Theoretical Assessment of AC Impedance Spectroscopy for Detecting Corrosion of Rebar in Reinforced Concrete* D. D. MACDONALD, M. C. H. MCKUBRE, and M. URQUIDI-MACDONALD* Abstract The applicability of AC impedance spectroscopy (ACIS) for detecting corrosion on rebar in concrete is explored theoretically. Corroding rebar is simulated as a one-dimensional electrical transmission line of twenty one-meter segments embedded in a uniform concrete matrix, with the corrosion being restricted to one segment. The simulations indicate that corrosion can only be detected at very low frequencies (<1 mHz), but that the impedance and the peak voltage monitored at the concrete surface may be used to locate the site of the corrosive attack. Introduction The corrosion of rebar in reinforced concrete is now recognized t-3 as a major problem in maintaining the structural integrity of our infrastructural systems (bridges, tunnels, roads, etc). The principal problem, at least as far as bridges and roads are concerned, is the ever increasing use of salt as a deicing agent. Penetration of the porous concrete matrix by chloride ion, water, and perhaps oxygen, leads to corrosion of the steel to form corrosion products that are collectively referred to as rust. Because these corrosion products (Fe 304 , Fe 203 , o.- FeOOH, y-FeOOH, etc.) occupy a volume that is significantly greater (by a factor of more than two) than the iron from which they form, the concrete at the rebar/concrete interphase is cast info a state of tension. This results in cracking and spalling of the concrete, exposure of the underlying steel, and the establishment of differential aeration cells. Thus, the steel continues to corrode, preferentially in those areas with the least access to oxygen; i.e., attack occurs preferentially on that steel that remains embedded in the concrete. This cycle continues and ultimately weakens the structural integrity of the system. When analyzing corrosion processes that occur in concrete, it is important to note that concrete is not homogeneous, either on the microscopic or macroscopic scales. Microscopic inhomogeneities result from pores and from the use of aggregate. Also, the hydration processes that occur during the setting of concrete, particularly if excess water is present, result in both chemical and physical heterogeneities that possess different properties (e.g., diffusivities for Cl - and 0 2). On a macroscopic scale, inhomogeneities may be caused by the gradients in temperature, the non-uniform access by water and salt, and the non-uniformity in pouring and fabrication. The important point is that corrosion of rebar occurs in an inhomogeneous medium, and any analysis of corrosion problems in reinforced concrete must ultimately address this issue. "Submitted for publication November 1986; revised March 1987. *SRI International, 333 Ravenswood Ave., Menlo Park, CA 94025. In this paper, the use of AC impedance spectroscopy (ACIS) to detect corrosion of rebar in concrete and to locate the position at which the attack occurs is theoretically explored. ACIS has been used previously 4-6 to study the corrosion of steels in concrete but, to the present authors' knowledge, it has not been developed for the purpose of locating the point(s) of attack. If the technique can be developed for this purpose, it would represent a significant advance in surveying reinforced structures for corrosion damage. Only the theory and numerical analysis are presented here; the experimental feasibility of the technique will be reported at a later date. Theory In developing the theory presented here, the present authors assume that the system consists of parallel round reinforcing bars embedded in an infinite concrete matrix. In reality, the bars that are most susceptible to corrosion are those located closest to a free surface, particularly if the surface is exposed to water and salt. Accordingly, real reinforced structures seldom exhibit the axial symmetry characteristic of the ideal system used here. However, the present assumption reduces the mathematica) problem to one dimension, and hence greatly simplifies the analysis presented below without significantly compromising the physical principles. A more realistic and cumbersome three-dimensional description could be invoked, but it would add little to the points that the authors wish to make in this paper. In developing this model, it is assumed that the electrical properties of the steel and concrete are purely resistive in nature, with the resitivity of the concrete (but not that of the steel) possibly being dependent on position resulting from the macroscopic inhomogeneity of the matrix. On the other hand, the impedance of the steel/matrix interface is reactive, as indicated by various experimental studies 4-6 and from our genera) experience with the electrochemical properties of steels in contact with aqueous solutions. 7,8 The reactance results from the existence of capacitive, pseudo-inductive, and possibly 0010-9312/88/00001/$3.00/0 2 © 1987, National Association of Corrosion Engineers CORROSION—NACE