This study entails the development of a data-based decision model to support the selection of track system during the design phase of a new railway line. The method used in the study includes literature survey, degradation modelling, Monte-Carlo simulation and LCC modelling.

The first step in the study is to collect available cost data for the track system under consideration. Construction and maintenance costs for ballast system with speed up to 250km/hr was collected from literature and available database. Similar costs for slab track with operating speed up to 320 km/hr were obtained from benchmarking. Thus, these operating conditions became the baseline for both systems.

Furthermore, literature study was conducted to study how change in operating speed can affect the degradation, maintenance need and cost of ballasted track system. Several models were studied to capture the behaviour of ballasted track system under varying operating conditions. Based on relevance, robustness, model formulations, result accuracy as presented in the literature studied, 10 models were selected for detailed study. At the final stage, 1 model was exempted due to very high discrepancy in comparison to other models and poor performance with variation in speed, which is the parameter of interest. A list of the degradation model with simplified model formulation, remarks and literature source is given in Table 2. More information about these models can be found in the references provided.

Table 3

Degradation models [see references 2–20]

Model nr | Degradation Models (References) | Formulation | Comments |

1 | Sato, (1995); sveld and Esveld, (2001); Lichtberger, (2011) | \({N}_{S}=\text{2,04}*{10}^{-3}*{T}^{\text{0,31}}*{V}^{\text{0,98}}*{M}^{\text{1,1}}*{L}^{\text{0,21}}*{P}^{\text{0,26}}\) | V-velocity T- Annual Tonnage M-Structural factor L-CWR factor P-Subgrade factor |

2 | ORE : Doyle, (1980); Esveld and Esveld, (2001); Larsson, (2004); Lichtberger, (2011) | \({N}_{ORE}=1+ {\alpha }+\beta +\gamma\) | \({\alpha }, \beta , \gamma\)are dimensionless speed coefficients that depend on track and vehicle parameters |

3 | Bing and Gross, (1983) | \({N}_{BG}=\text{1,25}*{\left(\frac{TQI1}{TQI2}\right)}^{-\text{0,58}}*{\left(\frac{V1}{V2}\right)}^{-0.18}*{\left(\frac{RA1}{RA2}\right)}^{-\text{0,11}}*{\left(\frac{BI1}{BI2}\right)}^{\text{1,04}}*{\left(1+FS\right)}^{-\text{0,44}}\) | TQI- Track quality indices at time 1&2 V- Velocity at time 1&2 RA- Track age at time 1 and 2 BI- Ballast index at time 1 and 2 FS- Substructure factor |

4 | Indian formula: Doyle, (1980) | \({N}_{IN}=1+\text{0,5}*\left(\frac{V}{\text{58,14}*k}\right)\) | k- Track stiffness |

5 | South African formula: Doyle, (1980) | \({N}_{SA }= 1+\text{4,92}*\left(\frac{V}{D}\right)\) | D-Wheel diameter |

6 | Clarke: Doyle, (1980) | \({N}_{CL}=1+\text{0,5}*\left(\frac{\text{19,5}*V}{D*k}\right)\) | k- Track stiffness |

7 | WMATA formula: Doyle, (1980) | \({N}_{WHATA}={\left(1+\text{3,86}*{10}^{-5}* {V}^{2}\right)}^{\text{0,67}}\) | V-Velocity |

8 | British railway formula: Doyle, (1980) | \({N}_{BR}=1+\left(\frac{\text{8,784}*\left(a1+a2\right)*V}{Ps}\right)*{\left(\frac{Dj*Pu}{g}\right)}^{\text{0,5}}\) | g- Gravity Dj-sleeper pressure Pu Ps- axle load (a1 + a2)-total rail joint dop angle |

9 | AREA formula: Doyle, (1980) | \({N}_{AREA}=1+\text{5,21}\frac{V}{D}\) | D- wheel diameter |

It should be noted that the main aim of using these models is not to predict the exact evolution of the track system but to estimate a correction factor which will be used to adjust the maintenance and cost of the known baseline scenario.

For the data collection, different sources of data were used to obtain the input values for the LCC model. The default values of the degradation model parameters presented in Table 2 are collected from literature and the technical specification document for the construction of the route. Maintenance and cost data are collected from benchmarking and best practices. Line specification and system description are collected from the ongoing investment project within the Swedish Transport Administration, Trafikverket.

Correction factor is a common method used in engineering design and construction to compensate for changes or uncertainties in design parameters and operating conditions. Correction factor makes it possible to use the results of the different degradation models even though there are uncertainties in predicting the exact degradation value. The correction factor is estimated using the ratio of the predicted deterioration of the track system under 2 different operating speeds i.e., 250 and 320 km/h, see Eq. 1. It should be noted that other parameters remain unchanged in the study. The correction factor is then used to adjust the possible change in maintenance need, service life of track components and costs due to speed change.

$${CF}_{mod}=\frac{Degradation value 250 km/h}{Degradation value 320 km/h} \left(1\right)$$

CFmod is the correction factor for a given degradation model m.

A range of correction factors was obtained using the degradation models in Table 2. A normal distribution was assumed for the factors and then used for a probabilistic estimation of the values of the unknown LCC parameters under varying operational condition. These parameters include service life and intervention interval of track systems.

In the design of track system and selection of optimal operating parameters, the amount of possession time that will be required for the purpose of maintenance and renewal is a very vital criterion. This is a good indication of the availability performance that a track system can deliver over a given period. A benchmarking of existing maintenance plan of ballasted track with speed up to 250 km/h was carried out to create a realistic maintenance plan for the base scenario. The correction factors were used to adjust the intervention intervals for the different activities for ballasted track system with speed up to 320 km/h. A simplified formulation used to estimate the possession time requirement for the two systems is given in Equations 2 and 3. Note that this does not include the time required for the design, projection, and initial installation of the systems.

$$Possession time=Maintenance Possession Time+Renewal Possession Time \left(2\right)$$

$$Possession time=\sum _{m=1}^{M}\frac{120}{{Interval}_{m}}*{MPT}_{m}+\sum _{r=1}^{R}\frac{120}{{Interval}_{r}}*{RPT}_{r} \left(3\right)$$

Where MPTm and RPTr are maintenance possession time for activity m and renewal possession time for activity r respectively.

For the life cycle cost of the two track designs, the costs of acquisition, operation and maintenance, renewal and disposal of replaced items are summed up over the required period of 120 years. Only significant, distinctive, and future cost elements are included in the model since the purpose of the study is to compare the proposed alternatives and to provide input for decision making. A simplified formulation of the LCC model is given in Eq. 4.

$$LCC=Cost acquisition + Cost operation \& maintenance$$

$$+ Cost renewal and disposal \left(4\right)$$

For calculation without discount rate, LCCs for the alternative designs under consideration are estimated using the formulation below.

$$LCC=CA+\sum _{m=1}^{M}\frac{120}{{Interval}_{m}}*{CM}_{m}+\sum _{r=1}^{R}\frac{120}{{Interval}_{r}}*{CR}_{r} \left(5\right)$$

LCC estimation with discount can be estimated using the formulation in Eq. 6.

$$LCC=CA+\sum _{m=1}^{M}\sum _{n=1}^{\frac{120}{{Interval}_{m}}}\frac{{CM}_{m}}{{(1+i)}^{\left(n*{Interval}_{m}\right)}}+\sum _{r=1}^{R}\sum _{n=1}^{\frac{120}{{Interval}_{r}}}\frac{{CR}_{r}}{{(1+i)}^{\left(n*{Interval}_{r}\right)}} \left(6\right)$$

For ballast system with traffic speed equal to 320 km/h, the interval used in the LCC formulation is adjusted for speed change using the formular below:

$${Interval}_{m\_320}=\frac{{Interval}_{m}}{{CF}_{mod}} \left(7\right)$$

Where CA is the cost of acquisition of the different systems. CMm and CRr are the cost of maintenance for intervention m and cost of renewal for activity r respectively. Intervalm and Intervalr are the intervention intervals for maintenance and renewal activities m and r respectively. Intervalm_320 is the maintenance interval for activity m under an operating speed condition of 320 km/h.

The variation in the intervals of track intervention due to the impact of operational parameters was modelled using Monte Carlo Simulation assuming a normal distribution of the correction factor. 10 000 simulations were carried out to have a reliable estimate of the decision criteria.

Note that a discount rate of zero is used in the LCC calculation due to the long calculation period of 120 years required for technical specifications within the project.