ðx; yÞ ¼ r exp s ðx x0 Þ2 s ðy y0 Þ2
ð6Þ
where f ðx; yÞ is the externally applied ICCP (as indicated above); r is
a factor involving the impressed current applied; s is a factor proportional to the diameter of the AISI 304 SS anode; and x0 and y0 are
the rectangular coordinates of the AISI 304 SS electrode (see Fig. 1a).
3. Experimental
GBFS from the company ‘‘Acerías Paz del Rio”, located in Boyacá,
Colombia, was used with a chemical composition (% by weight) of
33.7 SiO2, 12.8 Al2O3, 3.09 Fe2O3, 45.4 CaO, 0.5 TiO2, 0.64 SO3, 1.79
MgO, and 2.08 ignition loss; a specific surface area of 398 m2 kg1;
and a specific gravity of 2860 kg m3. The basicity index (CaO +
MgO)/(SiO2 + Al2O3) and quality index (CaO + MgO + Al2O3)/
(SiO2 + TiO2) were 1.01 and 1.73, respectively. According to ASTM
C 989-99 this is grade 80 slag [19]. The waterglass used as the activating solution consisted of a mix of commercial sodium silicate
(31.7% SiO2, 12.3% Na2O, and 56.0% water) and a 50% NaOH solution to obtain a SiO2/Na2O ratio of 2.4. The Na2O concentration in
the waterglass activating solution added to the mortar was 5% by
weight of slag. The aggregates used were a siliceous gravel with
a maximum grain size of 19 mm, specific gravity of 2940 kg m3,
and 1.3% absorption. OPC according to ASTM C 150-02 was also
tested for comparative purposes [20], with a specific gravity of
2990 kg m3 and a specific surface area of 400 kg m3. AAS and
OPC mortars were prepared with a water/cement ratio of 0.4.
The AAS and OPC specimens were de-moulded after 24 h and cured
in a climatic cabinet for 28 days, at 90% relative humidity (RH) for
AAS specimens and at 100% RH for OPC specimens to prevent
leaching of the activating solutions and to assure that the hydration reaction and product formation processes were not affected.
Structural 1018 steel rebars of 6.35 mm diameter were used
according to ASTM A 706-08 [21]. Reinforced cylindrical mortar
specimens (10 cm length and 5 cm diameter) were used to perform
the experimental tests. An active surface area of 10 cm2 was
marked on the working electrode with an epoxy resin, thus isolating the triple mortar/carbon steel/atmosphere interface to avoid
possible localized corrosion attack due to differential aeration.
Carbonation exposure was performed by accelerated testing in
a cabinet with 3% CO2, 65% RH, and 25 °C (mortars AASA and OPCA)
and exposure in a laboratory environment (Universidad del Valle,
Cali, Colombia) with 0.03% CO2, 65% RH, and 25 °C (mortars AASL
and OPCL).
Polarization measurements were performed up to 49 days by
immersing the reinforced mortar specimens in a 3.5% NaCl electrolyte using a CSE reference electrode.
Fig. 1a shows the device used to perform CP, consisting of a
13 13 cm two-dimensional square plastic container with a reinforced cylindrical mortar specimen in the centre and an AISI 304 SS
anode of 9 mm diameter situated at the point at x0 = 12.5 cm and
y0 = 12.5 cm. Fig. 1b shows a scheme with the container/reinforced
mortar/AISI 304 SS anode system and the externally ICCP source
used for CP application. Table 1 lists the parameters used for the
numerical simulation.
4. Results and discussion
Figs. 2–5 show the calculated isopotential line and potential
distributions (top views in Figs. 2a, 3a, 4a, and 5a and side views
in Figs. 2b, 3b, 4b, and 5b) for reinforced AASA (Fig. 2), OPCA
(Fig. 3), AASL (Fig. 4), and OPCL (Fig. 5) using a 2-dimensional
numerical simulation.
The potential variation between isopotential lines was 0.1 V vs.
CSE for OPCL (Fig. 5a) and 0.2 V vs. CSE for AASA (Fig. 2a), OPCA
(Fig. 3a) and AASL (Fig. 4a).
The white circle (in the middle position) in Figs. 2a, 3a, 4a, and
5a indicates the position of the rebar, and the cone with the red
vertex in Figs. 2b, 3b, 4b, and 5b (initiation of cone in the latter)
indicates the potential value of the rebar.
Table 2 summarizes the rebar protection potential obtained
using the 2-dimensional numerical simulation, and Table 3
R. Montoya et al. / Corrosion Science 51 (2009) 2857–2862
2859
Fig. 1. (a) Schematic representation of the experimental design used for cathodic protection (CP) numerical simulation. C1 (j @/
¼ 0) and C2 (j @/
¼ hð/Þ) are the
@n
@n
boundaries of the structural 1018 steel rebar and square plastic container, respectively. The X1 and X2 domains refer to the NaCl conductivity and cylindrical reinforced
mortar conductivity, respectively. (b) Scheme with the container/reinforced mortar/AISI 304 SS anode system and the externally impressed current cathodic protection (ICCP)
source.
Table 1
Impressed current cathodic protection (ICCP) design parameters for reinforced alkaliactivated slag mortar in accelerated carbonation conditions (AASA), reinforced
ordinary Portland cement mortar in accelerated carbonation conditions (OPCA),
reinforced alkali-activated slag mortar in laboratory conditions (AASL), and reinforced
ordinary Portland cement mortar in laboratory conditions (OPCL).
Parameter
Description
AASA mortar
Average conductivity of AASA mortar
Average conductivity of 3.5% NaCl electrolyte
Anode axis location (x0, y0)
Impressed current cathodic protection (ICCP)
0.019 mS cm1
86.3 mS cm1
x0 = 12.5 cm; y0 = 12.5 cm
55 106 A cm2
OPCA mortar
Average conductivity of OPCA mortar
Average conductivity of 3.5% NaCl electrolyte
Anode axis location (x0, y0)
Impressed current cathodic protection (ICCP)
0.042 mS cm1
86.3 mS cm1
x0 = 12.5 cm; y0 = 12.5 cm
55 106 A cm2
AASL mortar
Average conductivity of AASL mortar
Average conductivity of 3.5% NaCl electrolyte
Anode axis location (x0, y0)
Impressed current cathodic protection (ICCP)
0.086 mS cm1
86.3 mS cm1
x0 = 12.5 cm; y0 = 12.5 cm
55 106 A cm2
OPCL mortar
Average conductivity of OPCL mortar
Average conductivity of 3.5% NaCl electrolyte
Anode axis location (x0, y0)
Impressed current cathodic protection (ICCP)
0.23 mS cm1
86.3 mS cm1
x0 = 12.5 cm; y0 = 12.5 cm
55 106 A cm2
includes the laboratory results of the rebar protection potential
measured after 49 days experimentation.
It was assumed that the 1018 steel rebar was cathodically protected according to the criterion of the measurement of polarized
potential values between 0.85 and 1.0 V vs. CSE [5]. The quantitative results of Fig. 2 for AASA mortar show that the
55 106 A cm2 externally applied ICCP originated an electrical
potential of 1.980 V vs. CSE (see Table 2). Nevertheless, an overprotection was reached which was visualized by the red colour in
Fig. 2. So the steel rebar may be cathodically protected using a lower external ICCP than the 55 106 A cm2 used.
In contrast to AASA, which has the lowest conductivity
(0.019 mS cm1), OPCL with the highest conductivity (0.23 mS
cm1) and whose quantitative results are shown in Fig. 5, represents the opposite case. On OPCL the externally applied ICCP,
55 106 A cm2, caused a shift in the electrical potential to
0.510 V vs. CSE (see Table 2), which means that the externally applied ICCP was not enough to protect the specimen and the steel
rebar was actively corroding, as visualized by the red colour in
Fig. 5. Thus, one order of conductivity, 0.019 mS cm1 for AASA
and 0.23 mS cm1 for OPCL, caused a difference of more than
1.4 V in the electrical potential. In the latter example (Fig. 5) the
ICCP required to protect the steel rebar was higher than the
55 106 A cm2 utilized. Comparing the results of Fig. 2 with
Fig. 5, the use of AASA was more attractive than OPCL from a CP
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R. Montoya et al. / Corrosion Science 51 (2009) 2857–2862
Fig. 2. (a) Calculated isopotential lines distribution using rectangular (x0, y0)
coordinates for reinforced AASA mortar. The polarized potential variation between
units was 0.2 V. (b) A 3-D view of the calculated potential distribution for reinforced
AASA mortar. The anode was in the position of x0 = 12.5 cm, y0 = 12.5 cm.
point of view because the former required a lower ICCP than the
latter.
Fig. 3 for OPCA and Fig. 4 for AASL show an intermediate situation between AASA (Fig. 2) and OPCL (Fig. 5). On OPCA and AASL
the externally applied ICCP (55 106 A cm2) originated an electrical potential of approximately 1.0 V vs. CSE (see Table 2),
which means that the CP of the steel rebar was effective, according
to the criterion of measured polarized potential values between
0.85 and 1.0 V vs. SCE.
Therefore, conductivity differences of one order of magnitude
between AASA (0.019 mS cm1) and OPCL (0.23 mS cm1) drastically influence the CP design of the steel/mortar system. OPCA
and
AASL
(conductivity
(conductivity
0.042 mS cm1)
1
0.086 mS cm ) were well cathodically protected (see Figs. 3 and
4). These results are of practical importance because they are a
good example of using CP engineering to save energy when protecting reinforced concrete structures. Numerical simulations
based on FEM calculations allow CP performance to be assessed
using conductivity as a variable in the numerical simulation. It
should be noted that the j parameter (conductivity) that appears
in Eq. (5) considers the use of X1 and X2 domains to model the
CP of the steel rebar/mortar system using the FEM technique,
which shows the great flexibility of this method in the X domain
conditions.
Comparing the rebar protection electrical potential calculated
using the numerical simulation (Table 2) with laboratory results
of the rebar protection electrical potential measured after 49 days
experimentation (Table 3), it may be indicated that the numerical
simulation approach utilised in the present paper is a good tool for
reinforced mortar CP design. Nevertheless, the discrepancy between the protection electrical potential yielded using the numerical method and the electrical potential measured in the laboratory
Fig. 3. (a) Calculated isopotential lines distribution using rectangular (x0, y0)
coordinates for reinforced OPCA mortar. The polarized potential variation between
units was 0.2 V. (b) A 3-D view of the calculated potential distribution for reinforced
OPCA mortar. The anode was in the position of x0 = 12.5 cm, y0 = 12.5 cm.
Fig. 4. (a) Calculated isopotential lines distribution using rectangular (x0, y0)
coordinates for reinforced AASL mortar. The polarized potential variation between
units was 0.2 V. (b) A 3-D view of the calculated potential distribution for reinforced
AASL mortar. The anode was in the position of x0 = 12.5 cm, y0 = 12.5 cm.
R. Montoya et al. / Corrosion Science 51 (2009) 2857–2862
2861
the required impressed current density, from low to high, was: AASA < OPCA < AASL < OPCL. This result is of practical importance because it is a good example of using CP engineering to save energy
when protecting reinforced concrete structures, and as expected
corroborates Ohm’s law. Numerical methods based on FEM calculation allow CP performance to be assessed using the conductivity
parameter. From a CP point of view, the carbonation process has a
positive influence on the conductivity parameter, favouring CP
design.
The accuracy of the proposed numerical results was assessed by
comparisons with laboratory results measured after 49 days experimentation. The simulation approach was a good procedure for the
design of AASL and OPCA CP with intermediate conductivity values
of the order of 0.06 mS cm1. However, the discrepancy between
the numerical method and the laboratory results for AASA and
OPCL, with low (0.02 mS cm1) and high (0.23 mS cm1) conductivities, respectively, may be attributed to the ‘‘ideal” and simple
situation simulated, considering conductivity as the only variable.
Acknowledgements
R. Montoya expresses his gratitude to the Subdivision of Academic Formation and the DGAPA of UNAM, Mexico, and CSIC,
Spain, for the scholarship granted to him. W. Aperador expresses
his gratitude to the Centre of Excellence in Novel Materials (CENM)
and COLCIENCIAS of Colombia, Project Geoconcret, for the scholarship granted to him. The authors express their gratitude to Project
BIA2008-05398 from CICYT, Spain, for financial support.
Fig. 5. (a) Calculated isopotential lines distribution using rectangular (x0, y0)
coordinates for reinforced OPCL mortar. The polarized potential variation between
units was 0.1 V. (b) A 3-D view of the calculated potential distribution for reinforced
OPCL mortar. The anode was in the position of x0 = 12.5 cm, y0 = 12.5 cm.
Table 2
Rebar protection electrical potential obtained using the numerical simulation.
Mortar
Potential, V vs. CSE
AASA
OPCA
AASL
OPCL
1.980
0.970
0.980
0.510
Table 3
Laboratory results of the rebar protection electrical potential measured after 49 days
experimentation.
Mortar
Potential, V vs. CSE
AASA
OPCA
AASL
OPCL
0.892
0.943
0.952
0.897
results for AASA and OPCL (with the lowest and highest conductivity, respectively) may be attributed to the ‘‘ideal” situation simulated numerically, i.e. the number of rebars, their geometry, and
the corroding and passive zones, etc. The presence of pores and
irregularities in the mortar was not considered.
5. Conclusions
AASA mortar presents the best conductivity properties for CP
engineering design. OPCL, with a conductivity that is one order of
magnitude higher than AASA, requires a high externally impressed
current cathodic protection. The order of the mortars in terms of
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