Upper bound and load displacement solutions for laterally loaded piles in clays based on energy minimisation

A. Klar, Mark Randolph

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    28 Citations (Scopus)


    An important part of any foundation design procedure is the evaluation of the ultimate capacity and displacements under working loads. The most widely used solution for ultimate loads of laterally loaded piles in clays is that of Broms (1964). Broms ignored the soil resistance down to a depth of one and a half diameters, and used a constant resistance value of 9sud along the remainder of the pile, where su is the undrained shear strength, and d is the pile diameter.While the value of 9sud closely corresponds to the best-known lower- and upper-bound solutions, 9·14sud and 9·20sud respectively (Randolph & Houlsby, 1984; Martin & Randolph, 2006), the omission of the upper soil resistance is somewhat arbitrary. On the other hand, associating a resistance value of 9sud with the upper soil would not be conservative, as a wedge-type mechanism will develop in that area (Murff & Hamilton, 1993). Reduction factors are therefore commonly applied to the ultimate soil resistance near the surface in p–y curves (e.g. Matlock, 1970; Fleming et al., 1992)Murff & Hamilton (1993) dealt thoroughly with this problem by suggesting an upper-bound failure mechanism comprising a conical wedge near the surface, and a flow-round (plane strain) mechanism below the wedge. Strictly speaking, their upper-bound solution is not rigorous, since the transition from the wedge to the flow-round mechanism is not continuous, and the associated dissipation due to the abrupt change in the velocity field was not taken into account. Also, energy dissipation due to relative shearing between the stratified flow-round mechanisms was not considered in their solution.In the present work, a wedge-type mechanism, following the methodology of Murff & Hamilton (1993) but eliminating the discontinuity at the outer boundary of the wedge, is combined with the continuous flow-round mechanism of Klar & Osman (2008a) to result in a fully compatible and continuous deformation field. This deformation field allows rigorous calculations of upper-bound values.In addition, since the mechanism is continuous, with strain and strain rates defined everywhere, the mobilisable strength design (MSD) method (Bolton & Powrie, 1988; Osman & Bolton, 2005) may be applied for estimation of displacements under working loads.
    Original languageEnglish
    Pages (from-to)815-820
    Issue number10
    Publication statusPublished - 2008


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