| 轨道附近地面振动模型中的饱和地层动力格林函数 |
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| 引用本文： | 王福彤,陶夏新,谢礼立,郑鑫,崔高航.轨道附近地面振动模型中的饱和地层动力格林函数[J].地球物理学报,2015,58(8):2948-2961. |
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| 作者姓名： | 王福彤 陶夏新 谢礼立 郑鑫 崔高航 |
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| 作者单位： | 1. 中国地震局工程力学研究所, 哈尔滨 150001;2. 黑龙江大学建筑工程学院, 哈尔滨 150001;3. 哈尔滨工业大学土木工程学院, 哈尔滨 150090;4. 黑龙江八一农垦大学工程学院, 黑龙江大庆 163319;5. 东北林业大学土木工程学院, 哈尔滨 150040 |
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| 基金项目： | 国家自然科学基金项目(50538030,51108163),黑龙江省自然科学基金项目(E201221,E201330),中国博士后科学基金项目(2013M531084)资助. |
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| 摘 要： | 列车引起场地振动的建模需要能够表达地层的动力格林函数.本文兼顾饱和土的流固两相耦合性、场地土的分层性和波动的三维传播性,构建了半解析的场地动力格林函数.首先,基于Biot方程,在傅里叶变换域求解固体骨架和流体的位移和应力.然后采用传递矩阵方法建立地表位移和应力间的关系,得到格林函数矩阵.进而讨论矩阵的一些固有特征,提出改善竖向位移计算效率的措施.最后利用推导的格林函数计算了几个典型算例.数值结果与文献中其他方法得到的结果十分接近,与场地振动的现场观测试验基本符合.软土场地振动的计算结果高于饱和砂土场地,高速列车场地振动强度高于低速列车.当车速接近场地瑞利波速,模拟结果中显示出马赫锥.数值结果还显示,即使车速略低于瑞利波速,马赫锥也可能出现.本文推导的格林函数将有助于深入理解列车等移动激励作用下层状饱和土场地的振动特征.
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| 关 键 词： | 波动 多孔弹性介质 层状半空间 格林函数 列车 |
| 收稿时间： | 2014-03-13 |
Dynamic Green's function of stratified ground with saturated soil layers for modeling ground vibration near railway track |
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| WANG Fu-Tong,TAO Xia-Xin,XIE Li-Li,ZHENG Xin,CUI Gao-Hang.Dynamic Green's function of stratified ground with saturated soil layers for modeling ground vibration near railway track[J].Chinese Journal of Geophysics,2015,58(8):2948-2961. |
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| Authors: | WANG Fu-Tong TAO Xia-Xin XIE Li-Li ZHENG Xin CUI Gao-Hang |
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| Institution: | 1. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150001, China;2. School of Civil Engineering and Architecture, Heilongjiang University, Harbin 150001, China;3. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;4. School of Engineering, Heilongjiang Bayi Agricultural University, Daqing, Heilongjiang 163319, China;5. School of Civil Engineering, Northeast Forestry University, Harbin 150040, China |
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| Abstract: | The modeling of ground vibration from trains requires a Green's function to represent the dynamic characteristics of the ground. Because of the existence of groundwater, dynamic coupling vibration of soil skeleton and pore water may propagate in a naturally stratified ground. This paper proposes a semi-analytical Green's function that is able to model the fluid-solid coupling in saturated soil, stratification of ground configuration and three-dimensional propagation of waves.#br#The Biot's equation was Fourier transformed with respect to time and two horizontal cartesian components. General solutions of displacements and stresses of solid skeleton and pore fluid were worked out in the Fourier transformed domain. The relationship between displacement and stress on the ground surface was formulated by the transfer matrix technique, so that the matrix of the Green's function was derived. Improvements of computational efficiency for vertical displacement were achieved by taking advantage of some relevant matrices' properties. The proposed Green's function was added into a sophisticated train-track-ground interaction model to include the ground water effect. Validation of the Green's function was shown by computing several typical examples in the literature and simulating a field observation near the Beijing urban railway. Vibrations of two typical layered grounds with saturated clay and sandy soil, excited by low speed and high speed trains, respectively, were analyzed based on computation results.#br#The calculated amplitudes of ground vibrations were very close to those of some references, in both cases of a harmonic load with a fixed position and a moving load. For the field test in Beijing, the simulated ground vibration levels agreed largely with the observational data. The comparison of numerical results for the two kinds of saturated soil shows that the vibrations of soft clay were higher than those of saturated sand, and the vibration intensities of ground caused by high speed train are larger than those by the low-speed train. The Mach cone appeared in the simulated wave field of the ground surface in the case that train speed approached the phase velocity of Rayleigh waves.The numerical results also show that the Mach cone can still be generated even the train speed is slightly lower than the Rayleigh wave velocity.#br# The proposed Green's function is able to represent such mechanisms as fluid-solid interaction between two phases of saturated soil, geometric and physical stratification of soil deposit and three-dimensional propagation of viscoelastic waves in a ground. Some train-induced vibration features of the water-saturated layered ground can be simulated by the train-track-ground vibration model based on the Green's function, which will be helpful to understand the propagation and attenuation of the ground-borne vibrations caused by moving trains. |
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| Keywords: | Wave Propagation Poroelastic Medium Layered Half-space Green's Function Train |
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