International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
datum point, the group of datum points is divided in to two 
parts: the first part includes the datum points, which are 
assumed as stable and the second part includes the datum point, 
which is assumed as instable. And all the computation steps are 
repeated for each datum points. By this way, for all of the 
datum points, the probability of to be stabile or not has been 
tested. At the end, the exact datum points are derived. 
5.2 Determining the Deformation Values 
After determining the significant point movements, the block of 
datum points, which don’t have any deformations, are to be 
determined. By the help of these datum points, both epochs are 
shifted the same datum and deformation values are computed as 
explained below. 
The deformation vector for point P: 
i .1 
Xk Xk d, 
d-ly1-»k |7|d, 
J i d 
Z2 7k 2 
and the magnitude of the vector: 
d=yd'd 
To determine the significance of these deformation vectors, 
which are computed according to above equations, the Ho null 
hypothesis is carried out as given below. 
Hy qd =0 
And the test value: 
dTQ ld 
_# Out 
2 
380 
T 
While this test value is compared with critical value, 
FS f -« and if TE. f1-a* it is said that there is a 
significant 3D deformation in point P (Denli, 1998). 
After GPS Data evaluation, 3D deformation analysis was 
carried out as it is mentioned. After the analyses, the founded 
horizontal displacements can be seen in Figure 5. 
tie eer, 
4550622 45 " 
4552464 265 i 
Northing 
Northiag 
455464 35-| 
  
> e 
22 43 
à : 5 4662022310 + Y 
35a 377775465 kas 495 39440 376443505 375443510 376443515 
Easting 
317175480 
em 
Eastng 
Figure 5: Horizontal displacements in points 2 and 4. 
6. RESULTS and CONCLUSION 
As is very well known that, the weakest component of a 
position obtained by GPS is the height component. This is 
mainly because of the weakness of geometric structure of GPS. 
Because of this GPS technology in determining vertical 
deformations, it has to be supported by precise levelling 
measurements in vertical positioning. 
In the first step of the process, the data, which were handled 
from both measurement methods, were processed for each 
epoch separately. By this way, the results, which had been 
derived from the independent solutions for each epoch, were 
compared. This was done to obtain an impression of the quality 
of the data, of possible inherent problems and to get first hints 
on instable points, thus, allow applying a suitable deformation 
analysis strategy. This operation covers the only height 
component. In the result of this comparison, the benefits of the 
precise levelling measurements have been seen. The precise 
levelling measurements have an effective role for checking the 
heights derived from GPS measurements and also for clarifying 
the antenna height problems, which could be occurred during 
the GPS measurements and effect the height component 
directly. 
After these processes, deformation analyses were carried out by 
using height differences from levelling measurements, fe 
GPS measurements and also by using combination of height 
differences from both GPS and levelling measurements 
respectively. In general meaning, the results were confirmed 
each other. In the results, it was surprisingly found that the 
maximum height changes were in point 2 and point 4 (as it is 
seen in the graphics), which were assumed as stabile at the 
beginning of the project and even though that their 
constructions are pillar. According to analysis of precise 
levelling data, on the contrary of the situation in point 2 and 
point 4, there weren't seen any changes in heights in the 
deformation points on the viaduct. On the other hand, 
according to the second evaluation (using GPS derived height 
differences) in some points on the viaduct, height changes were 
reported. 
In the third evaluation, as a result of the Helmert Variance 
Component Estimation it was computed that the weight of 
height differences from levelling equals to 30 times of the 
weight of GPS derived height differences. This result was 
reached in the third iteration step. 
In the graphics, height changes according to consecutive 
measurement campaigns are seen. As the graphics of the first, 
the second and the third evaluations are compared, it is not 
reliable enough to use GPS measurements without special 
precautions for the GPS error sources, such as multipath, 
atmospheric effects, antenna height problems etc., in vertical 
deformation analysis of engineering structures. According to 
investigation of the result of the second evaluation, it was seen 
changes in heights of some points on the viaduct. However, 
while the first and third evaluations are considered, it is 
understood that these changes, seemed to be deformations on 
the object point of the viaduct according to results of the second 
evaluation, were not significant and caused by the error sources 
in GPS measurements especially antenna height problems. 
Thereafter, the 3D deformation analysis were carried out 
according to theoretical aspects that were explained in section 5 
and the results of the priory adjustments and 1D deformation 
analysis aid to the decision phase of 3D deformation analysis, 
while the network points are being grouped as stable or instable. 
According to analyses results, horizontal displacements were 
investigated in point 2 and point 4 in the outside of the viaduct 
(see Figure 5). 
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