Impact of Plane Waves on Lining in Elastic Medium with Transparent Artificial Boundary

To effectively address dynamic problems related to underground structures subjected to wave ac-tions, it is necessary to introduce artificial boundary conditions. Establishing conditions at these boundaries is crucial to ensure transparency of internal and external waves as they reflect off these structures. This paper pro-poses the use of exact non-reflective wave conditions at these boundaries. The authors explore the behavior of linings under longitudinal and shear waves using a mathematical model. The numerical implementation em-ploys the finite element and Bathe time integration methods. Examples of circular concrete linings subjected to longitudinal and shear waves are provided. The article considers the spacing between the linings and the di-mensions of the artificially defined region. The numerical results demonstrate the effectiveness and reliability of the transparency conditions at the artificial boundaries, allowing for a thorough investigation of wave im-pacts on underground structures under plane strain conditions.