弹性波在准饱和土和弹性土界面的反射与透射
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摘要
考虑土颗粒和孔隙流体的压缩性,根据准饱和土体的变形连续条件和平衡条件,推导了P1波(快压缩波)、P2波(慢压缩波)和S波的计算公式．根据Snell定理,研究了平面P1波从准饱和土体入射到弹性土层时在界面上的反射和透射,并绘制了反射系数、透射系数和界面应力、位移随入射角的变化曲线,结果表明:饱和度是影响界面效应的一个重要因素,当饱和度低于99％时,反射和透射系数以及应力和位移基本相等,变化不大,但当饱和度为100％时,虽然饱和度比99％提高了1％,但反射和透射系数以及应力和位移值比饱和度为99％时明显降低．
The calculation formulas for the wave velocities of P1 wave (fast compressional wave), P2 wave (slow compressional wave) and S wave were derived from continuity of deformation and equilibrium conditions and considering the compression of soil grains and pore fluid. According to Snell theorem, the reflection and transmission of incident plane P1 wave from the nearly saturated soil at the interface of elastic soil was studied, and curves of reflection coefficients, transmission coefficients, stresses and displacements of the interface were numerically obtained. The results show that the saturated degree is an important factor that affects the reflection and transmission. The reflection coefficients, transmission coefficients, stresses and displacements change little when the saturated degree increases by 4% from 95% to 99%, but they change obviously when the saturated degree increases by only 1% from 99% to 100%.
The calculation formulas for the wave velocities of P1 wave (fast compressional wave), P2 wave (slow compressional wave) and S wave were derived from continuity of deformation and equilibrium conditions and considering the compression of soil grains and pore fluid. According to Snell theorem, the reflection and transmission of incident plane P1 wave from the nearly saturated soil at the interface of elastic soil was studied, and curves of reflection coefficients, transmission coefficients, stresses and displacements of the interface were numerically obtained. The results show that the saturated degree is an important factor that affects the reflection and transmission. The reflection coefficients, transmission coefficients, stresses and displacements change little when the saturated degree increases by 4% from 95% to 99%, but they change obviously when the saturated degree increases by only 1% from 99% to 100%.
引文
1 Biot MA. Mechanics of propagation of elastic waves in a fluid-saturated porous solid. J Acoust Soc Am, 1956, 28(2): 168~191
2 Hajra S, Mukhopodhyay A. Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid saturated porous solid. Bull seism soc America, 1982, 72: 1509~1533
3吴昆裕,薛强．弹性波在两种流体饱和多孔介质界面上的反射和透射．中国科学技术大学学报, 1992,22(1):44~50(Wu Kunyu, Xue Qiang. Reflection and transmission of elastic waves at the interface of two fluid-saturated porous media. Journal of China University of Science and Technology, 1992, 22(1): 44~50 (in Chinese))
4杨峻,吴世明．地震波在饱和土层面的反射与透射．地震学报, 1997, 10(1): 29~35 (Yang Jun, Wu Shiming. Reflection and transmission of seismic wave at the interfaces of saturated soils. Acta Seismologica Sinica, 1997, 10(1): 29~35 (in Chinese))
5胡亚元,王立忠,陈云敏等．弹性波在横向各向同性弹性土和饱和土界面上的反射与透射．地震学报,1998,20(6):598~606(Hu Yayuan, Wang Lizhong, Chen Yunmin, et al. Reflection and transmission of elastic at the interface of transversely isotropic elastic soils and saturated soils. Acta Seismologica Sinica, 1998, 20(6): 598~606 (in Chinese))
6赵成刚,高福平,崔杰．波在饱和多孔介质与弹性固体介质交界面上界面效应,地震工程与工程振动, 1999,19(1):1—6 (Zhao Chenggang, Gao Fuping, Cui Jie. Boundary effect of wave propagation from liquid-filled porous medium to solid medium. Earthquake Engineering and Engineering Vibration, 1999, 19(1): 1~6 (in Chinese))
7叶陈江,史焱永,蔡袁强．S波由饱和土入射弹性土时在界面上的反射与透射．振动与冲击,2005,24(2):41~45(Ye Chenjiang, Shi Yanyong, Cai Yuanqiang. Reflection and transmission of incident S wave at the interface from saturated soils to elastic soils. Journal of Vibration and Shock, 2005, 24(2): 41~45 (in Chinese))
8李伟华．饱和度对波在土层交界面的反射,透射系数的影响．西北地震学报,2002,24(4):303~306(Li Weihua．Influence of water saturation on seismic reflection and transmission coefficients at a mainly water-saturated porous soil interface. Northwestern Seismological Journal, 2002, 24(4): 303~306 (in Chinese))
9薛松涛,陈诗惹,陈镕等．P1波入射准饱和土的波型转换问题．力学季刊,2005,26(1):128~133(Xue Songtao,Chen Shihui, Chen Rong, et al. Analysis on wave mode conversion of Incident P1 wave in nearly saturated soil. Chinese Quarterly of Mechanics, 2005, 26(1): 128~133 (in Chinese))
10 Vardoulakis I, Beskos D E. Dynamic behavior of nearly saturated porous media. Mechanics of Materials, 1986, 5: 87~108
11吴世明．土介质中的波．北京:科学出版社, 1997．62~65 (Wu Shiming. Wave Propagation in Soils. Beijing: Science Press, 1997. 62~65 (in Chinese))
12杨桂通,张善元．弹性动力学．北京:中国铁道出版社, 1988．110~117 (Yang Guitong, Zhang Shanyuan. Elastic Dynamics. Beijing: China Railway Press, 1988. 148~149 (in Chinese))
2 Hajra S, Mukhopodhyay A. Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid saturated porous solid. Bull seism soc America, 1982, 72: 1509~1533
3吴昆裕,薛强．弹性波在两种流体饱和多孔介质界面上的反射和透射．中国科学技术大学学报, 1992,22(1):44~50(Wu Kunyu, Xue Qiang. Reflection and transmission of elastic waves at the interface of two fluid-saturated porous media. Journal of China University of Science and Technology, 1992, 22(1): 44~50 (in Chinese))
4杨峻,吴世明．地震波在饱和土层面的反射与透射．地震学报, 1997, 10(1): 29~35 (Yang Jun, Wu Shiming. Reflection and transmission of seismic wave at the interfaces of saturated soils. Acta Seismologica Sinica, 1997, 10(1): 29~35 (in Chinese))
5胡亚元,王立忠,陈云敏等．弹性波在横向各向同性弹性土和饱和土界面上的反射与透射．地震学报,1998,20(6):598~606(Hu Yayuan, Wang Lizhong, Chen Yunmin, et al. Reflection and transmission of elastic at the interface of transversely isotropic elastic soils and saturated soils. Acta Seismologica Sinica, 1998, 20(6): 598~606 (in Chinese))
6赵成刚,高福平,崔杰．波在饱和多孔介质与弹性固体介质交界面上界面效应,地震工程与工程振动, 1999,19(1):1—6 (Zhao Chenggang, Gao Fuping, Cui Jie. Boundary effect of wave propagation from liquid-filled porous medium to solid medium. Earthquake Engineering and Engineering Vibration, 1999, 19(1): 1~6 (in Chinese))
7叶陈江,史焱永,蔡袁强．S波由饱和土入射弹性土时在界面上的反射与透射．振动与冲击,2005,24(2):41~45(Ye Chenjiang, Shi Yanyong, Cai Yuanqiang. Reflection and transmission of incident S wave at the interface from saturated soils to elastic soils. Journal of Vibration and Shock, 2005, 24(2): 41~45 (in Chinese))
8李伟华．饱和度对波在土层交界面的反射,透射系数的影响．西北地震学报,2002,24(4):303~306(Li Weihua．Influence of water saturation on seismic reflection and transmission coefficients at a mainly water-saturated porous soil interface. Northwestern Seismological Journal, 2002, 24(4): 303~306 (in Chinese))
9薛松涛,陈诗惹,陈镕等．P1波入射准饱和土的波型转换问题．力学季刊,2005,26(1):128~133(Xue Songtao,Chen Shihui, Chen Rong, et al. Analysis on wave mode conversion of Incident P1 wave in nearly saturated soil. Chinese Quarterly of Mechanics, 2005, 26(1): 128~133 (in Chinese))
10 Vardoulakis I, Beskos D E. Dynamic behavior of nearly saturated porous media. Mechanics of Materials, 1986, 5: 87~108
11吴世明．土介质中的波．北京:科学出版社, 1997．62~65 (Wu Shiming. Wave Propagation in Soils. Beijing: Science Press, 1997. 62~65 (in Chinese))
12杨桂通,张善元．弹性动力学．北京:中国铁道出版社, 1988．110~117 (Yang Guitong, Zhang Shanyuan. Elastic Dynamics. Beijing: China Railway Press, 1988. 148~149 (in Chinese))
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