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Influence of conductivity on cathodic protection of reinforced alkali-activated slag mortar using the finite element method

2009, Corrosion Science

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 2858 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 2860 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. 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