Beam on Nonlinear Winkler Foundation and Modified Neutral Plane Solution for Calculating Downdrag Settlement

Abstract

The neutral plane solution has been widely used to estimate downdrag settlements and drag loads mobilized in piles in consolidating soil profiles. Pile settlement is typically assumed equal to soil settlement at the neutral plane depth corresponding to effective stress conditions at the end of consolidation. This paper demonstrates that, in general, pile settlement is not equal to soil settlement at the neutral plane depth; rather, it is the relative velocity between the pile and soil that is zero at the neutral plane depth. A beam on nonlinear Winkler foundation (BNWF) solution, in which the shaft friction capacity is proportional to effective stress, is utilized to demonstrate that pile settlement is not equal to soil settlement at the neutral plane depth, because the neutral plane depth evolves as consolidation progresses. The BNWF solution also shows that pile settlement depends on drainage conditions, with more settlement occurring when consolidation occurs first near the top of the consolidating soil layer, and less settlement occurring when consolidation initiates at the bottom. A modified neutral plane solution that is amenable to hand calculation is formulated to account for the evolution of neutral plane depth on pile settlement. Finally, the proposed BNWF and modified neutral plane solutions are compared with measurements of downdrag settlement from a centrifuge test program. The proposed methods produced more accurate estimates of pile settlement than the traditional neutral plane solution.