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4 TABLE 1 Factor of safety on ultimate __ axial geotechnical capacity based on level Q FS = R / Q of construction control (AASHTO, 1997) Qn Basis for Design and Type Increasing Design/Construction of Construction Control Control Subsurface Explora- Load Eff ect (Q) X X X X X tion Static Calculation X X X X X fR(R), fQ(Q) Dynamic Formula X __ Wave Equation X X X X Rn R CAPWAP Analysis X X Static Load Test X X Resistance (R) Factor of Safety (FS) 3.50 2.75 2.25 2.00* 1.90 *For any combination of construction control that includes a static load test, FS =2.0. Within LSD, two types of limit states are usually considered, Ultimate Limit State (ULS), and Serviceability Limit State (SLS). ULS pertains to structural safety and involves struc- tural collapse or, in relation to piles, the ultimate bearing R, Q capacity of the soil. SLS pertains to conditions, such as exces- Figure 1. An illustration of probability density sive deformations and settlement or deterioration of the struc- functions for load effect and resistance. ture that would affect the performance of the structure under expected working loads. The formula for ULS is failure (Pf = P (R < Q )) is related to the extent to which the Factored resistance Factored load effects (2) two probability density functions overlap (although not sim- ply to the area of overlap). The formula for SLS is In LRFD, partial safety factors are applied separately to the load effect and resistance. Strength is reduced and load effects Deformation Tolerable deformation to are increased, by multiplying the corresponding characteris- (3) tic (or nominal) values by factors called strength (resistance) remain serviceable and load factors, respectively. Using this approach, the fac- tored (i.e., reduced) strength of a pile must be larger than a 1.3 LOAD AND RESISTANCE FACTOR DESIGN linear combination of the factored (i.e., increased) load effects. (LRFD) The nominal values (e.g., the nominal strength, Rn) are those calculated by the specific calibrated design method and are 1.3.1 Principles not necessarily the means (i.e., the mean loads, Q, or mean The design of a pile depends upon predicted loads and the resistance, R (Figure 1). For example, R might be the mean pile's capacity to resist them. Both loads and capacity have of dynamic signal matching analysis predictions calculated various sources and levels of uncertainty. Engineering design in many case histories, while Rn is the predicted value for the has historically compensated for these uncertainties by using specific analyzed pile. experience and subjective judgment. On the other hand, these Based on considerations ranging from case histories to uncertainties can be quantified using probability-based meth- existing design practice, a prescribed value is chosen for prob- ods aimed at achieving engineered designs with consistent ability of failure. Then, for a given pile design based on the levels of reliability. The intent of Load and Resistance Fac- application of resistance and load factors, the probability for tor Design (LRFD) is to separate uncertainties in loading from failure, that is, the probability that the factored loads exceed uncertainties in resistance and then to use procedures from the factored resistances, should be smaller than the prescribed probability theory to ensure a prescribed margin of safety. value. In foundation practice, the factors applied to load effects Figure 1 shows probability density functions (PDFs) for are typically transferred from structural codes, and then resis- load effect, Q, and resistance, R. "Load effect" is the load tance factors are specifically calculated to provide the pre- calculated to act on a particular element, (e.g., a specific pile). scribed probability of failure. As loads are usually better known than are resistances, the The importance of uncertainty regarding resistance can be load effect typically has smaller variability than resistance seen by reference to Figure 1. In this figure, the mean factor (i.e., a smaller coefficient of variation, translating to a nar- of safety is FS = R /Q , whereas the nominal factor of safety rower probability density function). Since failure is defined is FSn = Rn /Qn. Consider what happens if the uncertainty in as the load effect exceeding the resistance, the probability of resistance is increased, and thus the PDF broadened, as sug-