Mathematical modelling of the periodicity of geodetic observations of the displacements of the 'gas pipeline – ground foundation' system

Geodetic and Satellite Technologies for Engineering and Deformation Monitoring

Authors

First and Last Name Academic degree E-mail Affiliation
Igor Trevoho Sc.D. trevoho [at] gmail.com Lviv Polytechnic National University
Lviv, Ukraine
Ievgen Ilkiv Ph.D. evgen_ilkiv [at] ukr.net Ivano-Frankivsk National Technical University of Oil and Gas
Ivano-Frankivsk , Ukraine
Kira Nikitenko Ph.D. Kira_N85 [at] ukr.net LLC "It-transit"
Kyiv, Ukraine
Olha Hromova No hromova.0372 [at] gmail.com Lviv Polytechnic National University Lviv, Ukraine
Lviv, Ukraine
Petro Herasymchuk No gerasim4uk53 [at] ukr.net individual entrepreneur
Lviv, Ukraine

I and my co-authors (if any) authorize the use of the Paper in accordance with the Creative Commons CC BY license

First published on this website: 31.07.2026 - 13:19
Abstract 

The article presents a detailed study of the justification of accuracy and the optimal frequency of geodetic observations for monitoring the spatial displacements of the ground foundation and the main gas pipeline. The relevance of the research is associated with the lack of comprehensive normative guidance and detailed design calculations for predicting pipeline deflections during operation. To address this issue, the authors analyse the factors influencing deformation processes and consider the results of stress–strain state calculations for the structure–ground foundation system.

The study is based on mathematical models employing an exponential function to describe displacement stabilisation over time, taking into account final deflections and empirical coefficients related to soil filtration and density. The authors also calculate deformation velocities as the time derivative of the displacement function and propose an algorithm for determining the intervals between observation cycles based on the principle of equal influence of error sources.

Particular attention is given to evaluating the root mean square errors of deformation velocities, enabling the timely detection of accelerated and uneven deformation processes. The proposed monitoring methodology includes the selection of control mark locations and spacing, the assessment of measurement accuracy, and the determination of observation intervals, thereby improving both the reliability of monitoring results and the cost-effectiveness of monitoring.

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