层状非饱和土中端承桩竖向振动响应的半解析算法

doi:10.13722/j.cnki.jrme.2022.0678

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摘要为了探究层状非饱和土中桩基的竖向振动响应，基于非饱和土动力控制方程，考虑基质吸力、三相(固相、液相和气相)压缩特性和饱和度对动剪切模量的影响，结合Euler-Bernoulli杆理论，建立三维轴对称简谐荷载作用下层状非饱和土中端承桩的竖向振动响应模型。利用Laplace变换、势函数法和算子分解法求解土体波动方程，通过桩–土耦合条件和阻抗函数传递性求解桩顶动力阻抗频域响应的解析解，利用傅里叶逆变换和卷积定理得出桩顶时域响应的半解析解。验证所得解的正确性后，研究分层土的模量比和厚度比对桩顶动力响应的影响。计算结果表明：土层上硬下软时，桩顶动刚度与阻尼的波动性减弱，导纳存在“小峰夹大峰”现象，峰值变大，反之，导纳呈“大峰夹小峰”。相比于上下均质土，桩底反射信号明显减弱。软土层越厚，桩顶动力响应的振荡幅值越大，土层厚度不一时，速度时程曲线中土层分界面出现反射信号，反射位置与土层分界位置密切相关。

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	马文杰1
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	王长丹1
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	王炳龙1
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	周顺华1
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关键词 ：土力学, 成层非饱和土, 桩基础, 竖向振动, 动力阻抗

Abstract：Based on the dynamic governing equations of unsaturated soils，and considered the effects of matrix suction，three-phase(solid phase，liquid phase and gas phase) compression characteristics，as well as the effect of the degree of saturation on dynamic shear modulus，the vertical vibration response of end-bearing pile in layered unsaturated soils was investigated. Combined with Euler-Bernoulli bar theory，the vertical vibration response model of an end-bearing pile in layered unsaturated soils under three-dimensional axisymmetric harmonic load was proposed. The governing equation of unsaturated soils was derived by utilizing the Laplace transform，potential function and operator decomposition methods. In the frequency domain，the analytical solution of the dynamic impedance of the pile top was solved through the pile-soil coupling condition and impedance function transfer method. The semi-analytical solution of the pile top was obtained by using the inverse Fourier transform and convolution theorem in the time domain. After the correctness of the solution was verified，the effect of modulus ratio and thickness ratio of layered soil on the dynamic response of pile was investigated. The results shown that when pile in upper-hard-and-lower-soft two-layered soil，the fluctuation of dynamic stiffness and damping of the pile decreased，and the admittance had the phenomenon of“small peak sandwiching large peak”，the peak became larger. Conversely，the admittance presented“large peak sandwiching small peak”. Compared with the upper and lower homogeneous soil，the reflected signal at the pile bottom was obviously weakened. The thicker the soft soil layer was，the greater the oscillation amplitude of the pile. When the thickness of the soil layer was different，there was a reflection signal at the interface of the soil layer in the velocity time history curve，and the reflection position was closely related to the boundary position of the soil layer.

Key words： soil mechanics layered unsaturated soils pile foundation vertical vibration dynamic impedance

引用本文:

马文杰1，2，王长丹1，2，王炳龙1，2，周顺华1，2. 层状非饱和土中端承桩竖向振动响应的半解析算法[J]. 岩石力学与工程学报, 2023, 42(S1): 3767-3777.
MA Wenjie1，2，WANG Changdan1，2，WANG Binglong1，2，ZHOU Shunhua1，2. Semi-analytical method for vertical vibration response of end-bearing pile in layered unsaturated soils. , 2023, 42(S1): 3767-3777.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2022.0678 或 http://rockmech.whrsm.ac.cn/CN/Y2023/V42/IS1/3767

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