Rayleigh波在饱和半空间中圆形洞室周围的散射

doi:10.16285/j.rsm.2017.08.031

›› 2017, Vol. 38 ›› Issue (8): 2411-2425.doi: 10.16285/j.rsm.2017.08.031

Rayleigh波在饱和半空间中圆形洞室周围的散射

徐颖^{1, 2}，梁建文^{1, 2}，刘中宪³

1. 天津大学建筑工程学院，天津 300072；2. 天津大学天津市土木工程结构及新材料重点实验室，天津 300072； 3. 天津城建大学天津市软土特性与工程环境重点实验室，天津 300384

收稿日期:2015-09-08 出版日期:2017-08-11 发布日期:2018-06-05
通讯作者: 梁建文，男，1965年生，教授，博导，主要从事地震工程方面研究工作。E-mail: liang@tju.edu.cn E-mail: yingxu_civil@tju.edu.cn
作者简介:徐颖，女，1987年生，博士，主要从事钢结构及地震工程方面研究工作。
基金资助:
国家自然科学基金项目（No. 51378348）

Diffraction of Rayleigh waves around a circular cavity in poroelastic half-space

XU Ying^{1, 2}, LIANG Jian-wen^{1, 2}, LIU Zhong-xian³

1. School of Civil Engineering, Tianjin University, Tianjin 300072, China; 2. Tianjin Key Laboratory of Civil Engineering Structures and New Materials, Tianjin University, Tianjin 300072, China; 3. Key Laboratory of Tianjin Soft Soil Character and Engineering Environment, Tianjin Chengjian University, Tianjin 300384, China

Received:2015-09-08 Online:2017-08-11 Published:2018-06-05
Supported by:
This work was supported by the National Natural Science Foundation of China (51378348).

摘要/Abstract

摘要： 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。

关键词: 饱和半空间, 圆形洞室, 散射, Rayleigh波, 间接边界积分方程法

Abstract: In this paper, the diffraction of Rayleigh waves around a circular cavity in poroelastic half-space was investigated by indirect boundary integral equation method based on the Biot’s two-phase medium theory. The impacts of incident wave frequencies, porosities, drainage boundary conditions and depths of cavity on the displacement and pore pressure responses were discussed in detail. The results show that the existence of circular cavity amplifies the surface displacement and pore pressure in poroelastic half-space. The peak values of horizontal and vertical surface displacement were enlarged by 10.1 times and 11.2 times respectively for drained boundary, and enlarged by 12.0 times and 9.6 times respectively for undrained boundary. The peak value of surface pore pressure increases by 2.1 to 3.0 times compared with the free field responses. The peak values of displacement and pore pressure responses were both found at the cavity boundary close to the incident wave. With the increase of incident wave frequency or cavity depth, the amplification effect was weakened. The maximum pore pressure around cavity was found at the top of the cavity. For constant porosity, the pore pressure around cavity will reach the highest level when the incident frequency is 1.0 and reach the lowest level when the incident frequency is 2.0.

Key words: poroelastic half-space, circular cavity, diffraction, Rayleigh waves, indirect boundary integration equation method

中图分类号:

P 315.9

徐颖，梁建文，刘中宪,. Rayleigh波在饱和半空间中圆形洞室周围的散射[J]. , 2017, 38(8): 2411-2425.

XU Ying, LIANG Jian-wen, LIU Zhong-xian,. Diffraction of Rayleigh waves around a circular cavity in poroelastic half-space[J]. , 2017, 38(8): 2411-2425.

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Rayleigh波在饱和半空间中圆形洞室周围的散射

Diffraction of Rayleigh waves around a circular cavity in poroelastic half-space

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