deformation analysis( CODA). For example, the principle of complex deformation analysis has been applied in [ 28 ] for the analysis of dam deformation with four methods. The identification of movements using different geodetic methods led to the conclusion that the modified Karlsruhe Method and the method implemented in the JAG3D software yielded satisfactory results in deformation analysis [ 27 ].
1.1. Numerical example
A leveling network consisting of four points has been analyzed( fig. 1). The standard deviation of the height measurements per km is adopted at 0.8 mm / km. The preliminary known displacement of point 10 is-2.4 mm. The first and second epoch deformation measurements are presented in tab. 1 and tab. 2.
Fig. 3. Leveling network
After four sequential adjustments with fixed points one by one- with points 10, 11, 12 and 13, the displacements and related mean square errors computed with respect to points 10, 11, 12 and 13 indicate statistically changed height differences.
Table 1. First epoch deformation measurements |
From |
To |
height difference [ m ] |
leveling line [ m ] |
10 |
11 |
-0.3274 |
211 |
10 |
12 |
-0.1887 |
60 |
10 |
13 |
-0.4187 |
216 |
11 |
12 |
0.1392 |
169 |
11 |
13 |
-0.0915 |
205 |
12 |
13 |
-0.2304 |
68 |
Table 2. Second epoch deformation measurements |
From |
To |
height difference [ m ] |
leveling line [ m ] |
10 |
11 |
-0.3250 |
211 |
10 |
12 |
-0.1861 |
60 |
10 |
13 |
-0.4163 |
216 |
11 |
12 |
0.1394 |
169 |
11 |
13 |
-0.0916 |
205 |
12 |
13 |
-0.2306 |
68 |
119