Geostatistical Investigations of Displacements on the Basis of Data from the Geodetic Monitoring of a Hydrotechnical Object

Barbara Namysłowska-Wilczyńska 1  and Janusz Wynalek 1
  • 1 Wrocław University of Science and Technology, Faculty of Civil Engineering, 50-370, Wrocław, Poland

Abstract

Geostatistical methods make the analysis of measurement data possible. This article presents the problems directed towards the use of geostatistics in spatial analysis of displacements based on geodetic monitoring. Using methods of applied (spatial) statistics, the research deals with interesting and current issues connected to space-time analysis, modeling displacements and deformations, as applied to any large-area objects on which geodetic monitoring is conducted (e.g., water dams, urban areas in the vicinity of deep excavations, areas at a macro-regional scale subject to anthropogenic influences caused by mining, etc.). These problems are very crucial, especially for safety assessment of important hydrotechnical constructions, as well as for modeling and estimating mining damage.

Based on the geodetic monitoring data, a substantial basic empirical material was created, comprising many years of research results concerning displacements of controlled points situated on the crown and foreland of an exemplary earth dam, and used to assess the behaviour and safety of the object during its whole operating period. A research method at a macro-regional scale was applied to investigate some phenomena connected with the operation of the analysed big hydrotechnical construction.

Applying a semivariogram function enabled the spatial variability analysis of displacements. Isotropic empirical semivariograms were calculated and then, theoretical parameters of analytical functions were determined, which approximated the courses of the mentioned empirical variability measure. Using ordinary (block) kriging at the grid nodes of an elementary spatial grid covering the analysed object, the values of the Z* estimated means of displacements were calculated together with the accompanying assessment of uncertainty estimation – a standard deviation of estimation σk. Raster maps of the distribution of estimated averages Z* and raster maps of deviations of estimation σk (in perspective) were obtained for selected years (1995 and 2007), taking the ground height 136 m a.s.l. into calculation. To calculate raster maps of Z* interpolated values, methods of quick interpolation were also used, such as the technique of the inverse distance squares, a linear model of kriging, a spline kriging, which made the recognition of the general background of displacements possible, without the accuracy assessment of Z* value estimation, i.e., the value of σk. These maps are also related to 1995 and 2007 and the elevation.

As a result of applying these techniques, clear boundaries of subsiding areas, upthrusting and also horizontal displacements on the examined hydrotechnical object were marked out, which can be interpreted as areas of local deformations of the object, important for the safety of the construction.

The effect of geostatistical research conducted, including the structural analysis, semivariograms modeling, estimating the displacements of the hydrotechnical object, are rich cartographic characteristic (semivariograms, raster maps, block diagrams), which present the spatial visualization of the conducted various analyses of the monitored displacements.

The prepared geostatistical model (3D) of displacement variability (analysed within the area of the dam, during its operating period and including its height) will be useful not only in the correct assessment of displacements and deformations, but it will also make it possible to forecast these phenomena, which is crucial when the operating safety of such constructions is taken into account.

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  • [1] Clark I., Practical geostatistics, Appl. Sc. Publishers, London, 1979, 1–129.

  • [2] David M., Handbook of Applied Advanced Geostatistical Ore Reserve Estimation Developments in Geomathematics, Elsevier Science Publishers, B.V., Amsterdam, the Netherlands 1988, 1–216.

  • [3] Journel A.G., Huijbregts C.J., Mining Geostatistics, Academic Press, London, New York, San Francisco, 1978, 1–600.

  • [4] Kiciak P., Podstawy modelowania krzywych i powierzchni, Wydawnictwa Naukowo-Techniczne, Warszawa 2000.

  • [5] Matheron G., Traite de Geostatistique Appliquee: Memoires du Bureau de Recherches Geologique et Minieres, vd. 14, Editions Technip., Paris 1962, 1–333.

  • [6] Mucha J., Metody geostatystyczne w dokumentowaniu złóż, AGH, Kraków 1994, 1–155.

  • [7] Namysłowska-Wilczyńska B., Zmienność złóż rud miedzi na monoklinie przedsudeckiej w świetle badań geostatystycznych, Prace Naukowe Instytutu Geotechniki i Hydrotechniki Politechniki Wrocławskiej nr 64. Seria: Monografie nr 21, Wrocław 1993, 1–207.

  • [8] Namysłowska-Wilczyńska B., Geostatystyka. Teoria i zastosowania, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2006, 365.

  • [9] Namysłowska-Wilczyńska B. (ed.)., Modelowanie Procesów Hydrologicznych, Praca zbiorowa Namysłowska-Wilczyńska B., Modelowanie i prognozowanie (3D) wysokości opadu atmosferycznego i zawartości siarczanów SO4 w opadzie na obszarze dorzecza środkowej Odry z zastosowaniem geostatystyki, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2008, 526, 35–74.

  • [10] Namysłowska-Wilczyńska B., Pyra J., Integration of Data from Soil and Underground Waters Monitoring Grids by Kriging with External Drift, Processing of Terra Nostra, 8th Annual Conference of the International Association for Mathematical Geology (IAMG 2002), Berlin, 15–20 September 2002, 475–480.

  • [11] Namysłowska-Wilczyńska B., Pyra J., Rola precyzji ocen parametrów środowiskowych w edukacji ekologicznej, Polskie Towarzystwo Inżynierii Ekologicznej, Edukacja Ekologiczna. Podstawy Działań Naprawczych w Środowisku. Wydawnictwo Naukowe Lublin, Nałęczów 2004, 199–213.

  • [12] Namysłowska-Wilczyńska B., Rusak K., Geostatistics description of heavy metal content variation in soil of Olkusz region against a background of geological structure by GIS metod, Mathematische Geologie, Vol. 7, Mathematical Methods Applied to Geology and Mining, Mining. Mathematische Methoden in Geologie und Bergbau, CPress Verlag. Band 7, Dresden, December 2003, 51–63.

  • [13] Namysłowska-Wilczyńska B., Rusak K., Zastosowanie geostatystyki i GIS do analizy wpływu czynników naturalnych i antropogenicznych na koncentrację metali ciężkich w glebach rejonu olkuskiego, Polskie Towarzystwo Informacji Przestrzennej, Warszawa. III Ogólnopolskie Sympozjum Geoinformacyjne “Geoinformacja w Badaniach Przestrzennych”, Warszawa, 7–9.11.2005, Roczniki Geomatyki, 2005, z. 2, t. III, 115–124.

  • [14] Namysłowska-Wilczyńska B., Wynalek J., The analysis of vertical displacements for a hydrotechnical facility using geostatistics. Part 2. Determining the probability of displacement occurrence and its prediction, Studia Geotechnica et Mechanica, 2011, Vol. 33, No. 2, 67–75.

  • [15] Namysłowska-Wilczyńska B., Wynalek J., The analysis of vertical displacements for a geotechnical facility using geostatistics. Part 1. Structural analysis and estimation of displacements, Studia Geotechnica et Mechanica, 2011, Vol. 33, No. 1, 33–54.

  • [16] Namysłowska-Wilczyńska B., Skorupska B., Wieniewski A., Analiza geostatystyczna zmienności parametrów technologicznych popiołożużli zdeponowanych na składowisku odpadów przemysłowych, Ochrona Środowiska, 2012, Vol. 34, nr 2, 43–48.

  • [17] Namysłowska-Wilczyńska B., Geostatistical methods used to estimate Sieroszowice cop per ore deposit parameter, Zeitschrift für Geologische Wissenschaften, Journal for the Geological Sciences, Berlin, 2012, 40(6), 329–361.

  • [18] Namysłowska-Wilczyńska B., Geostatistical hydrogeochemical 3D model for Kłodzko underground water intake area. Part I. Estimation of basic statistics on quality parameters of underground waters, Studia Geotechnica et Mechanica, 2013, Vol. 35, No. 1, 157–181.

  • [19] Namysłowska-Wilczyńska B., Szacowanie parametrów jakościowych wody podziemnej z wykorzystaniem krigingu zwyczajnego dla obszaru ujęć w rejonie Kłodzka, Monografia XX KK KOWBAN 2013 Krajowej Konferencji “Komputerowe Wspomaganie Badań Naukowych”, Polanica Zdrój, 23–25.10.2013.

  • [20] Namysłowska-Wilczyńska B., Wynalek J., Analiza przestrzenna pola przemieszczeń na podstawie monitoringu geodezyjnego, Infobazy 2014, Inspiracja – Integracja – Implementacja: VII Krajowa Konferencja Naukowa, Gdańsk–Sopot, 8–10 września 2014, Gdańsk: Politechnika Gdańska, [2014], Dokument elektroniczny (pendrive), 1–12.

  • [21] Namysłowska-Wilczyńska B., Wynalek J., Badania geostatystyczne przemieszczeń na podstawie danych z monitoringu geodezyjnego obiektu hydrotechnicznego, Zeszyt Streszczeń Referat: XI Konferencja Naukowo-Techniczna KNTPH “Problemy Hydrotechniki”, Świeradów-Zdrój, 10–12 maja 2017, 52–53.

  • [22] Osada E., Analiza, wyrównanie i modelowanie geo-danych, Wyd. Akademii Rolniczej we Wrocławiu, 1998.

  • [23] Rejman J., Woźniak J., Geograficzne Systemy Informacyjne w badaniach współczesnych ruchów skorupy ziemskiej, Materiały III Krajowej Konferencji – Komputerowe Wspomaganie Badań Naukowych III KK KOWBAN ’96, Wrocławskie Towarzystwo Naukowe, Wrocław, 17–19 października 1996, 193–198.

  • [24] Wackernagel H., Multivariate Geostatistics, Springer-Verlag, Berlin, Heidelberg, New York, 1995, 256.

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