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Limit states
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Limit states, as discussed in previous chapters, are de ned as those conditions under which a structure or its components no longer perform an intended function (Allen 1994; Simpson et al. 1981). Whenever a structure or a part of a structure fails to satisfy one of its designated operational criteria, it is said to have reached a limit state. The two limit states of interest for most foundations are (1) ultimate limit state (strength limit state), and (2) serviceability limit state. Ultimate limit states pertain to structural safety and collapse. For foundations, the ultimate limit state is typically taken to be ultimate bearing capacity of the soil. Serviceability limit states pertain to conditions under which performance requirements under normal service loads are exceeded. Such conditions might include excessive deformations or deterioration of a structural foundation system such as piles. Serviceability limit states are typically checked using a partial factor of unity on all speci ed or characteristic service loads and load effects (Meyerhof 1994). In ASD, the concept of allowable soil bearing pressure may be controlled either by bearing capacity (ultimate state) or by settlement (serviceability limit) considerations. ASD implicitly accounts for both of these, but generally does so only implicitly (Becker 1996). In other words, the ASD method usually does not require that calculations be made to check both limit states but instead resorts to charts that show whether a design needs to be checked for ultimate limit state or for serviceability limit state. Common wisdom holds that serviceability limit states have a higher probability of occurrence than do ultimate limit states, principally because they occur at lower absolute loads (Duncan et al. 1989). As a result, the allowable settlement of a structure rather than the ultimate bearing capacity of the soil generally controls the design of shallow foundations. Accordingly, most routine design is based on speci c serviceability limits, and ultimate limits are checked subsequently (Becker 1996). However, this in not always the case; in the design of piles ultimate limit state often controls the design.
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18.2 Load and Resistance Factor Design
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In contrast to working stress design with its single safety criterion the factor of safety, FS Load and Resistance Factor Design (LRFD) takes into consideration the variability in loads and resistances separately by de ning separate factors on each. A load factor, , is assigned to variability or uncertainty in loads, while a resistance factor, , is assigned to variability or uncertainty in resistances. Thus, in LRFD the comparison of loads and resistances is formulated for strength limit states in an equation of the form (Withiam et al. 1997) Rr = Rn i Qi (18.6) in which Rr is factored resistance, Rn is ultimate resistance, Qi is force effect, stress, or stress resultant, is resistance factor, i is load factor, and = D R I > 0.95 is a series of dimensionless factors (taken from the structural code) accounting for the effects of ductility ( D ), redundancy ( R ), and operational importance ( I ). For the serviceability limit states, i i n (18.7)
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LOAD AND RESISTANCE FACTOR DESIGN
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in which i is the estimated displacement, and n is the tolerable displacement. The method for determining the ultimate geotechnical resistance (Rn ) is basically the same for both the LRFD and ASD methods. The difference between the methods is the separation of factors for load and resistance in the LRFD method. The use of LRFD in geotechnical engineering is a relatively recent development, which has been in large part driven by the development of LRFD codes for structural engineering, especially in application to highway structures. To date, the principal use of LRFD in geotechnical engineering has been in foundation design. The approach has not enjoyed extensive use in the design of earth structures, such as dams, or of underground works. Early development of the LRFD codes for structural design grew out of efforts at the Nationals Standards Institute to develop probability-based load criteria for buildings (Ellingwood et al. 1980); some of this was summarized and later republished by ASCE (1993). The American Petroleum Institute sponsored research on LRFD methods for the design of offshore structures during the 1980s. Much of the publicly available parts of this work is reported in API sources (API 1989; Moses 1985; Moses and Lind 1970). Other contemporary efforts to incorporate LRFD in codes for the structural design of buildings are reported by Sui et al. (1975), the National Research Council of Canada (1977) and CIRIA (1977). In more recent years, LRFD has begun to be introduced to structural designs in traditionally non-civil engineering applications, such as ship structures (Ayyub et al. 1997, 1995), although its introduction in machine design and other traditionally mechanical engineering applications continues to lag behind. Early applications of LRFD to transportation structures (e.g. highway bridges) which in recent years has led to more attention paid to the use of LRFD for the foundations of those structures were encouraged by the American Association of State Highway and Transportation Of cials (AASHTO), and by 1994 the AISC Manual of Steel Construction itself had adopted LRFD (AASHTO 1994; AISC 1994; Galambos and Ravindra 1978). This move to LRFD appears to have allowed signi cant savings in structural system costs on highway bridges, with some studies suggesting savings of from 5 30% in steel weight, with average savings of about 10% (Stenersen 2001). In an effort to harmonize design between structural systems and the foundations on which those systems rest, AASHTO and the Federal Highway Administration again led the effort to develop geotechnical codes similarly based on LRFD (AASHTO 1997; Withiam et al. 1998). These codes have primarily focused on the design of shallow foundations, piles and drilled shafts, and earth retaining works. The bene ts of moving to LRFD for foundations has been a more ef ciently balanced design with corresponding improvements to reliability, a more rational approach to accounting for load and resistance uncertainties in design codes, and a broadening of the bene ts of reliability-based design into routine design problems where speci c reliability calculations are not cost-effective (i.e. LRFD-based codes deliver optimized design formulas without the need for repeating reliability calculations for each particular design situation). Other applications of LRFD to geotechnical engineering principally for foundation design have been published by Barker et al. (1991), Fellenius (1994), Meyerhof (1994), O Neill (1995), Kuhlhawy and Mayne (1990) and Goble (1998), among others.
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