层状横观各向同性地基变形问题的一个近似解  

Approximate solution for deformation problems of transversely isotropic multi-layered soils

作　　者：朱桂春 史培新[1] 王占生 ZHU Gui-chun;SHI Pei-xin;WANG Zhan-sheng(School of Rail Transportation,Soochow University,Suzhou 215000,China;Yangzhou Polytechnic Institute,Yangzhou 225000,China;Suzhou Rail Transit Group,Suzhou 215000,China)

机构地区：[1]苏州大学轨道交通学院,江苏苏州215000 [2]扬州工业职业技术学院,江苏扬州225000 [3]苏州市轨道交通集团有限公司,江苏苏州215000

出　　处：《岩土工程学报》2020年第4期790-796,共7页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(51778386);苏州市2018年度第十六批科技发展计划(民生科技)项目(SS201831)。

摘　　要：从横观各向同性平面问题的基本弹性方程出发,利用扩展的瑞利-里兹法,将层状横观各向同性土体划分为多层有限区域及无限区域,每层土体作为一个块体,构造泛函,依据最小势能原理,对泛函进行变分求其驻值,结合边界约束条件,最终求得其近似解。求解过程采用高阶多项式及无穷坐标变换的方法实现了对无穷远处边界的高精度描述,克服了传统有限元方法对无穷远处结构盲目截断的缺点,同时又具有解析法精确求解的优点。根据公式,编制了Mathematica计算程序,得到了非对称荷载作用下层状横观各向同性地基变形的解答,并分析了横观各向同性参数和层状性质对地基变形的敏感程度,最后将其应用到某地连墙成槽施工引起的地层变形计算,研究表明该计算程序可快速简便地求解地连墙成槽施工引起的地层变形,具有较强的工程实用性。This study starts with the fundamental elastic equations for transversely isotropic plane problems by dividing the soil strata into a multi-layered finite region and an infinite region using the extended Rayleigh-Ritz method.Each layer of soil mass is treated as a block,and a function is constructed.The stationary values of the function are sought via the variation method in accordance with the principle of minimum potential.Boundary conditions are considered to seek the approximate solution.The solving process adopts higher-order polynomials and the transformation of infinite coordinates,achieving high accurate description of infinity boundary and overcoming the weakness of blindly truncating the infinity structures by the traditional finite element methods.A Mathematical computation program is compiled based on the formula and the solution to the plane strain problems of layered foundation under asymmetric loading is obtained.The sensitivity of the transversely isotropic parameters and layered properties to the deformation of the multi-layered soils is analyzed.Finally,it is applied to the calculation of ground deformation caused by the construction of a diaphragm wall.The research shows that the proposed program can quickly and easily calculate the ground deformation during slurry trench excavation,and is of engineering significance.

关 键 词：横观各向同性 层状地基 瑞利-里兹法 近似解 

分 类 号：TU433[建筑科学—岩土工程] TV642[建筑科学—土工工程]