Discussion of "Single piles in lateral spreads: field bending moment evaluation"

DISCUSSIONS AND CLOSURES Discussion of “Single Piles in Lateral Spreads: Field Bending Moment Evaluation” by Ricardo Dobry, Tarek Abdoun, Thomas D. O’Rourke, and S.H. Goh October 2003, Vol. 129, No. 10, pp. 879–889. DOI: 10.1061/ASCE1090-02412003129:10879 Scott J. Brandenberg 1 ; Ross W. Boulanger 2 ; and Bruce L. Kutter 3 Graduate Student, Univ. of California, Davis, Dept. of Civil and Environmental Engineering, Davis, CA 95616, E-mail: sjbrandenberg@ucdavis.edu Professor, Univ. of California, Davis, Dept. of Civil and Environmental Engineering, Davis, CA 95616. Professor, Univ. of California, Davis, Dept. of Civil and Environmental Engineering, Davis, CA 95616. The authors should be commended on their contribution to the study of pile foundations in liqueﬁed and laterally spreading ground. The data collected in their centrifuge tests and their sub- sequent analyses contribute to the understanding of soil-pile in- teraction during liquefaction-induced lateral spreading. An ana- lytical model based on limit equilibrium LE and elastic solutions referred to as an LE model for predicting bending moments in single piles subjected to loads from a laterally spread- ing crust was calibrated with centrifuge test data presented in a companion paper Abdoun et al. 2003. The ﬂexible pile founda- tion in centrifuge Model 1 experienced head displacements that would be considered too large in most design applications. The applicability of the LE model for stiffer piles that would exhibit satisfactory behavior in lateral spreads with a crust was left un- explored. In particular, the limiting state for z ps = 0 was not ob- served in the centrifuge tests and was not highlighted in the as- sociated LE solutions. Comparisons of LE and beam on nonlinear Winkler foundation BNWF analyses for stiffer piles are used in this discussion to bring attention to the practical importance of this limiting state and supplement the utility of the authors’ meth- odology. ment between the free-ﬁeld soil and the pile, so the gripping action is associated with a pile head displacement that is larger than the free-ﬁeld ground surface displacement. The LE model was calibrated to the test data by assuming elastic perfectly plastic soil-pile interaction behavior such that the evolution of bending moment with increasing D H is approxi- mately bilinear see Fig. 7 in the original paper. The values of M A , M B , H A shear force at point A, and z ps are calculated in the original paper by simultaneously solving Eqs. 3, 4, 5, and 6 at the yield point and Eqs. 3, 4, 5, and 9 after the yield point. At the yield point, the ultimate subgrade reaction is mobi- lized against the pile in the downslope direction below z ps and in the upslope direction above z ps . As D H increases after yield, z ps gradually shifts upward decreases in magnitude such that a larger portion of the crust exerts downslope loading on the pile, which causes M A to linearly decrease and M B and H A to linearly increase. The model was calibrated out to the peak crust displace- ment for the centrifuge test D H = 0.8 m, at which point the pre- dicted moments M A = 142 kN· m , M B = 356 kN· m match reason- ably well with the measured data M A Ϸ 140 kN· m , M B = 305 kN· m. The model predicts z ps = 1.29 m at D H = 0.80 m, which is only a slight decrease over z ps = 1.34 m at the yield point. Limiting State When z ps = 0 The LE model reaches a limiting state when z ps = 0 because the transition depth must lie somewhere within the soil layer. This limiting state did not develop for the ﬂexible pile in centrifuge Model 1 but is of practical interest for stiffer piles, as will be shown subsequently. Although the limiting state can be found by simultaneously solving Eqs. 3, 4, 5, and 9 in the original paper for different values of D H until z ps = 0, the limiting bending moments M A,lim and M B,lim limiting shear load at point A H A,lim and ground surface displacement at the limiting state D H,lim can be more easily calculated by setting ␣ = z ps / h = 0 in Eqs. 3 and 4, then solving Eqs. 5 and 9. The resulting equations are M A,lim p 0 · h 3 H A,lim 1 p 0 · h 2 2 M B,lim L p 0 · h 3 2 · h 6 L L EI EI 2 · D H,lim = p 0 · h · L 6 · h 12 k r · L 2 · h 6 Characterization of Observed Loading Mechanics for Flexible Pile in Model 1 Centrifuge Model 1 contained a single pile diameter, d = 0.60 cm, EI = 8,000 kN· m 2 in a soil proﬁle consisting of a non- liqueﬁable cemented sand crust over liqueﬁable loose sand over nonliqueﬁable cemented sand. As the crust spread laterally on top of the liqueﬁable sand, it caused a gripping action on the pile in which the crust below a transition depth z ps pushed the pile downslope, and the crust above z ps restrained the pile from mov- ing downslope. When crust displacement D H was 0.29 m, the pile head “snapped” downslope through the nonliqueﬁed crust, which veriﬁed the gripping action on the pile. The direction of subgrade reaction loading is controlled by the direction of relative displace- For practical purposes, knowing the values of M A , M B , and D H at the yield point from Eqs. 3, 4, 5, and 6 in the original paper and at the limiting point from Eqs. 1–4 in this discussion is sufﬁcient to characterize the relationship of moment versus crust displacement because its shape is approximately trilinear. JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / APRIL 2005 / 529