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24 Table 11. Table 3). Figure 11(a) includes 150 data points and Figure 11(b) Computed includes 257 data points documenting the performances of corrosion rates galvanized reinforcements within good and high quality fills, for galvanized respectively. The highest rates of corrosion are observed from reinforcements elements that are equal to or less than 2 years old, but these at selected higher rates are less than half of the rate of 15 m/yr included resistivities. in the AASHTO model. The mean corrosion rate during the CR first 2 years is approximately twice the mean corrosion rate (-cm) (m/yr) measured from elements older than 2 years. 1,000 7.9 When reinforcements are greater than 2 years old, the means 3,000 3.5 10,000 1.4 of the observed corrosion rates are less than half of those antic- 20,000 0.8 ipated on the basis of the AASHTO model. Due to the low rate of zinc loss, most of the observations reflect corrosion rates prior to depletion of the zinc coating. However, zinc may have is limited to galvanized reinforcements that are less than been depleted when corrosion rates, observed from elements 20 years old: more than 16 years old, are greater than 4 m/yr. This applies to two points each for Figures 11(a) and 11(b) where the aver- CR 1400-0.75 (16) age rates of steel loss for good and high quality fill may be inferred as approximately 6 m/yr and 4 m/yr, respectively. Table 11 is a summary of corrosion rates computed with Considering a factor of 2 to relate observations of average Equation (16) for selected resistivities. The corrosion rate (uniform) metal loss to tensile strength suggests that steel computed at = 3,000 -cm is consistent with the AASHTO losses of 12 m/yr and 8 m/yr may be used to model corro- model for corrosion of zinc after 2 years in service (i.e., sion rates for steel after zinc has been depleted from galva- 4 m/yr) and the corrosion rates computed at = 10,000 -cm nized reinforcements, considering good and high quality fills, and 20,000 -cm are consistent with the statistics presented respectively. in Figure 7. The AASHTO model is used to compute the nominal metal It also appears that corrosion rates for galvanized reinforce- loss and corresponding sacrificial steel for the calibration of ments are not necessarily lower than plain steel considering fill resistance factors when considering galvanized elements in materials with low min. This is not surprising because it is well both good and high quality fills. A Monte Carlo analysis was known that zinc does not perform better than steel for all performed to assess the probability that metal loss in excess environments. of the nominal amount may occur (pf). This analysis uses the Reliability analyses and resistance factor calibrations were means and standard deviations of the observations as described performed on data groups according to selected ranges of fill in Figure 7. A lognormal distribution was also assumed to resistivity, including 1,000 -cm < min < 3,000 -cm; 3,000 describe the variations in measurements, and the validity of this -cm min < 10,000 -cm; and min 10,000 -cm. Due to assumption is verified as described in Appendix E. Because the relatively high variability, marginal fills (with 1,000 -cm the majority of observations reflect corrosion rates for zinc, < min < 3,000 -cm) should be used with extreme caution. these measurements are best suited of estimating zinc life. Considerably more effort is needed to sample and test these Results from the Monte Carlo analysis render a 99% prob- materials to reliably characterize them and select appropri- ability that zinc coating with an initial thickness of 86 m ate corrosion rates for use in design (Elias et al., 2009). Use of will last 15 years considering good quality fill, and 32 years marginal material is not recommended, but guidance is devel- considering high quality fill. Thus, good quality fill supports oped to demonstrate the issues and level of effort required to zinc life similar to 16 years as predicted by the AASHTO properly manage the risk that is involved when used. Walls model for zi = 86m, and the zinc life appears to be twice as with fill material closer to the 3,000 -cm range may become long with high quality fill. The increased zinc life for high qual- more prevalent depending on whether or not recommenda- ity fill is due to the lower observed corrosion rates evident in tions from NCHRP Project 24-22 are adopted in practice. Figure 11(b). Steel loss, X, is assumed to commence subsequent to zinc Metal Loss Models and Reliability depletion. The mean steel loss is assumed to occur at a rate of 12 m/yr with a COV of approximately 0.66. Table 12 pre- AASHTO Model--Galvanized Reinforcements sents reinforcement ages corresponding to pf equal to 0.01 Figures 11(a) and 11(b) compare corrosion rates measured and 0.05, and the probability that the sacrificial steel will not via the LPR technique to the AASHTO metal loss model (see be consumed for the intended design life (75 or 100 years).

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25 16 14 Strip 12 Grid AASHTO CR (m/yr) 10 Mean 8 6 4 2 0 0 5 10 15 20 25 Age (Years) Figure 11(a). Corrosion rates vs. time and comparison with the AASHTO model for galvanized elements within good quality fill. 16 14 Strip 12 Grid AASHTO CR (m/yr) 10 Mean 8 6 4 2 0 0 5 10 15 20 25 30 Age (Years) Figure 11(b). Corrosion rates vs. time and comparison with the AASHTO model for galvanized elements within high quality fill. Based on the results in Table 12 it appears that the proba- points and Figure 12(b) includes 70 data points documenting bility of sacrificial steel being consumed within design lives of the performances of plain steel reinforcements within good 75 or 100 years is approximately 10% with good quality fill and high quality fills, respectively. Compared to data for galva- and 1.5% with respect to high quality fill (i.e., probabilities of nized reinforcements, the data for plain steel reinforcements 90% and 98.5% that design lives may be exceeded with good are less ambiguous because only the presence of one metal or high quality fills, respectively). type along these surfaces needs to be considered; whereas either zinc, steel or both may be present along the surfaces of galvanized reinforcements. Measured corrosion rates plotted Plain Steel Reinforcements in Figures 12(a) and 12(b) were multiplied by a factor of 2 Figures 12(a) and 12(b) compare corrosion rates measured to reflect higher rates of localized corrosion inherent to the via the LPR technique to the Elias and Stuttgart metal loss behavior of buried steel elements. Significant attenuation of models proposed for design. Figure 12(a) includes 53 data mean observed corrosion rates with respect to time is not Table 12. Occurrence of sacrificial steel consumption for galvanized reinforcements. Fill Quality tdesign X pf = 0.01 pf = 0.05 pf @ tdesign (years) (m) (years) (years) Good 75 708 54 69 0.075 100 1,008 65 84 0.116 High 75 708 75 102 0.010 100 1,008 86 118 0.022

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26 140 120 Data 100 Elias CR (m/yr) mean 80 60 40 20 0 0 5 10 15 20 Age (Years) Figure 12(a). Corrosion rates vs. time and comparison with the Elias model for plain steel elements within good quality fill. 140 120 Data 100 Stuttgart CR (m/yr) 80 mean 60 40 20 0 0 5 10 15 20 Age (Years) Figure 12(b). Corrosion rates vs. time and comparison with the Stuttgart model for plain steel elements within high quality fill. observed. However, more scatter is evident in these data com- A Monte Carlo analysis was performed to assess the prob- pared to galvanized reinforcements [Figures 11(a) and 11(b) ability that metal loss in excess of the nominal amount may compared to Figures 12(a) and 12(b)]. occur (pf). This analysis uses the means and standard devia- The Elias model described by Equation (3), and the Stuttgart tions of the observations as described in Figure 8. A lognor- model as described in Appendix A, are considered for design mal distribution was also assumed to describe the variations of plain steel reinforcements and the calibration of resist- in measurements and the validity of this assumption is veri- ance factors considering good and high quality fill conditions, fied as described in Appendix E. Design lives of 50 and 75 years respectively. Given the nonlinear form of Equation (3) (Elias are considered for plain steel reinforcements within good model) the differences between the mean of the observed and high quality fills, respectively. Given the uncertainty corrosion rates and the Elias model, depicted in Figure 12(a), associated with variations of observed performance, and lack are inversely proportional to age/design life. Considering a of data from reinforcements older than 20 years, estimations design life of 50 years, the Elias model renders a mean cor- of sacrificial steel requirements for longer service lives are rosion rate (averaged over 50 years) of 37 m/yr, compared considered dubious. Table 13 summarizes results from the to the observed mean of 25 m/yr based on measurements Monte Carlo simulations of service life. Due to the higher obtained from reinforcements with ages spanning 20 years. The variance inherent to the observed performances, probabilities mean of observed corrosion rates from reinforcements within of exceeding estimated metal losses are higher for plain steel high quality fill is similar to the Stuttgart model (12 m/yr) for reinforcements than for galvanized reinforcements (Table 12 plain steel reinforcements that are older than 2 years. Higher compared to Table 13). This will be reflected in relatively rates are used in the Stuttgart model for the first 2 years of ser- lower calibrated resistance factors used to achieve the same vice; however, this is not very important considering a service overall probability that MSE designs will meet the intended life of 75 years. service life.

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27 Table 13. Occurrence of sacrificial steel consumption for plain steel reinforcements. Fill Quality tdesign X pf = 0.01 pf = 0.05 pf @ tdesign (years) (m) (years) (years) Good 50 1,829 25 35 0.16 High 75 1,036 20 33 0.31 Marginal Quality Fill depending on location within the fill and the actual sources used during construction, there may be locations that have Figure 13 compares corrosion rates measured via the LPR resistivity higher than 3,000 -cm, or less than 1,000 -cm. technique to the metal loss model proposed for design [Jackura This is reflected in large scatter in the data as depicted in Fig- et al. (1987) and described subsequently with Equation 17(a)]. ure 13 where measured corrosion rates obtained from a par- These figures include approximately 200 data points docu- ticular site on the same day may vary from less than 4 m/yr menting the performances of galvanized reinforcements within to more than 25 m/yr. marginal quality fill. Performance data were obtained from Due to the paucity of data between 2 and 10 years of ser- 11 sites distributed amongst California, Nevada, New York, vice, statistics are generated for the first 2 years of service ( = and North Carolina. Much higher scatter is evident in these 2.4 m/yr and = 1.6 m/yr) and after 10 years of service ( = data compared to corrosion rates observed from good and high 4.6 m/yr and = 6.3 m/yr). These statistics demonstrate quality fills. Higher scatter may be attributed to uncertainties that the corrosion rates for marginal quality fill are approxi- with respect to fill resistivity. Samples, corresponding to these mately two to three times higher than those observed from 11 sites, were collected from different locations or sources good quality fills. (stockpiles) but the destinations of these fills relative to spe- A Monte Carlo simulation was performed to estimate zinc cific locations within MSE wall constructions are unknown. life assuming a lognormal distribution of corrosion rates. Furthermore, characteristics including salt content are not There are no data from reinforcements between the ages of homogeneous and can vary spatially with corresponding vari- 2 and 10 years so the statistics from reinforcements less than ations in the related resistivity. or equal to 2 years old are assumed to apply until the reinforce- Often results from five to 10 resistivity measurements are ments have been in service for 10 years. Results from the Monte available and used to represent fill conditions for a particular Carlo analysis render a 99% probability that zinc coating with site. These measurements depict a range with some measure- an initial thickness of 86 m will last 10 years considering ments above 3,000 -cm, and some below 1,000 -cm. This marginal quality fill. This compares with 16 years and 32 years is significant because resistivities neighboring 1,000 -cm for galvanized reinforcements within good and high quality appear to be a threshold, and substantially higher corrosion fills, respectively. Thus, the use of marginal quality fills appears rates are realized at resistivities below this threshold. Thus, to have a significant effect on zinc life, and zinc life is approx- although a site may be classified as having marginal quality fill, imately 60% of that expected with good quality fills. 70 60 Strip 50 Grid CR (m/yr) Model 40 Mean 30 20 10 0 0 5 10 15 20 25 30 Age (Years) Figure 13. Corrosion rates vs. time and comparison with the Jackura model for galvanized elements within marginal quality fill.