Theoretical $p\text{-}y$ Curves for Laterally Loaded Single Piles in Undrained Clay Using Bezier Curves

An alternative method was introduced for predicting the nonlinear $p\text{-}y$ curves for monotonic unidirectional laterally loaded single piles in uniform undrained clay. On the basis of numerical studies, closed-form solutions were developed for locating the start of yield $\left(y_e\right)$ ; the ultimate yield point $\left(y_u\right)$ ; and the initial stiffness, $K_i$ of the $p\text{-}y$ curve. The nonlinear section of the curve between the start of the yield and the ultimate yield point was represented by Bezier polynomials (also known as de Casteljau’s algorithm). Using these relationships, a direct method of constructing the $p\text{-}y$ curves was presented considering either tension failure or no tension failure of soils. For a typical pile configuration, the resulting load-deflection response was observed to compare favorably with the predictions from FLAC analysis and Matlock.