摘要
现有成层地基受荷问题求解方法尚不完善,传递矩阵法经常会出现病态矩阵和数据溢出,而解析层元法或刚度矩阵法存在高阶矩阵求逆很困难等缺陷。首先依据三维弹性静力学基本方程和Fourier正变换,推导得到含待定系数的土层状态变量矩阵形式解;然后结合成层地基边界条件、土层状态变量的待定系数转化关系以及Fourier逆变换,求得成层地基状态变量的已知系数解;最后针对均质半无限地基、三层不等厚地基及广义Gibson地基等算例进行方法验证及参数分析。结果表明:相较于传递矩阵法和解析层元法,提出的方法不仅合理且准确,同时具备数值计算稳定、求解速度更快、可自我校核以及适用土层数无限制等优点;层间接触面相对位移与界面滑移系数成正比,且与荷载作用面距层间接触面的尺寸成反比,界面相对位移变化值是荷载分布宽度变化值的2倍;广义Gibson地基分析时划分40层以上可满足计算精度要求,不同泊松比和荷载作用深度下土体体应变、位移均随非均质参数m的增大而减小;m对土体竖向状态变量的影响较为显著且m取值0.0~0.5时更值得关注。
The existing methods for solving the load problem of layered foundation are not perfect.The transfer matrix method often has ill conditioned matrix and data overflow,while the analytical layer element method or stiffness matrix method has some defects,such as difficult inversion of high-order matrix.Firstly,the matrix solution of soil state variables with undetermined coefficients is derived based on the basic equation of three-dimensional elastic statics and Fourier positive transformation.Then,combined with the boundary conditions,the transformation relationship of undetermined coefficients of soil state variables and the inverse Fourier transform,the known coefficient solution of layered foundation state variables is obtained.Finally,the method verification and parameter analysis are carried out for homogeneous semi infinite foundation,three-layer unequal thickness foundation and generalized Gibson foundation.The results show that compared with transfer matrix method and analytical layer element method,this method is not only reasonable and accurate,but also has the advantages of stable numerical calculation,faster solution speed,self-check and unlimited number of applicable soil layers.The relative displacement of interlayer contact surface is directly proportional to the interface slip coefficient and inversely proportional to the distance between loading surface and interlayer contact surface.The change value of interface relative displacement is twice the change value of load distribution width.The number of layers of generalized Gibson foundation is 40,which can meet the requirements of calculation accuracy.Under different Poisson’s ratio and load depth,the volume strain and displacement decrease with the increase of heterogeneous parameter m.The influence of parameter m on the vertical state variable of soil is more significant,and the value of m is more noteworthy when it is 0.0-0.5.
作者
王雨
王锦华
李尉
刘喆
WANG Yu;WANG Jinhua;LI Wei;LIU Zhe(China Academy of Safety Science and Technology,Beijing 100012,China;China Airport Planning and Design Institute Co.,Ltd.,Beijing 100029,China;School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China;Institute of Technical Standards,China Railway Economic and Planning Research Institute Co.,Ltd.,Beijing 100038,China)
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2022年第S02期3390-3401,共12页
Chinese Journal of Rock Mechanics and Engineering
基金
中央高校基本科研业务费专项资金资助(C21JB0500190)
关键词
土力学
成层地基
广义Gibson地基
层间接触
分层系数
优化方法
soil mechanics
multi-layered soil
generalized Gibson foundation
interlayer contact
stratification coefficient
optimization method
作者简介
王雨(1989-),男,2019年于北京交通大学土木工程专业获博士学位,现任工程师,主要从事结构与土体相互作用方面的研究工作。E-mail:wangyu198909@163.com;通讯作者:王锦华(1988-),男,现任工程师。E-mail:13522677087@139.com
