Abstract：Soil radial heterogeneity significantly impacts the low-strain integrity detection of pile foundations. Conventional computational models usually simplify soil variations to linear or quadratic functions. To address the inherent randomness of soil heterogeneity, this study develops a radial multi-layer random field model. It derives semi-analytical solutions for time-domain responses at any pile depth and analytical solutions for pile head frequency-domain responses, along with a corresponding solution procedure. The model’s validity is confirmed by comparing degenerate random field cases with classical models (e.g. homogeneous soil, construction-induced hardening/softening). Furthermore, the study systematically investigates how shear wave velocity ( ), its coefficient of variation (COV), fluctuation range ( ), construction influence zone ( ), and pile length (L) on the vibration characteristics and the failure probability of pile length detection. Results indicate that the random field model’s calculations are consistent with classical models under degenerate conditions,, highlighting its broader applicability. The degree of radial variability in soil positively correlates with the peak amplitude of the pile tip reflection velocity and the curve’s volatility around this peak. Moreover, increasing increases , while COV exhibits a dual effect. This model can be extended to analyze pile vibrations considering bidirectional and three-dimensional spatial soil variability, offering novel insights for probabilistic analysis in pile integrity detection.
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