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56 uncertainty. Figure 46 (borrowing from the concept presented depending on the quality and reliability of the database cases. by Ovesen, 1989) demonstrates the higher degree of uncer- The calibration, referring to soil type, specific model, and pile tainty associated with the design of a foundation. The material type combination as applied previously to deep foundations, properties are based on subsurface investigation and direct or has proven extremely effective compared to arbitrary selection indirect parameter evaluation. The loading of the foundation of parameters or WSD back-calculated values that defeat the and its distribution is mostly unknown as only limited infor- PBD principles as demonstrated in Section 1.4.4. The present mation has ever been gathered on loading at the foundation calibration is composed mostly of adopting the vertical load level. Because of this, the loading uncertainty is assumed as statistics established in NCHRP Project 24-17 (Paikowsky that attributed to the design of the structural element. The et al., 2004) and new development of horizontal load statistics main difficulty associated with the design of a foundation in and resistance for design methodologies based on the state of comparison with the design of a structural element remains practice established as outlined above. with the analysis model. While the calculation model in the The detailed calibration methodology and process are structural element is explicit (although becoming extremely presented in Section 4.3. complex and less definite as the element evolves in geometry and composition and requires the interaction with other units), 2.3 Execution and Presentation the analysis model for the evaluation of the soil resistance (i.e., bearing capacity) is extremely uncertain due to the as- 1. The execution of Unit I(a) (see Section 2.1, Figure 41) re- sumptions made during its establishment and the empirical sulted in the selection of the bearing capacity equations to data on which it is based. As such, the uncertainty of the geo- be analyzed, i.e., established the (calculated) limit state technical resistance model controls the resistance evaluation equations to be evaluated. Section 3.1 outlines the findings of the foundation. for establishing the state of practice in design and con- The concept adopted in this research (similar to that adopted struction leading to Section 3.4 presenting the selected by Paikowsky et al., 2004, for deep foundations) focused, there- bearing capacity methodology for soils and Section 3.8 the fore, on the calibration of selected bearing capacity (resistance) bearing capacity methodology for foundations on rock. models as a complete unit while reducing other associated 2. The execution of Unit I(b) (see Section 2.1, Figure 42) re- sources of uncertainty by following specific procedures, e.g., soil sulted in the development of case history databases, pre- parameter establishment. This approach is discussed in Section sented in Section 3.2. Examination and determination of 1.4, and demonstrated in the examples presented in Sections the measured strength limit state in these database case 1.4.4 and 1.4.5. The systematic analysis of many case histories histories are described in Sections 3.3, 3.6, and 3.7. Com- via a selected resistance model and their comparison to mea- parison of the calculated strength limit state (defined in sured resistance provided the uncertainty of the model applica- Item 1 above) to the measured strength limit state resulted tion, but also included in it the influence of the different sites in the statistical parameters of the resistance distribution from which the data were obtained as well as the uncertainty functions. These are described in Sections 3.5, 3.6, and 3.7. associated with the "measured" resistance. The distribution functions of the loads are defined and es- The assumption that the uncertainty obtained by the process tablished in Section 4.2. discussed above represents the variability of the model appli- 3. Selection of target reliability is described in Section 4.3.2. cation for a specific foundation analysis (i.e., the resistance 4. The development of resistance factors is described in Chap- variability as depicted in Figures 1 and 3) is reasonable and has ter 4 with summaries presented in Sections 4.10 and 4.13 for proven successful although it may contain some conservatism, foundations in/on granular soil and rock, respectively.