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Polarization of galvanic point anodes for corrosion prevention in reinforced concrete
h [electronic resource] /
by Margareth Dugarte.
[Tampa, Fla] :
b University of South Florida,
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Dissertation (Ph.D.)--University of South Florida, 2010.
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ABSTRACT: The polarization performance of two types of commercial galvanic point anodes for protection of reinforced steel around patch repairs was investigated. Experiments included measurement of the polarization history of the anode under constant current impressed by galvanostatic circuits and in reinforced concrete slabs. The tests revealed, for both types of anodes, a potential-current function (PF) indicating relatively little anodic polarization from an open circuit potential at low current levels, followed by an abrupt increase in potential as the current approached an apparent terminal value. Aging of the anodes was manifested by a continually decreasing current output in the concrete tests, and by increasingly more positive potentials in the galvanostatic tests. Those changes reflected an evolution of the PF generally toward more positive open circuit potentials and, more importantly, to the onset of elevated polarized potentials at increasingly lower current levels. There was considerable variability among the performance of replicate units of a given anode type. Modest to poor steel polarization levels were achieved in the test yard slabs. Modeling of a generic patch configuration was implemented with a one-dimensional approximation. The model calculated the throwing distance that could be achieved by a given number of anodes per unit perimeter of the patch, concrete thickness, concrete resistivity, amount of steel and amount of polarization needed for cathodic prevention. The model projections and aging information suggest that anode performance in likely application scenarios may seriously degrade after only a few years of operation, even if a relatively optimistic 100 mV corrosion prevention criterion were assumed. Less conservative criteria have been proposed in the literature but are yet to be substantiated. Other investigations suggest a significantly more conservative corrosion prevention may apply instead. The latter case would question the ability of the point anodes to provide adequate corrosion prevention.
Advisor: Alberto A. Sags, Ph.D
x Civil & Environmental Engineering
t USF Electronic Theses and Dissertations.
Polarization of Galvanic Point Anodes for Corrosion Prevention in Reinforced Concrete by Margareth Dugarte A dissertation submitted in partial fulfillment of the requirement s for the degree of Doctor of Philosophy Department of Civil and En vironmental Engineering College of Engineering University of South Florida Major Professor: Alber to A. Sags, Ph.D. Rajan Sen, Ph.D. Andrs Tejada-Martinez, Ph.D. Matthias Batzill, Ph.D. Venkat Bhethanabotla, Ph.D. Date of Approval: April 2, 2010 Keywords: zinc, cathodic protection, patch repair, reinforcing steel, potential Copyright 2010 Margareth Dugarte
ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Alberto Sags, whose guidance, supervision and support from the early stages to the c oncluding level of this project, allowed me to finish this disse rtation. Appreciation is given to my examining committee chairperso n Dr. Alex Volinsky and me mbers, Dr. R. Sen, A. Tejada-Martinez, M. Batzill, and V. Bhethanabotla for their interest. The author appreciates the financial s upport provided from the Florida Department of Transportation and the U.S. Department of Transportation for the research discussed in this dissertation. I wish to thank my colleagues fr om Corrosion Laboratory at USF, Kingsley Lau, Ezeddin Busba, Andrea S anchez, Adrienne Accardi, Mersedeh Akhoondan and Brandon Berke, they all a ssisted and encouraged me in various ways during my permanency in the l aboratory. The author thanks Maria Constanza Suarez and Gary Spicer for their collaboration in the experimental phase of the project. Finally, I would like to thank my husband, Ulises Orozco, who provided support throughout this dissertation process, as well as confidence and love. My parents, Daniel Dugarte and Yaneth Coll an d my sisters, Elisama, Yamile and Mercelena, for their love, support, and pat ience over the last 5 years. This dissertation is dedicated to them.
i TABLE OF CONTENTS LIST OF TABLES .................................................................................................iii LIST OF FI GURES...............................................................................................iv ABSTRACT .........................................................................................................vii 1. INTRO DUCTION..............................................................................................1 1.1 Backg round...............................................................................................1 1.2 Literature Revi ew......................................................................................2 1.2.1 Corrosion of St eel in C oncrete...........................................................2 1.2.2 Cathodic Protection and Cathodic Pr eventio n....................................4 1.2.3 Corrosion Macrocells and Effect of Pa tch Repai rs.............................6 1.2.4 Anodes for Controlling Corro sion Around Patc h Repair s...................7 1.2.5 Open Issues to be Addre ssed............................................................8 1.3 Object ives.................................................................................................9 1.3.1 Regarding Durabili ty..........................................................................9 1.3.2 Regarding E ffectivenes s....................................................................9 2. INVESTIGATION METHODOLOGY...............................................................10 2.1 Appr oach.................................................................................................10 2.1.1 Laboratory Experiment s...................................................................10 2.1.2 Mode ling..........................................................................................10 2.2 Products Selected for Evaluat ion............................................................11 2.3 General Aspects of the Anode Evaluation Approac h..............................15 2.4 Anodes in Galvanostatic Regime in Concre te.........................................18 2.4.1 Materials and Preparat ion................................................................18 2.4.2 Test C onditi ons................................................................................19 2.4.3 Data Measurement for Performance Ev aluatio n..............................20 2.5 Anodes Coupled to Reinfo rcing Steel in Concre te..................................21 2.5.1 Materials and Preparat ion................................................................22 2.5.2 Test C onditi ons................................................................................22 2.5.3 Data M easurement s.........................................................................24 220.127.116.11 Concrete Resistiv ity.................................................................25 18.104.22.168 Anode to R ebar Resist ance.....................................................26 22.214.171.124 Steel D epolariza tion................................................................26 126.96.36.199 Slow Anode Cyc lic Polari zation ...............................................26 2.5.4 Corrections and Adjustm ents...........................................................27 188.8.131.52 Potential and Current -Temperature Co rrections.....................27 184.108.40.206 Resistivity Â–Tem perature Corre ctions ......................................31
ii 3. RESULT S.......................................................................................................32 3.1 Results, Anodes in Galvanos tatic Regime in Concrete...........................32 3.2 Results, Anodes Coupled to Re inforcing Steel in Concrete....................36 3.2.1 Anode Pola rizati on...........................................................................36 3.2.2 Rebar Po larizati on...........................................................................50 3.2.3 Concrete Resistiv ity and Anode Re sistanc e....................................62 4. DISCUS SION.................................................................................................64 4.1 Anode Potential-Current Functions (PFs)................................................64 4.2 Rebar Pola rization...................................................................................71 5. MODELI NG....................................................................................................73 5.1 Introdu ction.............................................................................................73 5.2 Anode Rebar S ystem Mode led.............................................................74 5.3 Principles and Assump tions ....................................................................75 5.4 Implementation of the Model ...................................................................77 5.4.1 Model Inputs....................................................................................77 220.127.116.11 Overall Dimensions and Global Concrete Properties..............77 18.104.22.168 Local Resistan ce.....................................................................78 22.214.171.124 Polarization Function Â– Steel...................................................79 126.96.36.199 Polarization F unction A node (PF) ..........................................81 5.4.2 Implementation of the Mode l Computational Procedure................82 5.4.3 Model Appl ication Scope .................................................................83 5.4.4 Sensitivit y Analys is..........................................................................83 5.4.5 Model Va lidatio n..............................................................................88 5.5 Model Re sults.........................................................................................88 5.6 Model Di scussio n....................................................................................95 CONCLUSION S...............................................................................................101 REFERENC ES.................................................................................................105 APPENDICESÂ…Â…Â…Â…Â…Â…Â…......... .................. .................. .................. ............ 112 Appendix A: Computation of Polarization Distribution in a Reinforcing Steel Member Â– Model Validatio n...............................................................113 ABOUT THE AUTH OR............................................................................End Page
iii LIST OF TABLES Table 1 Materials and test cond itions for anodes in galvanostatic regime in c oncrete..............................................................................20 Table 2 Nomenclature of mo del variables and parameters.............................85 Table 3 PF, steel and other par ameters for model cases................................87 Table 4 General model paramet ers for calculat ed cases................................87 Table 5 Effect of current demand by the pat ch zone.......................................97 Table 6 Model output and expe rimental data for C anodes at ages 4 and 13 months ......................................................................118 Table 7 Model output and experi mental data for W anodes at ages 4 and 13 months ......................................................................119 Table 8 Deviations between model output and experim ental data................122
iv LIST OF FIGURES Figure 1 External appearance of anode types (C on top, W on bottom).....12 Figure 2 Ty pe C anode spec imens..............................................................13 Figure 3 Ty pe W anode spec imens.............................................................14 Figure 4 Idealized potential-current diagram of the evaluation approach....15 Figure 5 Anode test arrangement (sketc h)..................................................19 Figure 6 The 95% RH test chamber ............................................................19 Figure 7 Yard slab test c onfiguration showing 1st and 2nd set anode positions ........................................................................................23 Figure 8 Installed yard slab with c onnection box .........................................24 Figure 9 EIO evolution for both test m edia and anode types exposed in the 95% RH c hamber. ...................................................................34 Figure 10 EIO evolution for both test m edia and anode types exposed in the 60% RH c hamber....................................................................35 Figure 11 Anode current evolution wit h time for both sets of anodes............38 Figure 12 Anode potential (Instant -Off) evolution with time for both sets of anodes ......................................................................................39 Figure 13 Auxiliary anode potential evolution wit h time for both sets of anodes.......................................................................................... 41 Figure 14 Anode current as function of integrated anodic charge delivered for both se ts of anodes ..................................................42 Figure 15 Anode Potential as function of integrated anodic charge delivered for both se ts of anodes ..................................................43 Figure 16 PotentialCurrent trajectory for 1st set of anodes in test yard slabs..............................................................................................45 Figure 17 Potential-Cu rrent trajectory for 2nd se t of anodes in test yard slabs..............................................................................................46 Figure 18 EIO-log I curves of the 1st set of C anodes in test yard slabs........47 Figure 19 EIO-log I curves of the 1st set of W anodes in test yard slabs.......47 Figure 20 EIO-log I slow cyclic polarization data for 2nd set of Type C anodes.......................................................................................... 48 Figure 21 EIO-log I slow cyclic polarization data for 2nd set of Type W anodes.......................................................................................... 49 Figure 22 Rebar current along the yard slab main direction early in the exposure period (80 days) ............................................................51 Figure 23 Rebar current along the yard slab main direction later in the exposure period (400 days) ..........................................................52
v Figure 24 Rebar current along the yard slab main direction shortly after the 4 rebars in the chloride-contaminated zone were disconnect ed.................................................................................52 Figure 25 Four-hour rebar depol arization after 4 months of normal exposure.......................................................................................53 Figure 26 Four-hour rebar depol arization after 14 months of normal exposure .......................................................................................53 Figure 27 Four-hour rebar depol arization after 14 months of normal exposure plus several days of jointly connecting the Main and Auxiliary anodes .....................................................................54 Figure 28 Four-hour depolar ization of passive rebars after disconnection of the rebars in the chloride contaminated zone..............................................................................................55 Figure 29 Summary of 4-h depolar ization test result s for 1st set of anodes.......................................................................................... 58 Figure 30 Rebar current along t he yard slab main direction at two different anode ages..................................................................... 59 Figure 31 Four-hour rebar depol arization after 14 months of normal exposure .......................................................................................60 Figure 32 Summary of 4h depolarization test results for 2nd set of anodes.......................................................................................... 61 Figure 33 Combined EIO-log i representation of the individual InstantOff potential and current density val ues for passive rebars...........63 Figure 34 Concrete resistivit y of the zones with and without admixed chloride of all slabs as functi on of time since casting the concrete ........................................................................................63 Figure 35 Idealized evoluti on of anode PF with aging and effect on operating condi tions......................................................................68 Figure 36 Plan view of idealiz ed system chosen for implementation of the model ......................................................................................75 Figure 37 Model projections of throwing distance for C anodes at the indicated servic e times..................................................................90 Figure 38 Model projections of throwing distance for C anodes, as a function of serv ice time .................................................................91 Figure 39 Model projections of throwing distance for W anodes at the indicated servic e times..................................................................92 Figure 40 Model projections of throwing distance for W anodes, as a function of serv ice time .................................................................93 Figure 41 Sensitivity analysis of model projections to the choice of CS and iP, for 10 mo anode age. .........................................................94 Figure 42 Summary of informati on toward establishing a cathodic prevention polarizatio n criteri on..................................................100 Figure 43 Circuit network equi valent for model validation. ..........................114
vi Figure 44 Experimental and mo deled values of polarization and cathodic current for rebars c onnected to the main Type C anode 2nd Set (4 mont hs anode age) .........................................120 Figure 45 Experimental and mo deled values of polarization and cathodic current for rebars c onnected to the main Type C anode 2nd Set (13 months anode age) .......................................120 Figure 46 Experimental and mo deled values of polarization and cathodic current for rebars c onnected to the main Type W anode 2nd Set (4 mont hs anode age) .........................................121 Figure 47Experimental and modeled values of polarization and cathodic current for rebars c onnected to the main Type W anode 2nd Set (13 months anode age) .......................................121 Figure 48 One-on-one comparis on of model output and experimental values for C anodes ....................................................................123
vii POLARIZATION OF GALVANIC POINT ANODES FOR CORROSION PREVENTION IN REINFORCED CONCRETE Margareth Dugarte ABSTRACT The polarization performance of two types of commercial galvanic point anodes for protection of reinforced steel around patch repairs was investigated. Experiments included measur ement of the polarizatio n history of the anode under constant current impressed by gal vanostatic circuits and in reinforced concrete slabs. The tests revealed, for both types of anodes, a potential-current function (PF) indicating relatively li ttle anodic polarization from an open circuit potential at low current levels, followed by an abrupt increase in potential as the current approached an apparent terminal value. Aging of the anodes was manifested by a continually decreasing curr ent output in the concrete tests, and by increasingly more positive potentials in the galvanostatic tests. Those changes reflected an evolution of the PF generally toward more positive open circuit potentials and, more importantly to the onset of elevated polarized potentials at increasingly lower current le vels. There was considerable variability among the performance of replicate units of a given anode ty pe. Modest to poor steel polarization levels were achieved in the test yard slabs. Modeling of a generic patch configuration was implemented with a one-dimensional approximation. The model calculated the throwing distance that could be achieved by a given number of anodes per unit perimeter of the patch, concrete thickness, concrete resistivity, am ount of steel and amount of polarization
viii needed for cathodic prevention. The m odel projections and aging information suggest that anode performance in likely application scenarios may seriously degrade after only a few years of operation, even if a rela tively optimistic 100 mV corrosion prevention criterion were assu med. Less conservative criteria have been proposed in the literature but ar e yet to be subst antiated. Other investigations suggest a significantly mo re conservative corrosion prevention may apply instead. The latter case would qu estion the ability of the point anodes to provide adequate corrosion prevention.
1 1. INTRODUCTION 1.1 Background Corrosion of reinforcing steel in concre te is of major concern due to the associated cost and possible structural degradation. It has been estimated to cost billions of dollars per year to re store or replace damaged structures, and corrosion can result in failure of structural elements. The direct cost of corrosion in infrastructure is about $22.6 billion per year according to recent studies by the Federal Highway Administration. Indirect societal costs can be considerably higher [FHWA 2002]. There are approximately 600,000 highway bridges in the U.S and more than 15% of them are a ffected by corrosion damage [FHWA 2002]. These statistics underscore the impact of co rrosion on the economy of developed nations. The associated safety and financia l liability issues warrant the need for development of techniques and procedures to effectively control corrosion. The corrosion control of reinforcing steel in concrete is then a significance maintenance practice that government agencies and industry have address to reduce adverse impact. Chloride-induced corrosion of steel in c oncrete is one of the major causes of bridge deck and marine substructure deter ioration. The presence of chlorides results from exposure to sea water in coastal locations and application of de-icing salts on roadways in northern states. W hen chlorides reach the steel surface active corrosion ensures forming expans ive corrosion products that crack the concrete cover. The concrete delami nation, cracking and spalling if left
2 unmitigated can require costly maintenanc e of even eventually cause structural failure. Repairs often consist of removing the cracked concrete and replacing it with chloride-free concrete. It takes onl y a small amount of corrosion metal loss (e.g. ~0.1 mm (0.004 in)) at the reinforcing steel bar (rebar) surface to create corrosion products sufficient to generate inte rnal stresses that crack the concrete [Torres-Acosta 2004]. Thus, repairs often do not involve rebar replacement, as the remaining steel cross section is still adequate. However, patch repairs limited to the portions of the structure that showed conspicuous cracking may have detrimental consequences. As is o ften the case, zones adjacent to the patch have already had substantial chlori de contamination. As will be discussed in the following, corrosion can rapidl y develop there prom oted by the newly placed patch, and small ("point") anodes at the periphery of the new patch are often recommended as a means to alleviat e that problem. This investigation focuses in evaluating the performance of those anodes in concrete repair applications. 1.2 Literature Review 1.2.1 Corrosion of Steel in Concrete Steel in concrete is normally in t he passive condition (protected against corrosion by a nanoscale-thick oxide film) formed due to the highly alkaline nature of the pore water (pH 12.5 to 13). Ho wever, the film is disrupted by events such as a decrease in the pH of the pore water due to carbonation, or intrusion of chloride ions from the exter nal environment. The latter m odality tends to result in earlier distress in bridge applications and will be considered here. Corrosion starts when the chloride concentration at the rebar surface exceeds a critical value known as the chloride corrosion threshold (CT). Much of the information available on the value of CT concerns atmospherically exposed concrete. In that case the potential E between an isolat ed plain rebar steel segment and the immediately surrounding concrete tends to be, when passive, in the range -100
3 to -200 mV in the Copper/Copper Sulfate Electrode (CSE). In those conditions CT is typically >~0.4% of the mass of cement per unit value in the concrete [Li 2001]. The value of CT depends on many variables such as the rebar material [Hurley 2006], the pH of the concrete pore wa ter [Li 2001, Gouda 1970, Hausmann 1967] and the presence or voids [Glass 2007]. Of importance to the present work, CT has been found to depend also on the value of E for the passive steel in a manner that reflects the well known dependence between pitting potential and chloride content in other systems [Szklarska-Smialowska 1986]. The evidence available to date for steel in concrete is limited, but it suggests that if all other factors remain the same, CT tends to increase manifold when E decreases from ~-150 to ~-600mV CSE. There is uncerta inty as to the precise amount o polarization needed for a given effect [Presuel-Moreno 2005A, Alonso 2000, 2002; Izquierdo 2004, Pedeferri 1996]. There are four components present for co rrosion of steel reinforcement in concrete to occur: the concrete pore water or electrolyte, oxi dation of iron (Fe Fe++ + 2e-), oxygen reduction in presence of water (O2 + 2H2O +4e4 OH-), and an electronic path between anodic and cathodic regions in the steel rebar assembly. The value of E for an isolated rebar segment is determined by the interplay between cathodic electron-c onsuming reactions (principally the reduction of dissolved oxygen in the pore water indicated above) and anodic electron-producing reactions (such as t he dissolution of iron from the rebar indicated above). In the passive condition the rate of iron dissolution, or passive corrosion rate, is very small [Sags 2003] and the resulting mixed potential [Fontana 1986] for the system is in the re latively less negative value range given earlier. After CT is exceeded, the rate of the anodic reaction increases dramatically. The resulting mixed potential of steel that is corroding actively in atmospherically exposed chloride-contami nated concrete drops, typically to values EACT in the ~-300 mV to -600 mV SCE range [Bentur 1997, Broomfield 1997, Li 2001].
4 1.2.2 Cathodic Protecti on and Cathodic Prevention These modes of corrosion control and their differences and associated terminology are reviewed here as they pertain to the scope of this investigation. Cathodic protection in concrete is a method for decreasing the corrosion rate of steel that is already in the ac tively corroding stage. The decrease is achieved by lowering the steel potential to a value below that wh ich existed in the freely corroding condition. The rate of corro sion is that of the net anodic reaction, which decreases strongly as the potential becomes more negative following usual electrochemical kinetic la ws [Fontana 1986]. Assuming on first approximation Tafel kinetics and neglecting the effect of the metal deposition reaction, a decrease in potential by an am ount equal to one Tafel slope (typically in the order of 0.1V [Jones 1996] would lower the corrosi on rate by about 90%. It is then not surprising that practical criteria for achi eving cathodic protection, based on operating experience, specify a pol arization level of 100 mV below the freely corroding potential as a criterion for effective application of cathodic protection [Funahashi 1991]. In addition to direct action on anodic kinetics, the electric field driving the cathodic polar ization current tends over time to respectively decrease and increase the concentrations of chloride and hydroxide ions at the rebar surface. Depending on th e electric field strength [Glass 1997], those changes may actually restore pa ssivity on the rebar surface. Cathodic prevention is based on the entirely different concept from that of cathodic protection. In cathodic preventi on the potential of t he passive steel is shifted from its natural va lue in the negative direction before the onset of active corrosion, to substantially delay or prevent the initiation of such corrosion when the passive film is still in place. The change to a more negative potential has the effect, noted above, of in creasing the value of CT so that the steel can withstand significantly greater chloride content in the surrounding concrete before sustained passivity breakdown takes place. In other words, this preventive
5 cathodic polarization extends (sometimes indefinitely) the time period before any corrosion starts. The mechanism responsible for this effect is not precisely known, but it may involve phenomena obs erved in other systems such as improved resistance of the passive film to chloride ions [Macdonald 1992], or destabilization of incipient pits [Frankel 1998] as the polarization becomes less anodic. Such processes involve conditions quite different from those present on fully active rebar, so criteria such as the 100 mV shift for cathodic protection [Funahashi 1991] do not necessarily apply to cathodic prevention cases. As indicated earlier, there is uncertainty as to the value of the potential at which the passive rebar needs to be held to achieve a given increase in CT, an issue that will be addressed later in this document. There is agreement however that the current density needed to cathodically shift the potential by a given amount from the freely corroding condition is significantly less for passive than for active rebar [Glass 1997, Pedeferri 1996]. Thus, if t he required potential shifts were comparable, cathodic prev ention would be comparativ ely easier to implement than cathodic protection. For example, t he lesser driving potential of a galvanic system may suffice in a cathodic prev ention application, while an impressed current system may be needed for cathodic protection. The polarization needed for cathodic pr otection or prevention may be achieved either with impressed current or galvanic systems [Broomfield 1997]. Typical reported (independent confirmati on may be needed) steel protection current densities range between 2 to 20 mA/m2 for cathodic protection and a little as 0.2 to 2 mA/m2 for cathodic prevention [[Glass 1995]. In either case an anode or system of anodes in contact with the c oncrete is the physical source of the polarizing current, which travels through t he concrete to the rebar assembly. Given a certain polarization criterion va lue, the effectiveness of both cathodic protection and prevention depends also on how far away from the anode the polarization criterion is sati sfied. That reach is called the throwing distance. The throwing distance and its decrease with age are important descriptors of the capability of a protection or prevention system.
6 1.2.3 Corrosion Macrocells and Effect of Patch Repairs If a rebar segment is not isolated but is instead part of a larger rebar assembly, then because of electrochemical coupling the local value of E at the rebar segment is elevated or decreased if the potential in the surrounding zones is higher or lower respectively than that of the segment if it were isolated. This macrocell coupling effect is stronger if the el ectrical conductivity of the concrete is high (low resistivity) [Sags 1990, 2003, Broomfield 1997, Kranc 1994, Kranc 2001, Raupach 1996]. An important consequence of macrocell coupling is that any passive steel surrounding an actively corroding rebar z one may develop E values significantly more negative than if the rebar assembly were discontinuous. As a result, the corroding zone where corrosion had started at an earlier date, is effectively acting as a galvanic anode providing a degree of cathodic prevention to the surrounding passive steel. Thus, CT in that surrounding steel is increased and active corrosion would not take place there for some time, even if chloride contamination at the rebar depth were alre ady substantial. Such situation takes place in reinforced concrete structures such as for example a bridge deck in deicing salt service, where chloride c ontamination was more or less widely distributed and increased with se rvice time. Eventually active corrosion starts at a location where chloride buildup was fast est. The steel surrounding that zone, while still in the passive condition, may be nevertheless in contact with concrete with high chloride content. Corrosion ther e could have started soon afterwards without the prevention effect mentioned. Models providing visualizations of this effect have been presented elsew here [Sags 1998, 2009A, 2009B]. The zone experiencing corrosion may be patch-repaired by removing the chloride contaminated concrete there and replacing it with fresh, chloride-free concrete. As a result the previously active steel in the patch becomes passive and corrosion stops there. However, that transition to the passive condition also
7 elevates the potential of the steel in the patch from its former highly negative value to one that can be several hundred mV more positive. Consequently, the cathodic prevention effect on the surroundi ng zone is lost. The newly lowered value of CT in the surrounding zone then may be less than the existing local chloride concentration, and active corrosion c ould promptly start. This detrimental consequence is called a ring or halo damage around the patch [Broomfield 1997]. In those cases, prevention may be restored by insert ing a sacrificial galvanic anode (e.g. made of zinc, which develops a highly negative potential) in the patch-repair zone. That anode takes up the function of the previously corroding rebar and prevents corrosion from starting both in the patch area and its surroundings. 1.2.4 Anodes for Controlling Corrosion Around Patch Repairs Small galvanic anodes (Â“point anodes Â”) are available commercially for casting in patch repairs, for the int ended purpose of forestalling the halo damage effect [Bennett 2002, Sergi 2001,Whitmore 2003,Bennett 2006]. The anodes usually consist of a zinc alloy piece with steel connecting wires, and embedded in a mortar disk. Electronic connection to the rebar is necessary for these anodes to work, and it is made by tying the wires to the rebar in the patch. The mortar around the zinc alloy is formulated to obtain high pore water pH, increase water retention, or otherwise prom ote a regime where the form ation of a passive film on the alloy is hindered and the alloy stays in an active condition. The mortar may also be engineered to mitigate the effect of expansive anode corrosion products. The alloy composition itself may also be adjusted to promote activity. In such condition the isolated (open circuit) val ue of E for Zn alloys is highly negative (e.g. ~-1,000 mV CSE). Macrocell coupli ng with the rebar in both the patch and the surrounding zone then could allow for appreciable lowering of E and restoration of a cathodic prevention regime to a condition comparable to or greater than that existing before the repair. Proprietary patch concrete mixtures
8 are also marketed to increase the conductivity around the anode and maximize macrocell coupling with the ring zone. Point anodes as described above were t he subject of developmental work and commercial production in Europe durin g the previous decade [Sergi 2001] followed by introduction in North Americ a by two different companies. Typical production units are illustrated in Figure 1. Much of the marketing of those units has been aimed at residential or parking bu ilding applications, but recently there is increasing consideration for highway app lications. Of special interest is the mitigation of corrosion around repaired bridge deck spalls patches in inland as well as marine substructure components. 1.2.5 Open Issues to be Addressed The possibility of large scale applica tions in highway systems brings up several important performance and durability issues needing resolution. Among those, at the beginn ing of this investigation there was little documented information on the quantitative relations hip between the operat ing potential of point anodes and the amount of current delivered as func tion of that potential the polarization functi on (PF) of the anode. There was also a need to know how the ability of the anode to provide protective current would be degraded with se rvice time and the total amount of protective charge that coul d be delivered. It was also unknown over how long of a distance away from the repair patch the corrosion prevention effect may be obtained for a given potential-current anode function, anode age, and especially anode placement density so that a means of asse ssing the number of anodes needed (and hence cost) for a given desired effect could be assessed by the potential user.
9 1.3 Objectives The main objective of this study is therefore to evaluat e galvanic point anodes to determine their performance and applicability for concrete repairs. Based on the needs indicated in the previous section, the present investigation focused on durability and effectiveness as the two key factors deserving attention. 1.3.1 Regarding Durability a. Determine for selected commercially available point anodes the operating potential/current delivery function, and its dependence on relevant service variables and on service time. b. Establish anode cumulative capaci ty (total usable charge delivered) and associated ultimate service life capability. 1.3.2 Regarding Effectiveness a. Assess the anode ability to achieve cathodic prevention over a usable distance (throwing distance) under r ealistic service conditions and as a function of the number of anodes needed, so as to establish the means of conducting cost/benefits analyse s by potential users.
10 2. INVESTIGATION METHODOLOGY 2.1 Approach To achieve the investigation obj ectives the following two tasks were performed: laboratory expe riments addressing durability issues, and modeling addressing effectiveness. 2.1.1 Laboratory Experiments The polarization behavior of the anodes was examined by two types of tests in concrete. In one experiment t he anodes were under constant current impressed by galvanostatic circuits, wh ile in the other the anodes operated in natural macrocell conditions coupled to re inforcing steel in outdoor exposure test slabs. 2.1.2 Modeling Modeling of a generic patch configuration was implemented to project the performance of point anodes for patch repairs applications as function of service time. The model computations are int ended to evaluate the extent of steel polarization that could be achieved by these anodes in situat ions representative of highway applications. The findings will se rve to fill gaps in design criteria for galvanic point anode systems, and enable ra tional selection and application of corrosion prevention methods that best use limited public fiscal resources.
11 2.2 Products Selected for Evaluation In this investigation two types of point anodes in regular commercial production, each from a diffe rent manufacturer, were evaluated. These products are designated by the code names C and W. The manufacturers provided the anodes used for the laboratory tests directly to the University of South Florida, identifying those anodes as regular pr oduction units. Two sets of anodes from each manufacturer were evaluated. The fi rst set (1st) was provided in 2004 and the second set (2nd) in 2007. The anode model name for each manufacturer was the same for both sets. For C anodes the mortar pellet surrounding the anode proper was circular (Figure 1) and had an exte rnal diameter ~63 mm and thickness ~27 mm. The mortar mass was ~100 g. The zi nc alloy anode proper met ASTM B 418-95a Type I requirements according to the m anufacturer. The pellet was of highly alkaline mortar, reported by the manufacturer to have pH=14 or greater. The product Material Safety Data Sheet for this product model name identifies cement (no type specified) and lithium hydroxide as major constituents. Destructive examination of a unit of the 1st set revealed an internal solid zinc alloy disk (Figure 2) 44 mm in diameter and 12 mm thick. The zinc alloy mass (after subtracting that estimated for in ternal steel wires) was 103 g. The steel wires for external connection (~1.5 mm diameter) were embedded in the zinc alloy medallion and extending outwards. Examination of a unit of the 2nd set revealed a ribbed zinc alloy disk (Figure 2) 43 mm in diameter, 19 mm maximum thickness and 115 g alloy mass, with extern al connection wires as those in the 1st set. For W anodes the mortar pellet su rrounding the anode proper was roughly rectangular (Figure 1), 77 by 60 mm on t he sides and 33 mm thick. The mortar mass was ~ 170 g. The zinc alloy met ASTM B418-01 requirements according to the manufacturer. The pellet was of mort ar reported by the manufacturer to
12 contain humectants and proprietary zinc activators. The product Material Safety Data Sheet for this product model name identifies Portland cement and lithium bromide among major constituents, and ca lcium salt (a synonym for calcium hypochlorite but no clarification given), calcium nitrate and lit hium nitrate among minor constituents. Destru ctive examination of one unit from the 1st set revealed an internal zinc alloy element consisting of four piled rectangular expanded metal mesh squares, 34 mm on the side, with a combined height of 18 mm. A plastic sponge separated the squares into two pairs (Figure 3). The total zinc alloy mass was 48 g. Two steel wires (~1.5 mm di ameter) for external connection were wrapped tightly against the expanded metal squar es. Examination of three units from the 2nd set (Figure 3) revealed in a ll cases an internal zinc alloy element consisting of three piled rectangular expanded mesh squares, 34 mm on the side, with a combined height of 14 mm. There was no plastic sponge separating the squares. The total zinc alloy mass averaged over the 3 units was 40 g. Two steel wires (~1.5 mm diameter) for ex ternal connection were wrapped tightly against the expanded metal squares. Figure 1 External appearance of anode types (C on top, W on bottom).
13 Figure 2 Type C anode specimens. Zinc alloy anode appearance after embedded mortar was stripped; otherwise as-received. Left, 1st set; Right, 2nd set.
14 1s t Set 2n d Set Figure 3 Type W anode specimens. Zinc alloy anode appearance after embedded mortar was stripped. Top 1st se t. Bottom 2nd set. (Mortar only partially stripped).
15 ISBISA o.c ESBESAEr=f(I/Ar) t2>t1t1t=0 0 1 2 R ISBE I (log scale) ISBISA o.c ESBESAEr=f(I/Ar) t2>t1t1t=0 0 1 2 R ISBE I (log scale) 2.3 General Aspects of the Anode Evaluation Approach The investigation aims in large part to characterize anode performance by determining the potential/cu rrent delivery function (P F) of the anode, and its dependence on relevant service variables (e.g. moisture content and alkaline content of surrounding concrete) and on serv ice time. Implicit in this approach is determining the ability of the anode metal to remain in the active condition over long periods of time, as well as the cumula tive capacity of the anode (total usable charge delivered) and associated ulti mate service life capability. Figure 4 Idealized potentia l-current diagram of t he evaluation approach. Figure 4 shows the concepts involved and their application [Sags 2005]. Consider an anode being evaluat ed when initially placed in service. The anode is expected to develop under open circuit (OC) condition, a potential in the order of -1V CSE. If connected with a passive rebar assembly, the anode delivers some current and polarization causes the anode potential (as measured against a
16 reference electrode placed in close pr oximity to the anode) to become less negative than in the OC condition. The polar ization increases with larger current demand, as described by Curve 0 which is effectively the PF of the anode at the beginning of its service life. Curve 0 would also result from joining the locus of separate points corresponding to a number of similar newly placed anodes acting independently at different current dem ands. If current delivery of each anode were kept constant for a long time the anode performance is expected to degrade somewhat from causes such as zinc consumption (with consequent decrease in effective surface area) and a ccumulation of corrosion products that may impede the passage of ionic current or even promote pa ssivation of the anode surface causing eventually failure to deliver protection. The manifestation of such degradation would be a shift to more positive values in the anode potential, likely to a greater extent at longer services times and higher currents, as illustrated by PF Curves 1 (time = t1) and 2 (time = t2 > t1). Those curves can be obtained experimentally by operat ing the anodes while connected to an external galvanostatic control circuit. Bo th the ability of the anode to remain active and the cumulative capacity of the anode can then be characterized from the curves at each current regime and at different time intervals. A diagram thus obtained (family of PF curves as function of time) for a given anode type and environment, including mortar type and humidity condition, can serve as a standardized descripto r of the anode performance for those conditions. If a galvanic control circuit is used, this procedure eliminates the variability that appears when evaluating ano des, as it is often done [Sergi 2001], by coupling to a passive rebar asse mbly embedded in the same mortar or concrete. The variability in such cases stems from the current demand by the rebar assembly, which may sometimes be sustained at high levels for long periods of time, or drop rapidly early in the life of the test depending on the initial condition of the steel surface or small va riations in the pore water composition or concrete moisture.
17 The curves in a PF diagram obtained fr om a sacrificial anode may be used to obtain a bounding indication of how mu ch protective action may be expected from a rebar assembly for which t here is information on its polarization characteristics. As an illustration, the polar ization information can take the form of the long term potential-cathodic curr ent density polarization curve Er=f(i) for the reinforcing steel, determined by prior meas urements as illustrated in Figure 4. Thus if the anode placement density is such that each anode is to protect an area Ar of rebar surface area, the curve Er=f(I/Ar) describing the polarization characteristics of that area [Sags 2003] can be superimposed directly on the PF diagram to determine how much r ebar polarization may be achieved at different aging conditions (Figure 4). If the resistivity of the concrete path between anode and rebar is very small, the rebar receives a current ISA and is polarized down to potential ESA, which may then be compared with the minimum requirements for corrosion prevention in the specific application considered. ESA is the best polarization level to be expected; if concrete resistivity is finite so an effective circuit resistance R applies, the current is less (ISB) and the rebar polarization is only down to ESB. The amount of polar ization is proportionally less if the area to be polariz ed is greater, as the effect is the same as moving the rebar polarization curve to the right. This type of analysis, to project the extent of useful anode action based on the results of the test, can be ex tended to more complex system geometries by appropria te current distribution modeling [Presuel-Moreno 2005B, Sags 2003]. Those concepts have been applied in more detail in Chapter 5 of the pr esent document, dealing with performance modeling of sacrificial anodes in a reinforced concrete structure. Some content in this dissertation has been published in reports to the sponsoring agency (Dugarte and Sagues, 2010), and has been in part reproduced here.
18 2.4 Anodes in Galvanostatic Regime in Concrete These sets of experiments were c onducted using the above principles, where anode specimens were evaluated un der various galvanostatic regimes in controlled humidity chambers. 2.4.1 Materials and Preparation These tests involved the two anodes types to be evaluated (1st set only), in two different embedding media, two re lative humidity (RH) regimes, four galvanostatic regimes, and were conducted in triplicate for each condition for a total of 96 specimens. These specim ens were exposed for approximately 4 years. The basic test specimen arrangement (F igure 5) consisted of a prism 20 cm x 20 cm x 10 cm) with a test anode placed near the center. An embedded activated titanium rod (ATR) referenc e electrode [Castro 1996] (periodically calibrated against a Copper Sulfate Elec trode (CSE)) was placed against one of the external mortar faces of the anode. Al ternatively, an exte rnally placed CSE is used with appropriate compensation for electrolyte resistance if potential measurements are done with current on An activated titanium mesh of the type used for impressed current cathodic prot ection of steel in concrete was cast underneath one of the main faces of the pr ism. The specimens were kept in controlled containers at the desired re lative humidity. Connecting wires from anode and mesh led to a galvanostatic syst em capable of handling multiple independent channels.
19 GALVANOSTAT I electronicTi Mesh Anode Assembly Concrete EReference Electrode + GALVANOSTAT I electronicTi Mesh Anode Assembly Concrete EReference Electrode + Figure 5 Anode test arrangement (sketc h). Anode was placed centrally in specimen. 2.4.2 Test Conditions A summary of materials and test conditions is given in Table 1. A picture of the 95% RH chamber wit h test specimens is shown in Figure 6. Figure 6 The 95% RH test chamber.
20 Table 1 Materials and test conditions for anodes in galvanostatic regime in concrete. Anodes evaluated C and W 1st Set only. Embedding media A Portland-cement with polymers commercial product marketed for patch repairsA. Mixed per manufacturer's instructions, using 2 liter water per 50 lb bag of product plus 15 lb 3/8Â” Aggregate. Ordinary Repair Concrete (ORC) 0.41 w/c, 658 lb per cubic yard. Type II cement, 3/8Â” Aggregate. Test environments 95% R.H. and 60% R.H. Â– target values; typically controlled to +-5% Galvanostatic regime 0, 30, 100 and 300 A anodic current Replication Triplicate Total test blocks 96 2.4.3 Data Measurement fo r Performance Evaluation The potential EIO of the anodes is reported in the CSE scale in the instantOff condition (~ 1 sec after current interr uption) either measured directly against a CSE electrode placed on the block side, or against the internal activated Titanium rod calibrated against a CSE. Pot ential is reported as function of time t, with t=0 chosen to correspond to the mome nt of energizing of the anodes subject to galvanostatic control, which was 48 da ys after casting for the 95% R.H. tests and 81 days after casting for the 60% R.H tests. A Provided by the manufacturer of the W anodes.
21 The instant-Off potential, EIO, values of triplicate specimens were averaged. If the power-on potential of any specimen reached ~0V (i.e., clearly incapable of any protective action) at a given test time, testing of that specimen was discontinued and the EIO average value from that time on was computed only for the remaining specimens of that trio. 2.5 Anodes Coupled to Reinforcing Steel in Concrete These experiments determined the combined anode-rebar performance in outdoor exposure test yard slabs. These tests were intended to supplement the information provided by the galvanosta tic experiments by examining an anode aging trajectory closer to that expect ed in actual applications, and to have an opportunity to reveal possible effects of diurnal and seasonal variations in temperature and humidity that would have not been experienced in the laboratory tests. In addition, the reinforced concrete tests would serve to provide information on steel polarization data, and to offer a means to validate modeling predictions such as those described in the next par agraph. The outdoor tests served also to compare the behavior of the first and second sets of anodes from each manufacturer. For these tests and for the reasons indicated earlier, additional test strategies were needed to separate the information that pertains solely to the anode performance. One of those strategies was to in sert resistors of various sizes between the anode and the rebar asse mbly in a test system and monitor the resulting potential/current trajectory of the anode, thus yiel ding an alternative way of obtaining a PF diagram for the sa crificial anode samples at various stages of aging.
22 2.5.1 Materials and Preparation Figure 7 shows the test slab configurat ion. The steel rebars were regular production No.7 (nominal diameter 7/8 in (22mm)) bars complying to ASTM A615 Grade 60, with dark gray mill scale on the surface. Each rebar had a nominal 293 cm2 surface area, resulting in a 0.80 nominal ratio of steel area to concrete footprint area. The yard slabs were built using the same Ordinary Repair Concrete formulation as for the concrete blocks in the galvanostatic experiments, except that the shaded por tion near the center contained admixed sodium chloride to obtain 5.9 Kg/m3 (10 pounds per cubic yard (pcy)) chloride ion. Each slab contained two anodes of the each set provided by the manufacturers, placed as shown. Rebars were numbered from 1 to 12, starting from the left on Figure 7. Both anodes were of either Type C in triplicate slabs numbered 1, 3 and 5 or Type W in triplic ate slabs numbered 2, 4 and 6. 2.5.2 Test Conditions Six concrete slabs with embedded sacrif icial point anodes as indicated in Figure 7 were cured in the molds for one week and then demolded and placed horizontally, elevated 1 ft above ground, in the outdoor test yard at USF. The demolding date was designated as the start of the exposu re period (t=0). While curing, the main anode was kept provisiona lly wired to the four rebars in the Clrich zone. Since placement in the ya rd and until connections boxes were in place, the entire rebar assembly and the main anode were kept interconnected with provisional wiring. Due to casting diffi culties the concrete in the chloride-rich zone was at places poorly consolidated and exhibited some honeycombing. After placement in the yard the affected sl abs were fitted with partial forms and a cement-water grout was poured as needed to fill in the voids in the honeycombed spots.
23 Figure 7 Yard slab test configurati on showing 1st and 2nd set anode positions. Dimensions in inches. Rebars are numbered starting with No. 1 at left. The anode on the slab centerline (Main ) was normally always connected to the rest of the rebar assembly. The other anode (Auxiliary) was disconnected except when indicated. After 1045 days of operation of the 1st set of anodes an additional pair of externally wired dupl icate anodes, from the 2nd set provided by the manufacturers, was placed in each sl ab as shown and keeping the same slab assignment for each type of anode. The 2nd set of anodes was placed by first drilling two partially overlapping 2-in (5 cm) diameter core holes in the space indicated, inserting the anode in the openi ng and filling it with a proprietary mortar compound for placing point anodes as a retrofit in hardened concrete, applied per manufacturer's instructions. The connection to the previous Main anode was then switched to the Main anode of the 2nd set; all other anodes remained normally disconnected. 2 #7 bars on 4centers L = 16.5 18 48 20 16 6ClFREEMAIN AUX SLABS AS BUILT ClFREE Cl10 PC Y 2nd Set MAIN 2nd Set AUX 1st Set 2 #7 bars on 4centers L = 16.5 18 48 20 16 6ClFREEMAIN AUX SLABS AS BUILT ClFREE Cl10 PC Y 2nd Set MAIN 2nd Set AUX 1st Set
24 2.5.3 Data Measurements Externally wired switches permitt ed performing instant-Off potential measurements and measurements of current delivery to individual rebars. All rebars and the main anode were normally in terconnected. ATR electrodes were placed 12 mm away from the surface of each of the rebars. Figure 8 shows an installed slab. Figure 8 Installed yard slab with connection box. Measurements conducted typically on a weekly schedule included (a) anode and individual rebar curr ents; (b) potential of the anode-rebar assembly with anode energized (" Current -On" potential) with respect to a CSE placed on the concrete on top of each individual r ebar as well as over the anode position, and also with respect to each of the em bedded ATR electrodes; and (c) potential measured 1 second after disconnection ("In stant-Off potential) and immediate reconnection afterwards of each individual re bar as well as the anode, using both the CSE and the ATR electrodes. Air te mperature (and internal concrete temperature after the 2nd se t of anodes was installed) was measured each time
25 those tests were performed. The follo wing measurements and calibration tests procedures were conducted typically on a monthly or less frequent schedule. 188.8.131.52 Concrete Resistivity A Nilsson Model 400 Soil resistivity mete r (square wave alternating current ( ac ), 97 Hz). In this meter, current is applied with current terminals designated C1 and C2, and potentials are measured between terminals P1 and P2. The meter was employed with a 4-point configur ation that determined the concrete resistivity as function of distance along the main axis of the slab. All slab switches were temporarily placed in the open position. The rebars at each end of the assembly (No. 1 and 12) were connec ted to the meter terminals C1 and C2 respectively. The potential connections were made consecutively to pairs of rebars starting with meter terminal P1 to rebar No.1 and termi nal P2 to rebar No.2, then P1 to rebar No. 2 and P2 to rebar No.3 and so on. The resulting resistance for each of the other measurem ents was multiplied by a cell factor (68.6 cm, equal to the cross sectional area of the slab divided by the center-tocenter rebar distance) to obtain the concrete resistivity for the concrete slice between each the pair of r ebars. The raw measurement for the rebar pairs 1-2 and 11-12 were divided by a correction fa ctor of 1.2 to account for uneven current distribution at t he injection current rebarsB. The ac current path was uneven due to the presence of the main and auxiliary anodes between rebars No.4 and 5 for the 1st set of anodes, and in addition between rebars No. 3 and 4 and 10 and 11 after the 2nd set of anodes was placed. Thus, the resistivity of the chloride-free concrete is reported as the average of t hat obtained for rebar pairs 1-2 (corrected), 2-3, 3-4, 10-11 and 11-12 (corrected). After the introduction of the 2nd set of anodes, the values for pair 3-4 and 10-11 were not used for that B The cell factor was obtained as the average, for all slabs and for all test times up to the introduction of the 2nd set of anodes, of the raw re sistivity value for rebar pair 1-2 divided by that for pair 2-3, and similarly for pairs 11 12 and 10-11.
26 resistivity calculation. The resistivity fo r the concrete in t he chloride-containing concrete region is reported as the av erage for rebar pairs 5-6, 7-8 and 8-9. 184.108.40.206 Anode to Rebar Resistance These measurements were conducted at irregular intervals. The anode was temporarily disconnected from the rebar assembly to which it was normally connected. The soil resistivity meter wa s then used as a 2-point resistance measuring device, with one terminal connec ted to the anode and the other to the rebar assembly to which the anode was normally connected. 220.127.116.11 Steel Depolarization This test started with an instant-Off potential determination, after which the anode was left disconnected and remained so while the potentials of the anode and individual rebars ("Off potential) were measured 1h, 4h and 24h following disconnection. The anode was reconnected afterwards. The result of the depolarization test was normally reported as the difference between the 4h Off potentials and the Instant-Off potentials at the beginning of the test. Results for the other intervals were archived and discussed when appropriate. 18.104.22.168 Slow Anode Cyclic Polarization This test was conducted to obtain an approximation of the anode PF diagram at various aging periods. The te sts were conducted as slowly as practical to approximate stabilization of t he anode at each of t he potential/current points determined. Moreover, the tests were conducted first changing conditions in one direction and then again in the return direction. The extent to which any hysteresis effects appeared was an indicati on of how much the results obtained deviated from long term steady conditions. The test began after a regular set of Instant-Off measurements wa s conducted and is exemplified by the following
27 sequence. The connection between the anode and the rebar assembly was then opened and restored after introd ucing a 500 ohm resistor in the current path. After a typically 24 h wait period the curr ent and Instant-Off pot ential of the anode was determined and the resistor was repl aced by another about 2 times greater in value. The procedure was repeated in subsequent days. When a resistor value >=30 kohm was reached, the next daily step was in the open circuit condition so as to document the unpolarized potentia l of the anode. The subsequent daily steps were conducted with the same series of resistors but in reverse order, until reaching the direct connection condition. Th e test typically was completed over a period of 1-2 weeks. The Instant-Off potential vs current data with the forward and reverser data were reported as t he PF curve of the anode at the aging condition corresponding to the beginning of the test. 2.5.4 Corrections and Adjustments This section concerns corrections to measured variables in the yard slab inherent to the conditions of the experim ent. The purpose of the present section was to explore and analyze important sour ces of uncertainly in the potential measurements of reinforcing steel in c oncrete and temperature compensation in order to make the appropriate correcti ons. It is noted that the temperature corrections were intended primarily to assi st in smoothing t he data available to reveal long term trends. First the temper ature correction is analyzed, followed by a similar analysis of the potential correct ion. A third section deals with the resistivity corrections. 22.214.171.124 Potential and Current -Temperature Corrections Potential measurements conducted with a CSE on aged concrete surfaces are subject to artifacts including juncti on potentials induced by the gradient in OHconcentration due to carbonation or leachout of pore water [Myrdal 1996]. To
28 correct for those effects small (typically 1 cm2) portions of the upper slab surface of each slab were periodically chipped off or abraded to expose a fresh concrete surface next to each of the positions us ed for regular measur ements. Potential measurements taken with the CSE tip on the fresh surface were compared with measurements performed on an adjacent undisturbed surface. The difference was tallied as function of time and pror ated accordingly to build a potential correction (averaged for all slabs) that wa s globally applied to the raw potential data. Cross-checks against the internal ATR electrodes (not subject to the surface effects) validated t hat approach. All reported anode potential values in this document have been corrected accordingly. In addition to the systematic deviations noted above, potential measurements conducted on the concrete surface even in the absence of appreciable temperature variations (di scussed below) were subject to scatter from e.g. surface moisture variations and degree of contac t with the electrode sensing tip. Rebar potential measur ements spanned a narrower range than that of anode potentials, so the obscuring effects of random scatter were considerable when attempting to construc t a global steel polarization curve as shown in Section 3.2.2. In contrast, pot ential measurements of steel against the embedded ATR electrodes were found to be appreciably more stable. Consequently, the potentials reported in this document for constructing the steel polarization function were based on t he measurements against the embedded ATR, corrected by calibration performed at selected times against an external CSE. The calibration was conducted by carefully controlling surface conditions and performing repeated measur ements to minimize random error in the average of those measurements. As the steel potential meas urements were instant-Off values with only the current to a single rebar interrupted at a time, a compensation procedure was developed to a ccount in the calibration for residual ohmic drop between the respective potent ial measuring points of the CSE and the corresponding ATR.
29 Temperature of the test yard slabs spanned a wide range, from ~5 to ~35 oC. Measured values of galvanic current s, concrete resistivity and potentials showed appreciable day to day and season al fluctuations t hat correlated well with variations in temperature. Those fl uctuations obscured long term trends due solely to anode aging and other system evolution, and added scatter to determinations of anode PFs. Consequently, the data were analyzed to extract parameters that could serv e to approximately compens ate for the temperature variation effects. Following prior approaches documented in the literature [Virmani 1983, Pour-Ghaz 2009] the anode cu rrent, I, was assumed to follow an apparent Arrhenius relationship I(T1) = I(T2) exp [HA R-1 (T1 -1-T2 -1)] (1) Where T1 is the temperature for which a ll measurements are to be reported (chosen to be 298oK, 25oC which was the approximat e average temperature of the yard slabs at the time of the day measurements were conducted ), T2 is the temperature at the moment t he measurement was performed, HA is the apparent activation energy and R is the gas constant. The value of HA was obtained from the best fit slope of a modified Arrhenius plot of the cu rrent-temperature data for eac h anode type of the 2nd set of anodes. The modification consisted of plotting the value ( ln I)/R as function of T-1, where the differences are the change in measurement results for each slab of a given type of anode from the previous test date. The slope of the straight line best fitting the combined results for that anode was reported as the average effective activation energy. This approach emphasizes the changes due to temperature variations, which are relati vely short-term, and minimizes error in estimating HA introduced otherwise by the l onger-term changes due to system aging and not related to te mperature. Values of HA=53 kJ/mole and 32 kJ/mole were thus obtained for the C and W anodes respectively. Accurate concrete temperature records were kept only during the last half of the evaluation of the
30 1st set of anodes, when anode current values were generally small which tended to result in larger relative experimental scatter. Trial calculations showed that the resulting uncertainty in HA determination was considerably greater than that for the 2nd set of anodes. Consequently, it was decided instead to apply globally the HA values obtained for the 2nd set of anodes to the 1st set as well, recognizing that its correction is only roughly evaluated due to reduced confidence in both temperature and activation energy values. The temperature compensation descri bed above for the anode current is only a rough approximation that ignores the complex inte raction of the combined electrochemical processes at the anode and the rebar asse mbly, plus the effect of variation of electrolyte resistance with temperature. For example, the correction did not take into account the value of the potential at the time the current was measured. This simplified approach was adopted as it was felt that the uncertainty inherent in the instant -Off anode potential (where a relatively large ohmic potential drop is eliminated but never exactly) di d not merit further precision. A more sophisticated approach was used for temperature correction of the (mostly) cathodic current on the rebar, for which the instant-Off potential can be determined more accurately. Following a si mplified absolute reaction rate kinetics approach (see for example Kaesche 2003 a nd observations by Tanaka (1964)), the cathodic rebar current density was corrected for temperature taking into account the potential E as well by: I(T1, E) = I(T2,E) exp [ (H'A+P E) R-1 (T1 -1-T2 -1)] (2) Where H'A is a nominal corrected activation e nergy term and P is a parameter that adjusts for the value of the steel potential when the cu rrent measurement was made. The approach neglects also the complicating effect of any anodic reaction that took place on the rebar surface.
31 The values of H'A and P were obtained by a best fit procedure to be presented elsewhere [Dugarte 2010] that takes into a ccount the cathodic current density, temperature and potential changes between me asurements performed at consecutive test dates. The resulting average values of H'A and P were 40 kJ/mole and 10.4 kCoul/mole respectively, wit h no significantly different results from steel in the slabs that contained C or W anodes. Because of the small value of the products PE compared with H'A, the final correction is not much different that what would have been obt ained with a simpler relationship such as Eq.(1) with only the nominal acti vation energy term. 126.96.36.199 Resistivity Â–T emperature Corrections A procedure similar to that used for the anodic current temperature correction was used to obtain the apparent activation energies for the concrete resistivity, with a resulti ng value of 24 kJ/mole for t he concrete in the chloridefree zone. These apparent activation ener gy values and Eq.(1) were then applied to the entire data set. All anode cu rrent and concrete resistivity results reported in the following are temperatur e-compensated by that procedure. It is noted that the temperature corre ctions were intended primarily for data smoothing to assist in revealing tr ends in other system variables. Further analysis of this issue, including mec hanistic interpretation of the apparent activation energies values obtained is le ft for future contin uation work [Dugarte 2010].
32 3. RESULTS 3.1 Results, Anodes in Galvanostatic Regime in Concrete For the following, it is recalled th ese experiments were performed only with the 1st set of anodes prov ided by the manufacturers. The average Instant-Off potentials EIO from individual anodes of a given replicate trio were again averaged over 200 day periods from 0-200 days to 8001200 days, and the results are illustrated in Figures 9 and 10 for the 95% and 60% RH humidity conditions respective ly. The 0 mV vs CSE condition was reached in the high RH chamber for only a few of the specimens, most in the 300 A regime and then relatively late in the test. In contrast, in the low RH chamber the condition was reached relatively soon in more specimens and at lower current levels (10 and 30 A), effectively terminating the test early for those cases. The initial open circuit potentials (O CP) of the anodes ranged from values approaching that commonly expected for acti ve zinc (~-1V vs CSE) to sometimes markedly more positive values. In gener al both C and W anodes showed a more negative OCP in the proprietary mix medium than in the ordinary repair concrete, in both the high and low RH chambers. At 95% RH and for both embedding media the C anodes had more negative in itial OCP than the W anodes. In contrast, at low RH the initial OCP of both anodes were comparable and not so negative (~ -500 mV). Scatter in the OCP values was significant, obscuring determination by these measurements of a possible variation of OCP with time such as the increasing trend s uggested in the introduction.
33 The results for tests with galvanostati c current control typically showed clear increases in EIO with increasing current and ti me, culminating often in reaching the test-termination condition as noted above. At 95% RH the C anodes tended to polarize more, and faster with ti me, than the W anodes thus offsetting much of the difference in OCP betw een both types of anodes. At 60% RH both types of anodes (but more so the C anodes) tended to reach t he test-termination condition faster than at 95% RH. By 1200 days of exposure at 60% RH a majority of the anodes of both types had reached the te st termination condition at all three impressed current levels.
34 -1100 -900 -700 -500 -300 -100 1 10 100 1000I / AE IO vs CSE / mV 0 200 200 400 400600 600 800 800-1000 1000-1200 0-200 200-400 400-600 600-800 800-1000 1000-1200 C ORC EC -1100 -900 -700 -500 -300 -100 1 10 100 1000I / AE IO vs CSE / mV 0-200 200-400 400-600 600-800 800-1000 1000-1200 0-200 200-400 400-600 600-800 800-1000 1000-1200 W ORC EC Figure 9 EIO evolution for both test media and anode types exposed in the 95% RH chamber. Average results from multiple replicate anodes over each period (in days of exposure) indicated in the legend.
35 -1100 -900 -700 -500 -300 -100 1 10 100 1000 I / AEIO VS CSE / mV 0-200 200-400 400-600 600-800 800-1000 1000-1200 0-200 200-400 400-600 600-800 800-1000 1000-1200 W ORC EC -1100 -900 -700 -500 -300 -100 1 10 100 1000 I / AEIO vs CSE / mV 0-200 200-400 400-600 600-800 800-1000 1000-1200 0-200 200-400 400-600 600-800 800-1000 1000-1200 C 0 ORC EC Figure 10 EIO evolution for both test medi a and anode types exposed in the 60% RH chamber. Average results from multiple replicate anodes over each period (in days of exposure) indicated in the legend.
36 3.2 Results, Anodes Coupled to Reinforcing Steel in Concrete For the following, it is recalled that these experiments were performed with anodes from both the 1st and the 2nd sets provided by the manufacturers. The manufacturer product designations were the same in each case. The test schedule differed between both sets of anodes in that for the 1st set the 4 rebars in the chloride-contaminated region we re connected from day 0 to day 477 and disconnected from thereon until day 1045 when testing of the 1st set ended. For the 2nd set tests, that star ted immediately afterwards those rebars were never connected. Unless otherwise indicated, time reported in the following corresponds to the period starting at the beginning of the placement of the respective set of anodes. This report covers the evolution of the 1st and 2nd set of anodes through their first 1045 and 590 days respectively. Results from both series of experiments in the yard slabs are presented as follows. 3.2.1 Anode Polarization The current delivered by the anodes to the entire rebar assembly as a function of exposure time is shown in Figure 11 for both sets tested. In both instances there were high initial curr ents (sometimes > 3 mA) that decayed generally steadily to val ues in the range of 200-500 A after about 1.5 years for the C anodes of either set, and for t he W anodes of the 2nd set. Notably, the performance of the 1st set of W anodes deter iorated much faster than the rest, to values about one order of magnitude lower than those of the C anodes (e.g. 2090 A) at the end of the same period. For the 1st set of anodes of both types, there was a momentary lull in the long term decreasing trend after the active rebars were disconnected, but the trend was resumed afterwar ds. It is noted that for much of the test period the current delivered by anode C-1 of the1st set was consistently significantly greater t han that of its peers in the same set.
37 The evolution of Instant-Off potential s with time for both sets of anodes is shown in Figure 12. Initially potentials for all anodes in both sets were quite negative, ~-700 mV. For the 1st set the pot ential rapidly increased early on for both anodes, to reach a roughl y steady regime at ~-400 mV CSE. Disconnection of the active rebars at day 477 was followed by an increase of ~100 mV for the W anodes but little change for the C anodes. Of the latter, anode C-1, which had the highest currents as noted above had also the more negative potential, which began to drift toward even lower values (~ -600 mV) later in the exposure period. Both anode types in the 2nd set (with onl y passive rebars) showed a relatively slow increasing potential trend with time reaching average potentials of ~-450 mV and ~-600 CSE for W and C anodes respec tively by the end of the test period.
38 Figure 11 Anode current evolution with time for both sets of anodes. Results of anodes in individual test yard slabs. 10 100 1000 10000 010020030040050060070080090010001100 Time / daysI / uA C1 C3 C5 W2 W4 W6 All Rebars Passive rebars 1st Set 10 100 1000 10000 010020030040050060070080090010001100 Time /daysI / uA C1 C3 C5 W2 W4 W6 2nd Set Passive rebars
39 Figure 12 Anode potential (Instant-Off) evolution with time for both sets of anodes. Results of anodes in individual test yard slabs. -1100 -900 -700 -500 -300 -100 010020030040050060070080090010001100 Time /daysEIO CSE /mV C1 C3 C5 W2 W4 W6 All Rebars Passive rebars 1st Set` -1100 -900 -700 -500 -300 -100 010020030040050060070080090010001100 Time (days)EIO CSE (mV) C1 C3 C5 W2 W4 W6 2nd Set Passive rebars
40 The trends of potential ev olution with time of the auxiliary anodes, which were normally in an open circuit condition, are shown in Figure 13. For the 1st set, with one exception (C-1), the auxiliary anode potentials of both types started at values ~100 to 200 mV lower than those of the energized anodes, but increased at a much slower rate, r eaching on average a plateau at ~-600 mV after about 1.5 years. T he auxiliary anode in Slab 1 (C-1) stayed however at more negative potentials over much of t he test period. The 2nd set of anodes showed also a slow increasing potential tr end, but with starting values that were markedly more negative (~ -900 to -1200 mV) than those of the 1st set. The current and potential evolution of the energized anodes is shown in Figures 14 and 15 as function of the cumu lative amount of galvanic charge, Q, delivered by each anode up to the moment of each measurement. The value of Q was obtained by summation of the product of anode current-duration of all the previous test intervals up to the moment of measurement. The la rger the value of Q, the larger is the am ount of anode metal consumption due to the galvanic current, so Q serves as one descriptor for the extent of anode ag ing. For the 1st set of anodes there was a striking decreas e in current output of the W anodes Q reached ~10 k Coul to 20 k Coul. Two of the C anodes in the 1st set showed markedly decreased current delivery at Q ~10 k Coul to 20 k Coul, but anode C-1 was delivering ~500 A even at Q ~ 60 k Coul. Anodes in the 2nd set showed a more uniform decrease in current delivery with increasing Q, up to ~ 35 k Coul by the end of the test period. Unlike in the 1st set, performance of the W anodes di d not show early deterioration and was comparable up to the end of t he test interval to that of the type C anodes in both sets. Potential evolution trends as function of Q were obscured in the 1st set, especially for the C anodes. The 2nd set s howed a clearer trend, with potentials of both types of anodes increasing some what uniformly as Q increased.
41 Figure 13 Auxiliary anode pot ential evolution with time for both sets of anodes. Results of anodes in individual test yard slabs. -1300 -1100 -900 -700 -500 -300 -100 010020030040050060070080090010001100 Time /daysE CSE Aux/ mV C1 C3 C5 W2 W4 W6 1st Set -1300 -1100 -900 -700 -500 -300 -100 010020030040050060070080090010001100 Time /daysE CSE Aux /mV C1 C3 C5 W2 W4 W6 2nd Set
42 1 10 100 1000 10000 01000020000300004000050000600007000080000 Q int /Coul I /uA C1 C3 C5 W2 W4 W6 1st Set Figure 14 Anode current as function of integrated anodic charge delivered for both sets of anodes. 1 10 100 1000 10000 01000020000300004000050000600007000080000 Q / CoulI / uA C1 C3 C5 W2 W4 W6 2nd Set
43 -1200 -1000 -800 -600 -400 -200 0 01000020000300004000050000600007000080000 Q / CoulE IO CSE /mV C1 C3 C5 W2 W4 W6 1st Set Figure 15 Anode Potential as function of integrated anodic charge delivered for both sets of anodes. -1200 -1000 -800 -600 -400 -200 0 01000020000300004000050000600007000080000 Q / CoulEIO CSE / mV C-1 C-3 C-5 W-2 W-4 W-62nd Set
44 The potential-current trajectory of t he anodes in the test yard slabs is shown in Figures 16-17. Each symbol correspond to the average Instant-Off potential and corresponding current r eading for each anode, over a 100-day period starting with anode placement. The smallest symbol indicates the 0-100 day interval with increasingly large symbols for the subsequent in tervals. With the exception of data for anode C1 near the end of the test period, the trajectories correspond roughly to lines with a negativ e slope, small for the 1st set of anodes and steep for the 2nd set. The general direction of the trajectories (C-1 for 1st set excepted) is indicated by arrows. Results from the slow cyclic polarizat ion tests for the 1st set of anodes are illustrated in Figures 18 and 19. For this set the tests were conducted only near the end of the exposure period, so the curves reflect significant performance derating due to aging. The curves for the C anodes show little hysteresis, with the forward and return curves nearly over lapping, while the results for the W anodes tended to some hysteresis. The re sults show significant unit-to-unit variability, but the shape of the curv es generally resembles that of the galvanostatic test results, with a relati vely abrupt increase in anodic polarization once a given current level is reached. The slow cyclic polarization test resu lts for the 2nd set of anodes are given in Figure 20 and 21. The 2nd set tests of both C and W anodes tended to have as a whole small hysteresis, comparable to that observed for the C anodes in the 1st set tests. Therefore, for graphic si mplicity only the average values of the forward and reverse parts of the test ar e presented. Tests were conducted at anode ages of 1, 4 and 13 months. The star ting point of each curve generally matched the corresponding position in the pot ential-current trajectory (Figure 16 and 17) for the respective anode type. The results show increasing anodic polarization with anode age, with the C anod es having a more negative OCP (the zero current condition) than the W anodes but with a more abrupt polarization increase with increasing anodic current. Unlike the case of the 1st set, the results
45 -800 -700 -600 -500 -400 -300 -200 -100 0 110100100010000 I /uAE IO CSE/ mV W2 W4 W6 1st Set -800 -700 -600 -500 -400 -300 -200 -100 0 110100100010000 I /uAE IO CSE/ mV C1 C3 C5 1st Setfrom replicate anodes of a given type and aging condition showed relatively little variability. Figure 16 Potential-Current trajectory fo r 1st set of anodes in test yard slabs. Largest symbols indicate greater age. See te xt for explanation of other symbols and on behavior of anode C-1.
46 -800 -700 -600 -500 -400 -300 -200 -100 0 110100100010000 I / uAEIO CSE/ mV C1 C3 C5 2nd Set -800 -700 -600 -500 -400 -300 -200 -100 0 110100100010000 I / uAEIO CSE / mV W2 W4 W6 2nd Set Figure 17 Potential-Current trajectory fo r 2nd set of anodes in test yard slabs. Largest symbols indicate greater age. See te xt for explanation of other symbols.
47 Figure 18 EIO-log I curves of the 1st set of C anodes in test yard slabs. Polarization curves in the forw ard (a) and return directions (b) Figure 19 EIO-log I curves of the 1st set of W anodes in test yard slabs. Polarization curves in the forwar d (a) and return directions (b). -1500 -1300 -1100 -900 -700 -500 -300 -100 1 10 100 1000 I / uAEIO CSE / mV C1a C3a C5a C1b C3b C5b C 1st Set 0 -1500 -1300 -1100 -900 -700 -500 -300 -100 1 10 100 1000 I / uAEIO CSE / mV W2a W4a W6a W2b W4b W6b W 1st Set 0
48 1 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction C1 C3 C5 4 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction C1 C3 C5 10 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction C1 C3 C5 13 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 1.E-051.E-041.E-031.E-02 I / A Abstraction C1 C3 C5 0 Figure 20 EIO-log I slow cyclic polarization dat a for 2nd set of Type C anodes. Data for each of the corresponding test yard slabs (1,3,5), at approximate indicated anode age. Both forward and return data are displayed for each symbol.
49 Figure 21 EIO-log I slow cyclic polarization data for 2nd set of Type W anodes. Data for each of the corresponding test yard slabs (2, 4, 6), at approximate indicated anode age. Both forward and return data are displayed for each symbol. 1 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction W2 W4 W6 4 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction W2 W4 W6 10 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 Abstraction W2 W4 W6 13 mo -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 1.E-051.E-041.E-031.E-02 I / A Abstraction W2 W4 W6 0
50 3.2.2 Rebar Polarization The amount of current delivered by the 1st set of anodes to the rebars at different positions in the slab at various times is shown in Figures 22 and 23, for stages early and late respectively during the period when all bars were connected (before day 477). Cathodic (prote ctive/preventive condition) current is assigned a positive sign. Currents values are the average of t he three slabs of each type of anode. Both types of anode delivered about the same level of current at that time. All the passive rebar s were subject to a net cathodic current, and it was greatest for the bars immediatel y next to the anode. In contrast, some of the active bars in the chloride contaminated zone had negative current indicating that they were acting as net anodes. That effect persisted until the time in which the active bars were disc onnected. After disconnec tion of the active bars (Figure 24) the current to the re maining bars, all-passive, was always cathodic. The bars closest to the anode received the highest current, which decayed for rebars further away. A corre sponding pattern was observed at the far end of the slab. Four-hour depolarization test result s of the rebars performed during the evaluation for the 1st set of anodes, while all rebars were connected, are shown in Figures 25-28. The depolar ization level achieved was poor or nil on much of the rebar assembly both early on (Figur e 25) and after 14 months (Figure 26). Depolarization levels improved somewhat for the C anode yard slabs when both the main and the auxiliary anode were tem porarily connected together (Figure 27), but only on the side of the slab c ontaining the anodes and still yielding modest to poor results there. After disconn ection of the active rebars (Figure 28, top) the extent of depolar ization increased markedly for the C anode yard slabs, exceeding 100 mV on average for the slabs cl osest to the anodes. By that time the performance of the 1st set of W anodes had degraded dramatically and only poor depolarization levels were reached in those slabs even with an all-passive connected assembly. Later on, (Figure 28, bottom, for day 1000) the average
51 performance of the C anodes had degr aded significantly and average depolarization levels did not reac h 100 mV even next to the anode. Figure 22 Rebar current along the yard slab main direction early in the exposure period (80 days). 1st set of anodes. All rebars connected (average of triplicate slabs). -400 -200 0 200 400 600 800 04812162024283236404448 Position /inRebar Current /uA C W 80 days 1st Set A node 10 p c y ClA ll Rebars
52 Figure 23 Rebar current along the yard slab main direction later in the exposure period (400 days). 1st set of anodes (average of triplicate slabs). Figure 24 Rebar current along the yard slab ma in direction shortly after the 4 rebars in the chloride-contaminated zone were disconnected. 1st set of anodes (average of triplicate slabs). -400 -200 0 200 400 600 800 04812162024283236404448 Position /inRebar Current /uA C W 400 days 1st Set A node 10 p c y ClA ll Rebars 0 100 200 300 400 500 600 700 800 04812162024283236404448 Position /inRebar Current /uA C W 500 days 1st Set A node 10 p c y ClPassive rebars
53 -50 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 1st Set 100 days A node 10 pcy ClA ll rebars -50 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 1st Set 400 days A node 10 pcy ClA ll rebars Figure 25 Four-hour rebar depolarization after 4 months of normal exposure. 1st set of anodes. Average results of triplicate slabs. Figure 26 Four-hour rebar depolarization after 14 months of normal exposure. 1st set of anodes. Average results of triplicate slabs.
54 -50 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 1st Set 400 days A node 10 pcy ClA ll rebarsMain and auxiliary anodes together Figure 27 Four-hour rebar depolarization after 14 months of normal exposure plus several days of jointly connecting t he Main and Auxiliary anodes. 1st set of anodes. Average results of triplicate slabs.
55 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 1st Set 600 days A node 10 pcy ClPassive rebars 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 1st Set 1000 days A node 10 pcy ClPassive rebars Figure 28 Four-hour depolarization of pa ssive rebars after disconnection of the rebars in the chloride contaminated z one. 1st set of anodes. Average results of triplicate slabs.
56 Figure 29 summarizes the depolarization measurement results for the 1st set of anodes for the different condit ions and aging times evaluated. Rebar numbering starts at number 1 for the leftmost rebar as s hown in the plan view of Figure 7. Cathodic rebar currents and 4-h depolarization levels increased substantially when energizing the 2nd se t of anodes, which always acted only on the passive rebars. The effect decreased moderately with time over the ~500 days test period. Both types of anodes performed comparably although the performance of the W anodes appears to have degraded somewhat faster (relative to the initial levels) than t hat of the C anodes. Figures 30-32 document these trends. Each periodic measurement series of t he test yard slabs yielded individual Instant-Off potential and curr ent values for each of the passive rebars in every slab. At any given time those values covered a broad range depending on proximity of the rebar to the anode and condition of the anode, and the range varied further as the anodes aged. Sinc e the rebar material was the same throughout and the concrete surrounding t he rebar had (with exceptions noted below) the same composition, the combined results are expect ed to reflect the overall polarization behavio r of the steel surface under those conditions. The graph in Figure 33, with results expressed as current densities by dividing current by the nominal rebar surface area confi rms that expectation. There the data obtained from separate rebars in the six slabs, spanni ng a wide time period, generally delineate a cathodic polarization curve. The data in Figure 33 include results for rebars No. 1-5 and 10-12 for t he 1st set of anodes, and rebars No. 1-4 and 11-12 for the 2nd set of anodes. Data for rebars No.5 and 10 while evaluating the 2nd set of anodes are not in cluded since, as discussed elsewhere, there was some evidence of chloride le vels having increased there significantly by that time causing incipient rebar ac tivation in some cases. As expected, the large majority of the reco rded net rebar currents were cathodic. The data reflect
57 the typical scatter of test yard slab meas urements, of which uncertainty in the potential value is expected to be a major contributor. The solid line represents a fit to the results based on an abstraction consisting of an activation-limited cathodic reaction current density and a pot ential-invariant passive dissolution anodic current density, as descri bed in the Modeling section.
58 0 20 40 60 80 100 120 140 160 180 200 220 761141281492044284895877989111020 Time /days4h Depol./mV 1,2 2,3 3,4 4,5 1st Set All Rebars Passive rebars C 0 20 40 60 80 100 120 140 160 180 200 220 761141281492044284895877989111020 Time /days4h Depol./mV 1,2 2,3 3,4 4,5 1st Set All Rebars Passive rebars W Figure 29 Summary of 4-h depolarization test results for 1st set of anodes. Columns indicate average value for rebar pair indicated by numbers. Anode was located between rebars 4 and 5. Time indicates period since anode placement.
59 1 10 100 1000 04812162024283236404448 Position /inRebar Current /uA C W 200 days 2nd Set A node 10 pcy ClPassive rebars 1 10 100 1000 04812162024283236404448 Position /inRebar Current /uA C W 500 days 2nd Set A node 10 pcy ClPassive rebars Figure 30 Rebar current along the yard slab main direction at two different anode ages. 2nd set of anodes (average of trip licate slabs). Only passive rebars connected. Time indicates period since placement of 2nd set of anodes.
60 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 2nd Set 200 days A node 10 pcy ClPassive rebars 0 50 100 150 200 04812162024283236404448 Position / in4h Depol./mV C W 2nd Set 500 days A node 10 pcy ClPassive rebars Figure 31 Four-hour rebar depolarization after 14 months of normal exposure. 2nd set of anodes (average results of trip licate slabs). Only passive rebars connected. Time indicates period sinc e placement of 2nd set of anodes.
61 C Anodes0 20 40 60 80 100 120 140 160 180 200 220 2191200271362497 Time /days4h Depol./mV 1,2 2,3 3,4 4,5 2nd Set W Anodes 0 20 40 60 80 100 120 140 160 180 200 220 2191200271362497 Time /days4h Depol./mV 1,2 2,3 3,4 4,5 2nd Set Figure 32 Summary of 4-h depol arization test results for 2nd set of anodes. Columns indicate average value for rebar pair indicated by numbers. Anode was located between rebars 3 and 4. Time indi cates period since placement of 2nd set of anodes. Only passive rebars connected.
62 3.2.3 Concrete Resistivity and Anode Resistance Average values of concrete resist ivity of the zones with and without admixed chloride of all slabs as function of time since casting the concrete are shown in Figure 34. The resistivity increased with age toward a long term average value approaching 25 k -cm for the zone without chloride, and about half as much for the zone with admixed chloride. There was modest variability from slab to slab (standard deviation typically <20% of the average). Anode to rebar assembly resistanc e measurements for the 2nd set of anodes, averaged for a period between ~1 and ~1.5 years after placement were ~240 and 290 for the Type C and Type W anodes respectively. From calculations performed in the Modeling secti on, it is estimated that ~2/3 of the anode to rebar assembly resistance is due to the anode-concrete current spread resistance.
63 1.E+03 1.E+04 1.E+050300600900120015001800 t / daysResistivity / ohm-cm No Chloride Chloride -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 1.00E-091.00E-081.00E-071.00E-061.00E-05 i / A cm-2E CSE / V All C&W Set 1+2 Cath Abstraction Figure 33 Combined EIO-log i representation of t he individual Instant-Off potential and current density values for passive rebars. Data recorded during evaluation of both sets of anodes. Figure 34 Concrete resistivity of the zones with and wi thout admixed chloride of all slabs as function of time since casting the concrete.
64 4. DISCUSSION 4.1 Anode Potential-Current Functions (PFs) Both the galvanostatic RH chamber and the test yard slab revealed, for both types of anodes, comparably shaped PF s. The functions showed at low current levels relatively little anodic pol arization away from the open circuit potential, followed by an abrupt (in terms of a logarithmic current scale) increase in polarization as the current approached an apparent terminal value. The curves resemble the behavior expected from a system that is approaching a transportcontrolled limiting current density, or al ternatively, the presence of a sizable ohmic resistance [Jones 1996]. As the curves were constructed using Instant-Off potentials, it could be argued that the pr esence of an ohmic solution resistance component would have been cancelled by t he test method used. However, as noted elsewhere [Sags 1994] an Inst ant-Off (or a high frequency EIS) procedure may not completely cancel out all ohmic polarization components if the corrosion is localized to small parts of the metallic anode surface. That localization may affect vari ous parts of the anode surface as time progresses, so this effect could not be completely rul ed out even if autopsy tests were to show a cumulative, near uniform corrosion wastage of the metallic anode. A transportlimited polarization component could o ccur due to dynamic accumulation of anode corrosion products on its surface, which would effectively shift the equilibrium potential of t he anode toward a more positive value as observed. These issues merit attention in continuation research. For a given test condition and anode service history, the PFs showed notable variability among anodes of the same type in the 1st set of anodes
65 tested. Thus, in the aged condition two of the three type C 1st set anodes in the replicate test yard slabs had relatively elevated EOC values and low apparent terminal currents, while the remaining anode showed much greater activity. Significant variability, although at much lo wer performance levels, existed also for the aged type W 1st set of anodes. Unit-tounit performance variability among each type was much less for the 2nd set of anodes. In the test yard slab the 1st set of W anodes showed notably inconsist ent behavior with that of the 2nd set, even though both sets were nominally the same product. The 1st set, as a group, performed much worse than the 2nd sugge sting a production problem in the former. Consequently, in the following the discussion of the PFs of type W anodes will address principally the functi ons determined for the 2nd set, with the qualification that pr oduction uniformity may be an issue. In general and at moderate aging le vels and humid conditions, the C anodes tended to have more negative open circuit potentials, and faster polarization upon current delivery, than the W anodes. Nevertheless, both anodes tended to reach roughly the same operating point when coupled with passive steel in the test yard slabs. Similar behavior was observed in the galvanostatic tests at 95% RH. Initial tr ends in the 60% RH chamber (1st set of anodes only tested there) showed for both anode types comparable relative PF features to those seen in the other environments, but it should be recalled that early in that exposure the embedding medi um likely still retained much of the initial free water. Later behavior in the 60% RH chamber was obscured by data scatter. Aging of the anodes by delivering curr ent in service was manifested in the test yard slab, for both types and sets of anodes, by the continually decreasing current output. Increasing ohmic resist ance as concrete aged is expected to have been only a minor factor in this decay, since resistivity roughly stabilized in value after the first year, as shown in Figure 34. There was no indication either
66 of any important change in the polarizability of the steel bars that would have resulted in a strong decrease in cathodic current demand as time progressed. As implied by the slow cyclic polar ization test results, the current decreases most likely reflect primarily an evolution of the PF generally toward more positive open circuit potentials and, more importantly, to the onset of elevated polarized potentials at increasingl y lower current levels. That situation is explained in Figure 35 where idealized PF curves are shown for a fresh anode (t=0) and for increasingly aged conditions (t1, t2). The anode is coupled to a rebar assembly that creates a cathodic cu rrent demand as indicated. For each condition the operating point of the anode is denoted by the open circle. The effective ohmic drop between the steel and the anode is given by the vertical space between the open and filled circle s. As the anode ages, the operating point describes the trajectory indi cated by the arrowed red line, with corresponding decrease in current de livery and increase in anode potential denoted also by red arrows. That interpre tation is supported by the observation of such trajectories for both types and both sets of anodes in Figures 16 and 17. The evolution of anode potential with ti me toward more positive values was much faster for the 1st set of anodes than for the 2nd (Figures 12, 16 and 17). This behavior is explained in the fo llowing as a consequence of the steel bars in the chloride cont aminated zone having been co nnected to the anode for the first half of the evaluation period of the 1st set of anodes. Moreover, the Type C 1st set anode for Slab 1 (C-1) showed anomalous behavior in that its potential elevation trend was reversed at la ter exposure times (Figure 12). That anomalous behavior will be considered next as well. The chloride contaminat ed zone contained 1.5% Clion by weight of cement, about 4 times the value of commo nly assumed critical threshold values for corrosion initiation [Li 2001]. The st eel bars there were externally connected to the anode already during casting and curing of each slab, and were kept so
67 over the first 477 days of te sting. That coupling was however not sufficient to prevent corrosion initiation of the four r ebars in that zone, which were found to be in the active condition from the start. Active rebar has low polarizability, and given the quite low concrete resistivity duri ng the first year of operation (~7 to 10 k -cm, Figure 34) and the large steel surf ace area involved, that group of four rebars was an important contributor in deter mining the potential over much of the system. Indeed, as shown in Figure 23, some of those rebars were net anodes even though they were only about 15 cm (6 in) from the point anode. Thus, except for a very short initial period (Figur e 12), for much of the initial year or so of evaluation of the1st set of anodes the anode potential was more or less stabilized at a value not much below that of active reinforcing steel in chloridecontaminated concrete (e.g. ~-400 mV C SE). Consequently the potential-current trajectory for the first se t normally spanned a shorter potential range than if the anode would have been in contact with a more polarizable (i.e. passive) assembly. That latter scenario appli ed to the second anode set, for which the rebars in the chloride zone were never c onnected. Accordingly, the potentialcurrent trajectories for the 2nd set anodes were found to span a wider potential range (Figure 17) more fitting to the outcome described in Figure 33. The auxiliary anodes did not have a galv anic current load so in principle their potential history should be indicative of the effects of self corrosion plus any changes in the composition of the proprietary mortar in the pellet surrounding the metallic core. With the exception of the auxiliary C anode in Slab 1, the potential changes were significant over time (hundr eds of mV) and in the positive direction suggesting degradation. A possible cause for that evolution is diffusion into the surrounding concrete of the substances in the anode pellet that were responsible for zinc activation. For young concrete with the mixture pr oportions of the ORC in the humid outdoors environment used, diff usivity of ionic species typified by that of chloride ions is in the order of 10-8 to 10-7 cm2/sec [Sags 1994], and likely nearer to the high end of the range based on the low values of resistivity
68 o.c E o.c. EA (log scale)A0 A1 A2E E E o.c E o.c.A (log scale)A0 A1 A2E E E PCF t=t2>t1 APC F t=0 PCF t=t1 II IA0 A1 A2 t=t2>t1I t=0 t=t1 Rebar Cathodic Demand II IA0 A1 A2 o.c E o.c. EA (log scale)A0 A1 A2E E E o.c E o.c.A (log scale)A0 A1 A2E E E PCF t=t2>t1 APC F t=0 PCF t=t1 II IA0 A1 A2 t=t2>t1I t=0 t=t1 Rebar Cathodic Demand II IA0 A1 A2 observed [Berke 1992]. Consequently characte ristic diffusion distances of ionic species into the surrounding concrete a fter a year or so could amply exceed 1cm. That distance is in the order of the pellet thickness so substantial dissipation of anode activators with the test time interval would not be surprising. That dissipation could be an important c ontributor to anode performance derating over time, above and beyond any detrimental effects from galvanic current delivery. Figure 35 Idealized evolution of anode PF with aging and effect on operating conditions. EA, IA: anode potential and current; o.c.: open circuit condition. Black circles indicate the polarization conditi on of the anode. Filled circles correspond to the effective rebar polarization condi tion, at a potential equal to that of the anode plus an ohmic drop difference. Arrows indicate trends as aging time increases
69 The more straightforward anode degradatio n effect expected from current delivery is loss of anode mass. Based on the measurements r eported in Section 2.2, rounded-off values of 110g and 45 g will be assigned in the following to the initial anode metallic mass of Type C and W anodes respectively. Those masses correspond respectively to 1.68 and 0.69 mol of Zn, based on the atomic weight of Zn = 65.39 g/mol. Assuming dissolution as Zn+2 ions the maximum (also called the "theoretical") amount of galvanic charge QT that could be delivered can be calculated. The amount, equal to 2 F nM, where F=96.49 k Coul/equivalent is Faraday's constant and nM is the number of moles, is then QT=324 k Coul and QT =133 k Coul for C and W anodes respectively. Anode self corrosion and loss of physical continuity between parts of the anode or with the connecting wires often lower significantly the practica l amount of possible charge delivery by actual cathodic protection anodes, e.g. to ~0.5 QT. Thus, even if other factors have not already had significant derati ng consequences, by the time the anodes evaluated here deliver about 160 k Coul (C ) or 65 k Coul (W), they would be expected to be approaching the end of t heir effective service life. As shown in Figure 14, all type W anodes in the 1st set tested in the yard slabs showed substantial loss of the abili ty to provide galvanic current after having delivered only 10 to 22 kC oul, or only ~7% to 15% of QT. Two of the C anodes in the 1st set experienced faster current derating at Q ~10% of QT, but anode C-1 in that set still re tained appreciable current c apacity at Q ~20% of QT. Performance of the W anodes in the 2nd set showed considerable improvement over the 1st, as current remained at subs tantial levels for all three anodes with Q approaching 25% of QT. The 2nd set of C anodes performed, up to the final data acquired at Q ~10% of QT, similarly to the earlier stages of the1st set when only moderate current decay was taking place. The potential trends as function of Q shown in Figure 15 correlate well with the current trends only for the 2nd set of anodes, likely because of the obscuring effect of coupli ng to the active bars duri ng the first part of the
70 evaluation of the 1st set. The 2nd set potent ial and current trends, if they were to be sustained over later aging stages, w ould suggest that current delivery for these test conditions would reach values well below 100 A, and potentials approach ~-200 mV (thus providing little beneficial effect), at Q ~ to QT for the Type C and W anodes respectively. Such projection would be somewhat, but not extraordinarily less than the behavio r expected for m any galvanic anode systems as indicated earlier. The energized and the auxiliary 1st set Type C anodes in Slab 1 showed anomalous active behavior, as suggested by the highly negative potential of both anodes late in the test period, and by the high current and total charge delivery of the energized anode. This behavior is suggestive of anode activation beyond that expected from the effect of the anode pelle t mortar and the initially chloride-free ORC medium. Such activation is likely to have occurred because of chloride transport from the chloride contami nated zone into the nearby concrete surrounding the anode. As indicated earlier, the characteristic chloride diffusion distance in the sound concrete could eas ily be >> 1 cm after 1year, and it may have been even higher locally due to the in stances of poor consolidation noted earlier. Also as indicated earlier, there we re also signs of in cipient activation of rebars No. 5 and No. 10, (immediately on ei ther side of the chloride zone) in some of the slabs during the last stages of testi ng. Those observations are further indication of substantial chloride diffusion into the previously chloride free concrete. Consequently, the behavior of the 1st set of C anodes in Slab 1 may be explained by that slab being the firs t where chloride intrusion into the previously chloride-free concrete reac hed a sufficient level to promote enhanced activation of that anode. This explanation w ill be further exami ned in continuation testing of the auxiliary and disconnected 1st set anodes of the other slabs to ascertain if signs of activation develop there as well in the future. It is noted that the 2nd set anodes were intentionally pl aced one extra rebar step further than the 1st set from the chlo ride transition line, to minimize the chances of extraneous activation from Clions diffused in from the chloride-rich zone.
71 4.2 Rebar Polarization The poor rebar polarization levels ac hieved by the 1st set of anodes while all rebars in the yard slab were connected can be ascribed to the low polarizability of the acti ve rebars, as discussed ear lier. The rebar current distribution patterns along the slab main direction showed that, before their disconnection, rebars in the chloride-c ontaminated zone were often net anodes, contributing at times a total anodic curr ent comparable to or exceeding the current supplied by the point anode. Du ring that period, the rebar potential distribution along the slab main direction showed clearly that the rebars in the chloride contaminated zone, which exhi bited potentials typical of actively corroding steel, were a substantial polariz ing source for the rest of the system. The steel in the chloride zone of the slabs had potentials similar to, or even more negative than, the typical pot ential of the main anode, which in turn was more negative than that of the bars in the chloride-fr ee concrete zones. When conducting depolarization tests, the overall potentials relaxed relatively little, toward terminal values influenced by t hose of the active rebars. Consequently, the overall depolarization levels were poor. These results indicate also that point anodes of this size and at the placem ent density used, and for the amount of steel present in the slabs, are not likel y to provide substantial levels of conventional cathodic protection of an already corroding rebar assembly. After disconnection of the active rebar s in the 1st set tests, the anodes were indeed the most negat ive elements in the system and the only source of cathodic polarization of the remaining, passive, bars. The steel depolarization levels for the Type C anodes, which were still quite active at that time, improved accordingly to average levels in excess of 100 mV for the rebar group closest to the anode. The 1st set of Type W anodes ha d already degraded considerably by that time and failed to achieve appreciabl e levels of polarization even for only the passive rebars.
72 For the 2nd set of anodes polarization involved always only the passive rebars, and overall rebar polarization was consequent ly improved from the beginning compared with that of the 1st se t. Furthermore, the 2nd set of Type W anodes did not show the deficiency affecti ng the 1st set and steel polarization for those anodes improved accordingly. The composite cathodic rebar polar ization curve shown in Figure 33 shows features well establish by prev ious work, including an apparent Tafel region at low polarization levels followed by incipient indications of the establishment of a diffusion control regi me at greater polarization levels. The main cathodic reaction has the charac teristics of oxygen reduction, and the polarization/current func tion parameters match approx imately those reported elsewhere for steel in moderately hum id concrete [Sags 2003]. Further analysis of this curve is presented in the Modeling section (Chapter 5).
73 5. MODELING 5.1 Introduction A one-dimensional numerical model wa s developed to study the behavior of galvanic anode systems for patch repair app lications in reinforced concrete structures. The anode performanc e is measured by how far away from the patch perimeter (the Â“throwing distanceÂ” xT) an amount of cathodic polarization meeting or exceeding a required minimum (the Â“prevention criterionÂ” CP) can be provided to the passive rebar surrounding the patch3. A generic patch configuration with a 1-D approximation was used in the modeling to calculate the throwing distance that could be achieved by a given num ber of anodes per unit perimeter of the patch area, concrete thickness, concrete resistivity, amount of steel and amount of polarization needed for cathodic prevention. Several numerical models includi ng finite element and boundary element methods have been applied in the past to reinforcing steel corrosion [PresuelMoreno 2005B, Kranc 1994, Sags 1994]. The present model was based on the finite differences method using a r egular spreadsheet program. Experimental data on the anodic polarization as a function of service time (PF curves), and the polarization information for the steel coupled to the anode presented in the previous sections, were used as input parameters in conjunction with other variables that will be introduced later. Resu lts from the model allow determining the current and potential dist ribution on the cathode as a function of the distance from the anode element. 3 The value of CP is an input to the model, to be chosen based on the extent of chloride contamination in the concrete around the patch and how the chloride threshold depends on potential. This issue is discussed separately later on.
74 5.2 Anode Rebar System Modeled The simplified system chosen for implem entation of the model consists of a reinforced concrete slab (which may r epresent a bridge deck, parking structure floor, or a part of a wall) having a patch zone in which all the concrete has been replaced as shown in Figure 36. The patch is assumed to be roughly circular with anodes placed at uniform intervals w ( anode center-to-center distance) just inside the patch perimeter. It is assumed for simplicity that xT is not large compared with the dimensions of the patch so radial spread of the galvanic current is modest. The rebar mat (or mats) in the slab is treated as roughly corresponding to a uniform amount of steel surface to be polarized per unit area of the external concrete footprint. T hus, the problem can be considered on first approximation as a 1-D cu rrent distribution calculati on. Further simplifications involve assuming uniform concrete resist ivity, concrete thickness and rebar polarization properties. The latter include a time-and potential-independent anodic passive dissolution current dens ity and a time independent cathodic reaction (oxygen reduction) current density equal to that determined experimentally on the rebars in the yard slab tests, but constr icted by a limiting current density of fixed value. The polarization function (and its dependence on service time, t, or total charge delivered, Q) of the point anode correspond to that observed experimentally for each of t he two types of anode investigated. The current needed to polarize the region of st eel inside the patch area is neglected for simplicity. A variation of that treat ment was conducted as well to take into account for the presence of that steel and is presented later on. The base conditions outlined above then correspond to an anode placed at the end of a linear concrete beam, with the galvanic current running lengthwise and a distributed sink current density on t he steel given by the local concrete potential and the polarizati on function of the steel. At the anode end of the beam the potential is a function of the end potent ial and the polarizatio n function of the anode. The nomenclature to be used is listed in Table 2.
75 Patch AnodesDeck or Slab W xTL x ESU ES Cp W 0 Patch AnodesDeck or Slab W xTL x ESU ES Cp W 0 Figure 36 Plan view of idealized system chosen for implementat ion of the model 5.3 Principles and Assumptions Calling ESU the steady state potential that the passive rebar in the surrounding zone would achieve in the abs ence of any galvanic coupling with the rebar in the patch, and ES (x,t) the rebar potential at service time t and a distance x away from the patch perimeter, then the performance condition is given by ESU ES (xT,t) = CP (3) All electrode potentials are given in the CSE scale. As discussed earlier, within certain limits, anode aging may sometimes be better described not in terms of service ti me but rather by t he total amount Q of charge delivered since the moment of plac ement in service. In such case the performance condition can be alternatively given as ESU ES (xT,Q) = CP (4)
76 In the following, a formalism on Q will be presented for completeness alongside equations based on time as the aging parameter. However, calculations and examples will be limited for brevity to the case of time as the aging parameter. The desired projection model out put is therefore the value of xT for the chosen values of CP and t (or Q), as function of the other system conditions which serve as model inputs. Following the treatment described el sewhere [Presuel-Moreno 2005B] for similar conditions, at any given dist ance x charge conservation under the above assumptions requires that the concrete potential satisfies: d2EC/dx2 = SF tC -1 iS (5) The following boundary conditions apply: At the patch perimeter (anodes placed there), by Ohm's law: IA=w tC -1 dEC/dx |x=0 (6) At the outer slab edge (no current leaving the slab): dEC/dx = 0|x=L (7) The net steel current is assumed to depend only on potential, iS(ES). It is noted that given iS(ES), setting iS=0 yields the value of ESU. The anode current is assumed to depend on both potent ial and aging condition, IA(EA, t) (or IA(EA,Q)). Accounting for the presence of the cu rrent constriction resistances, and by using the configur ation parameters k1= SF tC -1and k2= SF w, the ruling equation and anode-end boundary condition become:
77 d2EC/dx2 = k1 iS (EC-RS iS) (8) IA(EC+RA IA)= k2 k1 -1 dEC/dx |x=0 (9) Thus, giving as inputs k1, k2, L, RS and RA as well as the functional relationships iS(ES) and IA(EA, t) (or IA(EA,Q)), solution of Equation (5) with the boundary conditions in Eqs. (6 to 9) yields EC(x, t) (or EC(x, Q)) as output. The use of the parameters k1 and k2 permits obtaining solutions that are roughly scalable for all systems having the same values of those parameters, and the same anode and steel polarizat ion properties. Generality is precluded however if, for example, the factors t hat determine local resistanc e vary sufficiently from system to system. Post-processing of that output then yields the value of the throwing power xT for any chosen criterion CP at the specified anode aging condition, therefore achieving the objective of the performance projection model. The sign convention used in writing the system equations is to declare iS < 0 when iS is a net cathodic current. T hat choice permits keeping the customary polarity designat ion when evaluating the re sults, with electrode potentials referred to the electrolyte and absolute values of activation-polarized anodic/cathodic current densities respec tively increasing/decreasing with potential. Interpretation of the findings is thus facilitated compared with other alternatives [Kranc 1994]. 5.4 Implementation of the Model 5.4.1 Model Inputs 188.8.131.52 Overall Dimensions and Global Concrete Properties The ranges of values for model inputs k1and k2 were chosen to bracket typical dimensional and concrete resist ivity conditions that may be encountered
78 in the field. L was fixed at 200 cm which approaches a semi-infinite condition compared with the throwing pow er values that may be usually expected; the solution is in that case conservatively evaluated and with low sensitivity to the precise value of L. 184.108.40.206 Local Resistance The following are rough estimates of the current constriction resistances of rebar and anode, intended to refine to some extent the throwing power calculations. More accurate solu tions would necessitate use of a multidimensional model, but such step ma y be premature consid ering the limited extent of the performance data base available at present. Model inputs RS and RA were estimated from geometric considerations and from the input values of k1 and k2 (Table 3). For RS the approach corresponding to the current flow betw een two concentric cylinders was assumed to apply on first approximation. In su ch case the length-specific current constriction resistance RSUL is given by [Sags 1994]: RSUL= (2 )-1 ln (tC/ S) (10) where S is the rebar diameter (diame ter of the inner cylinder) and tC is an approximation to the diameter of the outer cylinder, in this case taken to be in the order of the characteristic thickness of the system. Taking into account the problem scaling, the term RS in Eq. (8) is then RS= S RSUL (11) Complications in estimating RA stem from the metallic anode being surrounded by consecutive shells corresponding to corrosion products, proprietary anode pellet mo rtar, anode placement mortar/concrete if different
79 from the slab concrete, and finally the sl ab concrete itself. Moreover, current distribution can be highly complicated if t he metallic surface of the anode is not uniformly activated. In such ca se the polarization function IA(EA, t), even if determined by instant-Off measurements, may itself contain a considerable ohmic component per argument s described in detail by Sags  and as discussed elsewhere in this report. Assu ming that only the uniform part of the current constriction effect needs to be considered, the value of RA may be estimated on first approximation as corre sponding to that for the space between a sphere of effective diameter A in an spherical medium of diameter in the order of tC and resistivity equal to that of the sl ab concrete [Landolt 2007], so that RA ~ -1 [( A)-1 tC -1] (12) Assuming that the anode pellet mortar is highly conductive and that any ohmic effects due to corrosion product accumulation are already built into IA(EA, t), then the effect ive anode diameter A is considered to be in the order of the characteristic outer dimension of the anode mortar pellet, A ~ (pellet width + pellet thickness). A rounded-off value representative of both anode types evaluated was used (Table 3). 220.127.116.11 Polarization Function Â– Steel The function iS(ES) for the model realizations explored below is chosen to be representative of the behavio r of the steel used in the test yard slabs. The function is abstracted starti ng from the combined data set of instant-Off potential measurements as function of rebar curr ent given earlier in Figure 33. The abstraction consists of assuming for the cathodic reaction an increasing current density with decreasing potentia l following simple Tafel kinetics, until a nominal limiting current density value iL is reached. For more negative potentials the current is fixed at iL thus creating a simplified comb ined activation-concentration limited cathodic polarization curve. The anodic reaction on the rebar is assumed
80 to correspond to a potential-independent passive dissolution current density iP. Thus when i0S 10^((ES-E0S)/ CS) <= iL : iS = i0S 10^((ES-E0S)/ CS) iP (13) and when otherwise: iS = iL iP (14) Where i0S, E0S and CS are the nominal exchange current density, nominal equilibrium potential and nom inal Tafel slope respectively for the species undergoing the cathodic reac tion. The values of iP, i0S E0S 4 and CS were determined by least square fitting to the data shown in Figure 33 (Table 3), treating the portion of the polarization diagram spanned by the data as if the cathodic reaction were simply activati on-polarized. The resulting abstracted function is shown by the solid line in Figure 33. Application of the chosen parameter set resulted in a visually plausibl e fit function. However, it is cautioned that the fit procedure is prone to produce alternative parameter sets with nearly similar fit quality, so the set chosen for these calculations should be viewed only as a representative example of the st eel polarization function parameters. The value of iL is a preset parameter. A comparatively large value (iL = 2 A/cm2) was chosen to represent cases wher e cathodic diffusional limitation was unlikely (e.g. concrete atmospherically exposed at moderate relative humidity regimes [Sags 2003]). Smaller iL values were chosen based on previous findings [Sags 2003] to repres ent moist conditions. 4 The values of i0S E0S are not independent for the purposes of these calculations [Kranc 1992] so E0S was specified arbitrarily.
81 18.104.22.168 Polarization Function Anode (PF) As indicated earlier, the following applic ation is limited to the use of time as the anode aging parameter. The functions IA(EA, t) from instant-Off measurements for individual anodes at various t have been shown when presenting the PF results in Secti on 3. Tests with various abstraction representations showed that a function of the form shown in Eq.(15) yielded a reasonably fit to the experim ental potential-current curv es of individual anodes under nearly all circumstances. Eq. (15) is written with service time as the age parameter, but it is expect ed that on first approximation a comparable form could be used with Q as t he aging parameter. EA(IA,t) V-1= EA0(t) V-1 + (IA/IA0(t))n(t) (15) Here EA0 is the unpolarized potentia l of the anode, and IA0 is the anode current that, when delivered, results in 1V of anode polarization over EA0 (effectively corresponding to an anode potential close to that of isolated passive rebar, where the anode provides essent ially no protection). The exponent n indicates how steeply the anode output approac hes that level as current demand approaches that limit. It is em phasized that Eq.(15) is a convenient empirical fit function and no relationship with fundamental causes is implied. The parameters EA0, IA0 and n were obtained by least square fit from the polarization curve of each individual anode at various ages (Table 3). Those parameters exhibited significant variability for the replicate specimens of a given type of anode at a given age, reflecting the unit-to-unit vari ability in behavior noted earlier. For the purposes of obtaining a generic agedependent anode performance curve, the combined trends of EA0, IA0 and n with age for all anode specimens of a given type were displayed graphically and a repr esentative simplified variation function with age was abstracted in each case. Convenient empirical relationships thus found, again not necessarily reflecting basic issues were:
82 EA0(t) = EB + a (t/tu) (16) IA0(t) = IB (t/ tu) b (17) n(t) = nB (t/tu) c (18) Where tu is the time unit (e.g. months). Those relationships reflect the observation that the unpolarized potential tended to increase roughly linearly with time, while both the limit condition current and the steepness of approach to it tended to increase with time, but at a rate that decayed as time progressed (which resulted in parameters b and c being significantly <1). 5.4.2 Implementation of the Mo del Computational Procedure Numeric solutions of the ruling eq uation with boundary conditions were obtained by the finite differences method using a 20-element array and an iterative Jacobi technique with a re laxation factor between consecutive calculations chosen to achieve stability and prompt convergence of the solution. Separate calculations were performed for ea ch value of time t. The functions iS(ES) and IA(EA, t) were entered as numeric a rrays, which permitted manipulation to obtain reciprocal functions by lookup and interpolation as well as easily obtaining values of expressions such as iS (EC-RS iS) or IA(EC+RA IA). Entry by numeric array also provided flexibility to accommodate if desired functions other than the analytical expressions given in the previous section. General model parameters for calculated cases are given in Table 4.
83 5.4.3 Model Appl ication Scope The model is not intended for precise design purposes, but rather as an exploratory tool to obtain insight and i dentify broad operating conditions. As such sweeping simplifications were made su ch as the use of a one-dimensional representation, an approach t hat could be vastly improved if sufficiently accurate data on component properties be came available. The xT model output is obtained by interpolation between consecut ive spatial nodes, so reported values should be viewed as only approximate estimates with only marked changes meriting note. In these calculations t he spatial node array is not intended to replicate the placing of indivi dual rebars. Thus values of xT are reported nominally with cm resolution for com parison purposes, with the understanding that in an actual rebar gr id the polarization pattern would be strongly influenced by the local geometry. Fu rther model development is expected in continuation work [Dugarte 2010]. 5.4.4 Sensitivity Analysis A sensitivity analysis was performed to establish how model results may be affected by variations in the choice of assumed steel polarization parameters. The parameters selected for this analys is were the nominal Tafel slope for cathodic reaction on steel ( CS), and the anodic passive current density on steel surface (iP), both of which may be affected by considerable uncertainty. As a slave variable, the nominal exchange current density for the cathodic reaction of steel (i0S) was chosen coupled to the variations in iP and CS so that the value of ESU always remained fixed at the same value used for the baseline model computations. That way the calculations evaluated sensitivity to the polarizability of the steel without the added complicati on of changes in the unpolarized steel potential. The value of CS was varied from its centra l scenario conditions value of 138 mV downwards to 100 mV (an appr oximate low end of commonly reported
84 values [Glass 2000, Sags 2003]), and in to opposite direction, but by the same amount, to 176 mV to span a plausible r ange of conditions. The parameter iP was varied from its central sc enario choice of 2.6 E-08 A/cm2 to and 2 times that value (1.3 E-08 and 5.2E-08 A/cm2 respectively) to account for an appreciable uncertainty range. All ca lculations were performed with k1=1k and k2 =50 cm, for 10 mo age of both types of anode. Only cases with zero current to the patch region were explored.
85 Table 2 Nomenclature of m odel variables and parameters. _____________________________________________________________________________________ t (s) amount of time since anode placement and energizing Q (coul) integrated electric charge de livered by the anode since placement and energizing x (cm) distance away from perime ter of the patch (where anodes are placed) xT (cm) throwing power CP (V) cathodic prevention criterion value L (cm) distance from perimeter of t he patch to outer edge of the concrete slab. tC (cm) concrete slab thickness w (cm) anode center-to-center placem ent distance along patch perimeter SF(cm2-cm-2) steel placement density (amount of steel surface area per surface area of concrete slab footprint) S (cm) rebar diameter A (cm) effective anode diameter -cm ) concrete resistivity iS (A-cm-2) net current density on steel surface iP (A-cm-2) anodic passive current density on steel surface iC (A-cm-2) cathodic current density at the steel surface IA (A) galvanic current delivered by anode EC (V) potential of the concrete away from the immediate proximity of the steel surface or the metallic surface of the anode. ES (V) potential of the concrete at a point immediately adjacent to the steel surface ESU (V) unpolarized steel potential
86 Table 2 (Continued) ________________________ _____________________ ______________ EA (V) potential of the mortar at a point immediately adjacent to the metallic surface of the anode RSUL ( -cm) effective length-specific current c onstriction resistance of concrete at the steel surface RS ( -cm2) effective area-specific current cons triction resistance of concrete at the steel surface RA ( ) effective current constriction resistance of concrete around the active zone(s) of the meta llic portion of the anode. k1 ( configuration parameter: k1 = SF tC -1 k2 (cm) configuration parameter: k2 = SF w i0S (A-cm-2) nominal exchange current density, cathodic reaction on steel E0S (V) nominal equilibrium potent ial, cathodic reaction on steel CS (V) nominal Tafel slope, cathodic reaction on steel iL (A-cm-2) nominal limiting current density, cathodic reaction on steel EA0 (V) unpolarized anode potential EB, a(V) EA0 time dependence parameters E'B, a'(V) EA0 Q dependence parameters IA0 (A) anode current demand resulting in 1V polarization IB (A), b IA0 time dependence parameters I'B (A), b' IA0 Q dependence parameters n anode potential steepness of variation with current demand nB, c n time dependence parameters n'B, c' n Q dependence parameters tu (e.g. mo) time unit for parameter abstraction Qu (e.g. Coul) charge unit for parameter abstraction __________________________________________ ____________________
87 Table 3 PF, steel and other parameters for model cases. Table 4 General model param eters for calculated cases. Steel: i0S = 2.03 E-9 A-cm-2 E0S = -0.00 VCSE CS = 0.138 V iP = 2.59 E-8 A-cm-2 iL = 2 E-6 A-cm-2 ESU= -0.153 VCSE ** S = 2.2 cm *Nominal value **Value resulting from the other inputs Parameters used as base for k1, k2 cases and for constriction resistances A = 5 cm tc = 20 cm L = 200 cm SF = 1 Anode EB (V) a (V) IB (A) b nB c C -1.16 0.0057 2.0E-03 -0.43 2.7 -0.03 W -0.85 0.0085 5.4E-02 -1.7 0.81 0.33 k1 (k ) 3.33 1.00, 3.00 k2 (cm) 25, 50, 75 CP (V) 0.10, 0.15, 0.20 T (months) 1, 4 10, 13 Anode Current to Steel in Patch 0,
88 5.4.5 Model Validation Validation of the mode l projections by comparison against a well characterized actual system was per formed and results are presented in Appendix 1. There, t he model was applied to compute the extent of polarization delivered to the passive rebars in the yard slabs by the sacrificial point anodes at various ages. The results supported t he validity of the approach used here. 5.5 Model Results Figure 37 presents model results fo r the C anodes, showing the throwing distance xT as function of k1 and using the cathodic prev ention criterion value CP as a secondary parameter, for a fixed value of k2=50 cm and for anode ages of 1, 4, 10 and 13 months respectively. Those ages were chosen to correspond to the times for which PF data were collected in the yard slabs. Also for the C anodes Figure 38 shows as a function of time, and for a fixed value of k1=1k the effect of variations in the value of k2 on the throwing distance. Figures 39 and 40 show similarly displayed results for the W anodes In all cases, the polarization amount can be converted into steel current density by reference to Figure 33; the results are iS = 0.11, 0.29 and 0.70 A/cm2 for CP = 100, 150 and 200 mV respectively. It is noted that for these model calculati ons the area of steel inside the patch was considered to be relatively small, and the current needed to polarize this area was neglected. The resulting projections are consequently somewhat optimistic, and the derating effect of cu rrent flowing into the patch is discussed afterwards. The results can be best interpreted by recalling that a value of k1=1k at the center of the horizontal axis in Figures 37 and 39, corresponds to a reinforced concrete slab of thickness tC=20 cm (8 in), a steel density factor SF=1 and a concrete resistivity = 20 k -cm, baseline conditions that may be considered typical of many bridge deck or parking structure conditions. The other
89 k1 values for which results are given, 0.33 and 3.3 k correspond for the same tC and SF combination to concrete resistivities of 6.7 and 60 k -cm, or severe and mild corrosion propensity conditions respectively. Since SF was chosen as unity for theses examples, the parameter value k2= 50 cm corresponds to a placement density of one anode for every 50 cm of patch perimeter, which may be considered to be a reasonable practical value. Finally, CP values of 0.1, 0.15 and 0.2 V represent depolarizat ion criteria for cathodic prevention that are increasingly more conservative [Pre suel-Moreno 2005B]. In Figures 38 and 40 and for the above combinations, variations of k2 to values of 25 cm and 75 cm represent anode spacing near the tighter or wider extremes respectively of expected practical applications. Figure 41 presents the results from t he sensitivity analysis. Changes in CS in either direction from the central scenario resulted in moderate relative changes (by about a factor of 2 or less) in the value of the projected throwing distance for the 100 mV polarization crit erion. The effect was comparably moderate for the 150 mV crit erion when the excursion was toward greater values of CS, but if CS was reduced to 100 mV the result ing lower rebar polarizability became effectively prohibitive. For t he most demanding criterion, 200 mV, excursion of CS toward 176mV increased xT above the zero or nearly zero values at the central scenario, but not enough to exceed 10 cm. Analogous to the effect of variations in CS, changes in iP had moderate impact on the 100 mV criterion throwing distance, and stronger rela tive effect for the cases of the more demanding criterion values. Overall, the sensitivity calculations showed that relatively wide changes in key steel pol arization parameters induced no dramatic change in the highest projected values of xT for the age condition examined. Large relative changes in xT were projected for the more demanding polarization criteria cases, but the abs olute values in those case s tended not to be large.
90 Figure 37 Model projections of throwing distance for C anodes at the indicated service times. All graphs are for k2 = 50 cm, CP as shown. Absent symbol/line: polarization not achievable or xT < 1 cm. 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 02V 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 0.2V 10 mo 1 mo 4 mo 13 mo 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 0.2V 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 0.2V
91 CP = 0.1V1 10 100 110100x T /cm k2=25 cm k2=50 cm k2=75 cm CP = 0.15V1 10 100 110100x T /cm k2=25 cm k2=50 cm k2=75 cm CP = 0.2V1 10 100 110100Time / monthsx T /cm k2=25 cm k2=50 cm k2=75 cm Figure 38 Model projections of throwing distance for C anodes, as a function of service time. Legends indicate values of k2 (cm). Absent symbol/line: polarization not achievable or xT < 1 cm.
92 Figure 39 Model projections of throwi ng distance for W anodes at the indicated service times. All graphs are for k2 = 50 cm, CP as shown. Absent symbol/line: polarization not achievable or xT < 1 cm. 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 02V 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 0.2V 1 mo 4 mo 10 mo 13 mo 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15 V Cp = 0.2V 1 10 100 100100010000 K1 / x T /cm Cp = 0.1V Cp = 0.15V Cp = 02V
93 Figure 40 Model projections of throwing distance for W anodes, as a function of service time. Legends indicate values of k2 (cm). Absent symbol/line: polarization not achievable or xT < 1 cm. CP = 0.1 V1 10 100 110100x T /cm k2 = 25 cm k2 = 50 cm k2 = 75 cm CP = 0.15 V1 10 100 110100x T /cm k2 = 25 cm k2 = 50 cm k2 = 75 cm CP = 0.2 V 1 10 100 110100 Time / monthsx T /cm k2 = 25 cm k2 = 50 cm k2 = 75 cm
94 Figure 41 Sensitivity analysis of m odel projections to the choice of CS and iP, for 10 mo anode age. Dashed lines denote the central scenario. Absent symbol/line: polarizatio n not achievable or xT < 0.1 cm. 0.1 1 10 100 0.10.120.140.160.18 / Vx T / cm Cp = 0.1V C p = 0.15V Cp = 0.2V C Anodes 10 mo 0.1 1 10 100 012345ip / Acm-2x T / cm Cp = 0.1V Cp = 0.15V Cp = 0.2V W Anodes 1 0 mo 0.1 1 10 100 0.10.120.140.160.18 / Vx T / cm Cp = 0.1V Cp = 0.15V Cp = 0.2V 0.1 1 10 100 012345ip / Acm-2x T / cm Cp = 0.1V Cp = 0.15V Cp = 0.2V
95 5.6 Model Discussion Using the C anode cases as an ex ample, and for the above assumed baseline conditions, the 1 -month projections indica te an appreciable throwing distance, 33 cm for a 100 mV polarization cr iterion. For that polarization level reducing the anode spacing to 25 cm elevated xT to 40 cm, while it still reached 29 cm even for the 75 cm wide anode placem ent case. The projected throwing distance for k2=50 cm however degraded to less than 10cm when the wide anode spacing and a more conservative polarization criterion (200 mV) was used. A throwing distance of less than 10 cm may be considered to be quite ineffectual as it is in the order of rebar spacing in many applications. The other scenarios in the same figures can be similarly evaluated for insight. The projected throwing distance decr eased with service time to various extents as shown in figures 38 and 40, depending strongly on the polarization prevention criterion used. Thus, continuing with the above example, for baseline conditions and 13 mo age the projected 100 mV throwing distance for the 50 cm anode spacing was reduced to 23 cm. Fo r the same anode spacing Increasing the polarization criterion to 150 mV lowe red the projected throwing distance to less that 10 cm, and the model projected that the 200 mV criterion was no longer reachable. The 200 mV criterion could be met at 13 mo by reducing the anode spacing to 25 cm, but the projected throwing distance was poor (<10 cm). The projections for the W anodes (Figures 39 and 40) resulted in xT values that were comparable to those of t he C anodes at early ages, but generally smaller later on, in keeping with the re lative anode polarization behavior of the anodes in the yard slab tests as noted earlier. Otherwise, the same general trends and observations noted for the C anodes apply here as well. As indicated earlier, the projections would become more pessimistic when current demand by the steel in the patch area is considered. The extent of this
96 effect was addressed by evaluating model projections for the case where the region inside the patch required half of the galvanic current from the anode, so that the anode current is distribut ed equally between the patch area and the surrounding concrete. The results are pr esented in Table 5 for the baseline condition with k1=1k and a 50 cm anode spacing. As expected the projected performance degraded compar ed to the cases where the entire anode current flowed outside the patch. The extent of degradation depended particularly on the polarizability of the anode. T hus the projected effect was relatively small early on when the added current demand caused only a relatively small shift of the anode potential toward more positive values However, the shift would be more pronounced as later anode ages are consid ered, where a consequently steeper polarization curve applies. At age 13 m onths the projections indicated a substantial reduction in t he throwing distance to about to of the value obtained when no current to the patch was assumed depending on anode type. In an actual system the patch zone may be small compared to its surroundings, so the galvanic current partition and resu lting effect in polarization would be somewhat in between the two extreme situat ions (no current vs. of the current going to the patch) considered in Table 5.
97 C Anode Age CP / VXT /cmXT /cm 0.13326 0.151811 0.281 0.12819 0.15145 0.24Â– 0.12514 0.1510Â– 0.2Â–Â– 0.12312 0.158Â– 0.2Â–Â– 10 mo 13 mo 1 mo 4 mo A lternative ( current to patch) Base Cases (No current to patch) W Anode Age CP / VXT /cmXT /cm 0.12922 0.15158 0.25Â– 0.12719 0.15135 0.23Â– 0.12110 0.156Â– 0.2Â–Â– 0.1163 0.151Â– 0.2Â–Â– 10 mo 13 mo Base Cases (No current to patch) Alternative ( current to patch) 4 mo 1 mo Table 5 Effect of current demand by the patch zone. Projections over periods of time longer than 13 months are subject to considerable uncertainty as those would be beyond the testing period that yielded the PF data used as input to t hese model calculations. However, the trends from Figure 23 and the performance derating information as function of total charge in Figures 16 and 17 suggest that both types of anodes may settle, under conditions resembling those in the test yard slabs, into quasi-steady state operating currents in the order of ~0.1 mA after another year or two of operation. The corresponding charge delivery would be~3 .2 k Coul/year. Barring the effects of any other aging mechanism (such as di ssipation of pellet activator compound into the surrounding concrete), and based on the arguments made in previous section, anode operation at that rate might conti nue over about a decade of years range before approaching excessive consumption levels. Due to the relative shape of the anode and rebar pol arization curves, under the conditions modeled here the anodes tend to operate near the limit current condition defined by the upward leg of the PF. As show n in Figure 15, at age 13 months that current for both C and W anodes is in the order of to mA. As noted before,
98 by 13 months age the projected thro wing distance had begun to shorten considerably especially for the more dem anding polarization criteria. The effect on xT of further lowering the anode current by twofold or more toward ~0.1 mA may be inferred from the projected decrease of xT as anode spacing increased in comparable proportions (effectively loweri ng the anode current available per unit of patch perimeter) and also from the results of halving the anode current shown in Table 5. Such comparison suggests that as anode currents decay into the order of 0.1 mA the thro wing distance for satisfying the 100 mV polarization criterion would become two or more time s smaller than those projected for 13 mo, yielding quite poor pr ojected performance. By t he same argument, the more demanding polarization criteria (150 mV, 200 mV ) would result in even poorer or nil projected long performance. In summary, the model projections together with the aging information detailed in Chapter 3 suggest that anode performance in the likely scenarios discussed above, as measured by the th rowing distance, may seriously degrade after only a few years of operation even if a 100 mV corrosion prevention criterion were assumed. It has been proposed in the technical literature that, even with small polarization levels, significant corro sion control benefits can accrue from sustaining cathodic current densities with low values ranging from 0.2 A/cm2 to as little as 0.02 A/cm2 on passive steel [Pedeferri 1996, Sergi 2008]. The lower end of that range may not be relevant to atmospherically exposed concrete, for which a low end of 0.05 A/cm2 has been cited instead [Pedeferri 1996]. Those low end values would correspond to polarizat ion levels in the order of only 34 to 65 mV for 0.02 and 0.05 A/cm2 respectively (Figure 33), with consequently greater throwing distances than those obtai ned for the 100 mV cases. It is noted however that the 0.2 A/cm2 high end of the range does not improve prognosis relative to the situations addressed ear lier, as it corresponds in the present
99 model to a CP value approaching 150 mV (Figure 33). That case has already been addressed above, and yielded generally poor performance projections. There are indeed benefits from long term application of cathodic currents, in particular from an increase in pH near the surface of t he rebar and also a decrease in chloride content if contami nation already exists [Glass 1997, 2007]. Those effects are to be expected at s ubstantial cathodic current densities. However, the extent of benefits at the very low polarization levels that correspond to the low end of the current density-based cr iteria awaits suffi cient experimental demonstration. Should future research develop adequate supporting evidence, the less conservative criterion requirement s may merit further consideration. A contrary argument, for a more conservative corrosion prevention criterion, may be made based on t he analysis by Presuel-Moreno [2005A] summarized in Figure 42. As indicated ther e, polarization to as much as 400 mV below the normal open circuit potential (which is some -0.1 V vs SCE, or ~-0.18 V CSE) of passive steel in atmospheric ally exposed concrete may be required for an order-ofmagnitude increase in t he chloride corrosion threshold. If that were the case, cathodic polarization in t he order of 100 mV would only achieve a marginal threshold increase. In the li ght of such conservative scenario, the model projections would question the ability of point anodes of the size investigated here to provide a useful corrosion prevention effect. The precise dependence of corrosion threshold on potential of the passive steel is a critical issue in interpreting the results of t he present investigation. However, as evidenced from the scatter of availabl e data in Figure 42 there is much uncertainty as to the extent of that effect The issue is much in need of resolution by development of reliable dat a in future investigations.
100 Figure 42 Summary of information towa rd establishing a cathodic prevention polarization criterion*. Each symbol represents an instance of documented corrosion threshold for passive steel held in concrete at the pot ential indicated. Arrows indicate that the chloride threshold was equal or hi gher than the corresponding value. The dashed line yields the proposed cathodi c prevention potential for a given level of protection. Potentials are in the saturated calomel electrode scale; potentials vs CSE are 77 mV lower t han the value indica ted. See PresuelMoreno [2005A] for the referenc es cited in the figure. -600 -500 -400 -300 -200 -100 0 100 200 300 0.1110CT(Cl % by wt of cement)EpvsSCE (mV) Data spread in this range Lower bound. Presuel(OPC) -CPN Alonso-MPI Alonso(OPC)-MPI Arup(SRC)-CPI Breit-MPI Breit(OPC)-MFI Breit(BFSC)-MFI Breit(SRC)-MFI Pedeferri[6,77]-CPN&I Sandberg(SRC)-CPI Sandberg(SRC)-CFI Sags-CFN Soresen-MPI Sandberg(SRC)-CFN Sandberg(BFSC) -CFN Sandberg(BFSC) -CPN Sandberg(SRC)-CPN -600 -500 -400 -300 -200 -100 0 100 200 300 0.1110CT(Cl % by wt of cement)EpvsSCE (mV) Data spread in this range Lower bound. Presuel(OPC) -CPN Alonso-MPI Alonso(OPC)-MPI Arup(SRC)-CPI Breit-MPI Breit(OPC)-MFI Breit(BFSC)-MFI Breit(SRC)-MFI Pedeferri[6,77]-CPN&I Sandberg(SRC)-CPI Sandberg(SRC)-CFI Sags-CFN Soresen-MPI Sandberg(SRC)-CFN Sandberg(BFSC) -CFN Sandberg(BFSC) -CPN Sandberg(SRC)-CPN -600 -500 -600 -500 -400 -300 -200 -100 0 100 200 300 0.1110CT(Cl % by wt of cement)EpvsSCE (mV) Data spread in this range Lower bound. Presuel(OPC) -CPN Alonso-MPI Alonso(OPC)-MPI Arup(SRC)-CPI Breit-MPI Breit(OPC)-MFI Breit(BFSC)-MFI Breit(SRC)-MFI Pedeferri[6,77]-CPN&I Sandberg(SRC)-CPI Sandberg(SRC)-CFI Sags-CFN Soresen-MPI Sandberg(SRC)-CFN Sandberg(BFSC) -CFN Sandberg(BFSC) -CPN Sandberg(SRC)-CPN Presuel(OPC) -CPN Alonso-MPI Alonso(OPC)-MPI Arup(SRC)-CPI Breit-MPI Breit(OPC)-MFI Breit(BFSC)-MFI Breit(SRC)-MFI Pedeferri[6,77]-CPN&I Sandberg(SRC)-CPI Sandberg(SRC)-CFI Sags-CFN Soresen-MPI Sandberg(SRC)-CFN Sandberg(BFSC) -CFN Sandberg(BFSC) -CPN Sandberg(SRC)-CPN
101 CONCLUSIONS a. Galvanostatic tests under controll ed humidity and test yard slabs with reinforced concrete for both types of anodes revealed PFs with comparable features. The PF s showed relatively little anodic polarization from an open circuit potential at low cu rrent levels, followed by an abrupt increase in potential as the cu rrent approached an apparent terminal value. This limiting current for a new anode was in the order of 1.5 mA and 2.0 mA for C and W anodes respectively. For aged anodes (13 months service) it was in the order of ~0.6 mA and 0.4 mA for C and W anodes respectively. The curves resemble the behavior expected from a system that is approaching a diffusion-cont rolled limiting current density, or alternatively having a sizable ohmi c resistance polarization component. b. For a given test condition and anode service history, the PCFs showed significant variability among units of the same type within a given set of anodes delivered by the suppliers. For one of the anode types (W anodes), the 1st set tested performed notable worse as a group than the 2nd set (delivered 3 years later) s uggesting an initial manufacturing problem. For the 2nd set of anodes the unit-to-unit performance variability among each type was much less. c. Aging of the anodes by delivering cu rrent in service was manifested by a continually decreasing current output in the test yard slabs. As implied by Slow Cyclic Polarization test result s, those changes reflected an evolution of the PF generally toward more positive OC potentials and, more importantly, to the onset of elevated polarized potentials at increasingly lower current levels. The value of OC potential for a new anode (1 month)
102 was in the order of ~-1.15 V and -0. 85 V for C and W anodes respectively. When the anode was 13 months old t he OC potential decayed to ~-1.09 V and -0.75 V for C and W anodes respectively. d. Coupling of the anodes to rebar at the time of casting in concrete containing 1.5% Clby weight of cement was not sufficient to prevent corrosion initiation of the steel rebars in that zone. Testing for about 480 days in reinforced concrete slabs containing those corroding rebars in addition to passive rebars showed that the point anodes induced only modest to negligible polarization of the steel assembly. That effect was ascribed to the low polarizability of the actively corroding rebars. e. Upon disconnection of the actively corroding rebars wh ile evaluating the first set of anodes, one of the anode types produced cathodic polarization levels exceeding 100 mV in the passive rebars that were in close proximity to the anode. The other anode type (suspected of deficiency in the first set evaluated) had already exhausted mu ch of its polarizing ability in the preceding interval and produced only neg ligible effects on the surrounding passive steel. f. A continuation test with a second set of anodes of each type, coupled with only passive rebar, showed substantial polarization levels (100 mV to 200 mV) of rebar in the proximity of either type of anode. Current delivery decreased with service time but apprecia ble polarization levels were still achieved in nearby rebars after ~500 days of operation g. Most anode units of both types in the 1st set tested showed on average significant current delivery decrease after delivering a cumulative anodic charge that was only about 10% to 20% of the maximum theoretical amount (QT). Values of QT were ~ 324 k Coul and 133 k Coul for 1st set C and W anodes respectively. Anodes in the 2nd set tested showed less
103 aging effects over the dur ation of the test, wh ich was conducted until reaching up to about 25% of the theoretical limit. Estimates based on the extent of derating observed in the test interval suggest that in the absence of other degradation effects, anodes of this type may be able to function adequately up to about to of the theoretical consumption limit. h. Quantitative polarizati on functions of the steel rebar were found to agree with the results of previous investi gations. A steel PF abstraction was used as input for modeling projections of anode performance in a generic reinforced concrete system. i. A numerical abstraction of the PF graphs for the anode representative of the anodic behavior at various stages of anode aging was obtained using a mathematical function t hat reasonable fit to the experimental data. This function was written with service time as the age parameter. j. Improved perfo rmance of the 2nd over the 1st set of anodes was clearly observed. However, anodes from 2nd set were connected to passive rebar only, and enhanced performance may hav e resulted also from the low resistivity (nominally ~5000 -cm) medium cast around the 2nd set anodes. k. Modeling of a generic patch configuration with a one-dimensional approximation was used to calculate t he throwing distance that could be achieved by a given number of anodes per unit perimeter of the patch, concrete thickness, concrete resistiv ity, amount of st eel and amount of polarization needed for cathodic prev ention. The model projections together with the aging information determined experimentally suggest that throwing distance in likely ap plication scenarios may seriously degrade within a few years of operation, even if a relatively optimistic 100 mV corrosion prevention criterion were assumed. The model was
104 validated by comparison against the ex perimental results from the test yard slabs. l. Less conservative, current densitybased corrosion prevention criteria have been proposed in the literature t hat would result in improved throwing distance projections und er some conditions yet to be substantiated. However, other invest igations suggest that a significantly more conservative corrosion preventi on criterion than 100 mV polarization may be necessary instead. The latter case would question the ability of the point anodes to provide a useful corrosion prevention effect for reinforcement around the patch.
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110 Sags, A.A. and S.C. Kranc, S.C.Â“Model for a Quantitative Corrosion Damage Function for Reinforced Concrete Marine S ubstructureÂ”, Rehabilitation of Corrosion Damaged Infrastructure, Proceedings, Sympos ium 3, 3rd. NACE Latin-American Region Corrosion Congress, NACE Inte rnational, Houston, (1998), p.268. Sags, A.A., Pech-Canul, M.A., and Al-Mans ur, A.K.M., Â“Corrosion macrocell behavior of reinforcing steel in partially submerged concrete columnsÂ”, Corr. Sci. Vol. 45 (2003), p. 25-30. Sags, A.A, Balakrishna, V. and Powers, R .G, Â“An approach for the evaluation of performance of point anodes for corrosion prevention of reinforcing steel in concrete repairsÂ”, Paper 1083, International Federation for Structural Concrete (FIB) symposium: Â“Structural concrete and time: La Plata, Argentina., September 28-30, 2005. Sags, A., Kranc, S. and Lau, K. "Servi ce Life Forecasting for Reinforced Concrete Incorporating Potential-Depen dent Chloride Threhslold", Paper No. 09213, Corrosion /09, NACE Internat ional, Houston, (2009A), p. 22. Sags, A.A., Kranc S.C. and Lau, K., Â“Modelin g of Corrosion of Steel in Concrete with Potential-Dependent Chloride Thres hold", NACE International, Houston, (2009B). Sergi, G. and Page, C., "Sacrificial anodes for cathodic prevention of reinforcing steel around patch repairs applied to chlori de-contaminated concrete". In: Mietz, J. et al (eds.), Corrosion of Reinforcem ent in Concrete, IOM Communications, London, European Federation of Corrosion P ublications, No. 31(2001), p. 93-100.
111 Sergi, G., Simpson, D. and Potter, J. "Long-term performance and versatility of zinc sacrificial anodes for control of reinforcement corrosion", Proceedings of Eurocorr 2008, The European Corrosion Congress Â“Managing Corrosion for SustainabilityÂ”, Edinbur gh 7-11 September 2008. Szklarska-Smialowska, Z., Â“The Pitting Corrosion of Meta lsÂ”, Houston, TX: NACE International, (1986), p. 202-212. Torres-Acosta, A. and Sags, A. Â“Conc rete Cracking by Localized Steel Corrosion Geometric EffectsÂ”, ACI Mate rials Journal, Vol. 101 (2004), p.501 Virmani, Y.P, Clear, K. and Pasko, T., "Tim e-to-Corrosion of Reinforcing Steel in Concrete Slabs," FHWA-RD-76-70, Federal Highway Administra tion, Washington, DC (1983). Whitmore, D. and Abbott, S ., Â“Using Humectants to Enhance the Performance of Embedded Galvanic AnodesÂ”, Paper No. 03301, Corrosion/2003, NACE International, Houston, (2003).
113 Appendix A: Computation of Polarization Distribution in a Reinforcing Steel Member Â– Model Validation A.1 Objective and Approach While based on sound principles, the 1-D model that was used in Chapter 5 to estimate the extent of cathodic polarization pr ovided to a generic repair configuration involved numer ous simplifications and assumptions in the interest of practical implementation. Validation of the model projections by comparison against a well characterized actual system is therefore highly desirable. The test yard slabs have a simple reinforcement and concrete configuration suitable for such comparison. In this section, the m odel was applied to comp ute the extent of polarization delivered to the passive rebars in the yard slabs by the sacrificial point anodes at various ages. The model was adapted with minimum changes to simulate the actual physical system. The same computational array used for the model calculations was implemented but the number of cons ecutive nodes was changed to 12 to exactly match the existing number of r ebar segments in the slabs. Under those conditions Eq. 8 in finite di fference form is the same as that of a circuit network with resistance between concrete nodes co rresponding to the actual concrete resistance between planes centered on cons ecutive rebars, and potentials equal to those of the concrete on the nodes, as illustrated in Figure 43.
114 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 Cathodic Rebars Cathodic Rebars Anode R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I10 I11 I12Cathodic Rebars Cathodic Rebars Anode I6 I7 I8 I9 Disconnected Rebars R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 Cathodic Rebars Cathodic Rebars Anode R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I10 I11 I12Cathodic Rebars Cathodic Rebars Anode I6 I7 I8 I9 Disconnected Rebars R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 Cathodic Rebars Cathodic Rebars Anode R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I11 I12 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11I1 I2 I3 I4 I5 I10 I11 I12Cathodic Rebars Cathodic Rebars Anode I6 I7 I8 I9 Disconnected Rebars Appendix A: (Continued) Figure 43 Circuit network equivalent for model validation. Configuration modeled corresponds to the testi ng of the 2nd set of anodes. I6 to I9 = 0. The model in Chapter 5 was impl emented with one anode placed at the grid node corresponding to the repair patch end. For the validation calculations it was chosen to represent the case where the 2nd set of anodes was tested, so the anode position was located between rebars No. 3 and 4. This condition was modeled by associating nodes 3 and 4 each with one fictitious half-anode. For such half-anode, the PF has for a given pot ential one half of the current of the actual anode, and the current constriction re sistance is twice as large as that of the actual anode. Those provisions offer in ternal consistency since the parallel combination of both halves would then behave electrically equivalent to one full anode. Also as during the evaluation of the 2nd set of a nodes, where rebars 6 though 9 were disconnected, the corresponding nodes were assigned zero sink current. The boundary conditions at each end were specified similar to that of the remote end in the model in Chapter 5 (Eq.7). A.2 Procedure The validation calculations were m ade to correspond to conditions during the testing of the 2nd set of both types of anodes at ages 4 and 13 months. The following model inputs were used:
115 Appendix A: (Continued) a. PF for both ages calculated using t he global fit equations 15 to 18 with parameters listed in Table 3. b. Concrete resistivity for the ch loride-free and chloride-rich zones. The values used, 25 k -cm and 12.5 k -cm respectively corresponded to the average of the temperature-correct ed data for the period between days 1045 and 1550 in Figure 34, representativ e of the conditions prevalent at the two selected 2nd set anode ages. c. Steel polarization function as abstrac ted per Eq. (13) fr om the data in Figure 33, with parameters listed in Table 3. d. Slab dimensions per Figure 7. e. Steel placement density = 0.0906 co mputed from rebar nominal size and slab dimensions. The model inputs were used to calc ulate the secondary expressions for rebar and anode current constriction re sistances, and numeric solution was conducted in the same manner as indicated earlier. The model outputs for the purposes of validation comparisons were, for each rebar No. i that was connected to the anode at anode age t: a. The values of the potential Es (i,t) b. The values of the net ca thodic rebar current I(i,t) The difference P(i,t) = Esu Â– Es (i, t) for each rebar5 was calculated as a secondary output from the above and reported as the projected steel polarization in each case. 5 It is recalled the Esu is the value of the potent ial of unpolarized (open circuit) passive rebar.
116 Appendix A: (Continued) A.3 Results and Discussion The model output values of P(i,t) and I(i,t) were compared with the 4h steel depolarization values and individual temperature corrected rebar currents, averaged for each group of 3 slabs, measured at the respective anode ages. Tables 6 and 7 presents all the model results and the corresponding experimental data used for C and W anodes respectively. It is emphasized that other than adapting for system configuration and conc rete resistivity the parameter inputs used in the model calculat ions were the same as those used for the overall calculations in Chapter 5, and that no paramet er adjustment took place to normalize or condition the fit between the computed and measured amounts. The results are shown in graphic form in Figures 44 and 45 for the C anodes at ages 4 and 13 mo respectively, and similarly in Figures 46 and 47 for the W anodes. Comparisons are made only fo r the rebars that were connected to the anodes at the time, sinc e the others (No. 6-9) were in the open circuit condition and not forming part of the ov erall galvanic macrocell. Their open circuit potential values corresponded to a mixed potential determined in the anodic component by active steel dissoluti on in chloride contaminated concrete, a condition not addressed by the model so no comparisons for potential were made for those rebars. Mor eover, since those rebars were placed crosswise to the main electrolytic current flow and of small dimensions compared to the concrete bulk, they represented only a mino r disruption of the current distribution pattern so any residual effect on t he rest of the system was ignored.
117 Appendix A: (Continued) In all cases the pattern shapes of model steel polarization and galvanic current distribution matched well those obs erved experimentally. Those patterns included maxima at or between rebars No 3 and 4 which are on either side of the anode, and decay away from the anode in comparable proportions including substantially smaller amount s for the rebars at the ot her end of the slab. The model also replicated for both types of anodes the pattern of decreasing extent of polarization as anode age increas ed from 4 to 13 months.
118 12345101112 C Exp 1 0.1170.1350.1750.1570.1660.0630.0540.054 C Exp 3 0.1620.1890.2290.1950.1800.0910.1010.081 C Exp 5 0.1360.1300.1930.1740.1660.0980.0860.082 C ExpAverage 0.1380.1510.1990.1750.1700.0840.0800.072 C Model 0.1550.1770.2190.2190.1780.1080.0920.085 12345101112 C Exp 1 559927224891752813 C Exp 3 4886208258133261514 C Exp 5 387015224395271013 C ExpAverage 4785211250106431814 C Model 94138286286139392824 Current (uA) Rebar # C anodes 4 mo Depolarization(V) Rebar # 12345101112 C Exp 1 0.0970.1130.1510.1350.1290.0600.0590.057 C Exp 3 0.1560.1760.1870.1800.1660.0870.0860.087 C Exp 5 0.1460.1680.2100.1760.1630.1090.0950.093 C ExpAverage 0.1330.1520.1830.1640.1530.0850.0800.079 C Model 0.1230.1380.1680.1670.1360.0850.0740.068 12345101112 C Exp 1 488420216495712010 C Exp 3 345911613689211210 C Exp 5 2755971437622610 C ExpAverage 366613814887381310 C Model 526811711666241816 Rebar # C anodes 13 mo Depolarization(V) Rebar # Current (uA) Appendix A: (Continued) Table 6 Model output and experimental data for C anodes at ages 4 and 13 months.
119 12345101112 W Exp 1 0.1480.1660.2130.1650.1580.0790.0780.070 W Exp 3 0.1640.1750.2350.1660.1680.0920.0780.066 W Exp 5 0.1480.1620.2020.1590.1800.0750.0900.085 W ExpAverage 0.1530.1680.2170.1630.1690.0820.0820.073 W Model 0.1420.1610.1980.1980.1600.0980.0850.078 12345101112 W Exp 1 559927224891752813 W Exp 3 4886208258133261514 W Exp 5 387015224395271013 W ExpAverage 4785211250106431814 W Model 7410319819810331.5623.5920.35 Current (uA) Rebar # Depolarization(V) Rebar # W anodes 4 mo 12345101112 W Exp 1 0.1460.1660.1880.1630.1450.0750.0820.087 W Exp 3 0.1190.1300.1510.1120.1100.0490.0390.035 W Exp 5 0.1400.1420.1590.1540.1400.0900.0950.088 W ExpAverage 0.1350.1460.1660.1430.1310.0710.0720.070 W Model 0.1050.1160.1390.1380.1140.0720.0630.059 12345101112 W Exp 1 30428588462867 W Exp 3 334355725341-2012 W Exp 5 3036776467943 W ExpAverage 314072745526-47 W Model 3645696843181413 Rebar # W anodes 13 mo Depolarization(V) Rebar # Current (uA) Appendix A: (Continued) Table 7 Model output and experimental data for W anodes at ages 4 and 13 months.
120 0.00 0.05 0.10 0.15 0.20 0.25 020406080100120 Position (cm)E ( V ) Mod Esu Er Depol. Avg. C 0 100 200 300 400 020406080100120 Position (cm)I cath ( uA ) Mod I cath (uA) Avg C 000 005 0.10 0.15 020 025 020406080100120 Position (cm)E ( V ) Mod Esu Er Depol. Avg. C 0 100 200 300 400 020406080100120 Position (cm)I cath ( uA ) Mod Icath (uA ) Avg CAppendix A: (Continued) Figure 44 Experimental and modeled va lues of polarization and cathodic current for rebars connected to the main Type C anode 2nd Set (4 months anode age). Rebar positions measured from the slab edge next to Rebar No.1. Figure 45 Experimental and modeled va lues of polarization and cathodic current for rebars connected to the main Type C anode 2nd Set (13 months anode age). Rebar positions measured from the slab edge next to Rebar No.1.
121 0.00 0.05 0.10 0.15 0.20 0.25 020406080100120 Position (cm)E ( V ) Mod Esu Er Depol. Avg. C 0 100 200 300 400 020406080100120 Position (cm)I cath ( uA ) Mod I cath (uA) Avg W 0.00 0.05 0.10 0.15 0.20 0.25 020406080100120 Position (cm)E ( V ) Mod Esu Er Depol. Avg. W 0 100 200 300 400 020406080100120 Position (cm)I cath (uA) Mod Icath (uA ) Avg WAppendix A: (Continued) Figure 46 Experimental and modeled va lues of polarization and cathodic current for rebars connected to the main Type W anode 2nd Set (4 months anode age). Rebar positions measured from the slab edge next to Rebar No.1. Figure 47Experimental and modeled values of polarization and cathodic current for rebars connected to the main Ty pe W anode 2nd Set (13 months anode age). Rebar positions measured from th e slab edge next to Rebar No.1.
122 AverageSt De v A verageSt De v C / 4 mo0.0210.0111.4600.349 C / 13 mo-0.0090.0071.0600.370 W / 4 mo0.0020.0171.130.32 W / 13 mo-0.020.0121.410.83 Pmodel PexpI cath model / I cath exp Anode / Age Appendix A: (Continued) Quantitative agreement bet ween model and experimental observations is readily assessed in the graphic compar ison in Figures 48 and 49 for C and W anodes respectively, where the model and ex perimental values are plotted as function of each other and contrasted against an ideal 1:1 agreement line. In keeping with the Tafel-like beh avior of the cathodic reaction over much of the range of interest, comparisons between model and experimental polarization results were considered in terms of potent ials differences, while comparisons of currents were made in terms of rati os given the near exponential currentpotential relationship over the same range. In addition, the extent of agreement was evaluated numerically as shown in Table 8. There for each anode type and age condition examined the differences of model minus experimental polarization values of the 8 rebars (average of 3 slabs) were computed, and an average and standard deviation obtained. Similar calculati ons were performed for the ratios of model to experimental cathodic curren t. The results showed that model and experimental polarizations were typi cally on average within < 20 mV of each other, with standard deviation <20 mV. Likewise, model cathodic currents were typically within a multiplying/divi ding factor of 1.5 of those obtained experimentally. Table 8 Deviations between model output and experimental data.
123 y = 2.0833x0.9072R2 = 0.94491 10 100 1000 110100100 0 i cath exp./uAi cath model /uA 4 mo 13 mo y = 1.0797x + 0.0099 R2 = 0.9598 0 0.05 0.1 0.15 0.2 0.25 00.050.10.150.20.25 Dep. Model / VDep. Experimental / V 4 mo 13 mo Appendix A: (Continued) The quantitative comparison show ed agreement between model and experimental behavior that was generally close, comparable to the variability observed between the experimental results of replicate slabs in Tables 6 and 7. Together with the agreement wit h spatial polarization patterns and time evolution behavior documented above, these findings support the validity and applicability of the model. Figure 48 One-on-one comparison of model output and experimental values for C anodes. 4 mo (black circles) and 13 mo (open circles).
124 y = 0.7713x0.8599R2 = 0.93390 0.05 0.1 0.15 0.2 0.25 00.050.10.150.20.25 Dep Model / V Dep Experimental / V 4 mo 13 mo y = 2.2101x08297R2 = 0.9403 1 10 100 1000 1101001000 i cath exp. / uAi cath model /uA 4 mo 13 mo Appendix A: (Continued) Figure 49 One-on-one comparison of model output and experimental values for W anodes. 4 mo (black circles) and 13 mo (open circles). It is noted that the deviation between model and experimental results had often a moderate but clear ly systematic component that varied in extent and direction with the anode age considered. This is not surprising considering that the anode polarization functions used, and their time dependence parameters (Eqs. 15 to 18) resulted from a global fi t to the behavior of the group of three anodes evaluated in each set over the tota l test period. Moreover, the cathodic polarization function was also a global fit which had time invariant parameters and fixed concrete resistivity value for each slab zone was used in the model for all the calculations. Such global fits and flat approximations are expected to reasonably reproduce overall trends, but are less likely to precisely capture the instantaneous behavior of the system, therefore giving ri se to modest systematic offsets such as those observed here.
125 Appendix A: (Continued) In the foregoing the pot ential model output was considered only as a deviation from the unpolarized condition and compared to experimental results from the 4-hour depolar ization measurements which may underestimate to some extent the values that could be obta ined after longer disconnection times. Moreover, since the cathodic rebar asse mbly remained interconnected after the anode was disconnected, some residual ma crocell currents between individual rebars may have been still present af ter only 4 hours. Consequently, comparisons by the same methods used above were made using instead the individual instant-off rebar potentials determined experimentally and those predicted by the model. The extent of agreement between model and experimental values was comparabl e to that obtained when comparing polarization values, suggesting that the effe cts of those residual conditions were highly consequential in this case. A.4 Conclusion Comparison between model calculati ons and experimental observations generally supported the validity of t he modeling approach for the conditions examined.
ABOUT THE AUTHOR Margareth Dugarte graduated Summa cum laude from Universidad Del Norte (Colombia) in 2004 with a Bachelor Â’s Degree in Civil Engineering. She entered the Ph.D. program in the Civil Engi neering Department at the University of South Florida in fall 2005. While in the Ph.D. program, Ms D ugarte worked as a Graduate Research Assistant in the Corrosion Engineering Laboratory for almost 5 years, she was directly involved in a research projec t funded by the Florida Department of Transportation. She also worked in severa l occasions as Teaching Assistant for undergraduate classes. She has also participated several times in Student research poster presentations at international Conferenc es, where her hard work was recognized as a recipient of the prestigious Mars Fontana Award at the NACE International Corrosion/2007 conference. She also has published 3 papers in refereed international conference proceedings. S he is a student member of the National Association of Corrosion Engineers and the Electrochemical Society.