双重孔隙介质中P1波在自由边界上的反射

doi:10.16285/j.rsm.2016.06.028

›› 2016, Vol. 37 ›› Issue (6): 1753-1761.doi: 10.16285/j.rsm.2016.06.028

双重孔隙介质中P1波在自由边界上的反射

贺鹏飞^{1, 2}，夏唐代^{1, 2}，刘志军^{1, 2}，陈炜昀³

1. 浙江大学软弱土与环境土工教育部重点实验室，浙江杭州 310058；2. 浙江大学滨海与城市岩土工程研究中心，浙江杭州 310058； 3. 南京工业大学岩土工程研究所，江苏南京 210009

收稿日期:2014-11-24 出版日期:2016-06-13 发布日期:2018-06-09
通讯作者: 夏唐代，男，1965年生，博士，教授，博导，主要从事土动力学研究。E-mail: xtd@zju.edu.cn E-mail: perfect@zju.edu.cn
作者简介:贺鹏飞，男，1986年生，硕士研究生，主要是多孔介质波动理论研究。
基金资助:
国家自然科学基金资助（No.U1234204，No.51378463）。

Reflection of P1 wave from free surfaces of double-porosity media

HE Peng-fei^{1, 2}, XIA Tang-dai^{1, 2}, LIU Zhi-jun^{1, 2}, CHEN Wei-yun³

1. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University, Hangzhou, Zhejiang 310058, China; 2. Research Center of Costal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, Zhejiang 310058, China; 3. Institute of Geotechnical Engineering, Nanjing Tech University, Nanjing, Jiangsu 210009, China

Received:2014-11-24 Online:2016-06-13 Published:2018-06-09
Supported by:
This work was supported by the National Natural Science Foundation of China (U1234204, 51378463).

摘要/Abstract

摘要： 对双重孔隙介质波动中的体波及P1波在半空间自由透水和不透水边界上的反射问题进行了详细的理论求解。通过数值计算，对双重孔隙介质中4种体波的弥散和衰减特性，以及不同边界上反射波振幅反射系数随P1波入射角和频率的变化进行了分析。结果表明：（1）P1、P2、P3和S波均具有弥散和衰减特性，P1波传播最快而衰减最慢，P3波传播最慢而衰减最快；（2）随着入射角的增大，反射P2、P3和S波的振幅反射系数均先增大后减小，反射P1波则先减小后增大，且边界透水条件对反射P2和P3波的振幅反射系数影响显著，对P1和S波的影响较小，但透水和不透水边界下振幅反射系数随入射角的变化趋势一致；（3）反射P2、P3波的振幅反射系数均随频率的增大而增大，且不透水边界下反射P2波的振幅反射系数大于透水边界下的反射系数，而反射P3波则相反；（4）随着频率增大，透水边界下反射P1波的振幅反射系数先增大后减小，不透水边界下先减小后增大再减小，反射S波的振幅反射系数随频率变化情况则与P1波相反。

关键词: 双重孔隙介质, P1波, 自由边界, 入射角, 频率, 振幅反射系数

Abstract: The bulk waves in double-porosity media and the reflection of P1 wave at the free permeable and impermeable surfaces are theoretically derived and solved. The variations of the amplitude reflection coefficients of the reflecting waves with incident angle and frequency under different surface boundaries, as well as the dispersion and attenuation characteristics of the four kinds of bulk waves, are numerically studied. The results show that: (1) P1, P2, P3 and S waves all show dispersion and attenuation characteristics. Therein, P1 wave propagates fastest with lowest attenuation, and P3 wave attenuates fastest with lowest propagation velocity. (2) As the incident angle of P1 wave increases, the amplitude reflection coefficients of the reflecting P2, P3 and S waves increase at first then decrease, but the case of the reflecting P1 wave is just opposite. Moreover, the permeability of the surface has distinctive effect on the amplitude reflection coefficients of P2 and P3 waves and has slight effect on P1 and S waves. Nevertheless, whether the surface is permeable or impermeable, the changing tendency of the amplitude reflection coefficients is consistent. (3) The amplitude reflection coefficients of the reflecting P2 and P3 waves grow as frequency increases. In contrast with the reflecting P3 wave, for the reflecting P2 wave, the amplitude reflection coefficient in the case of free impermeable surface is larger than that in the case of free permeable surface. (4) For the reflecting P1 wave, with the increase of frequency, the amplitude reflection coefficient in the case of free permeable boundary increases firstly and then decreases, but fluctuates (decrease-increase-decrease) in the case of free impermeable surface. The amplitude reflection coefficients of the reflecting S wave just vary oppositely with the reflecting P1 wave.

Key words: double-porosity media, P1 wave, free surfaces, incident angle, frequency, amplitude reflection coefficients

中图分类号:

TU 435

贺鹏飞，夏唐代，刘志军，陈炜昀，. 双重孔隙介质中P1波在自由边界上的反射[J]. , 2016, 37(6): 1753-1761.

HE Peng-fei, XIA Tang-dai, LIU Zhi-jun, CHEN Wei-yun，. Reflection of P1 wave from free surfaces of double-porosity media[J]. , 2016, 37(6): 1753-1761.

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双重孔隙介质中P1波在自由边界上的反射

Reflection of P1 wave from free surfaces of double-porosity media

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