竖向入射S波作用下单桩水平地震响应简化解析方法

Simplified analytical solution for horizontal seismic response of single piles to vertically incident S waves

基于连续介质模型并考虑桩-土运动相互作用,将单桩视为一维线弹性梁,研究了竖向入射S波作用下的单桩水平地震响应问题。将竖向入射S波模拟为基岩水平位移,基于平面应变模型建立的土体控制方程,推导出地震作用下土体水平动力阻抗函数表达式。将土体阻抗代入单桩控制方程并联立桩-土接触条件及桩顶和桩底的边界条件,得出了竖向入射S波作用下单桩的地震响应解析解。通过将所得解与已有文献理论解和有限元结果进行对比,验证了该方法的合理性。基于所得理论解进行参数分析得出:桩-土模量比的增加可以明显降低桩-土运动相互作用因子的最小值,而较大桩身长径比以及土体滞回阻尼对桩-土运动相互作用因子的影响较小;对于桩顶水平地震放大因子来说,桩-土模量比的增加仅在高共振频率处抑制其幅值,较大桩身长径比对其影响较小,而滞回阻尼比的增加会显著抑制共振频率处的幅值;桩身地震响应仅在较小桩径比时受桩-土模量比的影响明显,并随桩-土模量比的增加而降低。

Based on the continuous medium model and the pile-soil interaction,the horizontal seismic response of a single pile subjected to vertically propagating S waves was investigated by regarding the single pile as a one-dimensional linearly elastic beam.The time-harmonic displacement of bedrock was introduced as the vertically propagating S waves,and the horizontal dynamic impedance function of the soil was derived by the governing equations of the plane strain model.Analytical solutions for the seismic response of the single pile subjected to vertically propagating S waves were obtained by subsuming soil impedance into the governing equation of the single pile and considering the boundary conditions at pile top and toe.The solution was verified by comparing it to the results of existing studies.Furthermore,as pile-soil modulus ratio increases,the minimum value of the kinematic response factor decreases.The kinematic response factor is not particularly sensitive to the large pile slenderness ratio and the soil material damping.For the horizontal amplification factor at the pile top,the increase of the pile-soil modulus ratio only suppresses the amplification at high resonance frequency,and the large pile slenderness ratio has the trivial effect on it.As the soil material damping increases,the amplification at resonance frequency gets considerably suppressed.The seismic response of the pile is obviously affected by the pile-soil modulus ratio only when the pile slenderness ratio is small,and it decreases with the increase of the pile-soil modulus ratio.