Simple Model for Nonlinear Response of 52 Laterally Loaded Piles

The response of a laterally loaded pile is normally dominated by the limiting force per unit length profile (LFP, ${\mathit{p}}_{\mathit{u}}$) mobilized along the pile to the depth of the plastic zone (e.g., maximum slip depth, max ${\mathit{x}}_{\mathit{p}}$) and depends on pile-soil relative rigidity (via the subgrade modulus of elasticity $\mathit{k}$). The values of ${\mathit{p}}_{\mathit{u}}$ and the shear modulus ($\mathit{G}$, thus $\mathit{k}$) were deduced extensively against the measured response of 32 and 20 piles tested in situ in clay and sand, respectively. In this paper, simplified closed-form solutions are presented for the design of laterally loaded piles. The parameters of the ${\mathit{p}}_{\mathit{u}}$ and the $\mathit{G}$ obtained previously are utilized to examine the impact of loading eccentricity on piles and to assess the validity of existing ${\mathit{p}}_{\mathit{u}}$-profiles. Expressions are also explored and provided regarding determinations of the ${\mathit{p}}_{\mathit{u}}$-profiles, the modulus of the subgrade reaction $\mathit{k}$ (via $\mathit{G}$), the ranges of the plastic zone (max ${\mathit{x}}_{\mathit{p}}$), and the depth of elastic influence (via the critical pile length ${\mathit{L}}_{\text{cr}}$), along with the correlations between the shear modulus of soil $\mathit{G}$ and undrained shear strength (${\mathit{s}}_{\mathit{u}}$) and/or the standard penetration test blow count ($\mathit{N}$). It is noted that the popularly adopted LFPs (such as Matlock’s LFP, Reese’s LFP, and American Petroleum Institute code methods) are not sufficiently accurate for 60–85% of the 52 piles investigated herein, especially for those with a diameter >1.5 m.