基于Rayleigh波理论的地基土动参数反演
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摘要
本文从环境振动的影响出发,基于Rayleigh波理论研究了层状地基土模型的频散曲线、截止频率等特性,利用遗传算法对地基土剪切波速进行了反演,进而得到地基土的其它动参数。
在均匀弹性水平层状介质的波传播分析中,常常采用传递矩阵的方法,本文分别介绍了直角坐标系下的传递矩阵法、柱面坐标系下的传递矩阵法、快速矢量和快速标量算法,以及有限元集成的薄层刚度法；主要针对快速标量法和薄层刚度法,利用Matlab编程计算了地基土模型的频散曲线和截止频率等基本特性,对比了两种方法的优缺点及适用范围。比较发现,薄层刚度法在低频范围计算效果比较好,但快速标量法计算速度较快,二者在高频范围的计算结果差异不大。本文进而采用薄层刚度法,编程计算并分析了环境振动中常见的几种地基土模型(递增型、软夹层)Rayleigh波的频散曲线、截止频率及相速度和波长关系等。
在参数反演方面,本文介绍了阻尼最小二乘法和遗传算法,利用假设的有效相速度-频率频散曲线,通过遗传算法计算了两种典型地基土模型(递增型、软夹层)的剪切波速,利用弹性介质转换关系得到地基土的其它动参数。
Considering the influence of environment vibration, and based on the Rayleigh Wave Theory, the frequency dispersion curves, cut-off frequency and some other characteristics of layered soil models are calculated, the shear wave velocities of foundation soil are inverted through genetic algorithm and some other parameters of foundation soil are obtained.
The transfer matrix method is often used in the analysis of wave propagation in homogeneously elastic medium with horizontal multilayer. Some analytical methods are introduced, such as transfer matrix method in rectangular coordinate system and fast vector and fast scalar algorithm in cylindrical coordinate, thin-layer method with stiffer matrix and so on.
The Rayleigh dispersion curves of multilayered soil are calculated by means of thin-layer method and fast scalar method, respectively, in which two-layered and three-layered soil model are adopted. In addition, the disperse properties of multilayered soil are analyzed, and it is found that the thin layer method is superior to rapid scalar method in low frequency domain, while in the high frequency domain it has little difference between each other. The Rayleigh wave's properties of four multilayer soil models are compared by means of thin-layer method particularly.
In the dynamic parameters inversion of foundation soil, by means of the genetic algorithm, the shear wave velocities for two common soil models are calculated based on the effective phase velocity-frequency dispersion curve, and then other parameters of multilayer foundation soil are acquired by the transformation relationship between the media's parameters.
在均匀弹性水平层状介质的波传播分析中,常常采用传递矩阵的方法,本文分别介绍了直角坐标系下的传递矩阵法、柱面坐标系下的传递矩阵法、快速矢量和快速标量算法,以及有限元集成的薄层刚度法；主要针对快速标量法和薄层刚度法,利用Matlab编程计算了地基土模型的频散曲线和截止频率等基本特性,对比了两种方法的优缺点及适用范围。比较发现,薄层刚度法在低频范围计算效果比较好,但快速标量法计算速度较快,二者在高频范围的计算结果差异不大。本文进而采用薄层刚度法,编程计算并分析了环境振动中常见的几种地基土模型(递增型、软夹层)Rayleigh波的频散曲线、截止频率及相速度和波长关系等。
在参数反演方面,本文介绍了阻尼最小二乘法和遗传算法,利用假设的有效相速度-频率频散曲线,通过遗传算法计算了两种典型地基土模型(递增型、软夹层)的剪切波速,利用弹性介质转换关系得到地基土的其它动参数。
Considering the influence of environment vibration, and based on the Rayleigh Wave Theory, the frequency dispersion curves, cut-off frequency and some other characteristics of layered soil models are calculated, the shear wave velocities of foundation soil are inverted through genetic algorithm and some other parameters of foundation soil are obtained.
The transfer matrix method is often used in the analysis of wave propagation in homogeneously elastic medium with horizontal multilayer. Some analytical methods are introduced, such as transfer matrix method in rectangular coordinate system and fast vector and fast scalar algorithm in cylindrical coordinate, thin-layer method with stiffer matrix and so on.
The Rayleigh dispersion curves of multilayered soil are calculated by means of thin-layer method and fast scalar method, respectively, in which two-layered and three-layered soil model are adopted. In addition, the disperse properties of multilayered soil are analyzed, and it is found that the thin layer method is superior to rapid scalar method in low frequency domain, while in the high frequency domain it has little difference between each other. The Rayleigh wave's properties of four multilayer soil models are compared by means of thin-layer method particularly.
In the dynamic parameters inversion of foundation soil, by means of the genetic algorithm, the shear wave velocities for two common soil models are calculated based on the effective phase velocity-frequency dispersion curve, and then other parameters of multilayer foundation soil are acquired by the transformation relationship between the media's parameters.
引文
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[2]Cao YM, Xia H, et al. Solution of moving-load-induced soil vibrations based on the Betti—Rayleigh Dynamic Reciprocal Theorem. Soil Dynamics and Earthquake Engineering, 2010,30:470-480.
[3]夏禾等.交通环境振动工程.北京：科学出版社,2010.
[4]曹艳梅,夏禾.运行列车对高层建筑结构的振动影响.工程力学,2006,23(3)：162-167.
[5]夏禾,曹艳梅.轨道交通引起的环境振动问题.铁道科学与工程学报,2004,1(1)：44-51.
[6]Xia H, Cao YM, De Roeck G. Theoretical modeling and characteristic analysis of moving-train induced ground vibrations. Journal of Sound and Vibration,2010,329:819-832.
[7]Xia H, CAO YM, Zhang N. Numerical analysis of vibration effects of metro trains on surrounding environment. International Journal of Structural Stability and Dynamics,2007,7(1): 151-166.
[8]夏禾,张楠,曹艳梅.列车对周围地面及建筑物振动影响的试验研究.铁道学报,2004,26(4)：93-98.
[9]曹艳梅,夏禾,战家旺.运行列车引起高层建筑物振动的试验研究及数值分析.工程力学,2006,23(11)：182-187.
[10]曹艳梅,夏禾,陈建国.运行列车引起地面振动的理论模型及振动特性分析.振动工程学报,2009,22(6)：589-596.
[11]曹艳梅,夏禾.基于Betti-Rayleigh动力互易定理求解移动荷载引起的地基土振动.岩石力学与工程学报,2009,28(7)：1467-1476.
[12]曹艳梅,夏禾.波数-频率域内地基土表面位移Green函数的理论分析.计算力学学报,2008,25(6)：833-838.
[13]Rayleigh L, On waves propagated along the plane surface of an elastic solid. Proceedings of the London Mathematic Society,1887,17:4-11.
[14]肖柏勋,李长征.瑞雷面波勘探技术研究述评.工程地球物理学报,2004,1(1)：38-45.
[15]Chang F K, Rayleigh wave dispersion technique for rapid subsurface exploration第42届国际地球物理年会,1973.
[16]佐膝长范.用GR-810激光激振系统进行地基勘察.日本VIC株式会社,1986.
[17]Stokoe, Ⅱ K. H., Nazarian S., Effectiveness of ground improvement from spectral analysis of surface waves[A]. In Pinc.8th Euro Conf on Soil Mech and Found Eng,1983.
[18]Xia J., Miller R. D., Park C. B., Estimation of near-surface shear-wave velocity by in version of Rayleigh waves [J]. Geophysics,1999,64(3):691-700.
[19]朱裕林.瑞利波勘探在工程勘察中的应用.工程勘探,1991,1：67-70.
[20]吴世明著.土介质中的波.北京：科学出版社,1997.
[21]吴世明,曾国熙,陈云敏等.利用表面波谱分析测定土层波速.地震工程与振动,1988,8(9)：27-32.
[22]夏唐代,陈云敏,吴世明.利用瑞利波速度弥散特性反演地基参数.振动工程学报,1991, 4(4)：31-37.
[23]陈云敏,吴世明,曾国熙.表面波谱分析方法及其应用.岩土工程学报,1992,14(3)：61-65.
[24]夏唐代,吴世明.流体-固体介质瑞雷波特性.水利学报,1994(1)：26-30.
[25]夏唐代,陈云敏,吴世明.匀质软夹层瑞利波弥散特性.振动工程学报.1993,6(1)：42-50.
[26]夏唐代,陈云敏,吴世明.道路结构瑞利波弥散曲线计算.第六届全国土力学及基础工程学术会议论文集.上海：同济大学出版社,1991,92-96
[27]杨成林等.瑞雷波勘探.北京：地质出版社,1993.
[28]刘云桢,王振东.瞬态面波法的数据采集处理系统及其应用实例.物探与化探,1996,20(1)：28-34.
[29]肖柏勋.三峡工程大坝建基岩体质量快速检测方法研究.“八五”国家重人科技攻关项日研究报告,1995.
[30]肖柏勋.岩体原位弹性波测试技术应用研究,“九五”国家科技攻关项目成果报告,2000.
[31]张碧星,肖柏勋等.瑞利波勘探中“之”形频散曲线的形成机理及反演研究.地球物理学报,2000,43(4)：557-567.
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