P波在饱和粗颗粒夹层界面上的反射和透射

摘要

In order to study the reflection and transmission of stress wave at interfaces of the sandwiched coarse granular structure in embedded pile-board subgrade,an interface effect model for the coupled elastic solid-saturated coarse granular layer-elastic solid sandwich structure is established according to the structure characteristic of embedded pile-board subgrade,taking into consideration the superimposed effect of plane P waves reflected from the coarse granular interlayer.Based on the Biot theory and the elastic wave theory,reflection and transmission coefficients at the upper and lower interfaces in the model are derived theoretically by introducing scalar and vector potential functions.Using the derived theoretical formulas,influences of various factors on the reflection and transmission coefficients are discussed through numerical examples.The results show that thickness,porosity and shear modulus of the sandwiched coarse granular structure will change the energy distribution on interfaces,and make it present a periodic resonance characteristic.As the porosity varies from 0.2 to 0.4,the reflection coefficient increases by about 25％.In addition,the propagation of shear wave causes the reflection coefficient to oscillate with damping at the resonant frequencies of the shear wave,and the permeability and flow conditions also have significant effect on the wave reflection.%为研究应力波在埋入式桩板路基饱和粗颗粒夹层结构界面的反射和透射效应,以平面P波为例,结合埋入式桩板路基的结构特点,基于Biot饱和多孔介质波动理论和弹性波动理论,建立了考虑饱和粗颗粒夹层反射波叠加影响的弹性介质-饱和粗颗粒夹层-弹性介质界面效应模型;采用引入势函数的方法推导了应力波在饱和粗颗粒夹层交界面上的反射和透射系数;通过数值算例研究了不同因素对反射和透射系数的影响规律.研究结果表明:夹层厚度、孔隙率、剪切模量改变了能量在交界面上的分配关系,且表现出周期性谐振特性,孔隙率由0.2变化到0.4时,反射系数增大了约25％;剪切波的传播引起反射系数在剪切波谐振频率处震荡且受阻尼作用,渗透率及透水条件对粗颗粒夹层的反射系数影响明显.