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基于Biot的两相介质理论,采用间接边界积分方程法,求解了Rayleigh波在饱和半空间中圆形洞室周围的二维散射问题,分析了入射波频率、孔隙率、边界渗透条件和洞室埋深等参数对地表位移幅值、洞室表面和地表孔隙水压力的影响。研究结果表明,由于圆形洞室的存在,饱和半空间地表位移幅值和地表孔隙水压被明显放大:在透水条件下,水平和竖向位移最大值分别比自由场放大了10.1倍和11.2倍;在不透水条件下,水平和竖向位移最大值分别比自由场放大了12.0倍和9.6倍,地表孔隙水压力放大了2.1~3.0倍。地表位移和孔隙水压力最大值均出现在入射波近端洞室边界附近。随着Rayleigh波入射频率的增大和洞室埋深的增加,地表位移幅值的放大作用有所减小。在相同孔隙率条件下,当入射频率为1.0时,洞室表面孔隙水压力最大;当入射频率为2.0时,洞室表面孔隙水压力最小,洞室表面最大孔隙水压力出现在洞室顶部。
Based on Biot’s theory of two-phase medium, the two-dimensional scattering problem of Rayleigh wave around a circular cavity in a saturated half-space is solved by the indirect boundary integral equation method. The effects of incident wave frequency, porosity, Depth and other parameters on the surface displacement amplitude, surface pressure and surface pore water pressure. The results show that the amplitude of surface displacement and the pore water pressure in saturated half-space are obviously magnified due to the existence of circular cavern: under the condition of water permeation, the maximum horizontal and vertical displacements are respectively 10.1 times and 11.2 times larger than the free field Times. Under impervious conditions, the maximum horizontal and vertical displacements were 12.0 times and 9.6 times larger than the free field and the surface pore water pressure was 2.1-3.0 times larger than the free field. The maximum of surface displacement and pore water pressure appears near the boundary of the cavern near the incident wave. With the increase of incident frequency of Rayleigh wave and the increase of burial depth, the amplifying effect of the amplitude of surface displacement is reduced. Under the same porosity, the pore water pressure is the largest when the incident frequency is 1.0. When the incident frequency is 2.0, the pore water pressure on the surface of the cavity is the smallest, and the maximum pore water pressure on the surface of the cavity appears on the top of the cavity.