互补算法在一维非线性固结求解中的应用  

Application of complementary algorithm for solving one-dimensional nonlinear consolidation

作　　者：邓岳保[1] 谢康和[1] 

机构地区：[1]浙江大学岩土工程研究所,杭州310058

出　　处：《岩土力学》2011年第9期2656-2662,共7页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.50878191)

摘　　要：以一维非线性固结为例,介绍了互补算法在固结问题求解中的应用。将地基土体的压缩特性曲线进行分段线性拟合并引入控制变量,得到土体孔隙比与有效应力间的统一关系式,并获得压缩曲线中的互补关系;详细推导了以孔隙比与有效应力为变量的一维非线性固结微分方程,通过对其进行差分求解,并结合压缩曲线中的互补条件,使得不同时刻的非线性固结问题转化为标准的线性互补问题。这样,非线性固结问题可通过在线性固结差分法中嵌入互补模型算法进行求解。该法的合理性通过与普通迭代算法进行对比获得证明。在此基础上,对一维固结问题线性与非线性解答的差异及影响非线性计算的因素进行了分析。计算中发现,互补模型算法在计算效率方面优于普通迭代法;线性计算程序中嵌入互补模型算法计算非线性固结在程序上容易实现;互补模型算法中通过对控制变量的求解,可判断地基土体所处的压缩状况。This paper focuses on solving a one-dimensional nonlinear consolidation problem with the complementary algorithm.Firstly,a piecewise linear function is used to fit the compression curve of foundation soil.With a control variable introduced,a unified relationship between the void ratio and the effective stress and complementarities of compression curve are obtained.After the differential equation of one-dimensional nonlinear consolidation derived in detail,which including void ratio and effective stress as variables,the problem of nonlinear consolidation at different stages is translated into a standard linear complementarity model by carrying out the finite difference method combined complementarities of compression curve.Consequently,problem of nonlinear consolidation can be solved by linear solving method with the complementary algorithm embedded in.Then,the method proposed here is validated by contrasting with general iterative method.On the basis,the difference of linear and nonlinear solution and all the factors of nonlinear calculation are investigated.And it is found that complementary model algorithm method is superior to general iterative method in calculation efficiency;and it is easy to carry out when embedding the complementary algorithm into a linear calculation program to compute nonlinear consolidation.Also,with the solution of control variables in complementary model algorithm method,the compression condition of foundation soil can be estimated.

关 键 词：一维固结理论 非线性分析 互补算法 线性互补模型 

分 类 号：TU433[建筑科学—岩土工程]