# Thermally Induced Displacements and Rotations of Pillars for Precise Geodetic Measurements
## 5 Conclusions  
Prior to the construction of large infrastructure projects (such as tunnels and viaducts), a network of geodetic points must be established. These points are used throughout the construction process and afterwards for all geodetic measurements. They are usually  
Figure 8: Comparison of the obtained data: (**a**) absolute values; (**b**) absolute errors of calculated results.  
stabilized with pillars, which should remain fixed during and after construction. In practice, however, many pillars have proven to be insufficiently stabilized as they have too small a cross-section and are encased in black-colored pipes. When exposed to sunlight, the sunlit side of these pillars heats up much more than the shaded side, which leads to thermal stresses and consequently to the pillar bending. The displacement of the forced-centering screw for the instrument can therefore be considerable. The key observations and contributions of our paper are as follows:  
1. Measuring the displacement of a column caused by thermal stress in the field is almost impossible, as isolating the displacement sensor mount from external influences is a major challenge. However, it is much easier to isolate an inclinometer mounted on the column, which measures the inclination of the plate that holds the screw for forced centering. From the measured inclination, the thermally induced displacement can be calculated without much effort.
2. In the laboratory, we heated a test column from one side and measured the temperatures on the hot and cold sides, the inclinations at the top of the column and on the side, as well as the displacements.
3. Using the equations presented, we calculated the displacements from the measured angles and adjusted them to the level of the displacement sensor so that the calculated displacements were directly comparable.
4. The displacement curves derived from the inclination measurements agree very well with the directly measured displacements over time.
5. During the heating phase, the temperature on the heated side of the pillar increased by 25.4 K, resulting in a lateral displacement of approximately 1 mm at the top of the pillar. The difference between measured displacements and the ones calculated from inclinations was less than 0.1 mm.  
Thus, this paper presents a reliable indirect method for determining the displacement of geodetic measurement pillars due to thermal loading, a common problem caused by inadequate pier design.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15094678/s1](https://www.mdpi.com/article/10.3390/app15094678/s1)]([https://www.mdpi.com/article/10.3390/app15094678/s1](https://www.mdpi.com/article/10.3390/app15094678/s1)), Inclinometer data; Temperature Displacement data.  
This work was achieved in collaboration among all authors. Conceptualization--[PERSON], [PERSON] and T.A.; Formal analysis--[PERSON] and [PERSON]; Investigation--[PERSON]; Methodology--[PERSON], [PERSON] and A.P.; Project administration--[PERSON]; Supervision--[PERSON]; Visualization--[PERSON] and T.A.; Writing, original draft--[PERSON], [PERSON], [PERSON] and T.A. All authors have read and agreed to the published version of the manuscript.  
The research was financially supported by the Slovenian Research and Innovation Agency (ARIS) through research core funding No. P2-0227 Geoinformation Infrastructure and Sustainable Spatial Development of Slovenia, No. P2-0260 Structural Mechanics and No. P2-0268 Geotechnology.  
Not applicable.  
The original contributions presented in this study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding author.  
The authors would like to express their gratitude to [PERSON] and [PERSON] from Igmat d.d., Slovenian Building Materials Institute, for conducting the measurements on the test column.  
[PERSON] is affiliated with Mariborski vodovod d.d. The authors declare that this affiliation had no influence on the design, execution, or interpretation of the research.