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130 5.1 Introduction Seven detailed design examples are presented in Appendix H. The presented examples include (1) Examples 1 through 4 of FHWAâs Geotechnical Engineering Circular No. 6 (GEC6), Appendix C (Kimmerling, 2002); (b) the foundations of the central pier and the east abutment of the Billerica, Massa- chusetts, B-12-025 Bridge; and (c) the foundation of the south abutment of the Marlborough, Massachusetts, N-08-013 Bridge. The ULS of bridge foundations (bearing capacity) is an- alyzed in the following examples according to the presented methodology and the AASHTO design specifications with LRFD resistance factors, as given in the current AASHTO (2007) specifications, as well as with the new resistance fac- tors for bearing resistance developed in this research proj- ect. The analysis is based on the conditions that are given in the examplesâ references, i.e., footing geometry as designed, soil conditions, and loading. For design completion, the SLS is analyzed as well, using several settlement analysis methods and a range of factors. Summary graphs and tables are provided for the calculations in all examples, and detailed calculations are shown for two design examples: (1) Exam- ple 1 from FHWA, in which the footing rests on natural soil and the applicable resistance factor depends on the way the soil parameters are derived and (2) the Central Pier of the B-12-025 Billerica Bridge, in which the footing rests on controlled soil. 5.2 Loading Conventions and Notations The loading conventions and the corresponding notation used in this report are as presented in Figure 120, unless otherwise stated in the design examples. The vertical-centric loading is F1; F2 and F3 are horizontal loadings along the transverse (x2-direction or z-direction) and longitudinal (x3-direction or y-direction) directions of the bridge, respec- tively. M3 is the moment about the longitudinal direction (x3- or y-axis) due to transverse loading and M2 is the moment about the z-axis (transverse direction) due to longitudinal load- ing. The load eccentricity across the footing width is eB = M2/F1 and across the footing length is eL = M3/F1. The resultant load inclination is given by . 5.3 Examples Summary In Appendix H, the figures present for the different exam- ples the performance versus footing size, referring to the effective footing size. The discussion in Appendix H of the example refers to geometrical size, which includes, for exam- ple, eccentricity. The limiting eccentricity in all examples was assumed to be e = B/6. Table 73 provides a summary of major findings from the design examples referring to the full geo- metrical width. Overall, the use of the new, recommended resistance factors for the strength limit states resulted in foun- dations with varied relations to the actual design, i.e., in five cases the designed foundations under the new factors are smaller, and in two cases the foundations are larger. In most cases, the foundations are controlled by limiting eccentricity, especially if the contribution of negative eccentricity is not adopted. As in other instances in which designs are compared to each other, the introduction of calibrated factors in RBD methodology provides mixed results in terms of econom- ics. Overall, no significant change in economics can be pointed out; the design improvement and the systematic approach are, however, a major improvement to the exist- ing guidelines. F F F22 32 1+ C H A P T E R 5 Design Examples
131 B 1x 2F 3M 1M 2M 1F 2x 3F L D 3x Design foundation size, B L (ft ft) Strength LS Service LS Ex am pl e Reference Foundation and soil condition Dominant limit state Maximum load eccentricity (ft) Eccentricity to footing side ratio Recommended = 0.45 = 1.0 Design in reference Settlement method used in reference 1 GEC6 - Exam ple 1 Bridge pier on natural soil deposits Service 0.36 e 2 /B = 0.23/ B e 3 /L = 0.36/L 9.75 ( = 0.35 to 0.40) 9. 5 9.5 50.0 .0 (Schm 78: 19.5 19.5) (Hough: 16.25 16.25) 16.0 16.0 Hough (1959 ) 2 Billerica Bridge Central Pier Pier footing on gravel fill Strength 0.50 e 2 /B = 0.50/ B e 3 /L = 0.095/52.4 = 0.0018 52.4 (C2 load, = 0.70) 8. 9 52.4 (C7 load, = 0.45) 52.4 4. 5 52.4 (Schm 78: 4. 3 52.4) (Hough: 2. 0 52.4) 13.1 52.4 Peck et al. (1974) 3 Billerica Bridge East Abut me nt Abut me nt footing on gravel fill Strength 2.31 e 2 /B = 2.31/ B e 3 /L = n.a. 15.5 61.65 ( = 0.45) 15.5 61.6 5 61.65 (including Schm 78 and Hough) 12.5 61.7 Peck et al. (1974) 4 GEC6 - Exam ple 2 Integral bridge abut me nt on structural fill Lim iting eccentricity 1.00 e 2 /B = 1.00/ B e 3 /L = n.a. 6. 0 82.0 ( = 0.45) 6. 0 82.0 82.0 (Schm78 and Hough: 6. 0 82.0*) 9. 8 82.0 Hough (1959 ) 5 GEC6 - Exam ple 3 Stub seat-type bridge abut me nt on structural fill Lim iting eccentricity 1.39 e 2 /B = 1.39/ B e 3 /L = n.a. 8.35 82.0 ( = 0.45) 8.35 82.0 82.0 (Schm 78 and Hough: 8.35 82.0) 10.5 82.0 Hough (1959 ) 6 GEC6 - Exam ple 4 Full height bridge abut me nt on natural soil Lim iting eccentricity 3.15 e 2 /B = 3.15/ B e 3 /L = n.a. 18.9 82.0 ( = 0.40) 18.9 82.0 18.9 82.0 (Schm 78 and Hough: 18.9 82.0*) 17.1 82.0 Hough (1959 ) 7 Marlborough Bridge South Abut me nt Single span abut me nt footing on rock Lim iting eccentricity if not considere d pos/neg contributio n 7.38 e 2 /B = 7.38/ B e 3 /L = 0 4. 0 38.4 4. 0 38.4 4. 0 38.4 AASHTO (2008) 10.5 38.4 AASHTO (2008) Eq. 10.6.2.4.4-3 Figure 120. Loading conventions and notation used. Table 73. Design example details summary.
