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 \(90^{\circ }\) along the circumferential direction.

中文翻译：

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具有多个缺陷的管桩中波传播的解析解

本文开发了一种分析解决方案，以对具有多个缺陷的管桩进行低应变完整性测试。通过考虑在垂直，圆周和径向方向上的波传播，导出的解决方案可以将管桩模拟为三维模型。通过拉普拉斯变换和变量分离获得桩的解析解。因此，通过逆傅立叶变换在数值上推导解的时域响应。该解决方案已针对已发布的完整桩和具有单个缺陷的桩的解决方案进行了验证。进行参数研究以识别和表征具有多个缺陷的管桩顶部的速度响应。数值结果表明，深缺陷产生的反射波受浅缺陷的二次反射影响。提出了一种新的检测方法，以减少高频干扰的影响并预测缺陷深度，这建议将接收器置于沿圆周方向\（90 ^ {\ circ} \）。