ACCURACY ASSESSMENT OF THE PRINCIPAL STRAINS IN DEFORMATION ANALYSIS

Abstract

Research Object and Relevance. The main components of the strain tensor and their accuracy assessment are the research objects in this work. When conducting monitoring using geodetic methods, it is usually not enough to determine only the displacements of reference points; it is also necessary to determine the presence and magnitude of deformations. This task is directly related to the accuracy assessment of such characteristics as principal strains, dilatation, shear strains, and rotation. Research Methods. In conducting this research, the authors used a system of equations arising on a local subdomain of triangular shape in the finite element method for a twodimensional deformation model. The parametric principle of accuracy assessment was applied, where the components of the strain tensor were taken as parameters. Results. More rigorous formulas for the mean square error functions of principal strains have been found. The influence on their accuracy assessment of both the triangle shape and the directions of principal strains is shown. Based on geodynamic monitoring data of a tailings dam, mathematical modeling of the influence of the finite element shape on the possible error in the accuracy assessment of principal strains was carried out. Discussion. The results of analyzing the influence of covariances that arise naturally between the components of the strain tensor show the most interesting results when assessing the accuracy of principal strain components. The non-symmetry of principal strain accuracy estimates for a triangular element shape other than an equilateral triangle is convincingly shown. Conclusion. This study demonstrates the need for more rigorous approaches to assessing the accuracy of deformation characteristics. Incorrect interpretation of monitoring results can lead to both unnecessary labor and financial costs, as well as fatal consequences due to incorrect assumptions in calculations.