锥形桩的纵向动力响应

Longitudinal Dynamic Response of Tapered Piles

主要研究了锥形桩这一典型变截面桩的桩顶纵向振动响应。桩身为均质线弹性有限长杆,桩顶受纵向冲击力作用。桩周土和桩底土用Kelvin?Voigt模型表示,假设桩周土剪切波速随深度线性变化。根据上述桩土模型,推导出简洁的波动方程。由Laplace变换得出了频域的解析解,然后采用快速傅里叶变换求解Laplace逆变换,得到了时域的半解析解。通过与差分法计算结果对比,表明本文求解方法的合理性。通过对计算结果的分析,了解了桩顶振动速度导纳曲线的变化特征,还说明了截面渐变程度对桩顶速度响应的影响,阐述了变截面效应。锥形桩的变截面效应表现为:桩身横截面的渐变会对频域响应的低频波部分产生影响;桩身横截面渐变时会引起桩身渐变的反射,而且截面渐扩(渐缩)程度越大,反射越明显。

Longitudinal dynamic response of tapered pile top is mainly presented.The pile is assumed to be a homogeneous linear elastic tapered bar with finite length,and its top is subjected to longitudinal impact force.Soil around and under the pile is represented by Kelvin-Voigt model.The shear wave speed of the soil around the pile varies linearly with depth.Simple wave equation is derived according to pile-soil model mentioned above.The analytical solution in frequency-domain is obtained by Laplace transform,while the semi-analytical solution in time-domain is computed by FFT（fast Fourier transform）.It is shown that FFT is an efficient method from the comparison with finite difference method.Not only characteristics of vibration velocity admittance curves of pile top are studied,but also influences of varying degree of cross-section on vibration velocity are discussed.Variable cross-section effects of tapered pile are shown as this： Reflection could be caused by the gradual variation of the cross-section.The larger the enlarging（or narrowing） degree of cross-section is,the stronger the reflection will become.Variable cross-section also has an effect on low-frequency wave of response in frequency-domain.