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The analysis of vertical displacements for a hydrotechnical facility using geostatistics. Part II. Determining the probability of displacement occurrence and its prediction

Namysłowska-Wilczyńska B., Wynalek J.

Studia Geotechnica et Mechanica

2011

Vol. 33, nr 2

67-75

The results of the geostatistical spatial analyses of measuring data that reflect the monitoring of vertical displacements of a small hydrotechnical facility are presented. Of some weirs on the Oder River the Opatowice facility was chosen due to the scale of the displacements measured. The databases of current displacements pa and total displacements pc obtained in the X-Y (2D) and X-Y-Z (3D) coordinate systems formed the basis for the geostatistical investigation. The application of variogram function enabled establishing the theoretical parameters of analytical functions that approximate the isotropic and directional empirical variograms of present and total displacements and, as a result, determining the variation of specified parameters for the geostatistical model. Consequently, using the ordinary block kriging method and the methods of quick interpolation, i.e., the inverse distance squared method and the linear kriging model, the raster maps of the mean estimated distributions Z*, estimated standard deviation ?k and also interpolated values of Z* were calculated for the facility analyzed. In further analyses, indicator variograms and raster maps of the probability distributions for displacement occurrence were constructed. This allows determining the subregions with various susceptibilities to exceeding particular probability thresholds of deformation occurrence. A spatial-time prognosis was also made enabling us to calculate of the predicted Z* values for the displacements in successive periods (block diagrams) of hydrotechnical facility operation.

The analysis of vertical displacements for a hydrotechnical facility using geostatistics. Part I. Structural analysis and estimation of displacements

Namysłowska-Wilczyńska B., Wynalek J.

Studia Geotechnica et Mechanica

2011

Vol. 33, nr 1

33-54

The effect of geostatistical studies, including structural analysis, modelling, estimation and forecast, is the cartographic characteristic of the displacements of the hydro-technical object - the Opatowice weir. In the nodes of the spatial grid, covering the object analyzed, the average estimated values Z* of displacements were calculated together with the assessment of the uncertainty of estimation - the standard deviation of estimation ?k. If necessary, the parameters Z* and ?k can be determined directly in the kriging calculation, at every point of the object. The obtained variograms, raster maps and block diagrams represent the spatial visualization of the results of the various displacements, derived from the geodesic monitoring of the dam. Applying an ordinary block kriging it is possible to separate the clear boundaries of the zones of the subsidences and to determine the elevations of the hydro-technical object, marking on the raster maps the distributions of the average Z* values, which can be interpreted as the areas of local deformation that are important when the safety of buildings is considered. The maps of quick interpolation allow identification of a general background of displacements, without the accuracy estimation of the interpolated values Z*. Probability maps enable us to predict the significant risk areas associated with a possible change in the geometry of an object, i.e., its local deformation. Due to an area-time prognosis we can determine the forecasted values Z* of displacements for the following year, with reference to the history of this process, i.e. the estimations from prior years. Taking account of a wide range of different applications of geostatistical techniques, we can conclude that they are also effective tools in the analysis of spatial displacement, in this case, for a relatively small hydro-technical object (weir). The research undertaken may be useful for a complete monitoring of relevant environmental factors, differing only "seemingly identical" objects, and not only for the results of successive control measurements of displacements. These concerns a proper treatment of all spatial and time factors associated with the interpretation of the displacements, which allows the deterministic safety operation of a hydro-technical object to be identified.