# Idealisations of Dynamic Modelling for Railway Ballast in Flood Conditions
## 1 Introduction  
Modern railway tracks have evolved over centuries with operational speeds and economic viability. Today, there are two types of modern railway tracks: ballasted and ballastless tracks. The use of railway ballast for rapid construction of low- to medium-speed tracks (<250 km/h) has been adopted over several decades [1]. Railway ballast or granular media is a main track component used in ballasted railway tracks worldwide [2]. It is mostly manufactured from crushed rock-based local materials from various sources such as crushed igneous rocks (granite, rhyolite, decite, basalt, quartzite or latite), crushed metamorphic rocks, crushed sedimentary rocks, crushed gravel (from rivers, lakes), or sometimes even from waste products (such as crushed slag, chitter) [3; 4; 5; 6; 7; 8]. Early railways did not place ballast as being highly significant to the makeup of a successful design of the permanent way. This position gradually changed and the performance of the ballast material is now considered important in the design process. Ballast is required to fulfil the task of maintaining the track in good alignment both horizontally and vertically. Track geometry deterioration can be rectified and restored quickly and cost-effectively over ballast [9; 10; 11; 12; 13; 14; 15]. To gain these benefits, railway ballast must have the following characteristics:* Durable to be able to absorb the loads imposed by the sleepers and transmit the loads to the sub-grade without undue breakdown;
* Hard-wearing with high abrasion resistance in both wet and dry conditions;
* Angular with sufficient bulk density to resist movement of the track both longitudinally and laterally; and
* Particle size to allow packing and transfer of the loads of the track but with sufficient void space to allow free draining to assist shedding of all moisture. Both the ballast and capping layer material can be seen in Figure 1. The functions or roles expected of the ballast layer have changed with time and the evolutionary development of railway technology. There is some discussion of the functions of ballast in the references, \"Railroad Engineering\" (Ch. 21) by [PERSON], \"British Rail Track\" (Ch. 2), by the Permanent Way Institution, \"A Review of Track Design Procedures\" (Vol. 2, Ch. 4) by [PERSON] and [PERSON], and \"Track Geotechnology and Substructure Management\", by [PERSON] and [PERSON] [2; 15]. The functions of ballast can be divided into two criteria:  
* Primary Functions: the original purpose of ballast; and
* Secondary Functions: the characteristics of the material that enable the ballast to fulfil and continue to fulfil its primary function and those functions that have been added with technology improvements and community expectations. The primary functions of the ballast are to provide a uniform elastic vertical support; to fix the track in position laterally and longitudinally; and to facilitate the correction of the track level and line enhancing constructability and maintainability of a railway network [1; 2; 3; 4]. The secondary functions of ballast are to allow surface water to drain rapidly; to inhibit the growth of vegetation; to compensate for the presence of fouling material, to reduce noise; to provide electrical insulation of one rail from the other; and, to moderate the effect of frost heave in cold climates and movement due to climate uncertainties [3; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Figure 1: A typical ballasted track (left). The capping layer called ‘sub-ballast’ is prepared by compacting roller prior to laying ballast. In reality, the capping layer and subgrade are non-homogenous and cannot be accurately modelled by a simple constant elastic half-space nor a continuous layer. These layers are thus designed under higher safety margin or higher factor of safety by the allowable stress design concept [16; 17]. The design takes into account the accumulated strains of these layers, which are often limited over a target design period (e.g., 15–25 years).