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4 are considered aggressive if one or more of the following con- constants k and n are identified depending on metal type (e.g., ditions are detected (PTI, 2004; Elias et al., 2009): galvanized or plain steel) and for fill conditions representative of MSE construction. Linearized versions of Equation (1) have pH < 4.5 for steel; or been adopted as a conservative approach to extrapolate obser- 4.5 > pH > 10 for galvanized elements; vations of metal loss over limited time frames and for design min < 2000 -cm; recommendations (Rehm, 1980; Jackura et al., 1987; Elias, presence of sulfides, sulfates, or chlorides; and 1990; AASHTO, 2009). presence of organics. Darbin et al. (1988) and Elias (1990) proposed equations, having the same form as Equation (1), to estimate steel loss Metal loss and service life models are correlated with under- for plain steel and galvanized elements, respectively. These ground conditions, particularly with respect to electrochem- models are developed using measurements of corrosion from ical properties of soil and groundwater. The National Bureau elements buried in fill representative of MSE construction. The of Standards (NBS) commissioned a study to observe metal loss following models apply to galvanized and plain steel rein- from steel and galvanized specimens that were buried under forcements, respectively: a variety of soil conditions for more than 50 years. Based on the results from the NBS study, Romanoff (1957) proposed the For galvanized elements: following power law to predict rates of corrosion of buried 1.54 metal elements: z m 0.65 if t f > i then X ( m ) = 50 t f ( yr ) 25 yr x = kt n (1) -2 z i ( m ) where z 1.54 x is loss of thickness per side or loss of radius, if t f i then X ( m ) = 0 (2) 25 k and n are constants, and t is time (years). For plain steel elements: Equation (1) applies to uniform-type corrosion and may m 0.8 also consider localized- or pitting-types of corrosion, but does X ( m ) = 80 tf (3) yr not consider more complex forms of corrosion, including hydrogen embrittlement or stress corrosion cracking (SCC) as where X is loss of steel (base metal) in units of m, and tf is described by Fontana (1986), FIP (1986), and Sabatini et al. service life in years. For Equation (2) loss of base steel occurs (1999). Equation (1) reflects observations that the corrosion subsequent to depletion of the zinc coating, and zi is the ini- rate is generally higher during the first few years and attenuates tial zinc thickness. Equation (2) is applicable to the range of with respect to time (i.e., n is < 1). This is due to the steel sur- fill conditions representative of MSE wall construction that face becoming "passivated" from stable corrosion by-products exhibit min greater than 1000 -cm. Data reviewed for Equa- that adhere to the surface and formation of a passive film layer. tion (3) are based on the NBS data set for plain steel and Equation (1) serves as the basis for several models used to esti- include a wider range of fill conditions. mate service life and associated sacrificial steel requirements. The service life of earth reinforcements is related to the These models differ in terms of the data sets (e.g., fill condi- remaining tensile capacity and not necessarily the maximum tions) used to regress the model parameters, and the time pit depth. This is because pit penetrations have a limited frame over which metal loss is considered. Note that in Equa- impact on the overall remaining cross section. Rather than tion (1) "x" describes metal loss that may include zinc and steel measuring and modeling pit depths, metal loss models and for galvanized elements. However, other metal loss equations measurements of corrosion rates for earth reinforcements presented in this report use "X" to denote loss of steel sub- are averaged over the surface area of the reinforcement. sequent to zinc deletion for galvanized elements. Metal loss Thus, metal loss is idealized as uniformly distributed over models for Type I and Type II reinforcements are discussed the surface. A factor of 2 is commonly applied to this uni- separately with due consideration given to differences in site form corrosion rate to consider the actual loss of tensile conditions, construction details, and metal type (e.g., use of strength capacity (Elias, 1990; Jackura et al., 1987); in other galvanized reinforcements for Type 1 reinforcements). words, the loss of tensile strength is twice that anticipated based on the average loss of section. Although the factor of 2 is often taken as a constant, Smith et al. (1996) describes Type I Reinforcements how the local factor may vary with respect to reinforcement Based on research conducted over the past several decades shape. Equations (2) and (3) include a factor of 2 to consider (e.g., King, 1978; Darbin et al., 1988; Elias, 1990) values for the the maximum metal loss and associated loss of tensile strength.

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5 Equation (2) considers that loss of zinc is uniform with Rehm (1980), Jackura et al. (1987) and Elias (1990) propose x = 25t0.65, but a factor of 2 is applied to the steel corrosion models for estimating metal loss of galvanized reinforcements rate to consider the maximum metal loss after zinc is con- in fill conditions applicable to MSE construction. Details of sumed as X = 50t0.65. these other models are described in Appendix A and are Although corrosion rates for both galvanized and plain referred to as the Stuttgart or Caltrans Interim models. These steel clearly vary exponentially with respect to time, a num- models consider fill conditions that are more severe relative to ber of models (including the AASHTO model) approximate the potential for corrosion compared to the AASHTO require- loss of steel using linear extrapolation for the purpose of ments, and are sometimes, but not always, associated with design. These models assume that the rate of zinc consump- correspondingly higher corrosion rates. Table 2 is a summary tion is higher in the first few years and then levels off to a of the different fill conditions, model parameters and cor- steady but significantly lower rate. Once the galvanized zinc responding estimates of zinc life, and estimates of steel loss coating is depleted, it is assumed that the base carbon steel considering a 75-year service life. corrodes at the carbon steel rate. This is a conservative assump- Considering a service life of 75 years and an initial zinc tion that does not consider that the insoluble by-product of thickness zi, equal to 86 m per side, the steel loss computed zinc corrosion continues to protect the underlying steel (Rehm, with the Darbin equation [Equation (2)] is 655 m per side. 1980). Calibration of LRFD resistance factors for galvanized For a 75-year design life, and zi equal to 86 m, the AASHTO, reinforcements assumes that the steel cross section is not con- Stuttgart-high salt, and Caltrans Interim-select models yield sumed before the zinc coating, which serves as the sacrificial estimates of steel loss close to that computed with the Darbin anode protecting the base steel. Since the zinc layers do not con- model. Differences between these models include the data tribute to the tensile strength of the reinforcements, strength sets that are used to regress model parameters (i.e., corrosion loss is also delayed until the zinc is consumed, and loss of steel rates). This demonstrates that the current AASHTO model section is described according to Equation (4). In general the uses corrosion rates that are applicable to fill conditions that thickness of steel, X, consumed per side over the design life, are more severe relative to those allowed by the specifications; tf, may be computed as in other words, the AASHTO model is conservative. For fill conditions that are considered marginal by AASHTO stan- m X ( m ) = ( t f ( yrs.) - C ( yrs.)) rs (4) dards, due to higher salts contents (models below the double yr line in Table 2), considerably higher steel losses are estimated. A complete comparison of steel losses computed with the ( zi - rz1 t1 ) models above the double line in Table 2 as a function of ser- where C is the time for zinc depletion C = t1 + , rz 2 vice life is presented in Figure 2. Comparisons with the Darbin which is computed based on the initial zinc thickness, zi, the model shown in Figure 2 imply that the factor of 2 described initial corrosion rate for zinc, rz1, the subsequent zinc corrosion by Elias (1990) is implicit in the piecewise linear models from rate, rz2, and the duration for which rz1 prevails (t1usually Stuttgart, AASHTO, and Caltrans. taken as 2 to 3 years). The corrosion rate of the base steel sub- Table 3 summarizes the AASHTO-recommended metal sequent to zinc depletion is rs. loss model for design of MSE structures (AASHTO, 2009) and Table 2. Summary of piecewise linear metal loss models for galvanized reinforcements. Electrochemical Parameters Metal Loss Steel Model Considered1 Parameters Loss/Side tf = 75 yrs. pH min Cl- SO4 rz12 rz2 rs C3 X4 -cm ppm ppm m/yr m/yr m/yr yrs. m Stuttgart-mildly corrosive 4.5 to 9 >1,000 <20 <50 6 2 9 39 324 Caltrans Interim-select5 >7 >1,000 <500 <2,000 NA NA 13 20 715 AASHTO-mildly corrosive 5 to 10 >3,000 <100 <200 15 4 12 16 708 2 Stuttgart-high salt, saturated 4.5 to 9 >1,000 <50 <500 17 2 12 20 654 Caltrans Interim-neutral >7 >1,000 <500 <2,000 NA NA 28 10 1820 Caltrans Interim-acidic 1,000 <500 <2,000 NA NA 33 10 2145 Caltrans Interim-corrosive >7 < 1,000 <500 <2,000 NA NA 71 6 4899 1 Electrochemical parameters considered for design by Caltrans have been updated since the Interim models were proposed in 1987. See Appendix A for details. 2 Applies to the first 2 years except for the Stuttgart high salt model where rz1 applies to the first 3 years. 3 C is the time to zinc deletion (i.e., initiation of steel loss) assuming zi is 86 m. 4 X is the steel loss per side for a 75-year service life. 5 Caltrans select fill is clean gravel with less than 25% passing the No. 4 sieve and less than 5% fines.

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6 1000 Darbin 800 Caltrans-select Steel Loss per side (m) AASHTO 600 Stuttgart-salt 400 200 0 0 20 40 60 80 100 Time (years) Figure 2. Comparison of metal loss models. the corresponding fill material requirements. The fill require- consideration. The number of samples required increases ments are intended to control corrosion potential with fills when evaluating more aggressive or marginal backfill materi- that are between noncorrosive and "mildly" corrosive. als, and when more confidence is needed for design (With- Based on the information in Table 3, the steel loss per side iam et al., 2002; Hegazy et al., 2003). Existing data involving (X) in m/yr for a given service life, tf , and initial thickness of frequent sample intervals at sites with poor conditions depict zinc coating, zi, is computed as a wide scatter in results (Whiting, 1986; Fishman et al., 2006). For moderate to large sized projects, with fill sources that are expected to be relatively nonaggressive relative to corrosion m ( zi - 30 m ) (i.e., mildly corrosive soils meeting AASHTO criteria), Table 4, X ( m ) = 12 t f - 2 yr - yr (5) yr m taken from Elias et al. (2009), can be used to determine the 4 number of samples that should be taken from each source yr and evaluated for electrochemical parameters. More samples The AASHTO model does not give any guidance for corro- should be retrieved if marginal quality reinforced fills are sion rates or metal loss modeling of plain steel (i.e., not galva- being contemplated for construction (not recommended), or nized) reinforcements or for fills that do not meet the stringent when undertaking performance evaluations at sites with poor electrochemical requirements. A significant effort was devoted reinforced fill conditions. In addition to the mean values used in this project to documenting the performance of in-service for design [i.e., the mean of the minimum resistivity (min) reinforcements and to verifying the reliability of the AASHTO values obtained from each test], the distribution and variabil- (and other) models used in MSE structure design. ity of the measurements is of significant interest from the The frequency and distribution of samples for assess- standpoint of reliability-based design (LRFD). ment of electrochemical parameters need to be given careful Table 4 places restrictions on the allowable standard devi- ations () of the resistivity and salt content (see comment 3) measurements. If these standard deviations are exceeded, then the sampling should be repeated. If the standard devia- Table 3. AASHTO metal loss model and tion, computed using the total numbers of samples, is still backfill requirements. outside the limits of Table 4, then the backfill source should Metal Loss Model Backfill Requirements not be used for MSE wall fill. If resistivity less than 3,000 -cm Component type Loss pH 5 to 10 is obtained from any test, obtain additional samples in the (age) (m/yr) Minimum 3,000 -cm resistivity vicinity of this sample location to identify if there are specific Zinc (<2 yrs), rz1 15 Chlorides <100 ppm areas wherein the material is unsuitable. Zinc (>2 yrs), rz2 4 Sulfates <200 ppm Stockpiles should be sampled from the top, middle, and Steel (after zinc), rs 12 Organic content <1% bottom portions and an excavator with a bucket should be