应力波在弹性软弱薄层传播的简化计算研究

Simplified Calculation Study on Stress Wave Propagation in Elastic Weak Thin Layer

应力波入射至软弱薄层后发生多重反射和透射现象,因波形叠加使反射和透射系数计算变得复杂。弹簧模型可以有效简化应力波在软弱薄层的多重反射和透射过程,给出反射和透射系数计算公式。通过建立考虑应力波在软弱薄层内多重反射和透射的实体模型,引入h/λ和Kn/Zω两个无量纲量分别描述应力波在软弱薄层传播过程中的几何特性和力学特性,讨论垂直入射条件下实体模型和弹簧模型的反射、透射系数变化规律。研究结果表明:当软弱薄层厚度与应力波波长相当时,应力波在软弱薄层的多重反射和透射过程引起透射系数和反射系数成"锯齿形"波动,波动周期和软弱薄层与岩层的阻抗比成线性关系;当软弱薄层厚度小于应力波波长时,随Kn/Zω值增加,采用实体模型和弹簧模型计算的透射系数逐渐接近,基于两者透射系数的差值确定等效门槛值ξ,ξ和软弱薄层与岩层的阻抗比成线性关系。

Multiple reflection and transmission occurred when stress wave propagated in weak thin layer.The calculation of reflection and transmission coefficient was very complex due to the superposition of stress waveform.By using spring model,the process of multiple reflection and transmission of stress wave propagation in weak layer could be effectively simplified,and the calculation formula of transmission and reflection coefficient would be deduced.The entity model was established considering multiple reflection and transmission of stress wave.The geometry and mechanical properties of stress wave propagation in elastic weak thin layer were described as two dimensionless quantities h/λ and Kn/Zω.Then,the change rule of reflection and transmission coefficients of spring model and entity model were studied under vertical incidence.The study results indicated that the transmission coefficient fluctuated in zigzag form when the thickness of weak thin layer was similar to wavelength of stress wave.The fluctuation period was almost linearly proportional to the impedance ratio of weak thin layer and rock stratum.When the thickness of weak thin layer was less than the wavelength of stress wave,with the increase of the value of Kn/Zω,the transmission coefficient using spring model gradually approached to that of entity model.The equivalent threshold valueξ,which was determined according to the Dvalue of two transmission coefficient,was linearly proportional to the impedance ratio of weak thin layer and rock stratum.