Degrading P-Y Spring Model for Laterally Loaded Piles in Soft Clay-Paper

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The paper presents a bounding surface plasticity model for predicting how soft clay resists laterally loaded piles during cyclic loading. Unlike a monotonic P–y curve, the model captures nonlinear response, permanent displacement, and stiffness degradation as repeated loading progresses toward a steady state.<br /><br />The model uses four parameters: ultimate soil resistance (Pult), yield load (Py), initial stiffness (Ke), and a hardening parameter (C). Pult can be estimated using established methods. Centrifuge test results indicate that Py and Ke are proportional to Pult and largely independent of depth and cycle count, while C varies with both depth and loading history. The authors provide parameter relationships calibrated to tests in kaolin.<br /><br />Coupled with a beam model of the pile, the spring model reproduces measured cyclic bending moments with good agreement: predictions are generally within about 10% in key comparisons, although accuracy declines somewhat after many cycles. The model also provides relationships for equivalent secant stiffness and damping as functions of displacement amplitude and cycle count. Both properties depend strongly on displacement, and stiffness degradation is most pronounced at intermediate amplitudes.<br /><br />The proposed approach offers a framework for analyzing cyclic pile response beyond conventional empirical curves. However, its calibrated parameter values are specific to kaolin tests, and further calibration is needed for other soil types.

Keywords

bounding surface plasticity

soft clay

laterally loaded piles

cyclic loading

P-y curve

stiffness degradation

permanent displacement

kaolin tests

secant stiffness

pile response