墙下条形基础与层状横观各向同性地基共同作用  

Interaction between strip foundation under wall and transversely isotropic layered soils

作　　者：艾智勇[1,2] 张逸帆[1,2] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《岩土力学》2016年第5期1243-1248,共6页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.50578121)~~

摘　　要：运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶(Fourier)变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比(Jacobi)正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。In this paper, dual integral equations are presented to solve the interaction problem between the strip foundation under wall and transversely isotropic layered soils. Starting with the governing equations of plane strain problem in rectangular coordinates, the transfer matrix solution of layered soils can be obtained through the Fourier transform and the continuity conditions between two adjacent layers. Based on the transfer matrix solution of layered soils and the mixed boundary conditions of the contact problem, a pair of dual integral equations of subgrade reactions and the deflection of the footing is derived. The deflection is solved by elastic thin plate theory in the case that the strip foundation is subjected to vertical concentrated load. Dual integral equations are further converted to linear equations by means of the Jacobi orthogonal polynomials and series expansions. The results of numerical calculation carded out by the corresponding computer program are compared and agree well with those by FEM software ABAQUS, which proves the correctness of the method in this paper. Further numerical examples prove that the plate-soil stiffness ratio and the stratification of soils have a significant effect on subgrade reactions, surface settlement and vertical normal stress along the z - axial.

关 键 词：横观各向同性 层状地基 墙下条形基础 对偶积分方程 

分 类 号：TU470[建筑科学—结构工程]