The spectral boundary integral (SBI) method has been widely employed in the study of fractures and friction within elastic and elastodynamic media, given its natural applicability to thin or infinitesimal interfaces. Many such interfaces and layers are also prevalent in porous, fluid-filled media. In this work, we introduce analytical SBI equations for cracks and thin layers in a 3D medium, with a particular focus on fluid presence within these interfaces or layers. We present three distinct solutions, each based on different assumptions: arbitrary pressure boundary conditions, arbitrary flux boundary conditions, or a bi-linear pressure profile within the layer. The bi-linear pressure solution models the flux through a thin, potentially pressurized, leaky layer. We highlight conditions under which the bi-linear SBI equations simplify to either the arbitrary flux or arbitrary pressure SBI equations, contingent on a specific non-dimensional parameter. We then delve into the in-plane pressure effects arising from a shear crack in a poroelastic solid. While such pressurization has been suggested to influence frictional strength in various ways and only occurs in mode II sliding, our findings indicate that a significant portion of the crack face is affected in 3D scenarios. Additionally, we investigate non-dimensional timescales governing the potential migration of this pressurization beyond the crack tip, which could induce strength alterations beyond the initially ruptured area.

中文翻译：

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时域和波数域中 3D 多孔弹性固体中裂纹和薄流体填充层的解析边界积分解

谱边界积分 (SBI) 方法因其自然适用于薄界面或无穷小界面而被广泛应用于弹性和弹性动力介质内的断裂和摩擦研究。许多这样的界面和层也普遍存在于多孔、充满流体的介质中。在这项工作中，我们引入了 3D 介质中裂纹和薄层的解析 SBI 方程，特别关注这些界面或层内的流体存在。我们提出了三种不同的解决方案，每种解决方案都基于不同的假设：任意压力边界条件、任意通量边界条件或层内的双线性压力分布。双线性压力解对通过潜在加压泄漏薄层的通量进行建模。我们重点介绍双线性 SBI 方程简化为任意通量或任意压力 SBI 方程的条件，具体取决于特定的无量纲参数。然后，我们深入研究多孔弹性固体中剪切裂纹引起的面内压力效应。虽然这种加压被认为会以各种方式影响摩擦强度，并且仅发生在 II 型滑动中，但我们的研究结果表明，裂纹面的很大一部分在 3D 场景中受到影响。此外，我们还研究了控制压力超出裂纹尖端的潜在迁移的无量纲时间尺度，这可能导致超出初始破裂区域的强度变化。