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This paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil