Analytical solution for dynamic interaction of end-bearing pile groups subjected to vertical dynamic loads
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摘要: 基于平面应变假定，建立了考虑被动桩散射效应的桩–土–桩竖向耦合振动响应分析计算模型。依托该计算模型，首先求解土体控制方程，得到桩周土纵向位移表达式、桩周土纵向复阻抗以及土体位移衰减函数，然后基于严格的桩–土耦合作用，求解外荷载作用下的主动桩位移和由主动桩振动产生的被动桩位移，并求出由被动桩振动产生的主动桩位移，由此得到考虑被动桩散射效应的桩–桩动力相互作用因子。基于求得的修正桩–桩动力相互作用因子，建立考虑被动桩散射效应的群桩竖向动力刚度矩阵，结合桩帽性质及叠加原理，推导得到竖向动荷载作用下的群桩竖向动力响应解析解。基于所得解进行算例分析表明：退化解与已有文献解吻合很好，验证了解的合理性；被动桩的散射效应对小间距群桩的振动响应有不可忽视的影响；桩间距和桩长径比对桩–桩动力相互作用因子、群桩竖向动阻抗有显著影响。Abstract: An analytical model for pile-soil-vertical coupled vibration of the pile considering the scattering effects of the passive pile is proposed based on the classical plane strain assumption. The governing equation for the soil is solved to obtain the expressions for the vertical displacement and resistance of the soil and the attenuation function of the soil displacement. Based on rigorous pile-soil interaction, the pile-interaction factor of the pile considering the scattering effects of the passive pile is obtained by solving the displacement of the active pile under vertical excitation and the displacement of the passive pile caused by the vibration of the active pile, as well as the displacement of the active pile caused by the scattering waves of the passive pile. Based on the modified pile-pile interaction factor, a stiffness-matrix is then established to derive the vertical dynamic responses of the pile groups by considering the scattering effects of the passive pile. Then the analytical solution for the vertical dynamic impedance of the pile groups is derived by incorporating the property of pile cap and the superposition principle. Finally, some arithmetical cases are presented to conduct the numerical analysis. It is found that the degenerated solution for the present solution agrees well with the existing one. The scattering effects cannot be ignored for the pile groups with small pile spacing. The pile spacing and slenderness ratio have considerable effects on the pile-interaction factor of the pile and the vertical dynamic impedance of the pile groups.
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Keywords:
- pile group /
- scattering effect /
- interaction factor /
- dynamic response /
- analytical solution
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图 2 桩–桩相互作用示意图
Figure 2. Schematic illustration of proposed model to account for pile-pile mutual interaction
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图 9 长径比对群桩相互作用因子影响
Figure 9. Variation of interaction factor with slenderness ratio of pile
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图 10 桩间距对群桩动力复阻抗影响
Figure 10. Variation of dynamic complex impedance with pile spacing
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