三维弹性半空间中圆弧形沉积谷地对弹性波的散射
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摘要
众所周知,历史上多次地震灾害给人民的生命安全和物质财产造成了巨大的损失。通过对震后灾情的考察,局部场地地形对于地震动,即场地反应有着重大的影响。因此,局部场地反应问题,一直是地震工程学界近年来研究的热点问题之一。
随着科学技术的发展,特别是计算机技术的发展,为人们从理论分析角度对局部场地反应问题进行研究提供了许多便利条件。沉积谷地形是工程中常见的局部场地类型,对这类场地的场地反应的研究,一直倍受科研人员的关注。随着研究的不断深入,对于沉积谷地形的场地反应的研究取得了一定的成果,但在这些成果中,多数是基于二维平面假设的情况下得到的,这对于全面认识沉积谷场地对于地震波传播的影响具有一定的局限性。
作为对前人研究成果的深入和补充,本文采用Fourier-Bessel级数展开技术和有限项Fourier级数展开技术,并将大圆弧假定拓展为大圆弧面假定来模拟半空间表面,从而将沉积谷地形对P波、SV波和Rayleigh波的散射的解析解,由二维拓展为三维。为进一步认识和研究地震波对沉积谷地形场地反应的影响奠定基础。
本文以上述研究工作为基础,在求得解析解的条件下,深入分析了利用级数展开法进行求解的精度问题,并从入射波的自身性质和沉积谷场地的性质出发,较为全面的分析了三维条件下P波、SV波和Rayleigh波对沉积谷地形场地反应的影响。研究表明,沉积谷地形对于地震波的放大效应与入射波的频率和入射角度密切相关,入射波频率较高和一些特定的入射角度,沉积谷地形对地震波的放大作用会比较明显;沉积谷地形弧深变化对地震波的放大作用影响比较大,也比较复杂,在不同的入射角度下,浅弧和深弧均有可能使地表位移放大较多;沉积介质的性质对沉积谷地形场地反应影响显著,一般来说,在各入射角度下,沉积介质的刚度相对于半空间介质刚度越小时,沉积谷地形对于地震波的放大作用越明显。
As we all have known, many earthquake hazards in history had brought tremendous losses to the safety of people's lives and property. Through the post-earthquake disaster investigations, the types of local sites have quite an effect on the surface motions of the local sites, which may be called the response of site. Therefore, the problem of the response of local venues has been a hot issue in earthquake engineering academics in recent years.
With developments of Science and technology, especially the development of computer technology, the advanced technologies provide people many convenient conditions to study the issue of local venue response from the perspective of theoretical analysis. The response of alluvial valley site which is a common type of local venues, have been paid much attention by the researchers. With the study continuously deepening, some results of response of the alluvial valley sites have been achieved. But the most of these results are based on the assumption that two-dimensional plane conditions are concerned. So it has contained limitations for us to comprehensively understand the effects that sedimentary Valley venues have on the propagation of seismic waves.
As the supplementary and expansion of previous Research results, In this paper, through using Fourier - Bessel series expansion methods and expanding the assumption from the large circular to the circular surface to simulate half-space surface, we expand analytical solutions of scattering of the P-waves, SV-waves and Rayleigh-waves on alluvial valley sites from 2D to 3D to lay the foundation of further understanding and studying the effects that alluvial valley sites have on the propagation of seismic waves.
in this paper, Based on the above studies, under the conditions of obtained the analytical solutions, the problem of accuracy of using method of series expansion to solve the issue is deeply analyzed and from the natures of the incident waves and the natures of alluvial valley sites, a more comprehensive analysis of effects that alluvial valley sites have on P-wave, SV-waves and Rayleigh-waves are made. Studies show that the amplification of the seismic waves by alluvial valley sites is closely related with the frequency and incidence angle of incident waves. The amplification of the seismic waves by alluvial valley sites is more obvious for relatively high frequency or some specific incidence angle of incident waves. The changes of the arc depth of alluvial valley have a major impact on the amplification of seismic waves by alluvial valley sites, and the effect is also complex. In different incidence angle of incident waves, the amplification of surface displacements may be more either in deep arc or in shallow arc. The nature of medium in alluvial valley has obvious effect on the surface motions of alluvial valley sites. In generally speaking, the stiffness of the deposition medium compared to the stiffness of half-space medium is the smaller, the amplification of seismic waves by alluvial valley sites is the more obvious.
随着科学技术的发展,特别是计算机技术的发展,为人们从理论分析角度对局部场地反应问题进行研究提供了许多便利条件。沉积谷地形是工程中常见的局部场地类型,对这类场地的场地反应的研究,一直倍受科研人员的关注。随着研究的不断深入,对于沉积谷地形的场地反应的研究取得了一定的成果,但在这些成果中,多数是基于二维平面假设的情况下得到的,这对于全面认识沉积谷场地对于地震波传播的影响具有一定的局限性。
作为对前人研究成果的深入和补充,本文采用Fourier-Bessel级数展开技术和有限项Fourier级数展开技术,并将大圆弧假定拓展为大圆弧面假定来模拟半空间表面,从而将沉积谷地形对P波、SV波和Rayleigh波的散射的解析解,由二维拓展为三维。为进一步认识和研究地震波对沉积谷地形场地反应的影响奠定基础。
本文以上述研究工作为基础,在求得解析解的条件下,深入分析了利用级数展开法进行求解的精度问题,并从入射波的自身性质和沉积谷场地的性质出发,较为全面的分析了三维条件下P波、SV波和Rayleigh波对沉积谷地形场地反应的影响。研究表明,沉积谷地形对于地震波的放大效应与入射波的频率和入射角度密切相关,入射波频率较高和一些特定的入射角度,沉积谷地形对地震波的放大作用会比较明显;沉积谷地形弧深变化对地震波的放大作用影响比较大,也比较复杂,在不同的入射角度下,浅弧和深弧均有可能使地表位移放大较多;沉积介质的性质对沉积谷地形场地反应影响显著,一般来说,在各入射角度下,沉积介质的刚度相对于半空间介质刚度越小时,沉积谷地形对于地震波的放大作用越明显。
As we all have known, many earthquake hazards in history had brought tremendous losses to the safety of people's lives and property. Through the post-earthquake disaster investigations, the types of local sites have quite an effect on the surface motions of the local sites, which may be called the response of site. Therefore, the problem of the response of local venues has been a hot issue in earthquake engineering academics in recent years.
With developments of Science and technology, especially the development of computer technology, the advanced technologies provide people many convenient conditions to study the issue of local venue response from the perspective of theoretical analysis. The response of alluvial valley site which is a common type of local venues, have been paid much attention by the researchers. With the study continuously deepening, some results of response of the alluvial valley sites have been achieved. But the most of these results are based on the assumption that two-dimensional plane conditions are concerned. So it has contained limitations for us to comprehensively understand the effects that sedimentary Valley venues have on the propagation of seismic waves.
As the supplementary and expansion of previous Research results, In this paper, through using Fourier - Bessel series expansion methods and expanding the assumption from the large circular to the circular surface to simulate half-space surface, we expand analytical solutions of scattering of the P-waves, SV-waves and Rayleigh-waves on alluvial valley sites from 2D to 3D to lay the foundation of further understanding and studying the effects that alluvial valley sites have on the propagation of seismic waves.
in this paper, Based on the above studies, under the conditions of obtained the analytical solutions, the problem of accuracy of using method of series expansion to solve the issue is deeply analyzed and from the natures of the incident waves and the natures of alluvial valley sites, a more comprehensive analysis of effects that alluvial valley sites have on P-wave, SV-waves and Rayleigh-waves are made. Studies show that the amplification of the seismic waves by alluvial valley sites is closely related with the frequency and incidence angle of incident waves. The amplification of the seismic waves by alluvial valley sites is more obvious for relatively high frequency or some specific incidence angle of incident waves. The changes of the arc depth of alluvial valley have a major impact on the amplification of seismic waves by alluvial valley sites, and the effect is also complex. In different incidence angle of incident waves, the amplification of surface displacements may be more either in deep arc or in shallow arc. The nature of medium in alluvial valley has obvious effect on the surface motions of alluvial valley sites. In generally speaking, the stiffness of the deposition medium compared to the stiffness of half-space medium is the smaller, the amplification of seismic waves by alluvial valley sites is the more obvious.
引文
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