关键词: 大坝沉降, 非确定性分析, 区间场有限元, Karhunen-Loève分解, Galerkin方法

Abstract: The settlement analysis of a dam faces a complicated nonlinear problem due to the coupling of internal and external factors during its construction and operation. The dam settlement interval established using the non-probability method helps the quantitative description of multi-source uncertain information, making the calculation more agreeable with the real case. This paper describes a new method of combining the Duncan-Chang model calculations of dam settlement with the Karhunen-Loeve decomposition, through extending the interval field finite element method from the linear elastic model to a nonlinear model. In this method, the variability of tangential modulus is described using a spatial dependence function in the form of square exponents; the Galerkin method with the Legendre polynomial basic functions is used to calculate the eigenvalues and eigenfunctions of variable modulus characteristics. We have coded an Abaqus user subroutine UMAT to implement the interval Duncan-Chang model, and adopted a Python script to calculate the response interval of dam settlement stress to the variations in modulus parameters, with the settlement interval so calculated being compared with the traditional vertex method. Analysis of engineering cases shows that our new method can effectively calculate the dam’s settlement interval that covers the vertex interval, and that the cost of finite element calculations is reduced from exponential to polynomial. The method can be further extended to the analysis of long-term dam deformation.

Key words: dam settlement, non-deterministic analysis, interval finite element method, Karhunen-Loève decomposition, Galerkin method