# Buckling Analysis of Interspersed Railway Tracks
## 1 Introduction  
Timber railway sleepers have often been used as railway sleepers worldwide [1, 2]. Such sleepers are expected to serve for about 15 to 20 service years, but the strength and serviceability of timber railway sleepers degrade over time. At present, the limited availability of reliable and high-quality timbers, and restrictions on deforestation, have inspired the world to explore more alternatives for the ageing timber sleepers [3, 4, 5]. Most countries have adopted concrete railway sleepers as the replacement. It is also important to note that the main function of \"spot replacement\" railway tracks (also called \"interspersed railway tracks\") is to enhance the performance of the lower-class tracks withlow operational speed. These can be found in various countries such as Australia, Japan, the United Kingdom, and the United States [2; 3; 4]. Although a partial replacement of aged, rotten sleepers is obviously more economical than complete track renewal or reconstruction, interspersed tracks have some drawbacks. According to open literature and industry knowledge, this practice could consequently undermine the existing ground foundations and also induce inconsistent local stiffness problems in the rail track system [5; 6; 7; 8; 9] and different track decay rates [10; 11; 12; 13; 14; 15; 16; 17]. It is clear that the long-term performance of interspersed tracks can be impaired. Studies of interspersed tracks have been carried out [18; 19; 20; 21]. Moving train loads were applied to interspersed tracks to study the vertical dynamic responses. It was observed that the replacement of timber sleepers by concrete tends to increase the deterioration rate of the railway track, as uplift behaviour occurs [21]. The condition of deteriorated interspersed track is presented in Figure 1.  
With the increase of global temperature, track buckling is a serious concern and has been found around the world [22; 23; 24]. Summer heat can significantly increase the rail temperature and cause the rail to expand, leading to a buildup of axial compression force in continuous welded rail (CWR). Although CWR provides a smooth ride and has a lower maintenance cost, it still suffers from drawbacks as the track tends to buckle easily when the rail temperature reaches a certain limit [25; 26; 27; 28]. Based on the evidence [29; 30; 31; 32], track buckling can cause derailment and cause huge loss of assets and passengers' lives. Moreover, for ballastless tracks, extreme temperatures may cause problems in the rail-structure interface by adding longitudinal stress in the rail and structure. It is noted that the additional stress on a structure should be controlled and not exceed the admissible stress capacity [33; 34; 35]. Although track buckling has been widely investigated [36; 37; 38; 39; 40; 41; 42; 43], interspersed tracks and their inconsistency have never been taken into account. It is interesting to note that timber and concrete sleepers have different properties and geometry, leading to inconsistency in resistance when it comes to interspersed tracks. Buckling resistance mainly depends on the specific type of sleeper, ballast, fastening system, etc. The sleeper type plays a role in track lateral resistance, especially on the friction base at the contact area between the ballast and sleeper [44; 45; 46]. Previous studies have shown that different types of sleepers provide different values of lateral resistance and the contribution of lateral resistance of each part is due to their properties [47; 48; 49; 50]. It was found that the lateral resistance of timber sleepers is about 60-80% that of concrete sleepers. Moreover, maintenance activities, such as ballast tamping, stone blowing, and sleeper replacement, can significantly reduce the compaction of ballast, leading to a reduction in the lateral resistance [49; 50]. Furthermore, torsional resistance also depends on the fastener and sleeper type.