分数阶黏弹性模型在饱和软土与单桩相互作用中的应用

Application of the Fractional Viscoelastic Model in Interaction of Saturated Soft Soils and Piles

摘要:

引入基于分数阶导数的Merchant模型，以描述饱和软土的黏弹性特征，并通过积分变换推导出变换域内的应力-应变关系；根据弹性-黏弹性对应原理，得到横观各向同性分数阶黏弹性饱和软土地基的解答，并将其作为地基边界元解的核函数；基于轴向受力的2节点桩单元的单元刚度矩阵，构建单桩的有限元解；将地基的边界元解和桩的有限元解进行耦合，以求解地基与单桩的相互作用问题；随后，设计算例验证本文理论的正确性，并对分数阶次对桩-土相互作用的影响进行分析。

Abstract:

To describe the viscoelastic characteristics of saturated soft soils， the fractional Merchant model is introduced， and the stress-strain relationship in the transformed domain is derived through integral transforms. Based on the elastic-viscoelastic correspondence principle， the solution of the fractional transversely isotropic viscoelastic saturated soft soils is obtained， which is the kernel function of the boundary element solution for the soils. Based on the stiffness matrix of a 2-noded pile element subjected to axial loading， the finite element solution for the pile is constructed. The boundary element solution for the soils is coupled with the finite element solution for the pile to solve the interaction between the soils and piles. Several examples are designed to verify the presented theory and to analyze the influence of the fractional order on the pile-soil interaction.