ANALYTICAL SOLUTION OF THE VERTICAL DYNAMIC RESPONSE OF ROCK-SOCKED PILE CONSIDERING TRANSVERSE INERTIAL EFFECT IN UNSATURATED SOIL
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摘要: 基于非饱和土的动力控制方程，考虑横向惯性效应，建立了三相非饱和介质中嵌岩桩的竖向动力响应连续介质模型，对桩侧非饱和土的动力控制方程进行Laplace变换，在频域内，通过引入势函数、算子分解等手段对控制方程进行解析，得到了桩侧土体剪应力及竖向振动位移的表达式.结合桩基的竖向振动方程及桩-土接触面的连续性条件，使桩土耦合振动系统得以解答，最终在频域内得到了桩顶复刚度、导纳、桩-土系统振动位移及应力的解析解，借助Laplace逆变换得到了半正弦激励载荷下桩顶的速度时程曲线.最后，通过算例分析验证了计算结果的准确性，分析了横向惯性、泊松比、饱和度、长径比、桩土模量比等因素对桩基动力响应的影响.结果表明：（1）单桩动刚度、阻尼、导纳等变量随频率变化发生周期性振荡，在桩基各阶固有频率处发生共振；（2）泊松比、饱和度、长径比、桩土模量比等因素对桩基的动力响应有较大影响，且频率越大，影响越明显；（3）泊松比越大，单桩动刚度、阻尼、导纳的波动幅值及对应的频率越小，桩顶时程曲线中的桩底反射信号越弱；（4）饱和度越大，对应各动力响应的波动幅值越大，且桩底反射信号的波峰越大.Abstract: Based on the dynamic governing equations of unsaturated soil, a continuous medium model regarding vertical dynamic response of rock-socked pile in three-phase unsaturated medium was established in this paper, taking the transverse inertial effect into consideration. The Laplace transformation is then used to solve the dynamic governing equations. In frequency domain, potential function and operator decomposition methods are also used to resolve the governing equations, thus obtained the expressions of soil vertical vibration displacement and shear stress. To solve the soil-pile coupling system, the vertical vibration equation of pile foundation and the continuity conditions are both adopted. Eventually, complex stiffness and admittance of the pile butt, vertical vibration displacement and shear stress of the model are obtained in frequency domain. And the travel curve of vibration velocity under half sine excitation load has also been deducted with the help of Laplace inverse transformation. The model is verified through the comparison with the saturated models. Finally, a case study of dynamic response of a pile in unsaturated soil is presented. The influences of transverse inertial effect, Poisson's ratio, saturation, pile length-diameter ratio and pile-soil modulus ratio on response of pile are investigated. The results show that:(1) Dynamic stiffness, damping and admittance oscillate with the frequency, and the pile resonance occur at the natural frequency of pile. (2) Dynamic response of the pile is sensitive to Poisson's ratio, saturation, pile length-diameter ratio and pile-soil modulus, while the sensitivity with higher frequency. (3) Larger Poisson's ratio causes smaller amplitude of dynamic stiffness, damping and admittance, as well as smaller reflection signal at bottom of the pile in its speed history curve. (4) Larger saturation leads to larger amplitude of pile response and peak value of reflection signal from the pile bottom.
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Key words:
- unsaturated soil /
- operator decomposition /
- transverse inertial effect /
- response of pile
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图 4 长径比对单桩动力响应的影响
Figure 4. The effect of pile length-diameter ratio on dynamic response
图 5 桩土模量比对单桩动力响应的影响
Figure 5. The effect of pile-soil modulus ratio on dynamic response
表 1 桩及桩周土物理力学性质
Table 1. Parameters of pile and soil
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