邓岳保, 谢康和. 基于互补算法的结构性软基一维非线性固结解[J]. 工程力学, 2012, 29(3): 163-169.
引用本文: 邓岳保, 谢康和. 基于互补算法的结构性软基一维非线性固结解[J]. 工程力学, 2012, 29(3): 163-169.
DENG Yue-bao, XIE Kang-he. SOLUTION FOR ONE DIMENSIONAL NON-LINEAR CONSOLIDATION OF STRUCTURED SOIL WITH COMPLEMENTARY ALGORITHM[J]. Engineering Mechanics, 2012, 29(3): 163-169.
Citation: DENG Yue-bao, XIE Kang-he. SOLUTION FOR ONE DIMENSIONAL NON-LINEAR CONSOLIDATION OF STRUCTURED SOIL WITH COMPLEMENTARY ALGORITHM[J]. Engineering Mechanics, 2012, 29(3): 163-169.

基于互补算法的结构性软基一维非线性固结解

SOLUTION FOR ONE DIMENSIONAL NON-LINEAR CONSOLIDATION OF STRUCTURED SOIL WITH COMPLEMENTARY ALGORITHM

  • 摘要: 以往采用半解析法及有限差分法计算结构性土一维非线性固结时,常需建立分段描述的控制方程,这给问题的表述及求解带来不便。该文以e、σ'为双状态变量进行推导,得到形式上统一的非线性固结方程。通过将互补算法嵌入到上述方程的差分求解过程,解决了地基土体结构性破坏界面难确定的问题。互补算法首先寻求分段线性e-lgσ'压缩曲线中的互补条件,并以此构造互补方程组,然后利用互补算法进行求解,进而可得各增量时间步差分进程中e-σ'关系所处阶段。该法的合理性通过与传统单变量差分解及解析解进行对比得到验证,并得到:双变量非线性固结控制方程形式上统一、推导过程较单变量法简单,且适用于任意的压缩模型;通过对压缩曲线中控制变量求解,可判断结构性软土地基所处的压缩状态;基于互补算法的差分解具有较高的计算精度,且求解效率优于一般迭代法。

     

    Abstract: Previous numerical methods such as semi-analytical solutions or finite difference method usually require solving equations described in subsection, which causes inconvenience in calculating nonlinear consolidation for structured soil. Different from traditional derivation process with single variable, this paper formulized governing equations of non-linear consolidation through introducing dual variables of e and σ'. For the purpose of ascertaining failure interface of structured soil, complementary algorithm was embedded into finite difference method. Firstly, complementary conditions were dug out from piecewise linear compression curve of e-lgσ'. Then, a series of complementary equations were established and the complementary algorithm was brought forward to solve them. Sequentially, relations of e-σ' which reflect the compression state of soil can be determined in the incremental time-step process of finite difference method. Lastly, traditional general single-variable method and analytical solution were used to demonstrate the reasonability of the proposed approach. And it can be seen that a unified two-state variable equations can be formulized into the equations derived from e-σ' and the derivation process of the equation is more concise than single-variable method. Also, the dual variable equations can be applied to any compression mode. With the solution of control variables in the new method, compression condition of foundation soil can be ascertained. In addition, the proposed method which based on complementary algorithm is of high accuracy and is superior to general iterative method in calculation efficiency.

     

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