Modelling fields of local displacement for estimating an analysis of tensor deformation

Abstract

The knowledge of the behavior of three-dimensional displacements fields is an
important requirement in the task of analysis of structures deformations, be them
natural or artificial. However, as the geodetic observations are usually accomplished
in a finite number of points of the study area, it is necessary to use a mathematical
tool of interpolation for the knowledge of such behavior. This way, the aim of this
work is to present the concepts involved in the modelling of local displacements
fields from three-dimensional displacements obtained by means of the Global
Positioning System (GPS). For the attainment of this objective a three-dimensional
polynomial model of second degree is used. The coefficients of this model are
calculated by a least square adjustment. After this stage, convenient statistical tests
are accomplished for the suitable analysis of the quality of the adjusted model, as
well as, for the verification of the significance of the estimated coefficients. Later,
these concepts werw applied in the three-dimensional displacements detected in the
region of Salto Caxias Hydroelectric Power Dam, where it was found out that the
results were satisfactory, once the polinomial function modeled was able to
determine, also, the deformation parameters in each one of the observation points.
Finally, the obtained results and its conclusion will be presented in this paper.