PROPAGATION OF ELASTIC WAVES IN UNCONSOLIDATED UNSATURATED GRANULAR MEDIUMS
PROPAGATION OF ELASTIC WAVES IN UNCONSOLIDATED UNSATURATED GRANULAR MEDIUMS
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DOI：
10.1029/jz069i002p00243
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发表时间：
1964-01-01
影响因子：
--
通讯作者：
BRUTSAERT, W
中科院分区：
文献类型：
--
作者：
BRUTSAERT, W
该理论使用三种不同的理想化模型。推导了连续体模型的一般运动方程。这个连续体由三种成分组成--固体、气体和液体;液体附着在固体上并具有表面张力。发生在运动方程中的弹性系数被确定为随机堆叠的不同大小的球体组成的模型;该模型的间隙包含气体和液体。在运动方程中出现的耗散系数确定为一个模型的短毛细管。九个运动方程被转换成旋转和非旋转方程，以产生平面、前进、正弦波。对于甚低频和甚高频的渐近情形，导出了波的速度和衰减。证明了存在三种类型的纵波和一种类型的横波。在非常低的频率下，只有一种类型的压缩波占优势，而在非常高的频率下，所有四种类型的波的耗散与频率的平方根成比例。
The theory makes use of three distinct idealized models. The general equations of motion are derived for a continuum model. This continuum consists of three components—a solid, a gas, and a liquid; the liquid adheres to the solid and has surface tension. The elastic coefficients occurring in the equations of motion are determined for a model consisting of randomly stacked spheres of different sizes; the interstices of this model contain both gas and liquid. The dissipation coefficients occurring in the equations of motion are determined for a model of short capillary tubes. The nine equations of motion are transformed into rotational and irrotational equations to yield plane, progressive, sinusoidal waves. The wave velocity and the attenuation are derived for the asymptotic cases of very low and very high frequencies. It is proved that there are three types of compressional waves and one type of shear wave. At very low frequencies only one type of compressional wave prevails, and at very high frequencies the dissipation for all four types of waves is proportional to the square root of the frequency.