## 4 Conclusions  
Cracking from dynamic loads at midspan is one of the most common forms of railway sleeper damage in conventional tracks. To prevent prestressed concrete sleepers from cracking caused by dynamic loads, the structural performance needs to be investigated and improved. The challenge for railway engineers is to improve the performance of railway sleepers to fulfil crack resistance requirements. In this study, numerical simulation of crack propagation was carried out using Ansys Workbench. The experimental program was used to validate and calibrate the numerical results. A full-scale model of the prestressed concrete sleeper was modelled and validated. Growth of crack length is a very important parameter to simulate crack propagation. Crack length was measured from a previous static capacity test in order to validate the crack model. The growth of crack simulation shows a fairly good agreement with the static capacity test results. Load-crack length response of sleepers is studied in this research. This paper also presents the time-dependent parameters including creep, shrinkage and relaxation which affect the crack behaviour of prestressed concrete sleepers with time. Based on the results obtained in this study, the key findings are as follows:  
* A reasonable numerical crack model in accordance with fracture toughness theory was developed. The Separating Morphing and Adaptive Remeshing Technology (SMART) crack growth simulation method is used. This method indicates the mesh changes occur around the crack-front region only, leading to a computationally efficient solution of the crack-growth problem. * Experimental and numerical results of crack propagation indicate the growth of cracks is sharp before 90 kN. After 90 kN, the growth of cracks slows. The structural performance of prestressed concrete sleepers is observed. * Effects of time-dependent behaviour including creep, shrinkage and relaxation are considered in the crack propagation analysis. Loss of prestress due to time-dependent behaviour reduces crack resistance of prestressed concrete sleepers. Figure 10: Effect of total time-dependent behaviour in terms of load-crack length response. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Loss of Prestress Due to** & & & & & \\
**Time-Dependent** & **No Loss** & **90** & **180** & **365** & **3650** \\
**Behaviour in Days** & & & & & \\ \hline Creep & 110.96 & 113.39 & 113.89 & 117.36 & 121.76 \\ Shrinkage & 110.96 & 113.68 & 114.27 & 118.13 & 122.60 \\ Relaxation & 110.96 & 112.49 & 112.64 & 114.57 & 117.37 \\ Combination of creep, shrinkage and relaxation & 110.96 & 117.76 & 119.08 & 129.00 & 142.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ultimate crack length due to time-dependent behaviour in days. * It is found that the crack lengths in sleepers are greater over time subject to time-dependent behaviour under the same loads. In the long-term, this effect becomes more significant. * Crack propagation subject to relaxation has less influence than creep and shrinkage. The effects of creep and shrinkage in crack propagation are similar to each other. This point demonstrates that the time-dependent behaviour of prestressed concrete sleepers in the concrete part has more influence than the tendon part. * A combination of the effect of time-dependent behaviour severely reduces the crack resistance of railway sleepers. In the static capacity test, a 116 mm long crack length under 140 kN was regarded as a failure. However, in this research, crack resistance of the prestressed concrete sleeper subject to all those time-dependent behaviours decreases over time. According to the numerical results, failure can happen under 100 kN external loads over a 10-year service life. The results show that crack propagation is heavily dependent on time-dependent behaviour. Therefore, a reliable approach for evaluating crack propagation subject to time-dependent behaviour needs to be developed to improve railway infrastructures in the future.