A theoretical model of the defective pile-beam system has been proposed. A three-dimensional continuous medium model is adopted for the surrounding soil

while a Rayleigh-love rod is employed for the pile shaft to account for the transverse inertial effect. The pile defect is simulated using segments with a radius different from the normal one. The impedance function recursive method

in conjunction with ring soil pile theory (RSPT) and amended impedance function transfer method (AIFTM)

is used to obtain the impedance function at pile head. The beam is simulated using Timoshenko beam

and transient excitation is applied at the pile-beam connection. The analytical solution for the dynamic response of the pile-beam system in the frequency domain is obtained

and a semi-analytical solution in the time domain is derived using the discrete Fourier transform. The obtained semi-analytical solution is compared with experimental and finite element method results to validate its reasonability. It is found that the pile-beam system is more suitable for excitation pickup at the pile-beam connection

although the influence of pile-beam parameters must also be considered. Finally

precautions for using low-strain testing on the pile-beam system are studied through parameter analysis.