Abstract We provide a theoretical analysis to support the presence of both slow and fast compression waves in an unconsolidated, fully saturated, granular material. We derive the constitutive relation for such an aggregate based upon a micro-mechanics analysis. In doing this, we take in account the coupling between the solid particles and fluid. As a consequence of this coupling, the lubrication layer provides a connection between particles, both when they are separating and when they are compressing. The predictions of the speed and attenuation of the fast compression waves compare well with experimental data over the range of frequencies for which the nonlinear dissipation associated with the relative velocities between solid and fluid is negligible. Slow waves are also predicted without comparison, because of the absence of clear experimental data. Predictions of the speed and attenuation for the shear wave are also provided and show a good agreement with experimental data when surface roughness is taken into account.

中文翻译：

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未固结颗粒材料中的波传播：一种微机械方法

摘要 我们提供了一个理论分析来支持在未固结的、完全饱和的粒状材料中同时存在慢速和快速压缩波。我们基于微观力学分析推导出这种聚集体的本构关系。在此过程中，我们考虑了固体颗粒和流体之间的耦合。作为这种耦合的结果，润滑层在颗粒分离和压缩时提供了颗粒之间的连接。快速压缩波的速度和衰减的预测与频率范围内的实验数据很好地比较，在这些频率范围内，与固体和流体之间的相对速度相关的非线性耗散可以忽略不计。慢波也被预测，没有比较，因为没有明确的实验数据。还提供了对剪切波的速度和衰减的预测，并在考虑表面粗糙度时显示出与实验数据的良好一致性。