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Scattering problems for a rectangular crack in a saturated porous material: application of the Chebyshev's functions
Waves in Random and Complex Media ( IF 4.051 ) Pub Date : 2021-03-08 , DOI: 10.1080/17455030.2021.1895453
Yongjia Song 1, 2 , Hengshan Hu 1 , Jun Wang 1 , Yongxin Gao 3
Affiliation  

Analytic solutions are derived for the problem of scattering of obliquely incident plane waves from a rectangular crack in a fluid-saturated porous solid. The propagation direction and polarization direction of the incident waves can be arbitrary. The solutions are based on expanding the crack opening displacements in terms of Chebyshev functions. Explicit expressions for the frequency-dependent stress intensity factors and scattering far fields are obtained. The poroelastic effects play a key role in determining the crack opening mode by changing the effective normal stress applied on the crack surfaces. Consequently, the dynamic responses of the crack can be quite different from those of conventional dry crack in an elastic solid. The effects of scattered slow-P waves as well as wave-induced crack fluid pressure on the dynamic stress intensity factors are clarified, and a corner effect is observed in the scattering patterns for moderately high frequencies. The comparisons of synthetic seismograms with the elastic model show the slow-P waves can cause significant energy loss and waveform change. This study can be used for fracture analysis of porous media and nondestructive testing for individual hydraulic fractures in reservoirs.



中文翻译:

饱和多孔材料中矩形裂纹的散射问题:切比雪夫函数的应用

推导了流体饱和多孔固体中矩形裂纹中倾斜入射平面波的散射问题的解析解。入射波的传播方向和偏振方向可以是任意的。该解决方案基于根据切比雪夫函数扩展裂纹张开位移。获得了频率相关应力强度因子和散射远场的显式表达式。孔隙弹性效应通过改变施加在裂纹表面上的有效法向应力,在确定裂纹张开模式方面发挥着关键作用。因此,裂纹的动态响应可能与弹性固体中传统干裂纹的动态响应有很大不同。阐明了散射慢 P 波以及波引起的裂纹流体压力对动应力强度因子的影响,并且在中等高频的散射图案中观察到角效应。合成地震图与弹性模型的比较表明,慢P波会导致显着的能量损失和波形变化。该研究可用于多孔介质的裂缝分析和储层中单个水力裂缝的无损检测。

更新日期:2021-03-08
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