2.5D prediction of soil vibrations due to railway loads by the isogeometric analysis with scaled boundary

Abstract

The 2.5D approach is an efficient tool for the dynamic analysis of half-space with longitudinally invariant properties. In this paper, a newly formulated 2.5D version of the NURBS-based isogeometric analysis (IGA) and the scaled boundary IGA (SBIGA) is proposed for analyzing the bounded and unbounded domains, respectively, of a soil-tunnel system subjected to moving railway loads. The bounded domain is discretized by IGA, since the NURBS used can exactly represent the variations in geometry and materials with negligible errors. The unbounded domain is discretized by SBIGA, which automatically satisfies the Sommerfeld radiation condition and can be easily connected with the bounded IGA domain. The 2.5D approach differs from the 2D approach in that both the in-plane and out-of-plane displacements of the profile of the soil-tunnel system are included in analysis. By applying the Fourier transformation, the IGA and SBIGA equations of the 2.5D version in the frequency-wavenumber domain are derived individually and then assembled at the interface of the bounded and unbounded domains. Two examples are prepared for the ground and underground trains moving at subsonic and transonic speeds. Both single and multi moving loads are considered. It was demonstrated that the wave propagation characteristics including the Mach cones at transonic speeds can be precisely predicted. The results in time and frequency domains have been compared with existing ones. It was shown that the proposed method is accurate and reliable for application to a wide range of soil-tunnel systems.