粘弹性场地地形对地震动谱特性的影响分析

【作者】 荣棉水；

【导师】 李小军；

【作者基本信息】 中国地震局地球物理研究所 ， 防灾减灾与防护工程， 2007， 硕士

【摘要】 大量的震害表明，地表地形对地面运动有很强的放大和缩小作用，因而直接影响到震害的分布。对地形条件进行研究的目的有两个，一是解释地震时地面运动的放大作用和空间变化，再就是预测在将来受地震时地面运动的特性。因此地形对地面运动的影响分析是地震工程学中非常重要且具吸引力的领域。通过大量研究，局部不规则地形对地震动峰值加速度的影响我们已有相当的了解，但是地形对地震动谱特性影响的研究相对较少。本文就以探讨地形对地震动谱特性的影响规律为研究目标，通过数值计算结果分析，着重开展了以下几个方面的研究工作，并初步得到了一些有意义的结果。1．数值计算方法的选择与分析本文选择的数值计算方法为李小军等提出的粘弹性场地地震反应分析的一种时域高精度显式有限元-有限差分方法。第二章系统回顾了显式有限元有限差分方法的理论框架。另外，这种时域高精度的显式有限元有限差分方法的优点在于采用了李小军等的显式逐步积分方法，而逐步积分方法的基本特性除了计算格式的收敛性、稳定性、精度以外还必须考虑数值计算的高频能耗特性(dissipation)和计算起步的幅值超越性(overshoot)。因此，作为前人工作的补充，本文还在第二章中分析了中心差分格式、中心差分结合单边差分的格式以及李小军等的积分格式这三种不同显式格式的能耗特性(对高频成分的抑制和消除作用)与幅值超越性(初始计算数据的放大特性)，并对三种显式格式显示出来的这两种特性做一综合评判。研究结果表明：李小军等的显式差分格式在物理阻尼比为0到1的范围内均具有较强的能耗特性，这种特性优于另外两种显式积分格式，能有效地克服透射边界的高频失稳，另外，这种格式也具有较小的速度幅值超越性，因此，在处理复杂场地地震反应方面是一种比较理想的显式积分格式。2．地形对地震动谱特性的影响分析由于实际工程遇到的场地地形条件是复杂多变的，地形对输入地震波的谱特性的影响也与很多因素有关，这些因素大体上包括场地特性和输入地震波特性两个部分。场地特性包括地形的特征尺寸如坡度和高度、介质的性质等，输入地震动特性包括输入地震波的频谱特性、入射角度等。为了便于总结规律，本文控制了若干影响因素以简化问题的分析。首先研究了坡地地形在高宽比不同、体波入射角度不同时出平面运动谱特性的差异，接着进一步研究了简单平台地形及凹陷地形对入射体波谱特性的影响，给出了若干定性及定量的结果。这些研究结果表明：地形的特征尺寸和入射角度不仅对地震动的峰值有影响，而且对地震动的谱特性有较大的影响，其中入射角度的影响尤为显著。另外，研究还表明基于脉冲输入研究粘弹性地形谱特性的影响仍不失为一种有效的方法。3．地形对输入地震动反应谱加速度峰值及特征周期影响规律的分析若干震害调查结果表明地形影响地震动的峰值及频谱特性，即影响反应谱的形状。现有的场地反应谱对地形的考虑是以地震力的形式给出的，实际工程中碰到局部不规则地形的问题时，工程师们无法从反应谱中直接获得特征周期或峰值加速度的调整方案，本文以一个具体的平台地形为算例，通过拟合的人造地震动输入，计算获得有地形影响的场地观测点的加速度时程，再利用美国抗震设计样本规范ATC3-06建议的方法以及双参数标定反应谱的方法确定观测点加速度时程所对应的场地反应谱特征周期值，进而简要分析了地形对输入地震动反应谱峰值加速度及特征周期的影响规律，并尝试着给出了特定条件下地形对观测点反应谱的调整方案。更多还原

【Abstract】 Many investigations of earthquake damages manifest that surfacetopography has significant amplification or reduction effects on groundmotion, and, therefore, it can influence the distribution of earthquakedamages directly. The purpose of studying on the influence of surfacetopography is to explain the reasons for the large amplifications andspatial variations of the ground motion and to predict some of the featuresof the ground motion during future earthquakes. So analysis of the effectof topography is one of the most important and attractive field inearthquake engineering. After a lot of investigation, we have know quite afew about the effect of surface topography on peak ground acceleration,but comparatively, the effect of surface topography on spectrum propertyof earthquake is still obscure for us. The objective of this thesis is todiscuss effects of topography on spectrum property of earthquakes,through numerical experiments and result analysis, the followingproblems are analyzed, and some applicable results are obtained.1. the choice and analysis of numerical integration methodsA numerical integration method executed in this thesis is the explicitfinite difference method suggested by Li Xiaojun et al. for analyzing theearthquake response of two-dimensional visco-elastic site. The systematicreview of this method is made in the second chapter. Besides, the virtue ofthis method is using the explicit integration formula also suggested by LiXiaojun. We know for a explicit integration formula, basic characteristicsincluding astringency、stability、precision、dissipation and overshootcharacteristic. So, as complementarity of former people’s work, dissipationand overshoot characteristics of three different integration formulas arediscussed in detail. The conclusions show that the explicit integrationformula suggested by Li Xiaojun and others has stronger numericaldissipation characteristic than the other 2 formulas while the real dampingvaries from 0 to 1, and the larger the real damping is, the phenomenon ismore obvious, this kind of formula can depress or eliminate the high-frequency instability induced by Local Transmitting Boundary, and,under the condition of the same precision, this kind of formula has lesservelocity overshoot characteristic, so it is an ideal integration formula forsolving the earthquake response of complex site.2. effect analysis of topography on spectrum property of earthquakeSurface topography is complex and various, actually, effect oftopography on spectrum property refers to many factors, such ascharacteristic dimensions of topography (including height and slope angleet al.)、characters of soil or rock、spectrum properties of input wavelets、angle of incidence et al. These factors can be classified into two sorts,characters of site and characters of earthquake. In order to summarizeconveniently, firstly, we discussed the difference of spectrum property ofanti-plane movement under the conditions of different topographic factorsand direction of the incident waves, then research expands to mesa andvalley. The conclusions show that the presence of topographic factors andthe direction of the incident waves not only significantly affect the peakground acceleration of site, but also affect the spectrum property of theincoming waves, and the effect of direction of the incident waves isespecially remarkable. The study also find that it is reasonable to analysespectrum properties with the input of impulse wavelets in the finiteelement simulation of wave motion.3. the effects analysis of topography on peak-acceleration andcharacteristic periodsInvestigations after earthquakes show that surface topography affectsthe peak-accleration and spectrum property of earthquake, so, it affectsthe shape of design spectra. Considerations of topographic effects in theseismic design code for buildings are suggested in form of earthquakeforce, while it is hard for engineers to get adjusting project throughseismic design code if they have to face topographic problems. In thisthesis, a model of mesa is established, a lot of artificial ground motions aregenerated and have been used as input movements, time histories of observation points are gained, finally, two methods (one is suggested byACT3-06 and another is suggested by Liao Zhenpeng and Li Dahua)areused to get the characteristic periods of sites. With these results, theeffects analysis of topography on peak-acceleration and characteristicperiods is executed and corresponding adjusting project for design spectrais suggested.更多还原