2025 , Volume 30, № 4, p.54-65

In numerical modelling of the behavior of underground objects in an infinite soil medium to wave effects, it is necessary to limit the study area. In this case, it is necessary to and ensure that both external and internal waves are not reflected atfrom the boundaries of the study area. In addition, front of the incident wave front may be at an angle to the study area, which requires additional transformations to correctly calculate the effects on the object. This article presents for the first time our approach presents the exact conditions of boundary transparency for plane elastic waves, taking intowhich account the incident wave front at any angle. Based on the proposed mathematical model, the behavior of linings under the action of a longitudinal wave incident at different angles is studied. The numerical solution of the dynamic problem is carried out using the finite element method and the Bate method in time.for transinient behaviour. As an example,circular and rectangular concrete linings are studied for the effect of plane longitudinal waves. The presented results show good qualityrobustness of transparency conditions at artificial boundaries at any angles of wave incidence, which allows reliable studies of the processes of wave action on deep underground structures in the case of plane deformation.