近断层地震作用下结构群动力响应研究
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摘要
近断层地震作用下结构群动力响应研究属于地震学和工程地震学的交叉领域,它需要综合考虑地震震源、地球介质、场地条件、土-结构相互作用以及结构-土-结构相互作用等因素。由于无法利用实验室条件,对包含震源、地球介质以及实际结构群的足尺模型进行实验研究,所以波动模拟是一种重要的研究手段。通过波动模拟方法研究可再现结构群的地震响应过程,进而透彻地解释结构群的震害现象。
本文首先梳理了建立有限断层震源模型的基本思路,介绍了地震断层的四个基本形态(包括走滑断层、正断层、逆冲断层和斜滑断层)和双力偶矩张量源,并推导了适用于本文平面应变问题的二维矩张量源表达式,整理了涉及有限断层震源参数(如断层尺寸、断层上的滑动位移和上升时间等)的经验公式,这些工作是本文相关章节建立有限断层震源模型的主要依据。
本文提出了一种近断层地震动模拟的被研究块体方法。该方法的基本思想是：首先通过四边形辅助计算网格,建立了连续介质中的被研究块体,再将应力沿被研究块体周围线段进行积分,得到了被研究块体周围所受内力的代数表达式,再将内力代入动力平衡方程可得被研究块体的位移、速度和加速度,最后通过编制程序实现了空间域内所有被研究块体动力平衡方程的求解。通过推导算法的差分方程,得到了该方法的频散方程,并给出了实际计算中适用于该方法的稳定性条件和网格离散可采用的允许最大空间步长。与Lamb问题解析解的对比结果证实了被研究块体方法具有良好的计算精度,同时验证了该方法的正确性。为使该方法适用于近断层地震动的模拟,将有限断层震源模型引入到算法中,与离散波数法对比结果证实了该方法引入有限断层震源的正确性。将该方法应用于1994年Northridge地震三个近断层观测台站地震记录的模拟,模拟结果与实际地震记录符合较好,并展示了断层的时-空破裂过程。本文提出的被研究块体方法可适用于分层介质、地表和地下不规则几何边界等复杂地质情况,并且方便引入有限断层震源模型,可作为模拟和预测近断层地震动的有效工具。
本文提出了一种可进行网格分级的被研究块体方法。在粗细网格的分界上,建立了由不同空间步长的四边形辅助网格构造而成的被研究块体,通过在粗细网格的连接处进行线性插值,使由粗网格组成的区域和由细网格组成的区域连接为整体,实现了波在两区域的相互传播。通过与Lamb解析解、Garvin解析解和无限域内两种分层介质解析解进行对比,验证了该方法不同荷载(包括单力源和爆炸源)、不同介质情况下的正确性。针对具有起伏地表的盆地问题,分别用双力偶震源和爆炸源作为荷载,得到了场地表面多点的水平峰值加速度,理论地震图和波传播的场图等,分析了不同倾角的震源对场地地震动的影响。该方法对于介质的空间离散具有较强的灵活性,网格分级大幅度提高了算法的计算效率；同时该方法适用于研究具有地表起伏的盆地问题以及其它复杂地质情况。
在被研究块体方法思想的基础上,本文最后提出了一种近断层地震作用下结构群动力响应模拟的一体化方法,该方法可将地震震源、地球介质以及结构群考虑为一个“整体”。基于被研究块体的概念,分别在结构中、地球介质中和地球介质与结构连接处建立了三种典型的被研究块体。针对第一种被研究块体(用于结构),根据受力分析建立了它的动力平衡方程,并给出了实际计算中适用于该方法的稳定性条件,用于模拟波在结构中传播。第二种被研究块体(用于地球介质)可用于模拟波在连续介质中传播。第三种被研究块体(用于结构-地球介质连接)用于解决上部结构与地球介质的连接问题,它是由结构的基础、结构第一层的半根柱子和基础下部的地球介质构成,可将结构柱端受到的剪力和轴力与周围来自第二种被研究块体的相互作用力连接起来,实现地震波在结构和土体中的相互传播。针对四个不同算例,用模拟一体化方法对近断层作用下结构群地震响应进行模拟,四个算例均使用同一半空间和同一有限断层震源模型,每个算例中都有三个相同的结构群分别位于断层附近的不同位置(上盘、破裂前方和下盘)。四个算例的不同之处是,算例一结构群中的所有结构均为6层框架结构；算例二结构群中既有6层框架结构又有24层框架结构；算例三结构群中结构均为24层框架结构；算例四结构群由三组不同动力特性的6层框架结构组成。模拟结果展示了结构的层间位移、结构屋顶的傅立叶谱、结构群的整体变形和结构群产生的波场等。分析了地震断层的破裂过程对断层附近不同位置结构群地震响应的影响。
最后,总结了全文,并展望进一步的研究内容和工作。
本文工作是国家自然科学基金项目“粘弹性介质中波动传播数值模拟的格子法(10972144)”的部分内容。
Research on the dynamic responses of building clusters caused by near-fault earthquakes need the combination of the seismology and the engineering seismology. The corresinfluences of earthquake source, earth medium, site conditions, soil-structure interaction (SSI), and structure-soil-structure interaction (SSSI) on the responses of structure clusters need to be considered comprehensively in the researchs. Because the full-scale experiments including earth medium, earthquake source, and building clusters can not be conducted under laboratory conditions, the wave simulation is an important approach in studying the dynamic responses of building clusters. The dynamic responses of building clusters during earthquake can be reproduced by employing the wave simulations and therefore the phenomena of earthquake disasters can be explained clearly.
In this paper, firstly, we review the basic idea of constructing finite-fault source model and introduce four basic configurations including strike-slip fault, normal fault, inverse or thrust fault, and oblique fault. The expressions of double-couple moment tensor are derived for the plane strain problem. The empirical relations of source parameters (such as the size of fault plane, slip on the fault plane, and rise time, etc.) of finite-fault source are also reviewed. According to these jobs, the finite-fault source model can be established in corresponding chapters.
The investigated lump method is presented to simulate near-fault ground motions caused by earthquake in this paper. The investigated lump is constructed from auxiliary quadrangular grid which consists of earth medium. The expressions of internal forces acting on around the investigated lump can be obtained by the integrations along contour of the investigated lump. Then the components of displacement, velocity, and acceleration of the investigated lump can be obtained by substituting the internal force into the dynamic equilibrium equation. Evaluation of the dynamic equilibrium equations of all the investigated lumps can be obtained by programming the FORTRAN code. The stability condition and allowed maximal spatial spacing employed in practical computation by using the proposed method can be obtained by the different equation and the dispersion equation of the algorithm. The numerical results comparing with Lamb's analytical solutions confirmed that is of good accuracy for the proposed method. The finite-fault source model is introduced to the proposed method for modeling near-fault ground motions. The results comparing with that of the discrete wave-number method confirmed the validity of the proposed method combining the finite-fault. The near-fault ground motions at three stations during the1994Northridge earthquake are synthesized by using the proposed method. The simulating results qualitatively match to the corresponding ground motion records. The Doppler effects produced by the earthquake can be seen clearly during the successive rupture of subfault on by one. The proposed method applies to the complex geological conditions including layered medium, surface and subsurface topography, and internal hole and so on, and is convenience to implement the introduction of finite-fault source model, and is an effective tool for simulating and predicting the near-fault ground motions.
An investigated lump method using mesh grading is presented to simulate complex site condition, especially for basin site condition. The investigated lump is constructed from the auxiliary quadrangular grid with different spatial spacing at the interface between coarser and fine grids. Nodal displacement components on the coarser grid can be obtained by linear interpolation technology, which implements mutual wave propagation in the region consisting of coarser and fine grids. The validity of the proposed method is confirmed by comparing respectively the results with Lamb's analytical solution, Garvin's analytical solution, and the analytical solution for layered medium in the cases of different loads (single-force and explosive source). Horizontal PGA, seismograms, and wave-fields of displacement for the complex site subjected to double-couple point source and explosive source are obtained. The influences of earthquake source different dip angel on the ground motions are studied. The investigated lump method using mesh grading is a high efficiency algorithem with unstructured grids and is applied to solve basin site and other complex site conditions.
An integrated method is presented to evaluate the dynamic responses of building clusters caused by near-fault earthquake. Earthquake source, earth medium, and building clusters are considered as a whole in the proposed method. Three types of typical investigated lumps are constructured from structure, earth medium, and the connection between soil and structure, respectively. In view of the first type of investigated lump simulating wave propagation in structure, the dynamic equilibrium equation is established according to stress distributions and the stability condition is given. The second type of investigated lump is used to model wave propagation in earth medium. The third type of investigated lump being constructured from foundation, half of column of the first floor of structure, and soil under the structural foundation is used to solve the connective problem between structure and soil. Mutual propagation of seismic wave in soil and structure is implemented by the third type of investigated lump which connects the shear and axial force acting on the top of column with the internal forces from the second investigated lump acting on earth medium. The simulative integrated method is applied to model the responses of building clusters caused by the near-fault ground motions in four different cases. In four cases, the same half-space and the same finite-fault source model are employed, and three clusters of buildings are located in the hanging wall, rupture forward, and footwall of the causative fault, respectively. The differences in four cases are:building clusters consist of some6-storey frame structures in the first case, building clusters consist of some6-storey and24-storey frame structures in the second case, building clusters consist of some24-storey frame structures in the third case, and build clusters consist of some6-storey frame structures with three types of dynamic features. The numerical results show the structural inter-story drifts, the Fourier amplitude spectra of horizontal accelerations of structural roofs, the deformations of building cluster, and wave-fields caused by building clusters, etc. The influences of the rupture process of causative fault on the building clusters located in the different positions are studied.
The main contributions of the dissertation are summarized and the further work is suggested.
The work carried out in the dissrtation is supported by National Natural Science Foundation of Chian (No.10972144).
本文首先梳理了建立有限断层震源模型的基本思路,介绍了地震断层的四个基本形态(包括走滑断层、正断层、逆冲断层和斜滑断层)和双力偶矩张量源,并推导了适用于本文平面应变问题的二维矩张量源表达式,整理了涉及有限断层震源参数(如断层尺寸、断层上的滑动位移和上升时间等)的经验公式,这些工作是本文相关章节建立有限断层震源模型的主要依据。
本文提出了一种近断层地震动模拟的被研究块体方法。该方法的基本思想是：首先通过四边形辅助计算网格,建立了连续介质中的被研究块体,再将应力沿被研究块体周围线段进行积分,得到了被研究块体周围所受内力的代数表达式,再将内力代入动力平衡方程可得被研究块体的位移、速度和加速度,最后通过编制程序实现了空间域内所有被研究块体动力平衡方程的求解。通过推导算法的差分方程,得到了该方法的频散方程,并给出了实际计算中适用于该方法的稳定性条件和网格离散可采用的允许最大空间步长。与Lamb问题解析解的对比结果证实了被研究块体方法具有良好的计算精度,同时验证了该方法的正确性。为使该方法适用于近断层地震动的模拟,将有限断层震源模型引入到算法中,与离散波数法对比结果证实了该方法引入有限断层震源的正确性。将该方法应用于1994年Northridge地震三个近断层观测台站地震记录的模拟,模拟结果与实际地震记录符合较好,并展示了断层的时-空破裂过程。本文提出的被研究块体方法可适用于分层介质、地表和地下不规则几何边界等复杂地质情况,并且方便引入有限断层震源模型,可作为模拟和预测近断层地震动的有效工具。
本文提出了一种可进行网格分级的被研究块体方法。在粗细网格的分界上,建立了由不同空间步长的四边形辅助网格构造而成的被研究块体,通过在粗细网格的连接处进行线性插值,使由粗网格组成的区域和由细网格组成的区域连接为整体,实现了波在两区域的相互传播。通过与Lamb解析解、Garvin解析解和无限域内两种分层介质解析解进行对比,验证了该方法不同荷载(包括单力源和爆炸源)、不同介质情况下的正确性。针对具有起伏地表的盆地问题,分别用双力偶震源和爆炸源作为荷载,得到了场地表面多点的水平峰值加速度,理论地震图和波传播的场图等,分析了不同倾角的震源对场地地震动的影响。该方法对于介质的空间离散具有较强的灵活性,网格分级大幅度提高了算法的计算效率；同时该方法适用于研究具有地表起伏的盆地问题以及其它复杂地质情况。
在被研究块体方法思想的基础上,本文最后提出了一种近断层地震作用下结构群动力响应模拟的一体化方法,该方法可将地震震源、地球介质以及结构群考虑为一个“整体”。基于被研究块体的概念,分别在结构中、地球介质中和地球介质与结构连接处建立了三种典型的被研究块体。针对第一种被研究块体(用于结构),根据受力分析建立了它的动力平衡方程,并给出了实际计算中适用于该方法的稳定性条件,用于模拟波在结构中传播。第二种被研究块体(用于地球介质)可用于模拟波在连续介质中传播。第三种被研究块体(用于结构-地球介质连接)用于解决上部结构与地球介质的连接问题,它是由结构的基础、结构第一层的半根柱子和基础下部的地球介质构成,可将结构柱端受到的剪力和轴力与周围来自第二种被研究块体的相互作用力连接起来,实现地震波在结构和土体中的相互传播。针对四个不同算例,用模拟一体化方法对近断层作用下结构群地震响应进行模拟,四个算例均使用同一半空间和同一有限断层震源模型,每个算例中都有三个相同的结构群分别位于断层附近的不同位置(上盘、破裂前方和下盘)。四个算例的不同之处是,算例一结构群中的所有结构均为6层框架结构；算例二结构群中既有6层框架结构又有24层框架结构；算例三结构群中结构均为24层框架结构；算例四结构群由三组不同动力特性的6层框架结构组成。模拟结果展示了结构的层间位移、结构屋顶的傅立叶谱、结构群的整体变形和结构群产生的波场等。分析了地震断层的破裂过程对断层附近不同位置结构群地震响应的影响。
最后,总结了全文,并展望进一步的研究内容和工作。
本文工作是国家自然科学基金项目“粘弹性介质中波动传播数值模拟的格子法(10972144)”的部分内容。
Research on the dynamic responses of building clusters caused by near-fault earthquakes need the combination of the seismology and the engineering seismology. The corresinfluences of earthquake source, earth medium, site conditions, soil-structure interaction (SSI), and structure-soil-structure interaction (SSSI) on the responses of structure clusters need to be considered comprehensively in the researchs. Because the full-scale experiments including earth medium, earthquake source, and building clusters can not be conducted under laboratory conditions, the wave simulation is an important approach in studying the dynamic responses of building clusters. The dynamic responses of building clusters during earthquake can be reproduced by employing the wave simulations and therefore the phenomena of earthquake disasters can be explained clearly.
In this paper, firstly, we review the basic idea of constructing finite-fault source model and introduce four basic configurations including strike-slip fault, normal fault, inverse or thrust fault, and oblique fault. The expressions of double-couple moment tensor are derived for the plane strain problem. The empirical relations of source parameters (such as the size of fault plane, slip on the fault plane, and rise time, etc.) of finite-fault source are also reviewed. According to these jobs, the finite-fault source model can be established in corresponding chapters.
The investigated lump method is presented to simulate near-fault ground motions caused by earthquake in this paper. The investigated lump is constructed from auxiliary quadrangular grid which consists of earth medium. The expressions of internal forces acting on around the investigated lump can be obtained by the integrations along contour of the investigated lump. Then the components of displacement, velocity, and acceleration of the investigated lump can be obtained by substituting the internal force into the dynamic equilibrium equation. Evaluation of the dynamic equilibrium equations of all the investigated lumps can be obtained by programming the FORTRAN code. The stability condition and allowed maximal spatial spacing employed in practical computation by using the proposed method can be obtained by the different equation and the dispersion equation of the algorithm. The numerical results comparing with Lamb's analytical solutions confirmed that is of good accuracy for the proposed method. The finite-fault source model is introduced to the proposed method for modeling near-fault ground motions. The results comparing with that of the discrete wave-number method confirmed the validity of the proposed method combining the finite-fault. The near-fault ground motions at three stations during the1994Northridge earthquake are synthesized by using the proposed method. The simulating results qualitatively match to the corresponding ground motion records. The Doppler effects produced by the earthquake can be seen clearly during the successive rupture of subfault on by one. The proposed method applies to the complex geological conditions including layered medium, surface and subsurface topography, and internal hole and so on, and is convenience to implement the introduction of finite-fault source model, and is an effective tool for simulating and predicting the near-fault ground motions.
An investigated lump method using mesh grading is presented to simulate complex site condition, especially for basin site condition. The investigated lump is constructed from the auxiliary quadrangular grid with different spatial spacing at the interface between coarser and fine grids. Nodal displacement components on the coarser grid can be obtained by linear interpolation technology, which implements mutual wave propagation in the region consisting of coarser and fine grids. The validity of the proposed method is confirmed by comparing respectively the results with Lamb's analytical solution, Garvin's analytical solution, and the analytical solution for layered medium in the cases of different loads (single-force and explosive source). Horizontal PGA, seismograms, and wave-fields of displacement for the complex site subjected to double-couple point source and explosive source are obtained. The influences of earthquake source different dip angel on the ground motions are studied. The investigated lump method using mesh grading is a high efficiency algorithem with unstructured grids and is applied to solve basin site and other complex site conditions.
An integrated method is presented to evaluate the dynamic responses of building clusters caused by near-fault earthquake. Earthquake source, earth medium, and building clusters are considered as a whole in the proposed method. Three types of typical investigated lumps are constructured from structure, earth medium, and the connection between soil and structure, respectively. In view of the first type of investigated lump simulating wave propagation in structure, the dynamic equilibrium equation is established according to stress distributions and the stability condition is given. The second type of investigated lump is used to model wave propagation in earth medium. The third type of investigated lump being constructured from foundation, half of column of the first floor of structure, and soil under the structural foundation is used to solve the connective problem between structure and soil. Mutual propagation of seismic wave in soil and structure is implemented by the third type of investigated lump which connects the shear and axial force acting on the top of column with the internal forces from the second investigated lump acting on earth medium. The simulative integrated method is applied to model the responses of building clusters caused by the near-fault ground motions in four different cases. In four cases, the same half-space and the same finite-fault source model are employed, and three clusters of buildings are located in the hanging wall, rupture forward, and footwall of the causative fault, respectively. The differences in four cases are:building clusters consist of some6-storey frame structures in the first case, building clusters consist of some6-storey and24-storey frame structures in the second case, building clusters consist of some24-storey frame structures in the third case, and build clusters consist of some6-storey frame structures with three types of dynamic features. The numerical results show the structural inter-story drifts, the Fourier amplitude spectra of horizontal accelerations of structural roofs, the deformations of building cluster, and wave-fields caused by building clusters, etc. The influences of the rupture process of causative fault on the building clusters located in the different positions are studied.
The main contributions of the dissertation are summarized and the further work is suggested.
The work carried out in the dissrtation is supported by National Natural Science Foundation of Chian (No.10972144).
引文
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