Development of Assessment Methodology for the Probabilistic Characteristics of Random Spatial Inhomogeneity of Geomassifs
摘要
The authors address the problem of accounting for spatial inhomogeneity of the properties of geomaterials using the theory of random fields. The limitations of the approach based on random variables is noted; thus, this approach fails to take into account the dimensions of structures and elements of geomassifs. Although being more adequate, the model of random fields is difficult to implement in practice not only due to the challenges of solving problems of the mechanics of randomly inhomogeneous media, but also due to the lack of reliable estimates of its probabilistic characteristics obtained from engineering survey data. A new methodology for assessing the correlation function for a two-dimensional random field is proposed. The proposed methodology is intended for processing data obtained on a regular grid (using the example of testing a concrete slab with a sclerometer). The algorithm, implemented in the Mathcad computational environment, permits the effective use of all statistical information about the mutual location of measurement points, compared to methods that analyze data solely along the coordinate axes. The developed methodology may serve as a basis for creating data processing algorithms for more complicated conditions (random point location, three-dimensional cases, etc.). In addition, the proposed methodology can be used to obtain validated estimates of the initial data when solving problems of structural reliability theory and geomechanics, taking the stochastic inhomogeneity of geomassifs into account.