Analytical Solution for Hydrodynamic Pressure Response in Tubes of Defective Piles Under Vertical Excitation

The tube seismic method evaluates pile integrity by analyzing the hydrodynamic pressure response in acoustic tubes embedded within piles under vertical excitation. However, theoretical research on this novel nondestructive testing technique for pile foundations remains limited. To address this gap, this study establishes a coupled vibration model for a large-diameter defective pile embedded in stratified soil. Analytical solutions for radial stress at any point within the pile in the Laplace domain are derived. By incorporating Biot's governing equations for fluid displacement potential, the time-depth hydrodynamic pressure response in the measurement tube is further formulated. The proposed theoretical model is validated through comparisons with existing analytical solutions. Additionally, the calculated hydrodynamic pressure wave patterns are compared with field-measured data, confirming the model's validity and rationality. Based on the validated analytical solution, a parametric analysis is conducted to investigate the effects of defect severity, burial depth of the defective section, and the presence of soil interlayers around the pile on the propagation characteristics of the Stoneley wave. The results reveal that abnormal K-shaped reflection signatures appear in wave patterns at depths corresponding to pile defects. Notably, soil interlayers exhibit negligible effects on the time-depth characteristics of hydrodynamic pressure responses in defective piles. The conclusions of this study not only provide theoretical support for the engineering application of the tube seismic method but also advance its standardized implementation in pile integrity test.