Cylindrical micro-pressure wave radiation from tunnel portals in deep cuttings

In high-speed railways, micro-pressure waves (MPWs) emitted from tunnel portals can cause significant problems. An MPW is typically a spherical wave. However, in infinitely deep cuttings, an MPW becomes a cylindrical wave and affects larger areas. In this study, the cylindrical MPWs emitted toward infinitely deep cuttings were analytically and numerically investigated. Analytical expressions were introduced, and a far-field approximation using the half-derivative of velocity at the tunnel exit was demonstrated. The analytical solutions agreed with the results of computational fluid dynamics. Finally, the strength of the main source term was demonstrated to be approximately proportional to Δpin(∂pin/∂t)max where pin is the pressure of the compression wave at the tunnel exit, and a linear formula is shown for engineering estimations.