平面P1波斜入射下海底洞室地震响应解析分析

基于无黏性可压缩理想流体介质波动理论和Biot流体饱和多孔介质波动理论,考虑水下饱和土的流固耦合,借助Hankel函数积分变换法(HFITM)给出入射平面P1波在海底洞室周围散射问题的解析解。相比传统研究中的"大圆弧假定",Hankel函数积分变换法可以较好地处理半空间表面边界条件。利用该解析解,计算分析了洞室表面透水条件、入射角度、入射频率、海水水深和饱和土的孔隙率等因素对水-土交界面处水平位移、竖向位移和洞室表面动水压力、环周总应力的影响。结果表明:洞室表面透水条件对水-土交界面处水平位移和竖向位移影响较小;随着斜入射角的增加,水-土交界面处竖向位移减小;随着入射频率的增加,水-土交界面处水平位移随之增加;海水水深为2.5倍SV波的波长时,水-土交界面处水平位移及洞室表面动水压力最大值最大;随着孔隙率的增加,水-土交界面处水平位移、竖向位移和洞室表面环周总应力减小,而洞室表面动水压力随之增加。

Analytical solution of seismic response of an undersea cavity under incident P_1-wave

Based on the wave propagation theory of saturated porous medium proposed by Biot and wave propagation theory of inviscid compressible ideal fluid, considering the fluid-mechanical coupling of underwater saturated soil, an analytical solution of the scattering problem of the incident plane P1-wave around the undersea cavity is presented using the Hankel function integral transformation method(HFITM). Compared with the "large arc hypothesis" in traditional research, the HFITM can better deal with the surface boundary of the half space. Using the analytical solution, the effects of permeability conditions of the cavity, incident angle, incident frequency, seawater depth and the porosity of saturated soil on the displacement(horizontal and vertical displacement) of the interface between water and saturated soil and the stress(hydrodynamic pressure and total circumferential stress) on the surface of the cavity. The results show that the permeability conditions on the surface of the cavity have a small effect on the displacement of the interface between water and saturated soil;as the oblique incident angle increases, the vertical displacement on the interface between the ideal water and saturated soil decreases;the horizontal displacement of the interface between water and saturated soil increases as the incident frequency increases;when the depth of seawater is 2.5 times the wavelength of the SV-wave, the maximum horizontal displacement on the interface between water and saturated soil and hydrodynamic pressure on the surface of the cavity are the largest;the displacement of the interface between water and saturated soil and the total circumferential stress on the surface of the cavity decrease with the increasing porosity, while the hydrodynamic pressure on the surface of the cavity increases.