## 1 Introduction  
As train speeds increase, safety becomes increasingly significant. Railway accidents are reported around the world every day. In particular, derailment accidents cause a lot of casualties and property damage. Derailment accidents have occurred frequently in Korea. Some coaches of the Korean high-speed train were recently derailed due to an error in the operation of a turnout. The derailment accident damaged rails, PC sleepers, the turnout and coaches although it did not cause any casualties as shown in Figure 1a [1]. In the United States, a derailment accident in a curve due to over-speed, as shown in Figure 1b, caused more than 170 dead or injured and property loss of $ 9 million [2]. Secondary collision accidents following derailment result in greater damage than derailment itself due to collision with surrounding structures or bridges falling down when wheels deviate from the tracks. For these reasons, a protective facility is usually installed to minimize damage due to secondary collision or falling [3, 4]. In Korea, it is a requirement to install protective facility in a sharp curve area and a bridge of over 18 (m) or other areas with high derailment risk. In the UK, the RSSB assume that, after a train is derailed, the inner wheel will be guided by the outer rail before wheels collide against the barrier walls. Based on this assumption, they suggested that the barrier wall height should be at least 350 (mm) from the head of rails, and the distance of the barrier wall must be greater than 1500 (mm). In Germany, guard-rails are usually applied to passenger and freight train lines. In the case of a high-speed train line, it is assumed that derailed wheels would be guided by rails. Therefore, the barrier walls must be kept from the running wheel-sets by a distance avoiding a collision against the walls. The height of the barrier walls is designed no higher than the rail head [5]. Even though barrier walls are installed on bridges or in curves to reduce damage after derailment for high-speed trains, the criteria for their locations and design loads are not clear, and studies on railway protective facilities are insufficient. In order to determine the construction locations and design loads of the protective facility, it is important to know the derailment behaviors of trains. Although it is ideal to check post-derailment behaviors through actual derailment tests, many research works generally simulate these using multi-body dynamics programs because of practical difficulties such as high cost and construction of a test facility. [PERSON] and [PERSON] [6] discussed appropriate modelling choices for suspension components, wheel/rail contact conditions and modeling input. [PERSON] and [PERSON] [7] considered a technique referred to as the 'Train 3D method' for simulation of trains as coupled derailed spatial and simplified one-dimensional models of rail vehicles to evaluate safety factors with dependence on the train operation regime. [PERSON] and [PERSON] [8] presented nonstiff method for computing the nonelliptical contact problem that can apply to the wheel rail contact problem. [PERSON] and [PERSON] [9] studied high-speed train crashes in three dimensions using multi-body dynamics to predict the crash behavior of trains. [PERSON] [10; 11] studied the impact forces in the case of a collision with a barrier wall using a three-dimensional finite element model of the KTX (Korean High Speed Train). [PERSON] [12; 13] developed a half-car test specimen of a vehicle and analyzed its derailment behaviors through experiments in the laboratory. In addition, they predicted the derailment behaviors of a derailed high-speed train using dynamic simulations. [PERSON] [14] conducted a series of low-speed derailment test under different test conditions for a Chinese train. This study confirmed that gearbox of train plays an important role in restricting the lateral motions of the derailed vehicle, and also the other influence factors such as speed, weight and track were considered.