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DOI: 10.15862/22SATS226 (https://doi.org/10.15862/22SATS226)

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Magomedov M.M., Ovchinnikov I.I. Parameterization of the random shape of debris in assessing the risk of collapse for mountain bridges. Russian Journal of Transport Engineering. 2026; 13(2). Available at: https://t-s.today/PDF/22SATS226.pdf (in Russian). DOI: 10.15862/22SATS226

Parameterization of the random shape of debris in assessing the risk of collapse for mountain bridges

Magomedov Mukhtar Magomedovich
Saratov State Technical University named after Y. Gagarin, Saratov, Russia
E-mail: magomedovmm751@mail.ru
ORCID: https://orcid.org/0000-0002-0049-3410

Ovchinnikov Ilya Igorevich
Tyumen Industrial University, Tyumen, Russia
Ufa State Petroleum Technical University, Ufa, Russia
Saratov State Technical University named after Yuri Gagarin, Saratov, Russia
E-mail: bridgeart@mail.ru
ORCID: https://orcid.org/0000-0001-8370-297X
RSCI: https://elibrary.ru/author_profile.asp?id=177132
SCOPUS: https://www.scopus.com/authid/detail.url?authorId=57191523104

Abstract. The article continues the research topic devoted to assessing the durability of mountain bridges under landslide impacts. In the previous part of the article, it was shown that the mining environment includes impacts in the form of dangerous geological processes, which are characterized by randomness of varying degrees. The next step in modeling uncertainty when developing a method for calculating durability for mountain bridges is to analyze the problem of parameterization of the collapse impact of the mountain environment.

The second part focuses on the parameterization of the shape of the stone, a key but least formalized factor determining local damage to the supports. A geometric apparatus is proposed based on the introduction of an invariant in the form of an equivalent radius, an arithmetic mean radius, and a radius variance forming the acuity parameter. It is shown that for a fixed mass of stone, the arithmetic mean radius is always equal to or less than the invariant in the form of an equivalent radius.

To generate random shapes with a fixed mass, a method of paired stochastic integration has been developed by analogy with the Kantorovich transport problem. A condition for a local balance of normalized volumes of protrusions and depressions is introduced, from which an analytical distribution of relative deviations is obtained, which reduces to a beta distribution. A conjugation parameter has been introduced within the framework of pair integration, which regulates the spatial correlation of stone shapes.

Based on a two-stage impact model (micro impact of the protrusion and macro impact of the main surface), a hazard parameter is constructed that shows how many times this scenario is more dangerous than the reference one. The effect of a «fingerprint» is taken into account — the dependence of the support response on accumulated damage. The total risk is expressed as an integral over the continuum of scenarios.

In this article, the authors describe the problematic points of parameterization of collapse loads in the form of a self-consistent shape of the impact object and the need to introduce a phenomenological connection into the apparatus.

Keywords: rockfall; mountain bridge; fragment shape; paired stochastic integration; beta distribution; two-stage impact model; hazard parameter; risk; Monte Carlo method; self-consistent problem

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