水平成层场地动剪应变与震动速度关系解析

Analysis of relationship between dynamic shear strain and vibration velocity of horizontal soil layers

以SHAKE2000为代表的频域等效线性化是目前主流的土层地震动计算方法。由于该方法在软土场地计算结果严重不合理,其改进方法成为目前研究热点,主要采用频率相关法,但一直没有取得实效。对频率相关法中土体动剪应变和震动速度成恒定比例关系的基本假定进行研究,从波动方程推导出了均匀全空间单向行波、单一均匀半无限场地、成层场地等3种典型场地中土体剪应变与震动速度关系的精确解答,通过数值试验研究了这一假定的合理性与偏差程度。结果表明:动剪应变和震动速度成恒定比例关系这一假定只有在无边界均匀介质单向行波情形下才成立,对于实际成层土场地,动剪应变与震动速度关系强烈依赖于波的频率和观察点的位置,如果在土层地震反应分析中忽略反射波而采用单向行波恒定比例假定将会使计算结果产生显著偏差;动剪应变与震动速度成恒定比例关系的假定导致的偏差达4个量级,即使对于单一均匀半无限空间模型偏差也十分显著;对实际土层地震动的求解,该假定在理论上定性错误,定量上偏差不可接受,必须放弃而另寻其他途径。

Equivalent linearization in frequency domain, represented by SHAKE2000, is the mainstream approach for seismic response analysis of soil layers. Due to the severe unreasonable results in soft soil sites, its improvement becomes a research hotspot, which mainly adopts frequency-dependent method（FDM）, but there has been no substantial improvement. This paper assumes that dynamic shear strain and vibration velocity present a constant proportional relationship in FDM. Based on wave equation, exact solutions for the relationship of the two variables were derived on three typical site models, i.e., the homogeneous half space with one-way traveling wave, the single uniform soil layer, and the layered soil site. The reasonability and deviation degree of the assumption were studied through numerical experiments. Results show that the constant proportional hypothesis only applies in the case of unbounded homogeneous medium with one-way traveling wave. For actual layered soil sites, the relationship between dynamic shear strain and vibration velocity strongly depends on the frequency of the wave and the location of the observation point. If we ignore the reflection wave in ground seismic response analysis, the use of constant proportion assumption under one-way traveling wave will make significant deviation to the results. The deviation caused by the assumption may span four orders of magnitude. Even for a single uniform deposit, the deviation is also very significant. For practical ground motion calculation, this assumption clearly exists qualitative error in theory, and the quantitative deviation can not be acceptable, so it must be abandoned and need to find another more reasonable approach.