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9 intervals, to pass through the specimen and return, is mea- tributed geographically. Approximately 40% of the walls sured. Return pulses may be either from a single reflection at constructed with strip reinforcements are located in the more a discontinuity, or from multiple reflections between a dis- temperate southern climates, where soils are normally slightly continuity and the end of the specimen. The patterns of the acidic. received pulses and the arrival times can provide valuable information about the nature of a defect, and of the integrity Load and Resistance Factor of the material being tested. Design (LRFD) LRFD is a reliability-based design method by which loads Performance Database and resistances are factored such that: An important component of this research is to organize and incorporate performance data from earth reinforcements into iQni Rn (6) a database. The database is analyzed to assess the reliability of current models for estimating metal loss and service life. The where New York State Department of Transportation (NYSDOT) Qni are nominal (i.e., computed) loads from sources that (Wheeler, 2002b), the Colorado Department of Transportation may include earth loads, surcharge loads, impact loads, (CDOT) (Hearn et al., 2004), the Association for Metallically or live loads; Stabilized Earth (AMSE, 2006), the Kentucky Transportation i is the load factor for the ith load source; Research Cabinet (Beckham et al., 2005), the Ohio Department Rn is the nominal (i.e., computed) resistance; and of Transportation (Timmerman, 1990), and the National Park is the resistance factor and is usually less than 1. Service (Anderson et al., 2009) have all developed databases Load and resistance factors are applied such that the asso- for retaining walls. In general, these databases follow a format ciated probability of the load exceeding the resistance is low. and protocol consistent with that employed by the FHWA The limit state equation corresponding to Equation (6) is mandated Bridge Management System (Hearn et al., 2004). These databases were considered and used as a basis to develop g ( R, Q ) = R - Qi = R Rn - Qi Qni > 0 (7) the framework for the performance database developed as part of NCHRP Project 24-28. The database developed for this proj- where ect provides input necessary for statistical analysis of perfor- g is a random variable representing the safety margin; mance data, reliability analysis, and calibration of resistance R is a random variable representing "measured or actual" factors for reliability-based design (i.e., LRFD). resistance; The AMSE has compiled an inventory documenting Q is a random variable representing "measured or actual" details of MSE walls constructed in the United States over the load; past 35 years (AMSE, 2006). The majority of walls con- Qi are random variables for "measured or actual" loads structed with grid reinforcements serve as retaining walls, from various sources that may include earth loads, sur- but approximately one-third of the walls with strip rein- charge loads, impact loads, or live loads; and forcements serve as part of a bridge structure (abutment or R and Qi are bias factors defined as the ratio of measured wing walls). Approximately half of the walls in the AMSE (actual) to nominal (computed) values of resistance and inventory are located in the western region of the United load, respectively. States, within an arid climate where backfill sources are alka- line. Approximately 80% of the fill materials included in the Figure 3 depicts the limit state equation described by Equa- AMSE database have a pH of between 6.5 and 8 (slightly tion (7) and the area beneath the tail to the left of g = 0 is the acidic to slightly alkaline) and min > 10,000 -cm. This is probability that g < 0 will occur, pf (i.e., pf = P[g R, Q] < 0). similar to data collected in France [Terre Arme Interna- This area is related to the reliability index, , which is defined tional (TAI), 1977] indicating that approximately half of the as the number of standard deviations between the mean value walls included in the French survey had min > 10,000 -cm of g(R, Q) and the origin of the g(R, Q) function. and 90% had pH values between 6 and 8.5. Thus, a large por- Table 6 describes the relationship between and pf. In tion of the inventory is constructed with fill material that general, = 0 corresponds to a 50% probability of occur- meets AASHTO requirements by a wide margin, and may be rence and the probability of occurrence is inversely propor- considered "high quality fill." tional to . The objective of LRFD is to find values for load Compared to steel grid-type reinforcements, which are and resistance factors, i and , to achieve a target reliability used predominantly within the western region of the United index, T, corresponding to an acceptable probability of States, use of strip reinforcements is more uniformly dis- occurrence, pf.