# Railway Substructure Modeling Approach for Modal Analysis Using Multibody Simulation
## 1 Introduction  
The railway sector is of major importance in today's society, which explains the continuous investment and research into the development of several relevant topics in this field. One such topic is the development and improvement of modeling solutions for railway vehicles and/or railway infrastructures, which can range from simple predictive maintenance-related models to digital twins of entire railway lines and vehicle fleets [1, 2]. Among their several benefits, these models are important tools for use by railway managers to support efficient and timely maintenance actions. Many of the available solutions dedicated to modeling the railway infrastructure are focused on either the plain railway superstructure or specific assets, such as bridges/viaducts or tunnels [3, 4, 5]. Common applications for these models include the Structural Health Monitoring of specific assets, the detection of track defects, or the prediction of track degradation [1, 2, 3, 6]. Despite the major focus on railway superstructure, the railway substructure is also the main goal of several modeling solutions. Most of them involve either lumped-elements theoretical models, where the substructure is represented by layers of spring-damper elements, or complex numerical simulations using the Finite Element Method(FEM) or other similar methods, where every component is modeled in detail [7; 8; 9; 10]. These modeling solutions can be used for several applications, such as to analyze noise and vibration propagation from the track [11; 12] or assess soil stability conditions under traffic loads [13]. However, there is a significant lack of modeling solutions for the railway substructure based on multibody simulation (MBS) models. This group of numerical simulation solutions is amply used to model railway vehicles and the railway superstructure [6; 14; 15], but to the authors' knowledge, there is no dedicated modeling solution focused on modeling the substructure with this type of software as a fully formed set of elements with their own independent and complete modal properties (mass, stiffness and damping). The common alternative modeling solutions either oversimplify the substructure representation by modeling it with only spring-damper elements, thus inherently coupling its modal properties and dynamic responses to the surrounding elements (e.g., coupled natural frequencies that depend on the mass of the elements above the substructure), or use FEM models to fully represent the substructure, which naturally involves higher development and computation costs [8; 9; 10]. The main objective of such a tool would be to enable proper modal analysis on a railway substructure model, where the uncoupled natural frequencies of this railway component could be extracted with significantly less computational effort than a FEM simulation. The need for such a modeling solution came during the development of a new track condition monitoring methodology (TCMM) that is based on the modal analysis of the natural frequencies of the multi-element system that encompasses an instrumented railway vehicle and the railway infrastructure under analysis [16; 17]. This methodology proposes the assessment of the railway infrastructure by monitoring the first vertical resonance frequency of the upper soil layer beneath the track (i.e., the first subgrade layer), thus taking into account the subgrade's major contribution to overall track support conditions, as opposed to the more common solutions that focus on superstructure conditions [4; 18; 19]. The development of this TCMM required a modeling solution that could provide adequate and realistic modal results from this multi-element mechanical system, but also simulate long stretches of railway track in a time-efficient manner (i.e., simulate track lengths of over 1 km).