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.