The paper presents an approximate solution to axial dynamic impedance calculation for group of square piles. Firstly, dynamic responses of the single pile-soil system are derived on the basis of Hamilton's energy principle and variation analysis. Then, the effects of square cross section on the pile-soil interaction are examined through the combination of theoretical deduction and numerical simulation. The vertical soil vibration around a square pile is found to be dependent on wave propagation directions in the near field (two times less than the side length of square pile). As the radial distance off pile axis increases, the soil vibration tends to be independent on propagation directions. Through superposition principle, the dynamic impedance of square pile group is calculated. This study could provide a reference to the problems with how the non-circular piles interplay with soil on vibration.

中文翻译：

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方截面桩的竖向振动

给出了方桩群轴向动力阻抗计算的近似解。首先，基于Hamilton能量原理和变分分析，推导出单桩土系统的动力响应。然后，通过理论推导和数值模拟相结合，研究了方形截面对桩土相互作用的影响。发现方形桩周围的垂直土壤振动取决于近场中的波传播方向（小于方形桩边长的两倍）。随着桩轴径向距离的增加，土体振动趋于与传播方向无关。通过叠加原理，计算出方桩群的动力阻抗。