Application of Multi-Parameter Transformation in Deformation of Dam

Abstract

Objects and engineering structures are subject to displacements resulting from numerous internal and external factors. Determination of the magnitude of these displacements is possible on the basis of cyclic measurements of changes in position of points determining the geometrical shape of the studied object. Processing the measurement results is aimed at determining the characteristics of the changes and assessment of possible hazards. The paper proposes a methodology for processing repeated GPS data from two-measurement epoch 2010 and 2011 using a model that utilizes multi-parameter transformation, relating original and repeated observations. The mathematical model was applied to original and repeated Global positioning system (GPS) station observations made to target points at Ikpoba Dam in Benin City. The transformation consisted of a parameter similarity transformation at the reference station (translations in the X-, Yand Z-directions at the instrument station, and rotations about the X-, Y-and Z-axes), plus a scale factor relating original and repeated instrument-target. Using MATLAB programme, three control points were transformed and the coordinates of all other monitoring and reference stations were obtained with reference to the transformed control points.Points displacement between the measurement epoch were then computed from the transformed coordinates. The results obtained showed a maximum error of 1mm on the X coordinate, 2mm on the Y coordinate and 7mm in elevation.