Instability of Back-Rotated Piles with Near Singularity Stiffness

The two-layer model previously established by the author is expanded to well capture the response of back-rotated and shape-distorted piles set with $P-{\mathrm{\Delta }}_o$ effect ($P$ is the vertical load on piles and ${\mathrm{\Delta }}_o$ is the initial lateral displacement) and subjected to lateral spreading. It is underpinned by sets of parameters of modulus ($k_{\mathrm{s}}$), modulus ratio ($m$), rotational stiffness ($k_{\theta }$), and limiting force per unit length ($p_b$), and calibrated using back-rotating four-pile groups ($1g$ model tests). The study shows that the imposed $P{\mathrm{\Delta }}_o$ values reduce the normalized stiffness ${\overline{k}}_{\theta }$ to $-(0.14–2.54)$ or (0.114–0.494). This ${\overline{k}}_{\theta }$ together with $p_b$ at $m=1.5–8$ incur the diverse response of (1) stable I2 and I5 piles for sufficient forward-rotating capacity; (2) stable I9 piles for a high ${\overline{k}}_{\theta }$; (3) distorted I14 piles at stiffness singularity (SS); (4) initially stable through to later distorted (at SS) I4 piles due to $p_b$ reduction; and (5) hinged I6 piles despite the largest $P{\mathrm{\Delta }}_o$ value and back-rotation. The flexible two-layer model should be adopted to design restrained piles subjected to lateral spreading.