上覆分数阶粘弹性饱和场地土位移地震放大系数

Displacement seismic amplification coefficient of overlying fractional derivative viscoelastic saturated site soil

考虑土体液相和固相的耦合作用,将基岩上覆场地土视为两相饱和多孔介质。为了考虑饱和场地土的粘弹性特性,其固相土骨架的应力应变关系利用分数阶Kelvin粘弹性模型来描述,建立了上覆分数阶粘弹性饱和场地土在简谐地震波作用下的运动控制方程。运用分数导数的性质并考虑上覆场地土的边界条件和透水性条件求解了上覆分数阶粘弹性场地土在简谐地震波作用下的振动问题,得到了饱和场地土的位移地震放大系数。采用数值算例分析讨论了分数导数的阶数、液固耦合系数、土体模型参数、基岩土体剪切模量比等参数对位移地震放大系数的影响。研究结果表明,分数导数的阶数、液固耦合系数、土体模型参数、基岩土体剪切模量比对饱和场地土的地震响应有较大的影响,通过压实场地土,可以达到增大液固耦合系数减小地震响应的作用,通过增大饱和场地土的粘性和剪切模量也可以减小地震反应。

Considering the coupling effect between fluid phase and solid phase, the site soil on bedrock is considered as two-phase saturated porous media. In order to consider the viscoelastic characteristics of thesaturated site soil, the stress-strain relationship of soil skeleton is described by fractional derivative Kelvin viscoelastic model, and the motion control equations of overlying fractional derivative viscoelastic saturated site soil under the action of harmonic earthquake wave are established. Using the properties of fractional derivative and considering the boundary conditions and permeable conditions, the vibration problem of overlying fractional derivative viscoelastic saturated site soil under the action of harmonic earthquake wave is solved, and the seismic displacement amplification coefficient of the saturated site soil is also obtained. The influences of the order of fractional derivative, liquid and solid coupling coefficient, model parameters of soil, and bedrock and soil shear modulus ratio on the seismic displacement amplification coefficient are analyzed and discussed by numerical examples. The results show that the order of fractional derivative, liquid and coupling coefficient, model parameters of soil, bedrock and soil shear modulus ratio have great effects on the seismic response of the site soil. The fluid and solid coupling coefficient could the increa of be increased and the seismic response can be decreased by compacting the saturated soil. Meanwhile, the viscosity and shear modulus of the saturated site soil can also reduce the seismic response.