# Thermally Induced Displacements and Rotations of Pillars for Precise Geodetic Measurements
## 1 Introduction  
The field of view of the pillar is a fundamental tool for understanding the dynamics of the pillar's motion and the dynamics of the pillar's motion. The measurement of the pillar's motion is a fundamental tool for understanding the dynamics of the pillar's motion and the dynamics of the pillar's motion. ## 1 Introduction  
Well-stabilized reference points are essential for precise geodetic measurements of ground movements and structural displacements. These points serve as the basis for measuring control points on or near the observed objects. The stabilization of these points is crucial to enable the often desired or even required accuracy of determining control point displacements within 1 mm. To achieve such high precision, we need to better understand the behavior of the reference points under different conditions. The reference points are often stabilized by reinforced concrete pillars equipped with bolts for forced centering of the instrument. When properly executed, this stabilization ensures the long-term stability of the reference point throughout the measurement period of the structure or its surroundings. Stabilization with reinforced concrete pillars offers many advantages if carried out correctly. However, in some cases, they are not performed correctly. A common problem occurs when a plastic pipe, usually of small diameter (sometimes only 20 cm), is inserted into the foundation of the pillar to serve as formwork. Reinforcement is placed inside the pipe, which is then filled with concrete. At the top of the pipe, a steel plate is anchored in the fresh concrete with a forced-centering screw. These pipes are available in various colors, including black (Figure 1). Relatively small diameters of the cross-sections and the dark, mainly black, color of the tube left on the pillar pose a considerable problem when exposed to sunlight. Temperature differences within the pillar can have a considerable influence on the position of the forced-centering screw, to such an extent that they cannot be ignored in precise measurements (see [1]). Local temperature variations in the reinforced concrete column, caused by one side being exposed to sunlight while the other is in the shade, lead to an expansion of the sunlit part and consequently to bending of the column. This bending leads to displacements of the forced-centering screw, which cannot be neglected under real conditions. Thermal effects on reinforced concrete columns can cause displacements up to 1 mm [2]. Measuring the displacement of a reference pillar in situ is a challenge, as it is difficult to thermally insulate the displacement sensor mount and the installation of such sensors would require considerable effort. On the other hand, the bending of the pillar also changes the inclination of the steel plate with the forced-centering screw. This inclination can be measured directly with a precise thermally insulated inclinometer, which is an interesting alternative and motivation for this study. Note, however, that the measured inclinations are only applicable if a simple correlation to displacements can be established. In our experimental setup, we performed inclination measurements on a test pillar where we could also measure displacements and temperatures to validate our numerical model. Our study focuses exclusively on the horizontal displacements of the pillar due to  
Figure 1: Examples of reference points for precise geodetic measurements: (**a**) first example; (**b**) second example; (**c**) third example; (**d**) fourth example. thermal loading, as the positional components of displacement are the main focus in 2D geodetic networks (the vertical component is negligible in 2D network analysis). This topic has already been recognized by the scientific community. In the work of [PERSON] et al. [3] and [PERSON] [4], the horizontal displacements of geodetic reference points due to thermal loads were considered in the context of monitoring bridge deformations. [PERSON] et al.