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Load and Resistance Factor Design (LRFD) for Deep Foundations (2004)

Chapter: Chapter 1 - Introduction and Research Approach

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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 1 - Introduction and Research Approach." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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3CHAPTER 1 INTRODUCTION AND RESEARCH APPROACH 1.1 BACKGROUND National Cooperative Highway Research Program Project NCHRP 24-17, “LRFD Deep Foundations Design,” was initi- ated to provide (1) recommended revisions to the driven pile and drilled shaft portions of section 10 of the AASHTO LRFD Bridge Design Specifications (AASHTO, 2001) and (2) a detailed procedure for calibrating deep foundation resistance factors. The current AASHTO specifications, as well as other existing codes based on Load and Resistance Factor Design (LRFD) principles, were calibrated using a combination of reliability theory, fitting to Allowable Stress Design (ASD— also called Working Stress Design, or WSD), and engineering judgment. The main challenges of the project were, therefore, the compilation of large, high-quality databases and the devel- opment of a procedural and data management framework that would enable LRFD parameter evaluation and future updates. Meeting these challenges required (1) organizing the resistance factors into a design-construction-quality- control sequence (i.e., independence in resistance factors according to the chronological stage and the evaluation pro- cedure) and (2) overcoming the generic difficulties of apply- ing the LRFD methodology to geotechnical applications, i.e., incorporation of indirect variability (e.g., site or parameters interpretation), judgment based on previous experience, and similar factors into the methodology. The project team, headed by the author, was divided into three groups dealing respec- tively with static analyses (University of Florida), proba- bilistic and structural analyses (University of Maryland), and dynamic analyses (University of Massachusetts Lowell). This chapter provides a background for design methodolo- gies and LRFD principles and usage. In Chapter 2, following a discussion of the major findings from a questionnaire and survey designed to discover the state of current practice, the databases that were developed for the project are presented and analyzed. Selected design methods are described, followed by an in-depth evaluation of the dynamic methods for the evalu- ation of the capacity of driven piles and an examination of their controlling parameters. The performance of different predic- tion methods, categorized according to the examined methods of analysis and controlling parameters, are also discussed in Chapter 2. In Chapter 3, the results of these analyses are used for the development of the resistance factors recommended for the revision of the AASHTO LRFD Bridge Design Specifica- tions. Statistical methods are used for the development of rec- ommendations for number of piles to be tested in quality assur- ance. Chapter 4 presents the conclusions supported by the study, suggestions for additional research, and a framework for LRFD for deep foundations that incorporates knowledge- based design. Detailed data and analyses are provided in the appendices available on the accompanying CD. 1.2 STRESS DESIGN METHODOLOGIES 1.2.1 Working Stress Design The working Stress Design (WSD) method, also called Allowable Stress Design (ASD), has been used in Civil Engi- neering since the early 1800s. Under WSD, the design loads (Q), which consist of the actual forces estimated to be applied to the structure (or a particular element of the structure), are compared to resistance, or strength (Rn ) through a factor of safety (FS): (1) Where Q = design load; Qall = allowable design load; Rn = resistance of the element or the structure, and Qult = ultimate geotechnical pile resistance. Table 1, from Standard Specifications for Highway Bridges (AASHTO, 1997), presents common practice, the traditional factors of safety used in conjunction with different levels of control in analysis and construction. Presumably, when a more reliable and consistent level of control is used, a smaller FS can be used, which leads to more economical design. Practically, however, the factors of safety in Table 1 do not necessarily consider the bias, in particular, the conservatism (i.e., underprediction) of the methods listed; hence, the valid- ity of their assumed effect on the economics of design is questionable. (These traditional factors of safety are further discussed and evaluated in section 3.5.2) 1.2.2 Limit States Design In the 1950s, the demand for more economical design of piles brought about the use of Limit States Design (LSD). Q Q R FS Q FSall n ult≤ = =

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

gested by the dashed curve. The mean resistance for this other predictive method remains unchanged, but the varia- tion (i.e., uncertainty) is increased. In calculating the prescribed probability of failure (Pf), a derived probability density function is calculated for the mar- gin of safety (R,Q), and reliability is expressed using the “reli- ability index”, β, which is the number of standard deviations of the derived PDF of R − Q separating the mean safety mar- gin from the nominal failure value of zero (Figure 2). Further discussion of the relationship of pf to β are given in section 2.7.1. For computational reasons, the margin of safety is taken as R − Q when the resistances and load effects have normally distributed uncertainty, but as ln(R) − ln(Q) when the uncertainties are logNormally distributed. 1.3.2 Background Information The concept of using the probability of failure as a crite- rion for structural design is generally credited to the Russians N. F. Khotsialov and N. S. Streletskii who presented it in the late 1920s, and it was introduced in the United States by Freudenthal (1947). The recent development of LRFD in civil engineering was initiated in structural engineering (see, e.g., Ellingwood et al., 1980). Reliability-Based Design codes using LRFD have been published by the American Institute of Steel Construction (AISC, 1994; Galambos and Ravindra 1978) and the American Concrete Institute (American Con- crete Institute, 1995). An effort was made by the National Standards Institute (ANSI) to develop probability-based load criteria for buildings (Ellingwood et al., 1982a, b) and ASCE 7-93 (ASCE, 1993). The American Petroleum Institute (API) extrapolated LRFD technology for use in fixed offshore plat- forms (API, 1989; Moses 1985, 1986). Comprehensive sum- maries of the implementation of probabilistic design theory in design codes include those by “Practical Approach to Code 5 Calibration” (Siu et al., 1975) for the National Building Code of Canada (National Research Council of Canada, 1977), Development of a Probability-Based Load Criterion for American National A58 (Ellingwood et al., 1980) for the National Bureau of Standards, and the Rationalization of Safety and Serviceability Factors in Structural Codes: CIRIA Report 63 (Construction Industry Research and Information Association, 1977). The AASHTO LRFD Bridge Design Spec- ifications (AASHTO, 1994), resulting from work in NCHRP Project 12-33 (Nowak, 1999), provide design guidance for girders. 1.3.3 LRFD Performance and Advantages Experience has shown that adopting a probability-based design code can result in cost savings and efficient use of materials. Reliability improvements are still under evaluation even though the new LRFD codes are designed to yield reli- abilities equal to or higher than those of earlier codes. Expe- riences are not yet well documented; but anecdotal evidence from naval architecture suggests that, relative to conventional WSD, the new AISC-LRFD requirements may save 5% to 30% of steel weight in ships (Ayyub, 1999). This may or may not be the case for civil engineering applications. Specific benefits for pile design include at least the following: 1. Cost savings and improved reliability because of more efficiently balanced design. 2. More rational and rigorous treatment of uncertainties in the design. 3. Improved perspective on the overall design and con- struction processes (sub- and superstructures); and the development of probability-based design procedures can stimulate advances in pile analysis and design. Figure 2. An illustration of a combined probability density function (g(R,Q)) representing the margin of safety and the reliability index, β. (σg = Standard deviation of g(R,Q)).

4. Transformation of the codes into living documents that can be easily revised to include new information reflect- ing statistical data on design factors. 5. The partial safety factor format used herein also pro- vides a framework for extrapolating existing design practice to new foundation concepts and materials where experience is limited. 1.3.4 LRFD in Geotechnical Engineering Early use of LSD for geotechnical applications was exam- ined by the Danish geotechnical institute (Hansen 1953, 1956) and later formulated into code (Hansen, 1966). Independent load and resistance factors were used, with the resistance fac- tors applied directly to the soil properties rather than to the nominal resistance. Considerable effort has been directed over the past decade on the application of LRFD in geotechnical engineering. LRFD approaches have been developed in offshore engi- neering (e.g., Tang, 1993; Hamilton and Murff, 1992), gen- eral foundation design (e.g., Kulhawy et al., 1996), and pile design for transportation structures (Barker et al., 1991; O’Neill, 1995). In geotechnical practice, uncertainties concerning resis- tance principally manifest themselves in design methodology, site characterization, soil behavior, and construction quality. The uncertainties have to do with the formulation of the phys- ical problem, interpreting site conditions, understanding soil behavior (e.g., its representation in property values), and accounting for construction effects. Uncertainties in external loads are small compared with uncertainties in soil and water loads and the strength-deformation behaviors of soils. The applied loads, however, are traditionally based on superstruc- ture analysis, whereas actual load transfer to substructures is poorly researched. The approach for selecting load and resis- tance factors developed in structural practice, though a useful starting point for geotechnical applications, is not sufficient. Work is needed to incorporate factors that are unique to geo- technical design into the LRFD formulation. Philosophically, the selection of load and resistance factors does not have to be made probabilistically, although in current structural practice a calibration based on reliability theory is commonly used. This approach focuses more on load uncer- tainties than resistance uncertainties and does not include many subjective factors unique to geotechnical practice. An expanded approach is needed if the full benefits of LRFD are to be achieved for foundation design. The National Research Council reports that the “subjective approach reflects the gen- eral lack of robust data sources from which a more objective set of factors can be derived” (National Research Council, 1995). The report continues, “realistically, because of the tremendous range of property values and site conditions that one may encounter, it is unlikely that completely objective factors can be developed in the foreseeable future.” 6 Today, the situation has changed somewhat, but not entirely. The present research team gathered robust data on pile capacity from which a more objective calibration of resis- tance factors could be made. Nonetheless, there remain uncer- tainties associated with (1) site conditions, (2) soil behavior and the interpretation of soil parameters, and (3) construction methods and quality. These factors are difficult to understand from the pile databases alone. Such knowledge-based factors should be combined with the reliability-theory-based cali- bration of the database records to achieve a meaningful LRFD approach, requiring a major research effort. These difficul- ties are addressed in the present research through the cali- bration of specific combinations of design and parameter interpretation methods. 1.3.5 LRFD for Deep Foundations Several efforts have been made to develop LRFD-based codes for deep foundation design. 1.3.5.1 2001 AASHTO LRFD Bridge Design Specifications for Driven Piles LRFD Bridge Design Specifications (AASHTO, 2001) states that the ultimate resistance (Rn) multiplied by a resis- tance factor (φ), which thus becomes the factored resistance (Rr), must be greater than or equal to the summation of loads (Qi) multiplied by corresponding load factors (γi), and a modifier (ηi). For strength limit states: (4) where: ηi = ηDηRηI > 0.95 (5) where ηi = factors to account for; ηD = effects of ductility; ηR = redundancy; and ηI = operational importance. The Specifications provide the following equations for determining the factored bearing resistance of piles, QR, QR = φQn = φqQult = φqpQp + φqsQs (6) for which: Qp = qp Ap (7) Qs = qs As (8) where φq = resistance factor for the bearing resistance of a sin- gle pile specified for methods that do not distinguish between total resistance and the individual contributions of tip resis- tance and shaft resistance; Qult = bearing resistance of a single R R Qr n i i i= ≥ ∑φ η γ

pile; Qp = pile tip resistance; Qs = pile shaft resistance (F); qp = unit tip resistance of pile; qs = unit shaft resistance of pile; As = surface area of pile shaft; Ap = area of pile tip; and φqp, φqs = resistance factor for tip and shaft resistance, respec- tively, for those methods that separate the resistance of a pile into contributions from tip resistance and shaft resistance. The resistance factors for use in the above equations are pre- sented in Table 10.5.5-2 of the Specifications for different design methods based on soil type and area of resistance (tip and side). The resistance factors for compression vary between 0.45 and 0.70. The table also incorporates a factor, λv, for dif- ferent methods and level of field capacity verification. As an example, if, in analysis, an α method is used to determine the pile’s friction resistance in clay, a resistance factor of 0.70 is recommended. If, in verification of the pile capacity, a pile driving formula, e.g., an ENR (Engineering News-Record) equation, is used without stress wave measurements during driving, a λv factor of 0.80 is recommended. The actual resis- tance factor to be used in the above analysis verification sequence is, therefore, 0.56 (i.e., 0.70 × 0.80). 1.3.5.2 2001 AASHTO LRFD Bridge Design Specifications for Drilled Shafts LRFD Bridge Design Specifications (AASHTO, 2001) provides detailed resistance factors for a large number of design methods for drilled shafts. Differentiation is made between base and side resistance, as for driven piles, with resistance factors varying between 0.45 and 0.65. Static test- ing is included with the same resistance factor as for driven piles (0.8). Resistance factors are not provided for drilled shafts in sand. The λv factor, used for field verification for driven piles, is not used for drilled shafts, and no distinction is made on the basis of construction method. 1.3.5.3 Worldwide LRFD Codes for Deep Foundations and Drilled Shafts A review of foundation design standards in the world was conducted by the Japanese Geotechnical Society (1998). A review of the development of LRFD applications for Geo- technical Engineering is presented by Goble (1999). A review of LRFD parameters for dynamic analyses of piles is pre- sented by Paikowsky and Stenerson in Appendix B. The present section provides a short review of non-US LRFD codes for deep foundations. The Australian Standard for Piling-Design and Installa- tion (1995) provides ranges of resistance factors for static load tests (0.7 to 0.9) and static pile analyses (0.40–0.65) related to the source of soil parameters and soil type (e.g., SPT in cohesionless soils). Detailed recommendations are provided for resistance factors to be used with the dynamic methods ranging between 0.45 to 0.65 for methods without dynamic measurements (including WEAP), and between 7 0.50 to 0.85 when utilizing dynamic measurements with sig- nal matching analysis. Selection of the appropriate resis- tance factor depends on driving conditions, geotechnical factors (e.g., extent of site investigation), and extent of test- ing (e.g., low range for <3% of the pile tested and high range for >15%). In traditional structural design specifications, a nominal value is given and the value used is based primar- ily on engineering judgment and cannot exceed the nominal value. The Australian Standard is therefore unique by pro- viding a guide for choosing the appropriate resistance fac- tor. Interestingly, no distinction is made regarding either soil type or time of driving (i.e. EOD, BOR) when referring to the signal matching based on dynamic measurements. The method by which the resistance factors were generated is not provided in the code. The AUSTROADS Bridge Design Code (1992) provides resistance factors for the construction stage alone including static load test (to failure φ = 0.9, proof test φ = 0.8), and four categories of dynamic methods. The range of resistance fac- tors is quite large and there is no explanation as to how the resistance factors were obtained. Goble (1999) postulates that the resistance factors were calibrated via the working stress design method. The Ontario Bridge Code (1992) recommends relatively low resistance factors with no differentiation between the individual static or dynamic analyses. For example, the resis- tance factors for static analyses and static load tests in com- pression and tension are 0.4, 0.3, 0.6 and 0.4 respectively. No information is provided on how the resistance factors were obtained. The Bridge Code (1992) is brief in its design requirements for deep foundations. Resistance factors are based on pile type, φ = 0.4 for all timber and concrete piles (precast, filled pipe, and cast in place) and 0.5 for steel piles. For dynamic load testing, resistance factors of 0.4 and 0.5 are recom- mended for routine testing and analyses based on dynamic measurements, respectively. Eurocode 7 (1997) deals with driven piles and drilled shafts at a single section. Factors for static load testing depend on the number of tested piles (irrelevant to the num- ber of piles at the specific site). Range of values from 0.67 to 0.91 is provided for one to three tests, related to the mean or lowest value of the test results. The code is quite complex with quantitative descriptions and limiting conditions. The code is presented with multiple component factors, and for comparison with the form used by U.S. codes, Goble (1999) inverted and combined the factors resulting in values rang- ing from 0.63 to 0.77 for base, skin, and total resistance of driven, bored, and CFA piles. DiMaggio et al. (1998) pre- sented a summary report of a geotechnical engineering study tour, stating “The team found Eurocode 7 to be a difficult doc- ument to read and understand, which may explain the various interpretations that were expressed in the countries visited.” Improvements in that direction were achieved through a text

that explains the methodology and provides design examples (Orr and Farrell, 1999; see also Orr, 2002). The final draft of the future Eurocode 7 (October 2001, see also Frank, 2002) is an extensive code that is expected to become an EN pub- lication by August 2004. This detailed document contains 12 sections dealing with all geotechnical design aspects rang- ing from geotechnical data (section 3), to construction super- vision (section 4), to hydraulic failure (section 10). Section 7 is dedicated to pile foundations. While not very detailed regarding a specific determination of the pile capacity, the code is elaborating for all cases (i.e., static load test results, static and dynamic methods) factors to be applied to both the minimum and average of the capacity as a function of the number of applications. For example, static load test capac- ity will have factors (to be divided by) ranging from 1.4 to 1.0 when applied to the results of 1 to 5 or over load tests. Specifically, if, for example, three static load tests are carried out, the mean value of the three will be divided by 1.2, and the minimum value by 1.05, and the lower of the two will determine the factored resistance to be used. Substantially fewer details are provided by the codes for LRFD design of drilled shafts. The two extremes being the aforementioned Bridge Code (1992), in which drilled shafts are included under a single category of cast-in-place piles (φ = 0.4 like all other concrete piles), and the AASHTO rel- atively detailed provisions described in section 1.3.5.2. 1.3.5.4 Difficulties with the Existing LRFD Codes All existing codes suffer from two major difficulties. One is the application of LRFD to geotechnical problems as described in section 1.3.4 (e.g., site variability, con- struction effects, past experience, etc.). The other problem is lack of data. None of the reviewed codes and associated resistance factors were consistently developed based on data- bases enabling the calculation of resistance factors from case histories. The current AASHTO specifications of driven piles reviewed in section 1.3.5.1 encounter additional difficulty due to the multiplication of the resistance factor by the mod- ifier λv. This procedure requires the interaction of two inde- pendent pile capacity evaluations (e.g., static analysis and dynamic methods) and results in unnecessary and confusing conservatism. A clear separation of the resistance factors on the basis of design and construction is required and is one aim of the present study. As a result of the aforementioned difficulties, the current AASHTO LRFD specifications for geotechnical applications are of limited use. Two surveys presented in this report (see section 2.1) found that only 14 states (30%) are currently committed to the use of LRFD in foundation design. In contrast 93% of the responding use WSD, suggesting that most of those that use LRFD are uti- lizing the methodology in parallel to WSD. 8 1.4 RESEARCH APPROACH 1.4.1 Design and Construction Process of Deep Foundations Figure 3 presents a flow chart depicting the design and construction process of deep foundations. Commonly, design starts with site investigation and soil parameter evaluation, assessments that vary in quality and quantity according to the importance of the project and complexity of the subsurface. Possible foundation schemes are identified based on the results of the investigation, load requirements, and local practice. All possible schemes are evaluated via static analyses. Schemes for driven piles also require dynamic analysis (drivability) for hammer evaluation, feasibility of installation, and structural adequacy of the pile. In sum, the design stage combines, therefore, structural and geotechnical analyses to determine the best prebidding design. This process leads to estimated quantities to appear in construction bidding documents. Upon construction initiation, static load testing and/or dynamic testing, or dynamic analysis based on driving resis- tance (using dynamic formulas or wave-equations) are carried out on selected elements (i.e., indicator piles) of the original design. Pile capacity is evaluated based on the con- struction phase testing results, which determine the assigned capacity and final design specifications. In large or important projects, the pile testing may also be used as part of the design. Two requirements are evident from this process: (1) pile evaluation is carried out at both the design and the construction stage, and (2) these two evaluations should result in foundation elements of the same reliability but pos- sibly different number and length of elements depending on the information available at each stage. 1.4.2 Overview of the Research Approach The complete application of LRFD to the process described in Figure 3 requires an integrated framework. For example, the method by which a field test (say SPT) is used to obtain soil parameters must be coordinated with the method used for static capacity of the pile, and both must be coordinated with the assessment of uncertainty. Independently, one needs to evaluate the design verification process during construction, i.e., static load testing and dynamic testing to assess and mod- ify the pile installation, as well as quality assurance (e.g., nondestructive testing of drilled shafts) and related issues. Previous LRFD developments, using back analysis of ASD and judgment, have addressed some of these issues (e.g., Withiam et al., 1998). The present effort to assemble a case history database adds other difficulties, for example determining a “predicted” capacity that can be compared with measured load-test values. The present effort was focused on calibrating the direct design and construction evaluation process. For the design, specific methods and correlations were chosen. Their results

(i.e., static capacity evaluations) were compared to measured pile performance under static load. In the dynamic analysis case, the database was used to identify controlling parame- ters, which were then calibrated. A description of the princi- ples used for the assessments of the three databases is pro- vided in section 1.4.3.3. Figure 4 presents a flowchart of the research approach for this study. The flowchart outlines the framework required for LRFD calibration of design and con- struction methods of analysis. The stages outlined in Figure 4 are described in the following sections; findings and evalu- ations related to the various stages of the framework are pre- sented in Chapter 2. 1.4.3 Principles and Framework of the Calibration 1.4.3.1 Determination of Analysis Methods To establish the state of practice, a questionnaire was devel- oped and distributed to all state highway and federal highway organizations. The material related to the questionnaire and detailed results are presented in Appendix A, on the accom- panying CD, and discussed in section 2.1. 1.4.3.2 Databases Three principal databases and six secondary databases were developed for the evaluation of the analysis methods and inter- pretation procedures. The major databases—drilled shaft, 9 driven piles, and PD/LT2000—are presented in Appendices B and C, on the accompanying CD, and discussed in section 2.2. The secondary databases are referred to and used as applicable. 1.4.3.3 Conceptual Evaluation of Driven Piles and Drilled Shafts Capacities Driven Piles—Static Analysis. The vast majority of the database case histories were related to SPT and CPT field testing. Four correlations of soil parameters from SPT and CPT were identified. The case histories were divided on the basis of soil condition (clay, sand, and mixed) and pile types (H pile, concrete piles, pipe piles). In summary, given field conditions were used via various soil parameter identifica- tions and pile capacity evaluation procedures to determine capacities. The capacities were then compared to measured static capacity. Details of the analyses are presented in sec- tion 2.3. Driven Piles—Dynamic Analysis. The dynamic evaluation of driven piles is the most common way to determine capacity during construction. Existing AASHTO specifications, as described in section 1.3.5.1, are complicated by the use of a factor, λv, which convolves the design stage and the construc- tion stage. Therefore, a fresh look at the basis for dynamic cal- ibration was required. Details are described in Paikowsky and Stenersen (2000) and in section 2.4. Yes Geomaterial Strength & Deformation Parameters Static Analysis of Deep Foundations Laboratory Testing Deformation and Settlement Bearing Capacity Vertical and Lateral Resistance Single/Group Deep Foundation Type/Construction Method Dynamic Analysis of Driven Piles Design • Geometry • Configuration • Installation Criteria Superstructure Loading Evaluation Substructure Loading Requirement Completed Substructure Testing • Material • Performance • Driving • Integrity QC Monitoring Construction Design Verification/ Modification • Dynamic testing • Static testing ? OK No Field Exploration & Testing Figure 3. Design and construction process for deep foundations.

Drilled Shafts—Static Analysis. Evaluation of the design of drilled shafts is difficult as limited data are available for the separation of capacity components (i.e., shaft and tip), and as both components of capacity are affected by the method of construction. The following procedure was used for the eval- uation of the measured skin capacities. The shape of the load- displacement curves was evaluated, and shafts for which more than 80% of the total capacity was mobilized in a displacement of less than 2% of the shaft diameter were considered as hav- ing resistance based on friction. Results of these procedures were compared to static analyses as described in section 2.6. 1.4.3.4 LRFD Calibration Existing AASHTO Specifications. Existing AASHTO spec- ifications are based on First-Order, Second-Moment (FOSM) analysis, using η = 1 in equation 4, and assuming lognormal distributions for resistance. This leads to the relation (Barker et al., 1991), (9)φ λ γ β= ( ) + +( ) +( )[ ]{ } ∑R i i Q R T R Q Q COVCOV Q COV COV 1 1 1 2 2 2 2 1 + exp ln 10 where: λR = resistance bias factor COVQ = coefficient of variation (the ratio of the standard deviation to the mean) of the load COVR = coefficient of variation of the resistance βT = target reliability index When just dead and live loads are considered, equation 9 can be rewritten as: (10) where: γD, γL = dead and live load factors QD/QL = dead to live load ratio λQD, λQL = dead and live load bias factors Present Project Calibration. LRFD for structural design has evolved beyond FOSM to the more invariant First-Order φ λ γ γ λ λ β = + + + + + + +   ( )( )     ( )( )[ ]{ } R D D L L Q Q R Q D L Q T R Q Q Q Q COV COV COV Q Q COV COV COV D L D L D L 1 1 1 2 2 2 2 2 2 1 + exp ln Database Build-Up Static – Driven Piles Dynamic – Driven Piles Static – Drilled Shafts Peripheral Databases Questionnaire Establish Common Design Methods and Procedures for Static Analyses Research and establish Recommended Pf Evaluation of the Static Capacity of DP and DS for all Methods/Correlation Combinations Evaluating Static Capacity DP based on Dynamic Analyses Establish Viable Methods and Controlling Parameters for the Dynamic Analyses Establish a Single Method for the Determination of Nominal Strength (capacity), its accuracy and LT procedure effect Calculating the Ratio of the Nominal Strength to Predicted Capacity LT-Static Load Test DP-Driven Piles DS-Drilled Shafts SGP 4/7/02 Evaluate the Nominal Strength of all casesDevelop Statistical Parameters for the Performance of each Analysis Method/Correlation Combination Calculating the Resistance Factors and Evaluating the Results Recommended Resistance Factors State of Practice Driven Piles and Drilled Shafts Design and Construction Figure 4. Stages of the research approach outlining the framework for LRFD calibration of the current study.

Reliability Method (FORM) approach (e.g., Ellingwood et al., 1980, Galambos and Ravindra, 1978), while geotech- nical applications have lagged behind (Meyerhof, 1994). In order to be consistent with the current structural code and the load factors to which it leads, it is necessary for calibra- tion of resistance factors for deep foundations to use FORM (Nowak, 1999). Following Ayyub and Assakkaf (1999), the present project calibrates LRFD partial safety factors using FORM, as developed by Hasofer and Lind (1974). FORM can be used to assess the reliability of a pile with respect to specified limit states and provides a means for calculating partial safety fac- tors φ and γi for resistance and loads, respectively, against a target reliability level, βO. FORM requires only first and sec- ond moment information on resistances and loads (i.e., means and variances) and an assumption of distribution shape (e.g., normal, lognormal, etc.). The calibration process using FORM is presented in Figure 5. In design practice, there are usually two types of limit state: ultimate limit state and serviceability limit state. Each can be represented by a performance function of the form, (11) in which X = (X1,X2,…,Xn) is a vector of basic random vari- ables of strengths and loads. The performance function g(X), often called the limit state function, relates random variables to either the strength or serviceability limit-state. The limit is defined as g(X) = 0, implying failure when g(X) < 0 (Figures 2 and 5). The reliability index, β, is the distance from the ori- gin of the space of basic random variables to the failure sur- face at the most probable point on that surface, that is, at the point on g(X) = 0 at which the joint PDF of X is greatest. This is sometimes called the design point and is found by an itera- tive solution procedure (Thoft-Christensen and Baker, 1982). The relationship of the limit states can also be used to back calculate representative values of the reliability index, β, from current design practice. The computational steps for determining β using FORM are the following: 1. In the regular coordinates, assume a design point, x*i , and, in a reduced coordinate system, obtain its corre- sponding point, x'*i , using the transformation: (12) where = mean value of the basic random variable Xi, =standard deviation of the basic random variable. The mean value of the vector of basic random variables is often used as an initial guess for the design point. The σ Xi µ Xi x x i i X X i i ' * * = − µ σ g X g X X Xn( ) , , ,= ( )1 2 K 11 notation x* and x'* is used to denote the design point in the regular coordinates and in the reduced coordinate system, respectively. 2. If the distribution of basic random variables is non- normal, approximate this distribution with an equiva- lent normal distribution at the design point, having the same tail area and ordinate of the density function, that is with equivalent mean, (13) and equivalent standard deviation (14) where µNX = mean of the equivalent normal distribution, σNX = standard deviation of the equivalent normal distribution, FX (x*) = original cumulative distribution function (CDF) of Xi evaluated at the design point, fX (x*) = original PDF of Xi evaluated at the design point, Φ(⋅) = CDF of the standard normal distribution, and φ(⋅) = PDF of the standard normal distribution. 3. Set x'*i = α*i β, in which the α*i are direction cosines. Compute the directional cosines (α*i , i = 1,2,...,n) using, (15) where (16) 4. With α*i , now known, the following equation is solved for β: (17) 5. Using the β obtained from step 4, a new design point is obtained from, (18)xi XN i XNi i* *= −µ α σ β g XN X XN X X XNn n nµ α σ β µ α σ β1 1 1 0−( ) −( )[ ] =* , , * *K µ σXN XNi i, ∂ ∂ ∂ ∂ σ g x g xi i X N i ' * *   =   α ∂ ∂ ∂ ∂ i i ii n g x g x i n* ' * ' * =     = ∑ 2 1 1 2for = , , ,K σ φ X N X X F x f x= ( )( )( ) ( ) −Φ 1 * * µ σXN X XNx F x= − ( )( )−* *Φ 1

12 Definition of Failure Define Limit States at Single Pile Level: Ultimate & Serviceability Define Statistical Characteristics of Basic Random Variables Resistance Load Determine Model Uncertainty for Strength (from database) MC Simulation or Probability Calculation to Get Statistical Properties of Scalar R Reliability Assessment Back-calculated Beta vs Load Ratio Curves in Practice Review Target Betas in the Literature and Practice µR Safe Region Failure Region Contours of fRS = fX(x) µS G(x)=0 GL(x)=0 Assign Target Betas Calculate Load and Resistance Factors Select Load and Resistance Factors Adjust for Mean/Nominal Parameters Case Study Designs for Comparison Determine Load Uncertainties from Superstructure to Foundation (from ST code) Notes: ST = structural MC = Monte Carlo µ = mean G(x) = performance function of the limit state = limit state function G(x) = 0 = limit defining failure for G(x)<0 GL(x) = linearized performance function Figure 5. Resistance factor analysis flow chart (after Ayyub and Assakkaf, 1999 and Ayyub et al., 2000), using FORM developed by Hasofer and Lind (1974).

6. Repeat steps 1 to 5 until convergence of β is achieved. This reliability index is the shortest distance to the failure surface from the origin in the reduced coordinate space. FORM can be used to estimate partial safety factors such as those found in the design format. At the failure point (R*,L*1 − … − L*n ), the limit state is given by, (19) or, in a more general form by, (20) The mean value of the resistance and the design point can be used to compute the mean partial safety factors for design as, (21) (22) In developing code provisions, it is necessary to follow current design practice to ensure consistent levels of reliabil- ity over different pile types. Calibrations of existing design codes are needed to make the new design formats as simple as possible and to put them in a form that is familiar to designers. For a given reliability index β and probability dis- tributions for resistance and load effects, the partial safety factors determined by the FORM approach may differ with failure mode. For this reason, calibration of the calculated partial safety factors (PSFs) is important in order to maintain the same values for all loads at different failure modes. In the case of geotechnical codes, the calibration of resistance fac- tors is performed for a set of load factors already specific in the structural code (see following section). Thus, the load factors are fixed. In this case, the following algorithm is used to determine resistance factors: 1. For a given value of the reliability index, β, probability distributions and moments of the load variables, and the coefficient of variation for the resistance, compute mean resistance R using FORM. γ µi i L L i = * φ µ= R R * g X g x x xn( ) *, *, , *= ( ) =1 2 0K g R L Ln= − − − =* * *1 0K 13 2. With the mean value for R computed in step 1, the par- tial safety factor, φ, is revised as: (23) where µLi and µR are the mean values of the load and strength variables, respectively, and γi, i = 1, 2,…, n, are the given set of load factors. Load Conditions and Load Factors. The actual load trans- ferred from the superstructure to the foundations is, by and large, unknown, with very little long-term research having been focused on the subject. The load uncertainties are taken, therefore, as those used for the superstructure analysis. LRFD Bridge Design Specifications (AASHTO, 2000) pro- vide five load combinations for the standard strength limit state (using dead, live, vehicular, and wind loads) and two for the extreme limit states (using earthquake and collision loads). The use of a load combination that includes lateral loading may at times be the restrictive loading condition for deep foundations design. Pile lateral capacity is usually controlled by service limit state, and as such, was excluded from the scope of the present study, which focuses on the axial capac- ity of single piles/drilled shafts. The load combination for strength I was therefore applied in its primary form as shown in the following limit state: Z = R − D − LL (24) Where R = strength or resistance of pile, D = dead load and LL = vehicular live loads. The probabilistic characteristics of the random variables D and LL are assumed to be those used by AASHTO (Nowak, 1999) with the following load factors and lognormal distributions (bias and COV) for live and dead loads, respectively: γL = 1.75 λQL = 1.15 COVQL = 0.2 (25) γD = 1.25 λQD = 1.05 COVQD = 0.1 (26) For the strength or resistance (R), the probabilistic charac- teristics are defined in Chapter 3, based on the databases for the various methods and conditions that are described in Chapter 2. φ γ µ µ= = ∑ i Li i n R 1

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 507: Load and Resistance Factor Design (LRFD) for Deep Foundations examines resistance factors for driven pile and drilled shaft foundations,and provides a procedure for calibrating deep foundation resistance.

Errata - Table 29 and Figure 47 in the pdf of NCHRP Report 507 contains incorrect information. An update to Table 29 and Figure 47 are available on-line.

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