Nonlinear Response of Lateral Piles with Compatible Cap Stiffness and $p$-Multiplier

Response of lateral pile groups is modeled using the more accurate (than any other numerical modeling) $p-y$ curves–based load transfer model. It is essentially underpinned by limiting force per unit length $p_m{p}_u$, modulus of subgrade reaction $p_{m}k$, and $p$-multiplier $p_m$ (to cater for pile-pile interaction, $p_m=1$ for single piles). With the model, new closed-form solutions are developed incorporating the cap-rotational stiffness $k_r$. The solutions are presented in nondimensional charts for free-head ($k_r=0$) through fixed-head ($k_r>10$ times the pile bending stiffness). The study reveals that the existing $p_m$ (bearing no link to the stiffness $k_r$) is inconsistent with $p_m=0.25$ for capped piles (at limiting state of elastic solutions). This casts doubt about the accuracy of available solutions, and a compatible stiffness $k_r$ and $p_m$ is required. The compatible normalized stiffness $k_{nr}$ is equal to 0.275–0.333 ($n=0.7$) and 0.333–0.564 ($n=1.7$) for the associated $p_m$ at the design level of (ground-level) bending moment specified in the JGJ code. Use of the solutions is elaborated for a typical offshore pile group against measured response, which largely substantiates the deduced stiffness $k_{nr}$. The coupled $k_r$ and $p_m$ revealed are fundamental to design of the capped piles using any methods. The new solutions using the $k_{nr}$ and $p_m$ values should be employed to conduct pertinent design.