The wave reflection characteristics of the pile tip-soil interface under the low-strain condition were studied for exploring the possible quantitative method of detecting and judging the support conditions of the pile base. Based on the one-dimensional wave theory, a new theoretical method was proposed for studying the relation between the upward stress wave (UW) and downward stress wave (DW) under different support stiffness (k′) of the base soil. The frequency response functions (FRFs) of the displacement, velocity, and axial force were derived, simulating the soil resistance with the viscoelastic model. When the downward velocity (v_d) was a semi-sinusoidal function, the upward velocity (v_u) under different support stiffness was calculated. It was shown that the FRFs reflects the reflection characteristics in the frequency domain. The FRF of velocity is the same as FRF of displacement but opposite to that of force. The relation between v_u/v_d and k′ is antisymmetric about the horizontal axis of logarithmic coordinate, and v_u/v_d decreases from 1 to −1 as k′ increases from 0 to +∞. The model experiment verified the theoretical calculation results. This research is useful for the theoretical study of the reflection characteristics at the pile tip and engineering applications.

研究了低应变条件下桩端-土界面的波反射特性，以探讨检测和判断桩基支护条件的可能定量方法。基于一维波动理论，提出了一种新的理论方法，用于研究基础土层不同支撑刚度（k '）下的上应力波（UW）和下应力波（DW）之间的关系。推导了位移，速度和轴向力的频率响应函数（FRF），并用粘弹性模型模拟了土的阻力。当向下速度（v _d）是半正弦函数时，向上速度（v _u）计算不同的支撑刚度。结果表明，FRFs反映了频域中的反射特性。速度的FRF与位移的FRF相同，但与力的FRF相反。v _u / v _d与k '之间的关系关于对数坐标的水平轴是不对称的，并且随着k '从0增加到+∞ ，v _u / v _d从1减小到-1 。模型实验验证了理论计算结果。该研究对于桩端反射特性的理论研究和工程应用很有帮助。