LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems (2011)

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12 Tasks The research approach includes nine tasks and the project was conducted in two phases. Tasks 1 through 5 were included in Phase I, and Phase II includes Tasks 6 through 9. Results from Phase I were described in the project interim report that was submitted in April 2007, and this report includes results from Phase II. A brief description of tasks from Phase I is summarized to help place the approach and results from Phase II into context. Task 1—Literature Review and Survey Task 1 consists of a review of existing literature and a sur- vey of owners, designers, and contractors to (1) identify exist- ing data on the past performance of metallic reinforcements; (2) trace the development of corrosion potential, metal loss and service life models that form the basis for the existing AASHTO specifications and FHWA recommendations; (3) document information relative to existing installations; and (4) solicit information regarding existing sites and planned construction/deconstruction where access to reinforcements could be gained for field studies, including opportunities to exhume reinforcement samples for observation and testing. Task 2—Prepare Performance Database Task 2 consists of (1) developing and populating a database using existing performance data identified in Task 1, (2) col- lecting information regarding the existing inventory of metal- lic earth reinforcements, and (3) studying attributes of the performance data and comparing attributes of the general population to those from sites with performance data. Task 3—Estimate Reliability of Service-Life Models Task 3 consists of analyzing the results from Tasks 1 and 2 to estimate the reliability and utility of promising models for predicting the corrosion potential, metal loss, and service life of metal-reinforced systems in geotechnical applications. Task 4—Develop Work Plan for Field Investigation Task 4 consists of preparing detailed plans for a compre- hensive field investigation to evaluate the performance of earth reinforcement systems. This plan addresses some of the deficiencies in the performance database identified in Task 2. These deficiencies include limitations with respect to geo- graphic distribution, range of fill characteristics, spatial and temporal variations, and corrosion rate measurements for Type II reinforcements. Task 5—Submit Interim Report Task 5 consists of preparing an interim report summariz- ing the results, conclusions, and recommended work plans developed during Tasks 1 to 4. This report was submitted to and approved by NCHRP in April 2007. Task 6—Implement Field Investigation Task 6 consists of implementing the workplan developed in Task 4 and approved in Task 5. Task 7—Identify Target Reliability Index for LRFD Using the data from Tasks 2, 3 and 6, statistical properties are computed to describe the variability of factors that affect metal loss and service life estimates of in-ground metallic reinforcement systems. This includes (1) reevaluation of the prediction model(s) to assess its accuracy and precision to esti- mate metal loss caused by corrosion and (2) development of appropriate resistance factors for use in LRFD that account for metal loss caused by corrosion. Calibration of the resistance fac- tors uses load factors from the AASHTO LRFD specifications C H A P T E R 2 Research Approach

and calibration methodology recommended by Allen et al. (2005). The resistance factors consider the nominal metal loss used in design and the redundancy of the design and load redistribution inherent to the identified limit states. The reliability index (β) for other systems that are vulnera- ble to metal loss (unprotected soil nails and rock bolts) will also be considered and compared to the βT values used in design. Task 8—Recommend Revisions to AASHTO LRFD Specifications Based on the results from Task 7, revisions to the current AASHTO LRFD specifications used in the design of metal- tensioned systems were reviewed and recommended. In particular, resistance factors for design of MSE walls are rec- ommended that take into account the estimated metal loss over the service life of the installation. Metal loss parameters will be updated as appropriate for galvanized and plain steel reinforcements, while taking into consideration different back- fill characteristics. Task 9—Submit Final Report This final report summarizes the findings of, draws conclu- sions from, and documents the research products, including • A performance database documenting the attributes and metal loss observed for a variety of metal-tensioned systems used in geotechnical applications, including the additional results from field studies conducted in Task 6. • Updated metal loss models that consider targeted levels of confidence, sources of error, and different types of elements and site conditions. • Recommended revisions to the current AASHTO LRFD specifications, including updated resistance factors for the design of MSE walls and other earth reinforcements. • Discussion of deficiencies in present knowledge and rec- ommendations for future work. Test Protocol Berkovitz and Healey (1997) and Elias et al. (2009) describe test protocols and procedures for sampling and testing Type I reinforcements. Withiam et al. (2002) present a recommended practice resulting from NCHRP Project 24-13 for condition assessment and service life modeling of Type II reinforcements. These procedures, protocols, and recommended practices were followed in the course of this research. Appendix B describes salient details of test procedures, sampling, data analysis, and interpretation for Type I and Type II reinforcements. In gen- eral, the protocols include (1) assessing the site and installation conditions; (2) sampling and testing backfill, groundwater, and in situ earth materials; (3) performing nondestructive testing (NDT) supplemented with visual observations; and (4) comparing results with expectations for service life mod- els (Fishman et al., 2005). NDT applied to Type I reinforcements includes measure- ment of half-cell potential and LPR. Half-cell potential mea- surements are useful to probe the surface and assess if corrosion has occurred and whether or not zinc coating remains on the surface of galvanized reinforcements. LPR is useful to estimate corrosion rate at an instant in time. Single measurements do not provide enough information and a sampling strategy is incorporated into the test protocol to consider random, spa- tial, and temporal variations in measurements. Additional NDT applied to Type II reinforcements includes impact and ultrasonic tests. Impact test results are useful to diagnose loss of prestress, assess grout quality, and indicate if the cross section is compromised from corrosion or from a bend or kink in the element. Ultrasonic test results are useful for obtain- ing more detailed information about the condition of elements within the first few feet from the proximal end of the element. Calibration of Resistance Factors for LRFD The procedure for reliability-based calibration of resistance factors for LRFD is as follows (Allen et al., 2005): 1. Consider limit state equation for yield of reinforcements. 2. Statistically characterize the data upon which the calibration is based. 3. Select a target reliability index. 4. Use reliability theory to compute resistance factors. Factors that impact the extent to which variability of metal loss affects probability of occurrence need to be included in the reliability-based calibration. To help identify these factors, Figure 4 illustrates how the steel incorporated into the design of a reinforcement cross section can be interpreted to include 13 Figure 4. Idealized reinforcement cross section.

14 three components: (1) steel needed to resist the applied load without yielding (nominal structural steel), (2) steel loss from corrosion (consumed steel), and (3) residual steel that was intended to serve as sacrificial steel, but not actually consumed by corrosion. Residual steel contributes to the reinforcement resistance, and consequently to the bias inherent to the design. Differences between the metal loss model used in design and the prevailing corrosion rates determine the amount of resid- ual steel at the end of the service life. Prevailing corrosion rates depend on the electrochemical properties of the fill, making fill quality an important factor to include in the calibration. Reinforcement size is also important because the significance of residual steel becomes less as the cross-sectional area of the reinforcement increases. In consideration of these factors, the reliability-based calibration is performed in terms of the fol- lowing design parameters: • service lives of 50, 75 and 100 years; • different reinforcement dimensions for strips 3 mm, 4 mm, 5 mm and 6 mm, or wire diameters for grids W7, W9, W11, W14; and • different backfill conditions (not all meet AASHTO speci- fications). Yield Limit State Loss of cross section affects the yield resistance of MSE reinforcements and is incorporated into the LRFD procedure in terms of the yield limit state equations. The yield limit state is reached when the reinforcement tension exceeds the yield resistance. Therefore, calculation of loads and yield resistance contribute to the yield limit state equations. Reinforcement loads may be computed via several differ- ent methods including the coherent gravity method, tieback wedge method, structure stiffness method, or the simplified method (Berg et al., 2009). Most metallic reinforcements are considered to be relatively inextensible, and, traditionally, loads have been computed via the coherent gravity method; however, the structure stiffness method and the simplified method have also been applied. For the purpose of this study the coherent gravity and simplified methods are considered and used to compute the load bias for the calibration of resis- tance factor. Reinforcement loads are computed based on the horizontal stress carried by the reinforcements computed as where σH is the horizontal stress at any depth in the reinforced zone, K is the coefficient of lateral earth pressure, σv is the factored vertical pressure at the depth of interest, and ΔσH is the supplemental factored horizontal pressure due to external surcharges. σ σ σH v HK= + Δ ( )8 The main differences between the simplified and the coher- ent gravity methods are with respect to the determination of K and computation of σv (Berg et al., 2009). The manner in which reinforcement loads are computed affects the load bias used in the calibration of resistance factor. Allen et al. (2001 and 2005) and D’Appolonia (2007) assessed the load bias for metallic MSE reinforcements using the simplified and coherent gravity meth- ods of analysis, respectively. We have used the load bias from these references to calibrate resistance factors for LRFD. The maximum reinforcement tension is computed from σH based on the spacing of the reinforcements as where Tmax is the maximum reinforcement tension at a given level per unit width of wall and SV is equal to the vertical spacing of reinforcements. Equations (8) and (9) describe the demand placed on the reinforcements; the capacity is the yield resistance of the rein- forcements computed as where R is resistance per unit width of wall, Fy is the yield strength of the steel, Ac is the cross-sectional area of the reinforcement at the end of the service life, and SH is the horizontal spacing of the reinforcements. For strip-type reinforcements: For steel grid-type reinforcements: where b is the width of the reinforcements, Ec is the strip thickness corrected for corrosion loss; Ec = (S − ΔS) for ΔS < S, and 0 for ΔS ≥ S, S is the initial thickness, ΔS is the loss of thickness (both sides) from corrosion, n is the number of longitudinal bars/wires, and D is the diameter of the bar or wire corrected for corrosion loss; D = Di − ΔS for ΔS < Di, and 0 for ΔS ≥ Di, where Di is the initial diameter. For galvanized reinforcements: Δ Δ S r t C C t S C t s f f f = × × −( ) < = ≥ 2 0 13 For For a( ) A n D c = × ×π 2 4 12( ) A bEc c= ( )11 R F A S y c H = ( )10 T SH Vmax ( )= σ 9

where rs is the corrosion rate of steel after zinc has been consumed, tf is the intended service life, C is the time to initiation of steel loss, zi is the zinc initial thickness per side, rz1 is the initial corrosion rate for zinc, and rz2 is the corrosion rate for zinc after the first two years. For plain steel reinforcements: Variables for the resistance calculation include Fy, Ac, rs, rz1, rz2, and zi. The spacings of the reinforcements (SH and SV) are considered to be constants. Using the statistics and observed distribution for measurements of corrosion rate, the bias of the remaining strength is computed and used as input for the reliability-based calibration of resistance factor. The bias is computed as The denominator includes nominal values used in design; Ac is based on the metal loss model recommended by AASHTO for design of metallic MSE reinforcements, and Fy is the nominal yield strength. The statistics of the observed corro- sion rates from the database described in Chapter 3 are used to describe the variable Ac, and the statistics for Fy are taken from Galambos and Ravindra (1978) and Bounopane et al. (2003). Bounopane et al. consider yield strengths to be normally distributed with mean 1.05 times the nominal and COV = 0.1. Resistance Factor Calibration Monte Carlo simulations are employed to compute the relationship between the reliability index, β, and resistance factor, φ. The Monte Carlo simulation method is used because the approach is more adaptable and rigorous compared to other techniques, and it has become the preferred approach λR y c y c F A F A =   ( )15 ΔS r ts f= × ×2 14( ) C yrs z r r i z z = + − ×( ) 2 2 13 1 2 ( )b for calibrating load and resistance factors for the LRFD spec- ifications (Allen et al., 2005; D’Appolonia, 2007). The simula- tions are performed in terms of a given load factor, γ, load bias, λQ, and resistance bias, λR. The Monte Carlo technique utilizes a random number generator to extrapolate the limit state function, g, for calibration of yield resistance. Random values of g are generated using the mean, standard deviation, and the distribution (e.g., normal, lognormal, or Weibull) of the load bias and the resistance bias. The extrapolation of g makes estimating β possible for a given combination of γ and φ. A value of γ is adopted that is compatible with the static earth load calculations (AASHTO, 2009). A range of φ values is assumed and estimated values of β (by iteration) are checked against a value of 2.3 as used in previous LRFD calibrations (Allen et al., 2005; D’Appolonia, 2007). Monte Carlo simula- tions were facilitated by the Lumenaut software package (Lumenaut, 2007), which performs Monte Carlo simulations through a link with Microsoft Excel. The vertical pressure due to the weight of the reinforced soil zone (σv in Equation 8) is assigned load type “EV” as described by Berg et al. (2009). AASHTO (2009) specifies γ equal to 1.35 for EV at the strength limit state, therefore, γ = 1.35 is adopted for calibration of the resistance factor similar to D’Appolonia Engineers (2007) and Berg et al. (2009). The load bias depends on use of the simplified or coherent grav- ity method and may depend on reinforcement type (strip or grid) as described by Allen et al. (2001), Allen et al. (2005), and D’Appolonia (2007). Results from these studies demon- strate that the load bias has a lognormal distribution, mean, and standard deviation as summarized in Table 8. Resistance bias is computed using Equations (10) to (15), nominal values for yield strength and remaining cross section, the yield strength variation, and the mean, standard deviation, and distribution from observations of metal loss archived in the performance database. Thus, the resistance bias depends on the nominal strength, which depends on the metal loss model used in design, as well as the manner in which observations of corrosion rate and metal loss are extrapolated to render the estimated remaining strength at the end of service. Monte Carlo simulations were performed using these values for load bias and load factor, and several different scenarios were considered. Different scenarios treat metal loss as deterministic or variable, and contrast “as built” versus Table 8. Mean (µ) and standard deviation () of lognormal load bias. Strip Grid Parameter Simplified Method1 Coherent Gravity Method2 Simplified Method1 Coherent Gravity Method2 0.973 1.294 0.973 1.084 0.449 0.499 0.449 0.737 1Allen et al. (2005). 2D’Appolonia (2007). μλQ σλQ 15

16 Figure 5. Monte Carlo simulation example showing input and output reports.

Figure 6. Typical Monte Carlo result from resistance factor calibration. -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 0 2 4 g (R,Q) z β = 2.27 17 design conditions. For each scenario different aspects of the design, including reinforcement size and service life, are con- sidered and 10,000 iterations are performed to arrive at the distribution of the limit state function. The Monte Carlo analysis for calibration of resistance factor computes values for the limit state function, g = R − Q, consid- ering the uncertainty of R and Q, and renders the probability that g < 0. The variables R and Q can be related to nominal values as Q = Qn × λQ, and based on the LRFD equation [Equation (6)], The analysis pro- ceeds by selecting a value for Qn; a value of unity is used for convenience. The Monte Carlo analysis then computes a range of values for g, using randomly generated values for λR and λQ based on their statistics, and a trial value of φ. The Lumenaut software outputs the results of the iterations in the form of a histogram and corresponding intervals are summarized in a table. Figure 5 is an example output from a typical Monte Carlo simulation for computing β based on a trial selection of φ. The top graph is a histogram depicting the distribution of g from results of the Monte Carlo simulation. The proba- bility that g < 0 may be computed by sorting and ranking these results and computing the cumulative probability at g = 0. The table beneath the histogram summarizes the statistics associated with g and the figures at the bottom of the page describe the statistics and associate distribution provided as input (in this case for λR and λQ). A worksheet, including the actual results from the 10,000 iterations, is also generated. The g values are then sorted and ranked in an ascending order and the cumulative probability at each g is calculated. Figure 6 shows a typical result depict- ing the standardized normal variable (z) versus randomly gen- erated g. The reliability index, β is equal to (−z) at g = o. For the example shown in Figure 6, β is equal to 2.27 correspond- ing to pf = 1.15E-02. The analysis is repeated with different trial values for φ until the probability that g < 0 corresponds to R R Q R n R Q n = × = × ×λ λ γφ . the target reliability index. Appendix E includes details simi- lar to Figures 5 and 6 in support of all Monte Carlo simula- tions described in this report. McVay et al. (2000) proposed representing design efficiency as the ratio of resistance factor and mean bias (φ/λR). This measure of efficiency accompanies computed resistance fac- tors to avoid the misconception that high resistance factors are correlated with the economy of a design method. Paikowski (2004) demonstrates that this ratio is systematically higher for methods that predict more accurately, regardless of the bias. Using different models for the nominal resistance in the denominator of Equation (15) may lead to different values of the mean bias (λR) and corresponding resistance factors (φ), but if the COVs are the same, the resulting efficiency factors are identical. Higher efficiency factors are only obtained with meth- ods that produce a lower COV with respect to the computed bias. This may be accomplished by improving the quality and quantity of measured or estimated resistance, the models and methods used to represent and extrapolate the data, or both. If the metal loss is assumed to be deterministic, the only vari- able (i.e., not a constant) describing the tensile strength remain- ing at the end of service condition corresponds to yield strength, Fy. Thus, the bias for remaining tensile strength is considered as normally distributed with mean equal to 1.05 and standard deviation of 0.105 (Bounopane et al., 2003). These results are presented to serve as a baseline to assess the impact that varia- tions in metal loss have on the computed values for φ. The calibration is performed to identify the resistance fac- tor corresponding to β of approximately 2.3 (pf ≈ 0.01). Resis- tance factors, summarized in Table 9, are rounded to the nearest increment of 0.05. These results may be compared to the current AASHTO specifications where φ is specified as 0.75 for strip-type rein- forcements and 0.65 for grids that are attached to a rigid wall facing. These factors are the same for the simplified and coherent gravity methods in the current edition of the speci- fications. It appears that the current AASHTO specifications implicitly consider some variation with respect to estimated sacrificial steel requirements for galvanized reinforcements. This is in spite of the fact that the resistance factors are not determined from a reliability-based calibration, but are cali- brated with respect to safety factors corresponding to the ear- lier specifications for ASD. Table 9. Resistance factors considering deterministic metal loss model. Type Simplified/Coherent Strip 0.55/0.45 Grid 0.50/0.35