# Effect of Track Irregularities on the Response of Two-Way Railway Tracks
## 1 Introduction  
Railways are a paramount and economical means for mass transportation and offer a suitable alternative to traffic congestion. However, in populated areas, ground vibrations induced by the moving trains is problematic. To examine this problem, various train-track models have been proposed to study the generation of ground vibrations and their propagation due to moving loads. Most of the early train-track models to study the effect of moving loads were based on analytical and semi-analytical methods [1; 2; 3; 4]. However, these methods are hard to formulate, limited to the specific types of problems, consider many simplified assumptions and difficult to implement to study the wave propagation due to moving loads. Therefore, a better understanding of the ground vibrations and wave propagation during the design and the construction of such facilities is highly desirable [5]. To study the ground vibration due to moving load, [PERSON] et al. [6] developed a theoretical train-track-subsoil interaction model and also considered track irregularities. This interaction model takes account of quasi-static as well as dynamic excitation between the vehicle and track. The results showed that the track unevenness could significantly increase the vibrations in the ground at a given speed. With the progress of computer technology, more sophisticated methods such as boundary element method (BEM), finite element method (FEM) and combined or hybrid methods have been introduced to solve ground vibration problems. Many researchers considered BEM [7; 8; 9] or combined methods [10; 11; 12; 13; 14] to study the effect of moving train on ground vibration and surrounding structures. Generally, these methods are mostly formulated in the frequency domain because of computationalefficiency. However, these methods are limited to linear problems and become inconvenient for solving complex geometries. The FEM precisely predict the ground vibrations and can give a replica of engineering insight of operational conditions. The FEM can easily solve nonlinear problems with complex geometries. [PERSON] et al. (2015) used three-dimensional finite element (FE) coupled train-track model to predict the track vibration at high speed. Their findings revealed that a series of waves radiating from the loading point formed a Mach cone, which caused the loss of symmetry in ground vibration at critical speed. The effect of rail surface irregularities was not considered in this study which is the main source of the increase in ground vibration in the train-track interaction problem. Moreover, to simplify the problem it was assumed that the track has symmetry all along the track. A half finite element domain with a single rail, half of the track and ground along the track was modeled to study the ground vibration due to moving load. This assumption is not useful while considering track irregularities. Furthermore, a lot of FEM based parametric studies have been carried out to investigate the effect of moving load under different track and ground conditions ([PERSON], 2014; [PERSON], 2015; [PERSON], 2016; [PERSON], 2017; [PERSON], 2018; [PERSON], 2019; [PERSON], 2020). The impact of train induced vibrations on adjacent structures and attenuation of ground vibration was studied by many researchers (e.g., ([PERSON], 2014; [PERSON], 2015; [PERSON], 2016; [PERSON], 2017; [PERSON], 2018)). In these studies, only one track or symmetry along the track (only one single rail) is considered to predict the track and ground vibrations due to moving loads. In real-world practice, two-way tracks are mostly constructed; and one track can easily be affected by the ground-borne vibrations induced by a moving train on the nearby track which has been ignored in previous studies. Therefore, for two-way tracks, the excitation on both tracks due to moving trains should be considered. To this end, a better model reflecting the overall responses, due to separate excitation on two tracks and the effect of waves propagating from one track to the other track needs to be studied.