岩土参数随机场离散的三角形单元局部平均法

将不确定性岩土参数建模为随机场而非传统意义上的随机变量,基于随机场的局部平均理论,提出了用于二维随机场离散的三角形单元局部平均法。通过面积坐标变换和高斯数值积分,给出了三角形单元局部平均随机场协方差矩阵的解析计算方法和数值计算方法。采用算例再现了所提方法的分析过程和有效性,并与传统二维随机场四边形单元离散法进行了对比。结果表明:提出的二维随机场三角形单元离散法能与有限元三角形单元离散法完美结合,随机场单元与有限元单元的对应关系清晰,易于随机有限元程序的编制;对于随机场单元的均值,传统四边形单元离散法与所提方法的计算结果相同;对于随机场单元的方差,传统四边形单元离散法计算结果偏小,所提方法显得更加科学、合理。

Local average method of triangular elements for discretization of random field of geotechnical parameters

By modeling the uncertain geotechnical parameters as spatially random fields instead of traditional random variables, a local average method of two-dimensional triangular elements is proposed based on the local average theory of random field. The analytical calculation and numerical calculation for the covariance matrix of triangular elements of the local average random field is provided by the transformation of area coordinates and the Gauss numerical integration. An illustrative example is presented to demonstrate the analysis process and the validity of the proposed method; and the advantage of the proposed method is proven by comparing these results with the results derived when the random fields of geotechnical parameters are divided based on arbitrary quadrilateral elements method. The results show that the local average method of triangular elements can perfectly combine with the finite element method of triangular elements; and the corresponding relation is clearer; and the program is simpler. For the mean of the random field mesh, the calculation results are the same based on the proposed method and the arbitrary quadrilateral elements method. For the variance of the random field mesh, the calculation results are smaller based on arbitrary quadrilateral elements method. Therefore, the local average method of triangular elements is more scientific and reasonable.