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28 Due to the high scatter inherent to these data and uncer- results from the Monte Carlo simulations of service life tainties with respect to fill properties, conservative assump- when nominal sacrificial steel requirements are estimated tions are made regarding zinc life and corrosion rates of base with Models I and II. steel subsequent to zinc deletion. For the purpose of estimat- Table 14 shows that the probabilities of sacrificial steel con- ing service life, zinc life is assumed to be constant and equal sumption are significantly affected by the nominally com- to 10 years (with zi = 86 m) and the observed corrosion rate puted sacrificial steel requirements (i.e., the amount of of steel subsequent to zinc depletion is taken as 32 m/yr sacrificial steel estimated for a 50-year design life according to with standard deviation of 21 m/yr and a lognormal distri- Model I or Model II). In principal, different resistance factors bution. The corrosion rate of steel is based on observations computed with different nominal models should offset the from galvanized reinforcements after 8 years of service with differences in nominal sacrificial steel requirements, render- the lower corrosion rates (i.e., < 4 m/yr) culled from the data ing similar design as long as the COVs of the different bias as described in Appendix E. distributions are also similar. Resistance factors will be cali- The model used to compute nominal sacrificial steel require- brated in the next section that will render the probability that ments for design is similar to the recommendations described reinforcements will be overstressed during their design life to by Jackura et al. (1987) for "neutral" fill with > 1,000 -cm be similar, independent of the metal loss model that is selected and salt contents limited as described in Table 2 (Caltrans- (i.e., resistance factors may be calibrated for each model to Interim model). This model assumes that steel is exposed on the render the same pf). The effect of the different models on steel surface of galvanized reinforcements (zi = 86 m) after 10 years requirements is illustrated in the design example presented in of service and that the base steel will corrode at an average rate Appendix F. of 28 m/yr subsequent to zinc depletion. Two different metal loss models are studied to illustrate how this affects the reliability of service life estimates. The Calibration of Resistance Factors first model (Model I) is from Jackura et al. (1987) for "neu- tral" fill and the second model (Model II) is a similar form, Galvanized Reinforcements but with double the corrosion rate for steel as follows: Data included in Appendix D include observations from galvanized reinforcements and coupons, and from plain steel m Model I : X ( m ) = ( t design - 10 ) years 28 (17a a) (i.e., not galvanized) elements. In-service reinforcements and year coupons are placed in the same fill conditions but have very m different dimensions, and coupons may be placed at both Model II : X ( m ) = ( t design - 10 ) years 56 (17 7 b) front and back locations with respect to the wall face. Data year from in-service reinforcements and coupons were compared, A Monte Carlo analysis was performed to assess the prob- and, on the basis of this comparison, the decision was made ability that metal loss in excess of the nominal amount may to include them in one data set, thus enhancing the quantity occur (pf). This analysis uses the means and standard devia- of data within each partition. tions of the observations as described in the preceding para- Metal loss is considered in the resistance factor calibration graphs and as depicted in Figure 7. A lognormal distribution where the bias of remaining strength (i.e., ratio of measure- was also assumed to describe the variations in measurements ments to nominal value used in design) is computed as Equa- and the validity of this assumption is verified as described in tion (15). The nominal remaining strength used in design and Appendix E. Design lives of 50 years are considered for galva- in the denominator of Equation (15) is computed as described nized steel reinforcements within marginal quality fills. Given in Equations (10) through (14) with values of rz1, rz2, and rs the uncertainty associated with variations of observed per- from the metal loss model recommended by AASHTO for formance, and lack of data from reinforcements older than assessing metal loss of galvanized reinforcements, and described 25 years, estimations of sacrificial steel requirements for longer in Tables 2 and 3. Since the oldest MSE walls are approximately service lives are considered dubious. Table 14 summarizes 40 years old, direct measurements of remaining strength after Table 14. Occurrence of sacrificial steel consumption for galvanized steel reinforcements in marginal quality fill. Design Model tdesign X pf = 0.01 pf = 0.05 pf @ tdesign (years) (m) (years) (years) Model I 50 1,120 18 24 0.44 Model II 50 2,240 28 40 0.11

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29 3 2 1 0 Z -1 -2 -3 0.10 1.00 10.00 Corrosion Rate, m/yr Figure 14. Probability plot depicting lognormal distribution for data describing corrosion rates of galvanized reinforcements within good quality fill. a service life of 75 or 100 years are not available. Therefore cor- Figures 14 and 15 are examples of inputs and intermediate rosion rate measurements must be extrapolated to estimate results from the calibration exercise. Tables 15 to 18 summa- "measurements" of remaining strength used in the numera- rize the final results from the calibration. The following list tor of Equation (15). The extrapolation also employs equa- describes the steps involved in the calibration process and gen- tions similar to Equations (10) through (14), but with eration of resistance factors using the Monte Carlo Technique: corrosion rates rz1, rz2, and rs from the observed performance of reinforcements during service. This approximation is con- a) Generate statistics from observations for corrosion rates sidered conservative due to the likely attenuation of corrosion including the mean (), standard deviation (), and the rate with respect to time. The corrosion rates used to extrap- shape of the probability density function (pdf). It is impor- olate metal loss are considered constants over prescribed time tant to select the correct shape of the pdf to represent the intervals, and are higher than those expected to prevail at the data. Probability plots similar to the one depicted in Fig- end of service. ure 14 are used to check the match between the empirical 1 Data Cumulative Probability 0.8 Weibull 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 Bias Figure 15. Typical plot showing Weibull distribution x f ( x ) 1 e for bias; galvanized strip reinforcement with S 4 mm, tf 75 years; 1.5, 1.6 corresponding to mean 1.35 and standard deviation 0.42.

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30 Table 15. Summary of for Table 17. Summary of for the conservative steel model. zinc residual steel model. Reinforcement Design Reinforcement Reinforcement Design Reinforcement Type Life Thickness Simple/Coherent Type Life Thickness/Size Simple/Coherent 4 mm 0.45/0.35 4 mm 0.70/0.65 75 years 5 mm 0.45/0.35 75 years 5 mm 0.65/0.55 Strip 6 mm 0.50/0.40 Strip 6 mm 0.65/0.55 4 mm 0.25/0.15 4 mm 0.55/0.50 100 years 5 mm 0.30/0.20 100 years 5 mm 0.60/0.50 6 mm 0.25/0.20 6 mm 0.65/0.50 W7 0.60/0.50 W9 0.60/0.50 75 years W11 0.60/0.50 data frequencies and the theoretical pdf. Probability grids W14 0.55/0.50 Grid W7 0.55/0.45 similar to Figure 14 are generated for each variable used to W9 0.55/0.45 describe corrosion rates and metal loss. In most cases log- 100 years W11 0.55/0.45 W14 0.55/0.45 normal distributions were found to fit well with the observed corrosion rates. b) Extrapolate metal loss to the end of the selected service life using the statistics of observed corrosion rates and corre- Good Quality Fill sponding assumptions regarding the trends of corrosion Good quality fill meets AASHTO requirements for electro- rates with respect to time. chemical and mechanical properties, and has min in the range c) Compute the remaining tensile strength, Trem, and the sta- of 3,000 -cm and 10,000 -cm. The statistics for reinforce- tistics of the resistance bias, R, via Monte Carlo simula- ments that are between 2 and 16 years, shown in Figure 7, are tions. The distribution of R is modeled with a pdf. The considered representative of the life of the zinc coating. Thus, bias distributions were modeled with either normal, log- the corrosion rate for zinc is assumed to be constant with normal, or Weibull distributions. Probability plots simi- respect to time with a mean rate of 1.7 m/yr (rz1 and rz2) and lar to the one depicted in Figure 15 are prepared to check standard deviation of 1.09 m/yr. The distribution is mod- the match between the empirical data frequencies and the eled as lognormal based on the probability plot depicted in theoretical pdf. Figure 14. The data shown in Figure 14 plot close to a straight d) Compute and corresponding pf for an assumed value line with a coefficient of correlation, R2 = 0.96. Probability of . plots, similar to Figure 14, depicting the distributions used for e) Iterate on to converge to the desired target reliability other corrosion rate measurements described in this report index, T. Tables 15 to 18 summarize the resistance factors, are included in Appendix E. , that converge to T for the different cases considered (e.g., Given the average rate of zinc loss (1.7 m/yr), and since galvanized reinforcements in good or high quality fill). measurements were made on reinforcements that are less As shown in Figure 7 and discussed in the previous section, the statistics of corrosion rate measurements are different Table 18. Summary of considering high quality fill. for fill materials that are considered good enough to meet AASHTO electrochemical requirements (good fill), and those Reinforcement Design Reinforcement Type Life Thickness/Size Simple/Coherent that exceed AASHTO requirements by a wide margin (high quality fill). Therefore, resistance factors are calibrated with 4 mm 0.85/0.70 respect to fill quality (i.e., good fill and high quality fill). 75 years 5 mm 0.75/0.65 Strip 6 mm 0.70/0.60 4 mm 1.0/0.85 100 years 5 mm 0.85/0.70 Table 16. Effect of zi on 6 mm 0.75/0.65 W7 0.75/0.65 computed ; S 4 mm, W9 0.70/0.60 tf 75 years. 75 years W11 0.65/0.55 W14 0.65/0.55 zi R Grid W7 0.90/0.75 (m) W9 0.80/0.70 86 1.35 0.42 0.35 100 years W11 0.80/0.65 150 1.54 0.26 0.65 W14 0.75/0.60

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31 than 30 years old, very few measurements are available to tor for zi = 150 m is 0.65 and compared to the case with zi = describe the corrosion of steel after zinc has been consumed 86 m, this result is closer to the current AASHTO specifica- from a galvanized reinforcement. Two different assumptions tions ( = 0.75). In this case zi has a significant effect on the are applied as described by Elias (1990) that either (1) con- computed , which demonstrates that zinc thickness is an sider the base steel to corrode at the same rate as plain black important variable to include in resistance factor calibrations. steel (i.e., not galvanized) or (2) assume that the base steel will However, data on initial zinc thickness are needed to prop- corrode at a rate similar to that prevailing as zinc is finally erly characterize the inherent variation and to incorporate the consumed (i.e., corrosion rate does not change abruptly after statistics into a reliability analysis. Use of zi = 86 m corre- zinc is consumed). In addition, "measured" corrosion rates sponds to the minimum requirement and is a conservative for steel were multiplied by 2 to render loss of tensile strength approach to modeling initial zinc thickness. from LPR measurements. The zinc residual model for steel consumption considers A conservative model for steel consumption assumes that that the corrosion rate of the base steel is affected by the pres- the base steel corrodes at the same rate as plain steel (i.e., not ence of zinc residuals. Zinc residuals passivate the steel sur- galvanized) after the sacrificial zinc layer is consumed. Most face and include a zinc oxide film layer adhered to the metal of the data used for corrosion rates of plain steel embedded surface and zinc oxides within the pore spaces of the sur- in fill materials meeting current AASHTO guidelines are from rounding fill. There are very few measurements describing plain steel coupons installed at MSE sites located in California, corrosion rates of base steel after zinc has been consumed. A New York, and Florida. The statistics of this data set render a few observations may be applicable from the data set col- mean corrosion rate and standard deviation of 27 m/yr and lected in Europe (Darbin et al., 1988) wherein zinc is con- 18 m/yr, respectively; and the distribution can be approxi- sumed relatively rapidly (i.e., within a few years) and from mated as lognormal. measurements made on walls in the United States that are A resistance bias is computed for different sizes of strip- approaching 30 years of age. Rapid zinc consumption from type reinforcements (4 mm, 5 mm, and 6 mm) and both 75- some of the earlier sites in Europe is due to a relatively thin and 100-year service lives. The bias tends to decrease with zinc coating (zi = 30 m) and moderately corrosive reinforced respect to increase in reinforcement size, and is higher con- fill materials. A review of these data renders corrosion rates sidering longer service life. The mean resistance bias, R, for steel that are close to 12 m/yr. This is the metal loss ranges between 1.2 and 1.5 with COV approximately 40% model recommended by AASHTO and is adopted as a basis and a distribution that is approximated as a Weibull distri- for comparison with calibrations performed by extrapolating bution (Vardeman, 1994). Figure 15 is a typical plot showing measured corrosion rates with the conservative steel model. the distribution of the computed bias. Similar to other data sets, a COV of 60% and a lognormal dis- Resistance factors are calibrated using the computed sta- tribution is used to describe the variation. tistics for resistance bias and load bias from the literature. The calibration was performed for both strip- and grid-type Table 15 summarizes the results of the resistance factor cal- reinforcements. The mean of the resistance bias is approxi- ibration applicable to the conservative steel loss estimate. mately 1.4 with COV approximately 20% and a distribution The resistance factors do not vary significantly with respect that is approximately normal. Table 17 is a summary of the to reinforcement size but are lower when considering longer resistance factors calibrated with metal loss measurements service life. Resistance factors of approximately 0.45 and 0.25 extrapolated with the zinc residual model for steel loss. These apply to 75- and 100-year service lives, respectively. Resis- resistance factors are significantly higher than those obtained tance factors calibrated using the coherent gravity model are with the conservative steel model (Table 15) and are in the slightly lower. The efficiency factor is approximately 0.38 for range of 0.60 to 0.70 for strip-type reinforcements, and 0.50 a design life of 75 years and 0.2 for a design life of 100 years. to 0.60 for grids. The efficiency ratio for this case is approxi- Additional calibrations were performed to investigate the mately 0.5 and represents an improvement compared to the effect of initial zinc thickness on the computed resistance fac- case in which metal loss measurements are extrapolated via tors. Table 16 compares results obtained with zi equal to 86 m the conservative steel model. and 150 m per side. The comparison considers 4-mm-thick galvanized strip reinforcements, a design life of 75 years, High Quality Reinforced Fill ( > 10,000 -cm) and the same statistics for metal loss (i.e., zinc and steel) as described for galvanized reinforcements with the conserva- High quality reinforced fills have min > 10,000 -cm and tive steel model. The load bias used in the calibration cor- corrosion rates corresponding to these conditions were responds to the coherent gravity method. In each case the observed from sites in Florida (Sagues et al., 1998; Berke and computed resistance bias has a Weibull distribution simi- Sagues, 2009) and North Carolina. These data render mean lar to that shown in Figure 15. The computed resistance fac- and standard deviation of corrosion rates for the zinc coating