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

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.