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A minimalist approach to polarization resistance measurements in a reinforced concrete structure

In the curriculum of future civil engineers, electrochemical concepts are often neglected, even though this knowledge is essential to adequately maintain reinforced concrete structures in a chloride‐exposed environment. Experiments are necessary to consolidate key theoretical concepts, but laboratory experience often involves complex and expensive electronic equipment that may obscure the basic procedures at work. This paper presents a simple minimalistic electrochemical test for polarization resistance measurements by which students can learn basic concepts of corrosion electrochemistry and estimate the corrosion rate as a key parameter for estimation of the remaining service life of concrete structures. The focus is on avoiding unnecessary complications and providing an experiment that can be readily implemented for a wider student reach.


| INTRODUCTION
Civil engineers are responsible for the built environment of our modern society, and they design infrastructure and modern transportation systems to ensure mobility and exchange of goods. Our infrastructure also ages and progressively deteriorates, challenging engineers to maintain and repair it under boundary conditions of depleting natural resources, environmental concerns, and cost constraints. A routine demolition and rebuilding of infrastructure is no longer a sustainable default option to address aging deterioration. Talented engineers with updated skills are needed to provide solutions for the maintenance of our infrastructure through more efficient management of materials and structures. Greater skills in extending remaining structure service life can be achieved through a better understanding of deterioration processes and more reliable condition assessment. The present paper contributes to this direction.
A major deterioration mechanism of reinforced concrete structures is reinforcement corrosion caused by the ingress of chloride ions from sources such as deicing salts and marine exposure. Chloride-induced reinforcement corrosion is an electrochemical process. Therefore, effective corrosion inspection and/or monitoring of reinforced concrete structures requires a certain amount of knowledge of electrochemistry on the part of the engineer, including understanding the basics of the corrosion mechanism and of the operation of electrochemical devices for condition assessment. However, exposure to electrochemistry is often neglected in the educational curriculum of future civil engineers.

| TEACHING AND LEARNING OBJECTIVES
The body of knowledge deemed necessary for licensure of future civil engineers, as articulated by the American Society of Civil Engineers, [1] includes electrochemistry, among other disciplines, as an important element to explain phenomena and to obtain solutions to problems related with construction materials. It is stated that a future civil engineer shall be able to "use the knowledge of materials science to solve problems appropriate to civil engineering" [1] such as knowledge of durability of construction materials and the maintenance of reinforced concrete structures. The corresponding level of achievement according to Bloom's taxonomy is "Application" to clarify what should be taught and learned. The term Application refers to the ability to use learned material in new situations. This paper does not intend to query if the level of achievement is appropriate regarding the upcoming engineering challenges. Rather, this paper presents a minimalistic experimental test to support the learning objective of understanding reinforcement corrosion, applying electrochemical methods and performing corrosion condition assessment of concrete structures.
A civil engineer should be able to conduct experiments on-site and in the lab to gather data that enables the evaluation of material performance and the interpretation of the structural conditions. The minimalistic test presented here aims to teach electrochemical skills to civil engineers without depending on sophisticated devices that may obscure the process used to obtain the necessary data. The setup may even be applied to the assessment of actual structures in the field to serve instead of, or as a verification supplement for, measurements conducted with complex commercial devices.

| EXPERIMENT-MINIMALISTIC TEST
Civil engineering students often encounter difficulty in abstracting material properties in a manner compatible with electrochemical basics. Difficulties may start while conceiving concrete as an electrolyte. In simple terms, concrete consists of solid mineral phases with pores spanning an enormous size range, the pores being partly filled with air, and pore solution having a pH value in the range of approximately 12.5-13.5. Depending on the moisture condition of the concrete, it can be abstracted as being equivalent to a macroscopically homogeneous medium with conductivity determined by the interconnectivity of the pore network and the amount of pore solution. Another challenge is envisioning the transport of electric charges through the concrete in the form of ions moving through the pore solution network. Challenges increase when moving onto higher-level concepts such as corrosion rate and corrosion potential. The minimalistic test is intended to assist civil engineering students to understand the corrosion of steel in concrete and to overcome some of those conceptual challenges. This is achieved through experiencing a direct manifestation of some of those elements in a simple setup, not obscured by the complex series of operations and instrumentation signal chain that is used in professional test devices.
The chosen subject for the experiment illustration is the measurement of corrosion rates of steel in concrete by a variation of the widely used polarization resistance method (PRM). It may be implemented, for example, near the end of a short course or teaching workshop on electrochemistry for civil engineers, when the students have already been introduced to the basic aspects of corrosion rate (CR), corrosion current density (i corr ), and steady-state corrosion potential (E corr ). The students have next been introduced to the concept of polarization resistance, as the ratio (after stabilization) between a small change ΔE from the potential E corr across a steel-concrete interface and the value of uniform current density i a = I a /A (where I a is the applied current and A is the steel area in contact with concrete) associated with the potential change: Next, students have been told that in many instances, a useful estimate of the value of i corr may be obtained by the Stern-Geary relationship [2] : where B is the Stern-Geary constant (of value typically estimated to be in the order of 0.026 V for steel in an actively corroding condition and 0.052 mV in steel not yet actively corroding). [3] The value of i corr , thus, obtained can then be converted into CR by Faradaic conversion, [4] as shown later, thus providing a rate of deterioration that is of direct relevance to durability estimates. It is noted that because ΔE is only measured as a difference, absolute determination of E corr is not needed as long as the reference electrode remains reasonably stable during the test. This circumstance is used to advantage here. Traditional experiments to illustrate the PRM use sophisticated, computer-controlled electronic potentiostats operated with some form of commercial software. Whereas those procedures are rapid and highly precise, the specimen wiring, automated apparatus operation, and software calculations can be complicated and distracting to the understanding of the student. She/he might concentrate on following prepackaged instructions, with little knowledge given of the actual paces that the system undergoes during the measurement. The approach presented here requires only a simple set of equipment, connections, and procedures. As a result, the student has direct knowledge at each step of what is being done to the system, how it is done, and what is the response to those actions. The student can then more directly focus on the principles at work and the significance of the outcome.

| Test specimens
The proposed test specimens for electrochemical measurements can be prepared easily by students in previous sessions or made ready by the instructor ahead of time in multiple replicates. The specimen represents a simple electrochemical half-cell with ordinary carbon steel rebar as the working electrode, embedded in mortar as the electrolyte. The cylinder is 100 mm high and 60 mm in diameter, with the reinforcement placed at the center to maintain symmetry; a cover depth of approximately 25 mm results with using a 10 mm diameter rebar. The bar has an electrical contact at the top for easy connection to external cables. The bar cut surfaces are also protected with a thin layer of polymer-modified cement mortar covered by a shrinkage tube to prevent crevice corrosion. The final exposed steel area is approximately 60 mm, which is degreased with acetone before casting. The mortar consists of Portland cement (CEM I 52.5R or other), the water-tobinder ratio of 0.5 and approximately <2 mm grain size sand (1,350 g sand, 450 g cement, and 225 cm 3 water; other mortar compositions are also suitable).
Two types of specimens are prepared to demonstrate the key electrochemical behavior regimes of reinforcement bars in concrete: actively corroding and passive (essentially noncorroding). Half of the specimens are produced with distilled water. The other specimens are produced with the same volume of water containing dissolved sodium chloride, resulting in a chloride mass content that is approximately 3% of the cement mass, to induce active corrosion on the steel. [5] Following demoulding approximately 2 days after casting, the specimens are kept immersed in trays containing tap water to continue curing and maintain a stable moisture condition. The chloride-containing and chloride-free specimens are kept in separate trays to avoid cross-contamination.

| Equipment
The equipment for the minimalistic test is widely available from consumer electronics sources, except for the reference electrode that may be replaced as indicated: • A small regular 9 V battery with a snap-on connector with short extension wires. • Five jumper cables, approximately 30 cm long, preferably thin gage (e.g., AWG 20) for easier handling, terminated in moderate size alligator clips, or banana plugs capable to fit alligator clips. • An ordinary digital multimeter capable of 1 mV (preferably 0.1 mV) DC resolution in the 1 or 2 V range, and the input impedance of 10 MΩ or greater. • Assortment of consumer electronic resistors, size ¼ to 1 W and 10% or finer precision (both not critical), at least values of 10 K, 100 K, and 1 MΩ, and 30 K, 300 K, and 3 MΩ are also desirable. • Cylindrical plastic container approximately 15 cm in diameter and height to hold specimen upright. Water (similar to that used during curing) should be placed in a container up to a level approximately 1 cm lower than specimen height. • The reference electrode can be copper/copper sulfate or other rugged variety. As a possible alternative, any stable metal electrode capable of retaining potential within ±1 mV over a period of approximately 3 min may serve as well. A piece of zinc or galvanized steel is allowed to stabilize in the solution, for example, >½ hr and not moved during the experiment, which might serve the purpose. • A makeshift counter electrode that may consist of an electrically separated piece of rebar or metal mesh (galvanized or stainless steel), or, if available, activated titanium cathodic.

| Experimental procedure
Students are expected to work in groups of two.

| Laboratory setup
• Specimen, reference and counter electrodes (RE and CE), should be placed in the test solution. There should be enough support for specimen and electrodes so that they shift is obtained. The resistor that achieved that effect should be kept in the circuit, with its value (R C ) being noted. • The control cable should be disconnected from CE and the system should be allowed to rest for at least 5 min.

| Test execution
• An entry table should be prepared for the data to be gathered in the next two steps. An ordinary watch, cell phone, or stopwatch should be used to keep track of time. One student should read the data and the other should enter it in the table.

| Data processing
The data postprocessing consists of the following steps. Explanation is provided in the next section: • Potential of the working electrode should be plotted as a function of time. • Estimated applied current (I a ) should be calculated (Equation 3, discussion next section): • From the graph, a ΔV estimate should be obtained as the difference between the average of the native potential readings and the terminal point (180 s) potential. It should be verified that ΔV is approximately <25 mV to reasonably approach the linear limit. [2] Otherwise, the test should be repeated with a resistor having a larger R C value. • Nominal polarization resistance R PN should be calculated (Equation 4, see next section): where CR is the corrosion rate (cm/s), M Fe is molar mass of iron (g/mol), i corr is corrosion current density (A/cm 2 ), z is valency number of iron (-), F is Faraday constant = 96,485 (C/mol), ρ Fe is iron density (g/cm 3 ; instructor may indicate that Fe is as a close proxy for carbon steel, given that the content of the other elements in rebar steel is quite small in comparison).

| Explanation of the basis of the test
Depending on how specialized the course using this experiment is, the students can be further introduced to some or all of the following more advanced concepts and qualifications of the meaning of the experiment and its outcome. These qualifications are among the reasons for the use of the "nominal" modifier in defining R PN , and they serve also to illustrate the importance of understanding that any indirect evaluation of corrosion rate in these systems is subject to some degree of uncertainty.
Conceptually, a PRM test could be conducted potentiostatically by controlling the potential change ΔE and finding out the value of i a needed for it, or galvanostatically by applying i a and determining the resulting ΔE. The potential/ current change can be implemented as a gradual change with time so as to determine the slope of potential versus current curve, in the manner of ASTM G96-90 or alternatively in the form of a step change, followed by a waiting period for stabilization. A galvanostatic step combination is among the simplest to implement and understand because it can be approximated, without need for electronic control, with the quasi-galvanostatic approach as used here. The battery voltage used (9 V) is large compared to the small typical WE-CE potentials associated with steel in concrete (e.g., approximately 0.5 V in either direction depending on the choice of CE) and the small potential deviations obtained (e.g., 20 mV). Hence, the error in applied current estimation as per Equation (3) is likely to be only in the order of 10%, which is minor compared to the usual uncertainties inherent in PRM tests. [3,[6][7][8][9] In a step method, one must wait until the dependent variable (in this case ΔE) has sufficiently approached a terminal value or make use of some form of estimate of the terminal condition based on knowledge of the parameters that are responsible for transient behavior, which may involve the effective interfacial capacitance or descriptors of transient transport phenomena that may be at work. These issues can be complicated and beyond the scope of introductory treatments of electrochemical diagnostic techniques. [6][7][8][9] In the minimalist test, an empirical approach has been used, based on indications from various sources, suggesting that for some reinforced concrete systems, the typical time constants (time transferred to attain a fraction 1 − e −1 of the final condition) can be in the order of several minutes. [6,9] As a practical compromise between accuracy and time limitations in the classroom, a waiting time of 3 min was chosen. More advanced students could be tasked with calculating a time constant by approximating the response to a simple exponential decay function and making a more refined estimate of ΔE by projection to the expected terminal value.
The value of ΔV includes yet another departure from the true interfacial potential change of the steel, in the form of an ohmic component ΔV S = I a ·R S (the "IR" effect), [6][7][8][9] where R S is the effective resistance of the electrolytic path present between the working electrode surface and the sensing point of the RE. [6][7][8][9][10] For the specimens used, which may be relatively cast recently and then kept in contact with tap water, ΔV S can be relatively small compared to the total value of ΔV even for the chloride-contaminated case (see discussion on the example below). Again, advanced students may be taught to make a rough estimate of R S by performing an extra "instant-on" potential measurement 1 s after current initiation. The value of the initial potential step ΔE i can then be used to obtain an estimate R s~Δ E i /I a .

| RESULTS AND DISCUSSION
The introduction and application of a minimalistic test in a course can be divided into different phases. First, a theoretical introduction shall provide the students with the background knowledge of corrosion of steel in concrete and associated characteristic electrochemical values. Students should discuss about consequences of reinforcement corrosion (durability, serviceability, load-bearing capacity, and limit states) and corrosion condition assessment of concrete structures: the parameters that can be measured in lab or on-site and the method by which the parameters can be interpreted in terms of whether reinforcement is in the active or in the passive condition.
The minimalistic test provides much teaching and learning material. On the basis of previous questions of students and discussion of common misconceptions, the instructor should be prepared to develop the prelab discussion customized to the class. Students may be encouraged to develop a sketch to prepare laboratory test specimens for corrosion tests of steel in concrete with the appropriate measurement setup. Thus, students shall discuss the function of each component, especially the transfer of the ions and electrons and the corresponding electrochemical reactions taking place. Often students find it difficult to explain which electrode is the anode or the cathode and which electrode is positive and which one is negative. Students shall indicate the transfer of electrons and ions, including their charge sign and the corresponding half-cell reactions.
Moreover, the particular initiation of reinforcement corrosion in concrete should be emphasized. Students shall be able to transfer the lab specimen condition to on-site condition and to discuss the location of the anode area and the cathode area on-site, and the kind of electrochemical data that can be measured in the lab and the data that can be measured on-site.
In the next step, students build the electrochemical test set. Civil engineering students are likely to have had limited exposure to the use of multimeters and reference electrodes. Therefore, it is of importance that the instructor provides support and is available for questions and examples on the use of a multimeter. Figure 2 shows students performing the minimalistic test during the workshop "Corrosion Electrochemistry for Civil Engineers," which was organized and conducted by the authors.
After the test setup is built, they measure its potential using the appropriate resistor during polarization, see Section 3 above. Then they plot the dependence of the potential versus time as shown in Table 1 and Figure 3, and estimate the potential drop before and after polarization. Figure 3 shows the potential data of a chloride-free and chloride-contaminated sample. The resting potential of both samples differs significantly (for these examples, a commercial SE 10 electrode [Sensortechnik Meinsberg] was used). The potential of the chloride-free sample is 45 mV SAE, whereas the potential of the chloride-contaminated sample is much more negative with a value of −519 mV SAE . Here, the students learn that the half-cell potential is one important indicator of whether reinforcement corrosion is active or not.
When conducting the LPM test, the potential drop was more pronounced in the chloride-free sample. The observation by itself is not particularly significant, as the magnitude of the potential drop is dependent on the intensity of the polarization, thus the used resistor. Instead, it is the ratio of a potential drop to the current density that is important, as will be seen later.
After the measurement itself, data postprocessing is required. Table 2 summarizes the measured data and postprocessed outcome of the example experiments.
Data postprocessing enables the corrosion condition assessment of the samples. The key parameter is i corr ; values well in excess of 0.1 µA/cm 2 are understood to be a clear indication that the system is corroding actively. [2] Here, the chloride-free sample is just below 0.1 µA/cm 2 , whereas the chloride-contaminated sample exceeds the value by more than an order of magnitude. This excess is much beyond the uncertainty that may be introduced by the qualifications noted earlier, so it can be concluded with reasonable assurance that the chloride-contaminated sample was corroding. It is noted in passing that independent impedance experiments showed that R S in these specimens was in the order of 100 Ω. After considering the electrode area, the error introduced by the IR effect in the evaluation of R p in the worst case (the chloride-contaminated sample) was only in the order of approximately 30%, not very consequential when considering the large relative behavior difference between the two specimen conditions examined.
In the next phase of the minimalistic test experience, students prepare a test report including the experimental results and all calculations. In postlab discussion, the students compare their results among each other. Students should discuss reasons for possible differences within their results. Afterward, the students can be prepared to discuss the consequence of reinforcement corrosion for reinforced concrete structures. What is the effect of the magnitude of the corrosion rate? When does a corrosion rate becomes critical? What kind of repair measures are applicable?
Another advantage of this setup is that the specimens, the reference, and counter electrodes can be used several times. It is noted that the potential of such a half-cell and the polarization currents may show significant variability with time. Corrosion of steel in concrete is a highly variable process. Even if the specimens were maintained in constant temperature and moisture conditions, the continuing hydration process of the mortar will increase the resistance of the electrolyte and probably cause the evolution of the steel-concrete interface. However, minor changes in absolute values of the potentials are only of secondary importance, as the focus of the test is on the short-term potential change due to external polarization.
Although chloride contamination is the basic requirement for chloride-induced corrosion, other factors can affect the corrosion activity as well, such as temperature, concrete resistivity, and so on. [3] These factors can be easily addressed in the student laboratory. To that end, specimens could be preconditioned in different climates with varying temperature and relative humidity. For such tests, an alternative CE and RE arrangement would be needed, using, for example, conductive polymers, possibly embedded electrodes, [10] and some temporary environmental controls.
Students should be reminded that the minimalistic test and similar transient polarization techniques provide only information about the corrosion propagation phasewhether it has actually started and an estimate of the corrosion rate. The test does not cover the initiation phase of corrosion of steel in concrete; the nature and rate of chloride transport in concrete, or the value of the chloride threshold, is of interest. Different kinds of specimens and techniques would be needed to address those issues, to be dealt with in other parts of the curriculum.
An important lesson from the minimalist test experience is that quantitative information on the rate of deterioration of steel in concrete can be extracted from an actual physical system with an extremely simple test. This information, albeit of low precision, is still enough to provide a key indication of the condition of steel that is embedded in concrete, without recourse to otherwise highly sophisticated non-destructive methods. The technique is evidence of how knowledge of fundamental aspects of a problem can be used to advantage by the engineer, even with access only to very limited resources. It is of interest to note that the minimalist test approach can serve in actual structural applications in the field if more advanced equipment experienced systematic or temporary malfunction. This was manifested in an extended survey of steel-reinforced earth walls in Florida, [11,12] where PRM procedures were normally conducted with state-of-the-art computer-controlled potentiostatic equipment. The result provided a corrosion rate estimate of the strips, from which long-term durability projections were made. The assessed structural elements consisted of galvanized steel strips embedded in the soil. Solid-state reference electrodes were embedded in the soil near the strips, some of which were used as counter electrodes to apply sampling current to other nearby strips. The procedure worked well in most walls, but in some instances, electric interference thought to result from stray ac current in the soil, interfered severely with the potentiostat operation, rendering the regular PRM measurement impossible. For those locations, the investigators developed a contingency minimal equipment method [11,12] that served as a model for the educational exercise presented here. Comparisons in the field study between R p values obtained with the minimal approach and with the computerized systems under normal conditions typically showed results within approximately 20% of each other, a highly favorable outcome. Thus, this simple and rapid method can serve as a desirable backup or confirmatory procedure in field operations, where the high cost of having personnel on-site could be wasted by the failure of or disabling artifacts inherent to the use of complex electronic devices.
The teaching experience may include exploring with the students the application of the method for on-site purposes if a suitable structure is available. In such an opportunity, students could learn directly the real-world problems in performing corrosion condition assessment on-site such as accessibility and weather condition issues, directly probing the reinforcement and much-related experience.

| CONCLUSIONS
This paper presents an educational laboratory experience for quantitative corrosion rate evaluation of reinforcing steel in a mortar, easy to construct with material available from ordinary consumer electronics and hardware sources. With the instruction, students learn to prepare a simple half-cell to apply electrochemical measurements to reinforced concrete, to assess whether a specimen is actively corroding or not, and to obtain an approximate estimate of the rate of corrosion. The minimalistic test does not require cost-intensive lab equipment nor sophisticated electrochemical devices. The experiment is easy to understand and simple to execute. Students get valuable hands-on experience to understand reinforcement corrosion in concrete as a major deterioration mechanism. They learn to prepare and execute electrochemical tests in the context of basic scientific principles and to assess corrosion conditions.