Analytical Solution for Negative Skin Friction of Pile Foundations Induced by Seismic Loess Subsidence

ABSTRACT

Negative Skin Friction (NSF) induced by loess subsidence can significantly impair the performance of pile foundations in seismic regions. However, existing studies have primarily focused on immersion-induced collapsibility, while the effects of seismically induced loess subsidence remain insufficiently understood and inadequately represented in current analytical models. To address this gap, this study develops a depthdependent analytical framework for evaluating NSF, based on a case study in Lanzhou, China. An exponential function is established to characterise the variation of seismic subsidence with depth and is incorporated into a tri-linear load-transfer model, enabling closed-form solutions for the axial force and shaft friction of a single pile in layered loess. The proposed solutions are validated against three-dimensional finite element simulations (PLAXIS 3D), showing good agreement and reliability. Results indicate that: under vertical loading, axial force decreases monotonically with depth, while shaft friction first increases and then decreases; under seismic loading, axial force reaches a maximum within the pile, and shaft friction transitions from negative to positive, forming a neutral point; under combined loading, these behaviours are further amplified. The neutral point is identified as a key parameter governing pile response and is significantly influenced by load combinations. These findings enhance the understanding of NSF development under seismic subsidence and provide a practical analytical tool for the design and assessment of pile foundations in seismic loess regions.