The propagation characteristics of F-(flexural) wave and the reflection from vertical cracks in pipe-piles subjected to an eccentric vertical excitation were numerically investigated using elastodynamic finite integration technique (EFIT). The accuracy of the self-written code was validated by comparing computed results against the measured data. The snapshots of circumferential, radial and vertical velocities in intact and cracked pipe-piles, as well as the velocity histories of the pile-top were presented. It is found that not only L-(longitudinal) wave (corresponding to axisymmetric mode) but also F-wave (corresponding to non-axisymmetric mode) can be excited in pipe-piles subjected to an eccentric vertical excitation. F-wave causes motion in all directions, while L-wave only causes vertical motion. The three-dimensional (3-D) interference is weak at 90° away from the excitation position for circumferential velocity response, while at 45° or 135° for radial velocity response. The reflected F-wave (RFW) from the pipe-toe has multiple peaks due to the dispersion effect of F-wave. Reflection occurs when F-wave encounters vertical cracks, while L-wave is not sensitive to vertical cracks. The intensity of RFW from vertical cracks varies with excitation-and-sensor modes. For shallow vertical cracks, the RFW strength varies with the sensor positions; while the intensity of the RFW caused by deep vertical cracks varies little with the sensor positions. With the increase of crack length, the strength of the first arrival RFW due to the vertical crack has no obvious change; however, the strength of RFW from the pile-toe decreases.

中文翻译：

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管桩完整性试验中弯曲波的传播特性和竖向裂缝的反射

使用弹性动力学有限积分技术（EFIT）数值研究了F-（弯曲）波的传播特性和管桩垂直裂缝反射的偏心垂直激励。通过将计算结果与测量数据进行比较，验证了自写代码的准确性。给出了完整和破裂管桩的圆周速度、径向速度和垂直速度的快照，以及桩顶的速度历史。研究发现，在垂直偏心激发的管桩中，不仅可以激发L-(纵向)波(对应于轴对称模式)，而且可以激发F-波(对应于非轴对称模式)。F波引起各个方向的运动，而L波只引起垂直运动。三维 (3-D) 干涉在距激发位置 90° 处的圆周速度响应较弱，而在 45° 或 135° 处的径向速度响应较弱。由于 F 波的色散效应，从管趾反射的 F 波 (RFW) 具有多个峰值。当 F 波遇到垂直裂缝时会发生反射，而 L 波对垂直裂缝不敏感。来自垂直裂缝的 RFW 强度随激发和传感器模式而变化。对于浅垂直裂纹，RFW 强度随传感器位置而变化；而由深垂直裂纹引起的RFW强度随传感器位置的变化很小。随着裂纹长度的增加，垂直裂纹引起的初至射频波强度无明显变化；然而，从桩趾开始的 RFW 强度会降低。