大直径管桩在瞬态集中荷载作用下的振动响应时域解析解

Time-domain analytical solution of the vibration response of a large-diameter pipe pile subjected to transient concentrated load

大直径管桩在低应变检测中应力波的传播是一个三维波动问题。将桩周土、桩芯土和桩底土对桩的作用简化为文克尔弹簧,将激振力用半正弦脉冲模拟,建立了大直径管桩在瞬态集中荷载作用下的振动响应计算模型,采用分离变量法和常数变易法求得了波动方程的时域解表达式。将该时域解与采用数值傅立叶逆变换计算得到的时域响应进行了对比验证,进一步将时域解析解计算结果与试验值进行了对比,验证了其合理性。采用得到的时域解计算分析了桩顶速度时域响应特性,结果表明:入射波到达时间和结束时间与波的传播距离成正比,从0°点到180°点基本呈线性变化;激振点的入射波结束时间等于输入脉冲宽度,其余测点的入射波结束时间与入射波到达时间的差值与输入脉冲宽度相等;入射波峰值对应的时间在激振点最小,从0°点到135°点逐渐增大,在135°点到180°点之间基本保持不变。

For a large-diameter pipe pile subjected to transient concentrated load in low strain testing, the wave propagation should be explained by three-dimensional wave equation. The effects of the soils on the pile are modeled by Winkler spring. The exciting force is simulated by a semisinusoidal impulse. A mechanical model for the vibration response of the large-diameter pipe pile subjected to transient concentrated load is established. The time-domain analytical solution is obtained by the separation of variables and the variation of constants. The results of the proposed analytical solution are compared with those calculated by numerical Fourier inverse transformation. The validity is also verified by the test results. The time-domain velocity responses on the pile top are analyzed by means of the analytical solution. The calculated results indicate that the arrival and terminative time of the incident waves is proportional to the propagation distance and it varies linearly from the point of 0° to that of 180°. At the exciting point, the terminative time of the incident waves is equal to the width of the input impulses, and at the other points, the difference between the terminative and arrival time of the incident waves is equal to the width of the input impulses. The peak time of the incident waves at the exciting point is the earliest and that from the point of 0° to that of 135° increases gradually. However, the peak time does not increase any more from the point of 135° to that of 180°.