河谷场地地震波传播解析模型及放大效应
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摘要
从形态上看,自然界存在平坦、凸起和凹陷3种常见的地形及场地条件,而河谷场地是一种常见的凹陷地形,且在河谷场地修建了大量工程(如土石坝、桥梁等)。实际震害调查表明地形及场地条件对地震灾害影响很大。针对河谷场地地震波传播解析模型及放大效应,全面总结了笔者及其课题组长期以来的研究成果。主要包括以下4个方面:(1)提出了近源地形与场地效应的概念,用线源柱面SH波模拟入射地震波,平面波是其远场入射的特例,构造了线源柱面SH波自由场,定义了近源激励下的放大因子,实现了入射波波前弯曲及其地形放大效应,为其它地形和场地引起的近源放大效应研究开启了新的可能。(2)构建了非对称V形河谷地震波传播解析模型,包括亥姆霍兹运动方程、河谷表面自由边界条件及虚拟辅助边界应力与位移连续条件,提出了区域分解与区域匹配分两步走的策略,首先将整个区域分解成3个符合极坐标系的子区域,在子区域中对运动方程进行求解获得相应的波场(含有未知系数),然后将各个子区域的波场在边界进行匹配,利用边界条件求解未知系数,从而获得整个区域的波场解答以及柱面SH波的二维散射规律,揭示了非对称V形河谷的差异放大效应,这将对建在非对称V形河谷上的长大跨度工程有着不可忽视的影响。(3)U形河谷在地球表面是普遍存在的,由于缺少实际地震记录和理论研究,U形河谷的地形放大效应仍然未知。构建了U形河谷解析模型,本质上也就是亥姆霍兹方程的边值问题,并得到了这个问题的波函数级数解,发现了U形河谷谷底对地震波的异常放大现象,改变了学术界以往认为凹陷地形底部地震动一定会衰减的不全面认识,并被用来解释中世纪暖期美国亚利桑那州的大量山体落石与滑坡现象。(4)河谷常有沉积物(覆盖层),覆盖层将进一步加剧地震放大效应。构建了线源柱面SH波半圆形沉积谷解析模型,并给出了其解析级数解,发现覆盖层对地震波有明显的放大效应,且覆盖层阻尼比较小时剧烈放大,这将加剧工程结构的破坏。最后,考虑河谷场地地震放大效应进行河谷两侧边坡地震稳定性分析,及土石坝地震反应分析与坝坡地震稳定性分析,认为河谷场地地震放大效应对边坡工程与土石坝工程抗震分析有着重要的影响。
Morphologically, there are three types of topographic and site conditions in nature: flat, convex and concave sites. The canyon(or valley) is a common concave site, and a large number of structures such as earth-rock dams and bridges have been built in such a site. Investigation of actual earthquake damage shows that the topographic and site conditions have great influences on earthquake disasters. Aiming at the analytical models and amplification effects of seismic wave propagation in canyon sites, the long-term research achievements of the author and his research group are summarized comprehensively. They include four aspects:(1) The concept of near-source topographic and site effects is proposed by simulating the incident seismic waves with a line source of cylindrical SH waves. The planewave is a special case of its far field incidence. The free wave field under the line source of cylindrical SH waves is constructed to realize the curvature of the incident wavefront. The amplification factor is defined to describe the topographic effects under near-source excitation, which opens new possibilities for studying the near-source amplification effects of other topographies and sites.(2) An analytical model for seismic wave propagation in non-symmetrical V-shaped canyon is constructed, including the Helmholtz equation, traction-free boundary conditions on canyon surface, and continuity conditions of traction and displacement on the auxiliary boundary. A two-step strategy for region decomposition and region matching is proposed. Firstly, the whole region is decomposed into three sub-regions in accordance with the corresponding polar coordinate systems. The corresponding wave fields(including unknown coefficients) are obtained by solving the equation of motion in the sub-regions. Then, the wave fields of each sub-region are matched at the boundary, and the unknown coefficients are solved by using the boundary conditions. The wave-field solutions of the whole region and the two-dimensional scattering patterns of cylindrical SH waves are obtained. The differential amplification effects of the non-symmetrical V-shaped canyon are revealed, which will have an unignorable influence on the large-span projects built in it.(3) U-shaped canyons are ubiquitous on the earth's surface. Due to the lack of actual seismic records and theoretical researches, the topographic amplification effects of the U-shaped canyons are still unknown. The analytical model for a U-shaped canyon is constructed, which is essentially the boundary value problem of Helmholtz equation. The wave function series solution to the problem is obtained. The anomalous amplification of seismic waves at the bottom of U-shaped canyon has been found. It has changed the incomplete understanding that the ground motion at the bottom of a concave topography is bound to attenuate, and has been used to explain the large number of rockfalls and landslides in Arizona during the warm period of the Middle Ages.(4) Sediments(overburden layers) often occur in canyons, which may further aggravate the amplification effects of earthquakes. An analytical model for a partially filled semi-circular alluvial valley under a line source of cylindrical SH waves is constructed, and its analytical series solution is given. It is found that the overburden layers have obvious amplification effects on the seismic waves, especially for those with a small damping ratio, which will aggravate the damage of engineering structures. Finally, the seismic stability analysis of the canyon or valley slopes, the seismic response analysis of earth and rockfill dams as well as the seismic stability analysis of the dam slopes are carried out considering the seismic amplification effects of the canyon or valley sites. It is believed that the seismic amplification effects of canyons or valleys have important influences on the seismic analysis of slope and dam engineering.
Morphologically, there are three types of topographic and site conditions in nature: flat, convex and concave sites. The canyon(or valley) is a common concave site, and a large number of structures such as earth-rock dams and bridges have been built in such a site. Investigation of actual earthquake damage shows that the topographic and site conditions have great influences on earthquake disasters. Aiming at the analytical models and amplification effects of seismic wave propagation in canyon sites, the long-term research achievements of the author and his research group are summarized comprehensively. They include four aspects:(1) The concept of near-source topographic and site effects is proposed by simulating the incident seismic waves with a line source of cylindrical SH waves. The planewave is a special case of its far field incidence. The free wave field under the line source of cylindrical SH waves is constructed to realize the curvature of the incident wavefront. The amplification factor is defined to describe the topographic effects under near-source excitation, which opens new possibilities for studying the near-source amplification effects of other topographies and sites.(2) An analytical model for seismic wave propagation in non-symmetrical V-shaped canyon is constructed, including the Helmholtz equation, traction-free boundary conditions on canyon surface, and continuity conditions of traction and displacement on the auxiliary boundary. A two-step strategy for region decomposition and region matching is proposed. Firstly, the whole region is decomposed into three sub-regions in accordance with the corresponding polar coordinate systems. The corresponding wave fields(including unknown coefficients) are obtained by solving the equation of motion in the sub-regions. Then, the wave fields of each sub-region are matched at the boundary, and the unknown coefficients are solved by using the boundary conditions. The wave-field solutions of the whole region and the two-dimensional scattering patterns of cylindrical SH waves are obtained. The differential amplification effects of the non-symmetrical V-shaped canyon are revealed, which will have an unignorable influence on the large-span projects built in it.(3) U-shaped canyons are ubiquitous on the earth's surface. Due to the lack of actual seismic records and theoretical researches, the topographic amplification effects of the U-shaped canyons are still unknown. The analytical model for a U-shaped canyon is constructed, which is essentially the boundary value problem of Helmholtz equation. The wave function series solution to the problem is obtained. The anomalous amplification of seismic waves at the bottom of U-shaped canyon has been found. It has changed the incomplete understanding that the ground motion at the bottom of a concave topography is bound to attenuate, and has been used to explain the large number of rockfalls and landslides in Arizona during the warm period of the Middle Ages.(4) Sediments(overburden layers) often occur in canyons, which may further aggravate the amplification effects of earthquakes. An analytical model for a partially filled semi-circular alluvial valley under a line source of cylindrical SH waves is constructed, and its analytical series solution is given. It is found that the overburden layers have obvious amplification effects on the seismic waves, especially for those with a small damping ratio, which will aggravate the damage of engineering structures. Finally, the seismic stability analysis of the canyon or valley slopes, the seismic response analysis of earth and rockfill dams as well as the seismic stability analysis of the dam slopes are carried out considering the seismic amplification effects of the canyon or valley sites. It is believed that the seismic amplification effects of canyons or valleys have important influences on the seismic analysis of slope and dam engineering.
引文
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