The Critical Frequency in Biphasic Media: Beyond Biots Approach
The Critical Frequency in Biphasic Media: Beyond Biots Approach
复制标题
双相介质中的临界频率：超越 Biots 方法
DOI：
10.1061/9780784412992.276
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发表时间：
2013
影响因子：
7.4
通讯作者：
J. Renner
中科院分区：
文献类型：
--
作者：
P. Kurzeja;H. Steeb;J. Renner
毕奥的双相介质中波的传播理论对当今的研究及其在工程和地球科学中的应用仍有重大影响。特别地，由毕奥引入的特征频率用于区分粘度主导的低频范围与惯性主导的高频范围。理解这些机制的对比优势范围之间的过渡对于解释实验和新理论的基础至关重要。毕奥得出的特征频率的微观和问题仍然存在关于其正确的转换到宏观尺度。具体而言，由于简化了微尺度上的假设，忽略了三个方面：固体的惯性，固体的弹性，和频率依赖的动量相互作用。这些方面的修正对具有弱固体骨架和不可压缩流体的系统特别重要。然而，对于典型的岩石或土壤系统，忽略这些校正似乎是合理的。进行了实验，其中波传播通过弹性管的不同材料（钢，硅树脂）充满了各种流体（空气，水，Na-聚钨）。这些实验被认为代表了单个孔隙中的微观机制。实验记录和理论预测之间的不匹配表明，在进行可靠的升级之前，需要进一步考虑当前理论处理问题中的一些假设。
Biot's theory for wave propagation in biphasic media is still of great influence on current research and its applications in engineering and geosciences. In particular, the characteristic frequency introduced by Biot is used to distinguish a viscosity-dominated low frequency range from an inertia-dominated high frequency range. An understanding of the transition between these ranges of contrasting dominance of mechanisms is of vital importance for the interpretation of experiments and the basis of new theories. Biot derived the characteristic frequency on the microscale and questions remain regarding its correct transformation to the macroscale. Specifically, three aspects are neglected due to simplifying assumptions on the microscale: inertia of the solid, elasticity of the solid, and a frequency-dependent momentum interaction. Corrections accounting for these aspects are particularly significant for systems with a weak solid skeleton and a rather incompressible fluid. Neglection of these corrections appears however often justified for typical systems of rocks or soils. Experiments were conducted in which waves propagate through elastic tubes of different materials (steel, silicone) filled with various fluids (air, water, Na-Polywolframat). These experiments are supposed to represent the micro-scale mechanisms in single pores. The mismatch between experimental records and theoretical predictions suggests that some of the assumptions made in current theoretical treatments of the problem require further consideration before a reliable upscaling can be undertaken.