上覆非线性场地土的振动分析

Vibration Analysis of Nonlinear Sites

采用一维波动模型,分析半空间上、受竖直向上传播的稳态剪切波激振下剪切模量沿深度按指数规律变化的单层非线性场地土横向自由振动问题,求得位移的闭合解,并由该解得到场地土地表与基岩露头位移幅值之比的放大系数.通过对此类单层非线性场地土的算例分析,讨论了场地土沿深度变化的剪切模量及半空间与场地土层底面之间的阻抗比对场地土放大系数的影响,并验证了剪切模量沿深度按指数规律变化的非线性场地土(0≤α≤1)的自振周期仍可估为剪切波穿过该场地土层所需时间的4倍.

By using the one-dimensional wave model, this paper analyzed the horizontal free vibration of a nonlinear site which was excited by the vertically propagating shear waves. First, we obtained its closed-form solutions of the displacement. Then, through these solutions, we obtained the amplitude amplification of the ground surface total displacement to the bedrock outcrop displacement. An example of such nonlinear sites with a single layer shows that the elastic shear modulus has effect on the amplication, and so does the impedance ratio of the half-space to the bottom surface of the layer. The example also verifies that the predominant period of the site is four times the time that the shear wave needs to travel through the layer.