分数阶黏弹性饱和地基与板的共同作用

Interaction Between Fractional Viscoelastic Saturated Soils and Plates

摘要:

基于层状分数阶黏弹性横观各向同性饱和地基的固结解答，采用边界元法与有限元法耦合的方法，探讨板与黏弹性饱和地基的共同作用。首先基于Mindlin中厚板理论，得到板的总刚度矩阵方程；随后引入分数阶黏弹性饱和地基的精细积分解答，获得地基柔度矩阵方程；最后利用板?土协调条件，得到黏弹性饱和地基与板共同作用的解答。与已有文献对比，验证了本文解的正确性，并讨论黏弹性饱和地基参数和地基加固深度等因素对筏板与地基共同作用的影响。

关键词:层状饱和地基;横观各向同性;分数阶黏弹性;Mindlin板;板‒土共同作用;时效性

Abstract:

Based on the solution of multilayered fractional viscoelastic cross-anisotropic saturated soils， the boundary element-finite element coupling method is utilized to investigate the interaction between the plate and viscoelastic saturated soils. First， based on the Mindlin’s plate theory， the total stiffness matrix equation of the plate is obtained. Then， the precise integration solution of fractional viscoelastic saturated soils is introduced to obtain the flexibility matrix equation of soils. Finally， according to the coordination conditions of the plate-soil nodes， the solution of the interaction between the viscoelastic saturated soils and the plate is obtained. The proposed solution in this paper is verified by comparing with that of the literature. Moreover， the effects of the soil parameters and the reinforcement depth of soils on the time-dependent interaction between the raft and viscoelastic soils are analyzed.

Key words:stratified saturated soils;transversely isotropic;fractional viscoelasticity;Mindlin plate;plate-soil interaction;time-dependent effect