An Analytical Solution for Wave Propagation in a Pipe Pile with Multiple Defects

An analytical solution is developed in this paper to conduct the low-strain integrity testing for a pipe pile with multiple defects. The derived solution allows simulating the pipe pile as a three-dimensional model by considering the wave propagation in the vertical, circumferential and radial directions. Analytical solutions of the pile are obtained by the Laplace transform and separation of variables. Accordingly, time-domain responses of the solution are deduced by the inverse Fourier transform numerically. The solution is validated against the published solutions for an intact pile and a pile with a single defect. Parametric studies are conducted to identify and characterize the velocity responses on the top of pipe piles with multiple defects. Numerical results suggest that the reflected waves generated by the deep defects are affected by the secondary reflections from the shallow defects. A new detecting method is proposed to decrease the influence of high-frequency interferences and to predict the defective depth, which suggests putting the receiver at the point of 90. along the circumferential direction.