1. THEORY AND PRACTICE OF DEFORMATION SURVEYING AND ANALYSIS
Measurements of deformations by surveying methods are of primary importance due to the risk of landslides, structural movements, stability assessments of buildings, etc. In Switzerland, the engineers Lang and Zölly employed geodetic methods for deformation studies in the 1920s [ 16 ]. In the 1950s, 1960s, and 1970s, Polish Professor T. Lazzarini applied new methods and solutions that contributed to the creation of the foundations of deformation analysis surveys. Prof. T. Lazzarini pioneering work also led to the creation of Working Group 6.1 of FIG Commission 6. He introduced the concept and method of differential deformation analysis. Analysis of deformation measurements may be made by using robust and non-robust methods [ 3 ], [ 8 ], [ 15 ], [ 21 ], [ 22 ], [ 32 ]. Analysis of deformation measurements can be performed with invariant( angle differences, distance differences, etc) [ 4 ], [ 18 ], [ 25 ] and non-invariant methods. The displacements of points can be obtained directly from measurements or after the adjustment. In the geodetic practice of stable point deformation analysis, the following known methods are used [ 11 ], [ 14 ], [ 29 ]– the Karpenko method, the Runov method, the Ganishin method, the Storozhenko method, the Costachel method, the Botyan method, the Martuszewicz, the Marchak and the Chernikov methods. Several of those methods are examined, and comparative analysis has been made [ 1 ].
Free or constrained network adjustment is used for deformation surveys [ 2 ]. An example of geotechnical engineering multi-criteria methods are the methods to analyze slope stability and critical slip surface – Fellenius, Bishop, Janbu, Spencer, Morgenstern and Price, etc. Similarly, the concept of multi-criteria methods can be applied to deformation analysis, which leads to the concept of complex deformation analysis( CODA), where the methods for analyzing deformation should be named after the names of their inventors. The scientific research pointed out the names of authors who created new methods for determining the reference points stability-Pelzer, Heck et al., Lazzarini, Polak, van Mierlo, Niemeier [ 9 ]. In some literature sources there is a so-called Caspary method named after Caspary [ 12 ]. These are some of the scientists who laid the foundations of modern deformation analysis and surveys. The five world-famous schools in deformation analysis called by the names of their locations are Delft, Fredericton, Hanover, Karlsruhe, and Munich [ 17 ], [ 26 ], [ 30 ]. The scientists behind the research centers are:-Delft( J. van Mierlo and J. J. Kok)-Fredericton( A. Chrzanowski, Y. Q. Chen, J. M. Secord)-Hanover( H. Pelzer and W. Niemeier)-Karlsruhe( B. Heck, E. Kuntz and B. Meier-Hirmer)-Munich( W. Welsch)
A central part of the methods of deformation analysis is the Hanover School( global congruency test) [ 20 ] and the Fredericton School( Iterative Weighted Similarity Transformation-IWST) [ 9 ], [ 10 ], [ 31 ]. This, respectively, laid the foundation for the methods employed in the study of the stability of points: the Pelzer-Niemeier method and the Chen-Chrzanowski-Secord method [ 13 ].
In practice, the Penev and Milev methods can be used for finding point stability. P. Penev created a rigorous theoretical justification of the methods for determining the stability of the reference benchmarks based on the use of constant average height [ 24 ]. With the Milev method to identify stable points and benchmarks from reference networks and to find the movements of the remaining points followed next strategy-leveling benchmarks one by one is accepted as stable and heights and mean square errors of the remaining points are calculated. After this process, every point will have several mean square errors. The minimal mean square error of every point is accepted in the analysis. This procedure increases the power of statistical tests [ 18 ].
For deformation analysis we need the displacement vector between two epochs and the mean square error of the displacement vector. The displacement vector is found from the coordinate differences. The displacement vector ' s mean square error is calculated using the mean square errors of the first and second epoch deformation surveys. The ratio greater than 2.0 is the test statistic for whether significant movements of the points have occurred at the 95 % confidence level [ 7 ]. The PhD thesis presented in [ 19 ] underlines the need for effective deformation analysis methods, because some deformation concepts aren ' t effective in deformation analysis. In the context of modern deformation analysis, to find stable points in geodetic networks, several methods can be used, which leads to the concept of complex
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