简谐荷载作用下层状饱和冻土地基动力响应分析

DYNAMIC RESPONSE ANALYSIS OF LAYERED SATURATED FROZEN SOIL FOUNDATION UNDER HARMONIC LOADING

  • 摘要: 基于含孔隙固体多孔介质理论,建立了二维层状饱和冻土地基的计算模型,研究了简谐荷载作用下层状饱和冻土地基的动力响应问题。通过Helmholtz定理和Fourier积分变换,采用传递矩阵法,结合边界及层间连续条件推导获得了层状饱和冻土地基的刚度矩阵,得到了层状饱和冻土地基在频域中的动力响应解答。通过快速傅里叶变换得到了层状饱和冻土中各相位移和应力的数值解。与已有文献进行对比后,通过数值算例分别分析讨论了上软下硬和上硬下软两种典型层状地基中表层土剪切模量、表层土温度、表层土孔隙率和荷载频率对动力响应的影响规律。研究结果表明:在上软下硬和上硬下软两种地基情况下,竖向位移和孔隙水所分担的应力幅值随着表层土剪切模量的增大而减小,随着表层土温度、表层土孔隙率和荷载频率的增大而增大;层状饱和冻土地基中软硬土层的排列次序对竖向位移和孔隙水所分担的应力影响显著。

     

    Abstract: Based on the theory of porous media containing porous solids, established is a two-dimensional calculation model for layered saturated frozen soil foundation, and studied is the dynamic response of layered saturated frozen soil foundation under harmonic load. Through Helmholtz theorem and Fourier integral transform, the stiffness matrix of layered saturated frozen soil foundation is derived by using one transfer matrix method and combining boundary and interlayer continuity conditions, and the dynamic response solution of layered saturated frozen soil foundation in frequency domain is obtained. The numerical solutions of displacement and stress of each phase in layered saturated frozen soil are obtained by fast Fourier transform. After comparing with the existing literatures, the effects of surface soil shear modulus, of surface soil temperature, of surface soil porosity and of load frequency on dynamic response in two typical layered foundations of upper soft and lower hard and upper hard and lower soft are studied by numerical examples. The computational results show that: the stress amplitude shared by the vertical displacement and pore water decreases with the increase of shear modulus of surface soil and, increases with the increase of surface soil temperature, of surface soil porosity, and of loading frequency. The arrangement order of soft and hard soil layers in the layered saturated frozen soil foundation has a significant effect on the vertical displacement and the stress shared by pore water.

     

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