基于分数阶导数的长期静荷载下群桩地基沉降研究  

Settlement of fractional order viscoelastic pile group foundation under long-term static load

作　　者：尹久仁[1] 代琳玲 李鑫[2] 吴郡 黄俊杰 YIN Jiuren;DAI Linling;LI Xin;WU Jun;HUANG Junjie(School of Mechanical Engineering and Mechanics,Xiangtan University,Xiangtan 411105,China;College of Civil Engineering,Xiangtan University,Xiangtan 411105,China;Sichuan Jiandao Engineering Design Co.,Ltd.,Chengdu 610051,China)

机构地区：[1]湘潭大学机械工程与力学学院,湖南湘潭411105 [2]湘潭大学土木工程学院,湖南湘潭411105 [3]四川建道工程设计有限公司,四川成都610051

出　　处：《湘潭大学学报(自然科学版)》2025年第2期180-186,共7页Journal of Xiangtan University(Natural Science Edition)

摘　　要：基于分数阶Merchant模型,引入Riemann-Liouville积分定义下的分数阶导数方程,推导了分数阶Merchant模型的本构关系和蠕变方程.为了描述长期静荷载下分数阶黏弹性群桩地基的受荷变形特点,根据分数阶Merchant本构方程,通过Visual Studio软件编写相关Fortran代码,实现了含有分数阶次的黏弹性本构模型在ABAQUS软件中的二次开发,并在二次开发的基础上,通过有限元数值模拟,分析了长期静荷载作用下不同位置桩的受力特点以及不同分数阶次对群桩地基的桩-土作用和地基沉降的影响.研究发现模型中分数阶次的改变对群桩地基的受荷变形影响不大,但会改变其变形速率,分数阶次越大,变形速度越快.Based on fractional Merchant model,the fractional derivative equation under the definition of Riemann-Liouville integral is introduced,and the constitutive relation and creep equation of fractional Merchant model are derived.In order to describe the load deformation characteristics of fractional-order viscoelastic pile group foundation under long-term static load,according to the fractional-order Merchant constitutive equation,relevant Fortran code was written by Visual Studio software to achieve the secondary development of the fractional-order viscoelastic constitutive model in ABAQUS software.On the basis of the secondary development,Through finite element numerical simulation,the loading characteristics of piles at different positions under long-term static load and the effects of different fractional orders on the pile-soil interaction and foundation settlement of pile group foundation are analyzed.It is found that the change of fractional order in the model has little effect on the load deformation of pile group foundation,but it will change the deformation rate.The greater the fractional order,the faster the deformation rate.

关 键 词：分数阶导数 黏弹性模型 ABAQUS二次开发 地基沉降 桩-土相互作用 

分 类 号：TU473[建筑科学—结构工程]