基于分数阶黏弹性地基模型的群桩时效行为研究

Time-behavior of pile groups based on fractional derivative soil model

基于有限单元法,将群桩划分为有限个2节点单元,从而构建了竖向受荷群桩的有限元求解方程;为了模拟饱和软黏土的流变特性,通过Laplace变换,推导了分数阶导数Merchant模型中的应力–应变关系;引入弹性-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边界元解答;考虑桩-土界面处的位移协调,将群桩有限元求解方程和地基边界元解答进行耦合,推导出群桩-土相互作用方程;再根据群桩承台的位移协调条件,求解得到群桩基础状态量的时变解答;基于以上理论,设计了数值算例,以验证方法的正确性,并分析了分数阶次对群桩时效行为的影响。

Based on the finite element method, the finite element equations for the vertically loaded pile groups are established by dividing the pile groups into a number of 2-node elements. To simulate the rheologic properties of saturated soft soils, the stress-strain relationship of the fractional Merchant model is derived by the Laplace transform. The elastic-viscoelastic correspondence principle is introduced to obtain the boundary element solutions for the fractional transversely isotropic viscoelastic saturated soft soils. In light of the displacement continuity of pile-soil interfaces, the governing equation for the interaction between the pile groups and the soils is derived by coupling the finite element equations for the pile groups and the boundary element ones for the soils. Later, the time behaviors of each state variable for the pile groups can be solved by introducing the displacement conditions of the pile cap. Based on the foregoing theory, numerical examples are griven to verify the rationality of the proposed method, and then the influences of fractional numbers on the time-dependent behaviors of the pile groups are discussed.