COUPLED DYNAMIC RESPONSES BETWEEN SATURATED SOIL AND PILE SYSTEMS UNDER VERTICAL EARTHQUAKES
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摘要: 为揭示竖向地震荷载作用下桩土系统的耦合动力特性,首先将基桩视为具有径向和竖向变形的三维轴对称杆件,采用Hamilton变分原理建立其运动方程,而桩周土体视为充满流体的三维多孔连续介质,采用Boer多孔弹性介质模型描述其动力学行为。在不引入势函数的情况下,先将土骨架的体积应变和孔隙流体压力作为中间变量处理土体运动方程,然后采用分离变量法求解土体和基桩的运动方程,进而结合桩-土系统的边界和连续条件,推导得到桩顶的运动放大系数和运动响应因子解析解。通过与相应有限元模型数值计算结果及已有解的比较,验证所提出解的正确性。最后分析桩土主要参数对桩土耦合系统动力特性的影响,得到了一些有意义的结论,可为相关工程实践提供参考。研究结果表明:当桩长径比较小时,基桩的径向变形对饱和土-桩系统的动力响应存在显著影响,忽略基桩的径向变形,将高估桩土系统的共振行为;对于单相土而言,在低频阶段,桩顶响应相对于自由场表面响应偏小,在高频阶段,其随着桩长径比的增大而偏大。桩土系统的共振行为发生于激振频率接近于土体自由场的自振频率。随着桩长径比的增大,桩土系统对基岩运动的放大效应呈增大趋势;对于饱和土而言,饱和土层表面的响应与基岩运动基本上一致。随着桩长径比的增大,桩土系统对基岩运动的放大效应呈减小趋势。
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关键词:
- 桩土相互作用 /
- 饱和土 /
- 三维轴对称杆 /
- 径向变形 /
- Boer多孔介质模型
Abstract: To reveal the coupling dynamic characteristics of pile-soil systems under vertical seismic loads, the pile foundation was firstly regarded as a three-dimensional axisymmetric bar with radial and vertical deformation, and its motion equation was established by using a Hamiltonan variational principle. The soil around the pile was treated as a three-dimensional fluid-filled porous continuous medium, and its dynamic behavior was described by using Boer’s poroelastic media model. Without the introduction of potential functions, the volumetric strain of soil skeleton and pore fluid pressure were taken as intermediate variables to deal with the soil motion equation, and then the motion equations of soil and pile were solved by the method of variable separation. Combined with the boundary and continuity conditions of the pile-soil system, the analytical solutions of the kinematic amplification factor and kinematic response factor of the pile top were derived. The correctness of the proposed solution was verified by comparing the numerical results of the corresponding finite element model with the existing solutions. Finally, the influence of the main pile-soil parameters on the dynamic characteristics of the pile-soil coupling system was analyzed, and some meaningful conclusions were obtained, which can provide a reference for related engineering practice. The results show that: when the pile length-radius ratio is small, the radial deformation of pile foundation has a significant effect on the dynamic response of saturated soil-pile system. If the radial deformation of the pile foundation could be ignored, the resonance behavior of the pile-soil system might be overestimated. For single-phase soil, in the low frequency range, the response of a pile top is smaller than that of a free field surface and, in the high frequency range, it is larger with the increase of pile length-radius ratio. The resonance behavior of a pile-soil system occurs when the excitation frequency is close to the natural frequency of a soil free field. As the length-radius ratio of piles increases, the magnifying effect of a pile-soil system on bedrock movement tends to increase. For saturated soil, the response of saturated soil surface is basically the same as the movement of bedrock. With the increase of pile length-radius ratio, the magnifying effect of a pile-soil system on bedrock movement tends to decrease. -
表 1 桩土参数
Table 1. Pile and soil parameters
类别 参数 取值 基桩 桩长L/m 10.00 桩半径r0/m 0.25 桩弹性模量Ep/GPa 20.00 桩密度 ρ p/(kg/m3) 2500.00 桩泊松比υp 0.10 饱和土 土弹性模量Es/MPa 20.00 土泊松比υs 0.20 土阻尼比ηs 0.05 土骨架实际密度ρsR/(kg/m3) 1800.00 孔隙流体实际密度ρfR/(kg/m3) 1000.00 孔隙流体体积分数nf 0.40 Darcy渗透系数kf/(mm/s) 0.10 -
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