The reflection and radiation of steep-fronted wavefronts at a tunnel exit to a deep cutting is studied and contrasted with the more usual case of radiation from over-ground portals. A well-known difference between radiation in odd and even dimensions is shown to have a significant influence on reflected wavefronts, notably causing increased distortion that complicates analyses, but that can have practical advantages when rapid changes are undesirable. Likewise, micro-pressure waves radiating from the portal into a cutting are shown to exhibit strong dispersion that does not occur in the corresponding radiation into an open terrain. In the latter case, formulae that represent the behaviour of monopoles and dipoles are commonly used to estimate conditions beyond tunnel portals, but no such simple formula exists (or is even possible) for cylindrical radiation that is characteristic of MPWs in cuttings. An important outcome of the paper is the development of an approximate relationship that predicts the maximum amplitudes of these MPWs with an accuracy that should be acceptable in engineering design, at least for initial purposes. The formula shows that peak pressure amplitudes decay much more slowly than those from an overground portal, namely varying approximately as r ^−0.5 compared with r ⁻¹, where r denotes the distance from the portal.

中文翻译：

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深部岩屑隧道洞口的微压波辐射

研究了隧道出口到深切削处的陡波前波前的反射和辐射，并与更常见的地面入口处的辐射情况进行了对比。众所周知，奇数维和偶数维辐射之间的差异对反射波前有显着影响，尤其会导致失真增加，使分析复杂化，但当不希望快速变化时，这可能具有实际优势。同样，从入口辐射到切割中的微压力波显示出强烈的色散，这在相应的辐射到开阔地形中不会发生。在后一种情况下，表示单极子和偶极子行为的公式通常用于估计隧道入口以外的条件，但是对于作为岩屑中 MPW 特征的柱面辐射，不存在（甚至不可能）这样简单的公式。该论文的一个重要成果是开发了一种近似关系，该关系可以预测这些 MPW 的最大幅度，其精度在工程设计中应该是可以接受的，至少对于初始目的而言。该公式表明，峰值压力幅度的衰减比来自地面入口的要慢得多，即大致变化为r ^-0.5与r ^-1相比，其中r表示与门户的距离。