Performance analysis of subgrade in asphaltic rail track design and Indonesia ’ s existing ballasted track

: Due to subgrade - related concerns, the perfor - mance of Indonesia ’ s ballasted track continues to be signif - icant impediments for the Indonesian railway stakeholders ’ intention to increase the speed of passenger train opera - tions. This study aims to examine the vertical compressive stress in the subgrade of Indonesia ’ s ballasted track and two asphaltic rail track designs, asphaltic overlayment and asphaltic underlayment, under various cyclic loading conditions based on three di ﬀ erent train speeds, 120 ( low speed ) , 240 ( medium speed ) , and 360 kph ( high speed ) . The AC layer thicknesses for each asphaltic rail track design are as follows: 0.1, 0.2, 0.3, and 0.4 m for asphaltic underlayment, and 0.075, 0.15, 0.225, and 0.3 m for asphaltic overlayment. 2D ﬁ nite element models and simulations were used to capture and predict the subgrade ’ s vertical com - pressive stress performance. The most obvious ﬁ nding to emerge from this study is that the asphaltic overlay - ment track has a greater capacity for transmitting and decreasing stresses from the top structure to subgrade layer than the asphaltic underlayment track and the Indonesia ’ ballasted track, respectively. This research can shed light on the prospective application of asphaltic rail track to the Indonesian rail network for the faster pas - senger trains operation.


Introduction
The increasing global demand for rail travel has resulted in increased line speeds on passenger lines. The performance of the railroad track under these circumstances is dependent on the interaction between the train carriages, the superstructure, and the track support [1]. Track support characteristics have a direct impact on railway track deterioration, which has significant cost and time implications for the rail industry via maintenance operations, track replacements, and line speed restrictions [2].
The railway track must serve two primary functions: first, to safely direct the train and second, to carry the train's load and distribute it over an area as large as possible on the subgrade [3]. Subgrade is an essential component of rail track structure, supporting the upper loads of the tracks and trains, and its stability has a direct impact on train safety and passenger comfort [4,5]. Additionally, subgrade provides the ultimate support for the track structure. Therefore, the geotechnical structure of the railway subgrade, which was created by excavation or filling, must be protected by the railway track superstructures, and have sufficient engineering stability and very minor permanent deformation to meet track laying and safe operating standards [6].
Ballasted track is the only option for rail track design in Indonesian railway lines due to its low construction costs and high flexibility. Due to subgrade-related concerns, the performance, durability, and maintenance costs of Indonesia's ballasted track system continue to be significant impediments for the government and railway stakeholders' intention to increase the train's speed and axle load. Although the design speed of the track section of Indonesia's ballasted track is 120 kph, passenger trains are not permitted to exceed 90 kph in order to minimize derailment risk [7].
Sadeghi and Askarinejad [8] conducted a sensitivity analysis utilizing several models of track degradation. They discovered that the permitted annual tonnage for a track with a high-quality subgrade is four times that of a track with a subgrade of poor quality. Therefore, low subgrade stiffness can dramatically increase maintenance frequency and decrease overall asset life [9].
Subgrade settlement is the leading source of track damage from a substructure perspective. Differential track settling can lead to defects in the vertical track geometry, which, if left untreated, might result in derailment. Several researchers [10][11][12][13][14][15] discovered that the subgrade is the primary source of both average and differential longterm settlement in the majority of track designs. The vertical compressive stress at the top of the subgrade shows possible long-term subgrade settlement failure performance and track maintenance costs. The greater the vertical compressive stress at the top of the subgrade layer, the greater the chance of subgrade failure and the higher risk of trackbed settlement.
In certain nations, including the United States [16][17][18], Japan [19], China [20], France [21,22], Italy [23], and Germany [24], railroad engineers have adopted the asphaltic underlayment track design. This asphaltic rail track design is favored because the asphalt is shielded beneath the ballast layer, minimizing the asphalt's exposure to sunlight and temperature fluctuations. Alternatively, a number of studies investigated another sort of asphaltic rail track design, namely asphaltic overlayment, in which the asphalt concrete (AC) layer is utilized and laid over the sub-ballast or roadbed layer [25,26]. Unfortunately, neither form of asphaltic rail track has ever been installed in Indonesia's rail networks [13].
Ramirez Cardona et al. [22] reported that bituminous sub-ballast layers reduced the vertical stress transferred to the soil layer by as much as 30%. Fang et al. [27] found that hot mix asphalt is an appropriate material for the railway substructure in order to increase the resilient performance and stress distribution. Liu [28] and Setiawan [13,15] also analyzed vertical compressive stress using a mechanistic-empirical technique to forecast the subgrade design life of the ballasted and asphaltic underlayment tracks. Setiawan [13] confirmed that the ballasted track has a shorter subgrade service life and greater subgrade vertical compressive stress than the asphaltic underlayment track, despite the fact that the sub-ballast beneath the ballast layer in the ballasted track is one hundred percent thicker than the AC beneath the ballast layer in the asphaltic underlayment track. Due to the decreased compressive stress at the surface of the subgrade layer, Setiawan [15] observed that asphaltic underlayment tracks had a longer subgrade service life than ballasted tracks. Setiawan [26] discovered, using the same mechanisticempirical technique, that asphaltic overlayment track is superior to ballasted track because it has a greater capacity for transmitting top loads, hence minimizing subgrade compressive stresses.
It is difficult to find research that compares the performance of various asphaltic rail track designs, in this case asphaltic overlayment and asphaltic underlayment track, in terms of the vertical compressive stress attenuation in the subgrade. Additionally, the majority of previous studies continue to rely on the mechanistic-empirical method. Therefore, it is proposed to use a more mechanistic method and finite element simulation, such as ABAQUS Software, to accurately capture and forecast the responses of ballasted track and asphaltic track-bed to varying passenger train operating speeds.
In this study, asphaltic overlayment tracks were those in which the ballast was replaced by AC layer, and asphaltic underlayment tracks were those in which the sub-ballast was replaced by AC layer. The impact of different train speeds on the subgrade behavior of these two asphaltic rail track systems was compared with that of the Indonesian ballasted track. Two-dimensional (2D) finite element models and simulations were applied to characterize and estimate the subgrade's performance in terms of vertical compressive stress.
This study aims to examine the vertical compressive stress curve in the subgrade of Indonesia's ballasted track and two asphaltic rail track designs, namely asphaltic overlayment and asphaltic underlayment, under various cyclic loading conditions based on three different train speeds, 120 (low speed), 240 (medium speed), and 360 kph (high speed). The AC layer thicknesses for each asphaltic rail track design are 0.075, 0.15, 0.225, and 0.3 m for asphaltic overlayment, and 0.1, 0.2, 0.3, and 0.4 m for asphaltic underlayment. This research can shed light on the prospective application of asphaltic rail track to the Indonesian rail network for the operation of faster passenger trains.

Indonesia's ballasted rail track
The typical thickness of the sub-ballast layer is 15 cm. In addition, certain railway systems do not use a sub-ballast layer and instead employ a thicker subgrade layer [3]. Nevertheless, according to Regulation No. 60 of 2012 of the Indonesian Minister of Transportation Concerning Railroad Technical Requirements, the design thickness of ballast and sub-ballast for conventional track is fixed regardless of the specific conditions [29]. The thicknesses of the ballast and sub-ballast layers are 0.3 and 0.4 m, respectively. Figure

Asphaltic overlayment track
The geometrical design and important location for the investigation of vertical compressive stress in the subgrade layer of asphaltic overlayment track can be observed in    Tables 1-3 give the material properties for the simulation of rail tracks in the present work. All three types of rail tracks are comprised of materials with a linear elastic behavior. The properties of sleeper, ballast, sub-ballast, and subgrade are the typical values based on Indonesian railway regulations.

Loading systems
According to Ghataora et al. [30], a frequency between 1 and 3 Hz corresponds well to the primary frequency of train-induced loading in the subgrade. This frequency depends on the train's speed and the distance between the axles, bogies, and coaches. Priest et al. [31] found that the pairs of bogies at the ends of adjacent wagons had a loading frequency of 1 Hz on a length of track with an average line speed of 50 kph, whereas individual bogies and axles had loading frequencies of 2 and 6 Hz, respectively.
In this study, the loading frequencies are precisely proportional to the train speed, and they fall within the range of loading frequencies typically experienced by low-, medium-, and high-speed trains. Each rail track design undergoes 5,000 loading cycles at three different frequencies, 2.4, 4.8, and 7.2 Hz, based on three different train speed levels, 120 (low speed), 240 (medium speed), and 360 kph (high speed), and the distance between single bogie to single bogie of the passenger coach is 14 m (Figure 4). Using Eqs. (1) and (2), a 28-ton static bogie load was translated into the dynamic load ( Table 4) and then applied as a concentrated force in the left and right rail positions.
where I p is the conversion factor, V is the design speed (kph), P s is the static wheel load of a train (kg), and P d is the dynamic wheel load of a train (kg).   14.0 m Figure 4: Distance between two single bogie in a passenger coach [32].
Performance analysis of subgrade in asphaltic rail track design  5

Numerical modeling
Using Abaqus software, a 2D simulation of Indonesia's ballasted track and two asphaltic rail track design types was created. Figure 5 illustrates the 2D mesh of the simulation models for the three analyzed tracks. For the ballast, sub-ballast, and subgrade, a mesh size of 50 mm × 50 mm was determined, whereas 55 mm × 50 mm was  used for the sleeper. As the boundary condition was given as the soil box condition, the vertical displacement at the bottom and the horizontal displacement at the side of the model were fixed. The interactions between the layers were anticipated to be firmly bound, and the sleeper was expected to be a rigid material.

Results and discussion
One of the most significant functions of railway track beds is to transfer the load to the formation or subgrade layer beneath the track. The subgrade stresses can be affected by axle load, formation thickness, sleeper spacing, rail bending stiffness, and the existence of any additional layer for load distribution [33]. As the train speed increases, the evaluation and influence of subgrade become ever more crucial to the performance of railroad track structures [4]. According to Uzarski [34], the subgrade permitted stress value for the conventional design is around 137 kPa, although AREMA (The American Railway Engineering and Maintenance-of-Way Association) recommends limiting the stress at the top of the subgrade to 172 kPa.   at the bottom of the subgrade was 82, 118, and 154 kPa. In accordance with AREMA's advice on the allowed stress at the top of the subgrade, Indonesia's ballasted track can only accommodate the 120 kph low-speed passenger train. Figure 7 displays the vertical compressive stress curve in the subgrade layer of asphaltic underlayment track at train speeds of 120, 240, and 360 kph for four different AC layer thicknesses, 0.1, 20, 30, and 40 cm, respectively. It has been confirmed that a thicker AC layer in asphaltic underlayment will not only result in lower stresses at the top of the subgrade, but also provide a steeper vertical compressive stress curve. In other words, as the AC layer becomes thicker, the magnitude difference between the vertical compressive stress at the top and bottom of the subgrade would decrease. In addition, the magnitude gap of vertical compressive stress in each measurement location between 120 and 240 kph (Blue Line vs Green Line) is proportional to the magnitude gap of vertical compressive stress in each measurement location between 240 and 360 kph (Green Line vs Red Line). Figure 8 shows the vertical compressive stress curve in the subgrade layer of asphaltic underlayment track with different AC layer thicknesses, 10, 20, 30, and 40 cm, under train speeds of 120, 240, and 360 kph, respectively. The greater the train speed, the greater the stress at the top of the subgrade and shallower the vertical compressive stress curve. In other words, when train speed increases, the magnitude difference between the vertical compressive stress at the top and bottom of the subgrade would increase. In addition, the decrease in vertical compressive stress due to the increase in AC layer thickness from 10 to 20 cm (Red Line vs Orange Line) is greater than the decrease in vertical compressive stress owing to the increase in AC layer thickness from 30 to 40 cm (Green Line vs Blue Line). Figure 9 compares the vertical compressive stress curve in the subgrade layer of Indonesia's ballasted track and asphaltic underlayment track with varying thicknesses of AC layer at train speeds of 120, 240, and 360 kph. Ballasted track in Indonesia continues to outperform asphaltic underlayment track with 10 cm of AC layer. The alternative rail track design is therefore restricted to asphaltic underlayment tracks with 20, 30, and 40 cm of AC layer. In addition, the vertical compressive stress at the top of the subgrade in asphaltic underlayment track with 30 cm of ballast and 40 cm of AC layer at 120, 240, and 360 kph of train speed is 96, 139, and 181 kPa, respectively, which is approximately 47% less than the vertical compressive stress at the top of the subgrade in Indonesia's ballasted track with 30 cm of ballast and 40 cm of sub-ballast layer. In other words, the asphaltic underlayment track is 47% stronger than the Indonesia's ballasted track in terms of vertical compressive stress attenuation in the subgrade, particularly when the AC layer replaces the sub-ballast layer. Several investigations revealed that the dynamic stresses in the subgrade beneath a slab track were four to five times smaller than those under a ballasted track, and that the stresses in the soil rose as train speeds increased [35][36][37][38][39]. In addition, it can be concluded that an asphaltic underlayment track with the same structural thickness as Indonesia's ballasted track can serve not only the low-speed but also the medium-speed passenger train, per AREMA's recommendation regarding the maximum allowable stress at the top of the subgrade. Figure 10 represents the vertical compressive stress curve in the subgrade layer of the asphaltic overlayment track at train speeds of 120, 240, and 360 kph for four different AC layer thicknesses, 7.5, 15, 22.5, and 30 cm, respectively. It has been confirmed that a thicker AC layer in an asphaltic overlay will not only result in less stress at the top of the subgrade, but also provide a steeper vertical compressive stress curve. In other words, as the AC layer becomes thicker, the magnitude difference between the vertical compressive stress at the top and bottom of the subgrade would decrease. In addition, the magnitude gap of vertical compressive stress in each measurement location between 120 and 240 kph (Blue Line vs Green Line) is proportional to the magnitude gap of vertical compressive stress in each measurement location between 240 and 360 kph (Green Line vs Red Line). Figure 11 exhibits the vertical compressive stress curve in the subgrade layer of asphaltic overlayment track with varying AC layer thicknesses, 7.5, 15, 22.5, and 30 cm, under train speeds of 120, 240, and 360 kph, respectively. The greater the train speed, the greater the stress at the top of the subgrade and shallower the vertical compressive stress curve. In other words, when the train speed increases, the magnitude difference between the vertical compressive stress at the top and bottom of the subgrade would increase. In addition, the decrease in vertical compressive stress resulting from an increase in AC layer thickness from 7.5 to 15 cm (Red Line vs Orange   Line) is more significant than the decrease in vertical compressive stress resulting from an increase in AC layer thickness from 22.5 to 30 cm (Green Line vs Blue Line). Figure 12 compares the vertical compressive stress curve in the subgrade layer of Indonesia's ballasted track and asphaltic overlayment track with various thicknesses of AC layer at train speeds of 120, 240, and 360 kph. All asphaltic overlay track variants perform better than the ballasted track in Indonesia. In other words, asphaltic overlayment tracks with 7.5, 15, 22.5, and 30 cm of AC layer can be used as an alternative rail track design due to their significantly lower vertical compressive stress and shallower vertical compressive stress curve in the subgrade. Moreover, the vertical compressive stress at the top of the subgrade in asphaltic overlayment track with 30 cm of AC and 40 cm of sub-ballast layer at 120, 240, and 360 kph of train speed is 90, 130, and 170 kPa, which is 57% less than the vertical compressive stress at the top of the subgrade in Indonesia's ballasted track with 30 cm of ballast and 40 cm of sub-ballast layer. In other words, asphaltic overlayment track with the same structural thicknesses is 57% stronger than Indonesia's ballasted track in terms of vertical compressive stress attenuation in the subgrade, especially when the AC layer replaces the ballast layer. The findings of field measurements of the dynamic stress at the subgrade surface were presented in a number of publications. The dynamic stress in the subgrade surface of a slab track was found to be between 13 and 20 kPa, whereas it was between 50 and 100 kPa for a ballasted track [35][36][37][38][39]. Furthermore, it  can be concluded that asphaltic overlayment track with the same structural thickness as Indonesia's ballasted track can serve all speed levels of passenger train operation, namely 120, 240, and 360 kph, in accordance with AREMA's recommendation regarding the allowable stress at the top of the subgrade. Figure 13 compares the vertical compressive stress curve in the subgrade layer of asphaltic underlayment track and asphaltic overlayment track with a 30 cm AC layer at train speeds of 120, 240, and 360 kph. In terms of vertical compressive stress attenuation in the subgrade and with the same AC layer thickness, the asphaltic overlayment track design outperforms the asphaltic underlayment track design. Under 120, 240, and 360 kph of train speed, the vertical compressive stress at the top of the subgrade is 109, 158, and 206 kPa, respectively, in asphaltic underlayment track with 30 cm of AC layer. Under 120, 240, and 360 kph of train speed, the vertical compressive stress at the top of the subgrade in asphaltic overlayment track with 30 cm of AC layer is 90, 130, and 170 kPa, respectively. Under a train speed of 350 kph, Lee et al. [25] discovered that an asphaltic rail track with AC layer thicknesses of 20, 27, and 35 cm below the sleeper produced vertical compressive stresses of approximately 140, 90, and 50 kPa at the top of the roadbed, respectively.

Conclusions
This research analyzed the performance of Indonesia's ballasted track in terms of the distribution of vertical compressive stress in the subgrade, then compared it to the two asphaltic rail track designs. According to the results, the asphaltic overlayment track is superior to the asphaltic underlayment track and the ballasted track in Indonesia in transmitting and decreasing stresses from the top structure to the subgrade layer. Also, the AC layer should be placed right beneath the sleeper, where the majority of the stress is concentrated, to better protect the subgrade.
In addition, it can be concluded that only asphaltic underlayment tracks with 20, 30, and 40 cm of AC layer are viable alternatives for Indonesian railways. In contrast, asphaltic overlayment tracks with all four different AC layer thicknesses can be utilized to replace the ballasted track for higher speed train operations in Indonesia. In accordance with AREMA's advice on the allowed stress at the top of the subgrade, Indonesia's ballasted track can only accommodate the 120 kph low-speed passenger train. On the other hand, asphaltic underlayment track with the same structural thickness as Indonesia's ballasted track can serve both low-speed and mediumspeed passenger trains, whereas asphaltic overlayment track can service all three speed levels of passenger train operation.
This analysis took into account the asphalt material's linear elastic characteristics. Future research should address the linear viscoelastic constitutive behavior of asphalt material to predict the performance of AC layer behavior and the influence of AC layer on the reduction of vertical compressive stress in the subgrade of asphaltic rail tracks.