**1. Introduction**

In a railway track structure system, sleepers (or ties) perform critical functions by transferring and distributing train loadings from rail to ballast or concrete slab. The critical components undergo repeated train loading and impact loading; however, the exact load transfer mechanism within the sleeper is still unclear due to uneven ballast support conditions and irregular surface conditions of rail and wheels. Due to inaccurately identified loads and support conditions, various parts of sleepers can have damages such as center-binding crack, and flexural and/or shear cracks at the rail-seat section. Nowadays, the railway industry has paid more attention to how to improve the service life of sleepers not only because of increasing axle loads, speed, and traffic volume, but also because of increasing maintenance costs including expensive sleeper replacing costs [1].

Concrete has been widely used for manufacturing sleepers in the world [2], and various attempts have been carried out to complement the brittle nature of the material. Cracks in concrete sleepers have been widely investigated and identified that it is mainly attributed to the material brittleness, particularly under dynamic loadings [1,3]. Although the tensile crack development in concrete is inevitable, it is revealed that the crack propagation can be effectively controlled by using various types of discontinuous reinforcements such as steel fibers [4]. Similarly, various efforts have also been made for concrete sleeper applications to enhance material ductility using fibers [5–8]. For example, Ramezanianpour et al. [5]

**Citation:** Shin, M.; Bae, Y.; Pyo, S. A Numerical Study on Structural Performance of Railway Sleepers Using Ultra High-Performance Concrete (UHPC). *Materials* **2021**, *14*, 2979. https://doi.org/10.3390/ ma14112979

Academic Editor: Bahman Ghiassi

Received: 4 May 2021 Accepted: 28 May 2021 Published: 31 May 2021

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used polypropylene fiber to enhance the tensile and flexural strength, and the durability of concrete by reducing chloride diffusion, water penetration, and sorptivity. Shin et al. [6] concluded that the use of 0.75% of steel fibers results in enhanced static and impact flexural capacity and toughness. Yang et al. [7] revealed that the concrete sleepers reinforced with steel fibers showed increased flexural and fatigue capacity at the rail-seat section compared with conventional concrete sleepers with conventional stirrups, since the concrete sleepers with steel fibers can mitigate crack propagation and prevent brittle shear failure.

For an efficient massive concrete sleeper production process in a precast concrete facility, high strength concretes are generally used in order to promote early demolding and applying prestressing forces. Therefore, many national and international standards require specified minimum compressive strength of concrete for sleeper applications, e.g., C45/55 MPa in European standards [9], 50 MPa in Australia [10], and C50/60 MPa in the International Union of Railways recommendation [11]. Ultra high-performance concrete (UHPC) is one of the most advanced cement-based materials showing a compressive strength at 28 days higher than 150 MPa [12], which possesses strong potentials to extend the service lives of structures with various engineering merits including high ductility [13], durability [14], abrasion resistance [15], and impact resistance [16]. Recently, the authors revealed that the adoption of UHPC in railway sleepers resulted in stable structural behavior and outstanding crack resistance capability even after initial cracks developed [17].

Wide-width concrete sleepers are one of the special types of sleepers, which can significantly reduce the burden of ballast and track substructures due to a larger contact area. The large contact areas of the wide sleepers enable to reduce vibration values, extends maintenance intervals, and the life of the track system [18,19]. With these advantages, the range of applications of the wide concrete sleepers is getting higher from general lines to highly loaded areas such as transitional zones between earthwork, bridges, and tunnels.

Recently, there have been great efforts to study the numerical models of reinforced concrete structures by considering the nonlinearity of concrete behavior, bond strength, the stochastic natures of concrete, etc. Sucharda et al. [20] presented the nonlinear behavior of reinforced concrete beams without shear reinforcement using a stochastic model. In their concrete model, they incorporated the uncertainties in the concrete properties and studied the sensitivity to input parameters including fracture energy, *Gf*. Instead of performing a direct tension test on concrete, they conducted splitting, three-point bending, and four-point bending tests. In their study, they reported that the ratio of the maximum to minimum loads is not necessarily corresponding to the limit of the input parameters. Valikhani et al. [21] studied numerical modeling of bonding of regular concrete and UHPC since UHPC can be used for the repair of concrete structures. In order to model the interface between concrete and UHPC, they used a zero-thickness volume element with post-failure tensionseparation laws. They demonstrated the importance of the interface between two different materials. Shin and Yu [22] presented a numerical study on the splitting performance of prestressed concrete prisms by incorporating bond-slip behavior of prestressed concrete using a cohesive element. They used a user-defined material model to describe the bondslip behavior at the interface.

In this research, a numerical model of wide-type UHPC sleepers with respect to different amounts of fiber contents are developed and compared to the experimental tests. A direct tension test is performed and used for obtaining nonlinear properties of UHPC in tension. Using the developed models, a parametric study is performed to investigate the structural performance of the sleepers with respect to the content of steel fibers, the diameter of the prestressing tendons, and the yielding strength of PS tendons. The commercial finite element program ABAQUS is used in this study [23].

#### **2. Mix Design and Fabrication of UHPC Sleeper**

Wide-width concrete sleepers were manufactured using UHPC mixtures with three levels of fiber contents, mainly 0.5%, 1.0%, and 1.5%. The detailed mix proportion of the UHPC mixtures and the mixing procedures can be found in Bae and Pyo [8]. The

compressive strength was evaluated using a 50 mm cubic specimen and averaged from at least three specimens. The compressive strengths of 0.5%, 1.0%, and 1.5%-UHPC specimens at 28 days were 149, 160, and 159 MPa, respectively. In addition, tensile strength results were adopted from Pyo et al. [24], where the tensile behavior of the similar UHPC mixture without ground granulated blast furnace slag (GGBFS) was characterized by following the JSCE recommendation [25]. The thickness of the tested tensile specimens was 30 mm-thick according to the recommendation. Figure 1 shows the averaged stress-strain relationships of UHPC with three levels of fiber contents under the direct tension test. For numerical constitutive models, the experimentally obtained constitutive relationship data were used to calibrate the uniaxial tensile behavior of three different concrete models. The solid lines represent the experimental data [24] and the dashed lines the numerical models.

**Figure 1.** Experimentally obtained averaged stress-strain relationships under the direct tensile test on the UHPC with various fiber volume contents and the corresponding numerical constitutive models.

Figure 2 shows the detailed layout of the fabricated UHPC sleepers in the previous research [8,17], in which four PS tendons with diameters of 9.2 mm were used. Six sleepers with the 1.0% fiber volume case and three sleepers with the 0.5% and 1.5% fiber volume cases each were fabricated and tested. The fresh UHPC mixture was cast in the mold with external vibration, similar to the conventional sleeper production protocol. The casted UHPC sleepers were demolded after 24 h of curing and the sleepers were air-cured for an additional 24 h. Then, the prestress forces were introduced with the post-tensioning method. It is important to note that the prestress force was introduced without a post-tension duct and a thin layer of coating was applied to the surface of the PS tendons.

**Figure 2.** *Cont.*

**Figure 2.** Geometrical dimension of L-150 series sleeper (unit: mm): (**a**) top view; (**b**) front view; (**c**) rail-seat section; (**d**) center section.

#### **3. Finite Element Modeling**

The brittle cracking model available in ABAQUS [23] is adopted to describe the brittle failure nature of the concrete. Since the direct tensile stress and strain relationships were available for three different levels of the steel fiber contents, the direct stress after cracking and direct cracking strain data were computed and used to define concrete cracking behaviors. Figure 1 shows the comparisons between the numerical and experimental stress-strain relationships for the cracking models. The inelastic tensile strain is computed by Equation (1).

$$
\epsilon\_t^{in} = \epsilon\_t^{current} - \frac{\sigma\_t^{current}}{E\_o} \,\,\,\,\tag{1}
$$

where *in <sup>t</sup>* is the inelastic strain (direct cracking strain) in tension, *current <sup>t</sup>* is the total strain, σ*current <sup>t</sup>* is the current stress level (direct stress after cracking), and *Eo* is the initial elastic modulus of concrete [23]. For the simplicity and the elastic nature of the UHPC (with the compressive strength of 150 MPa), the compression region of concrete is modeled as a linear elastic model. Table 1 summarizes the important mechanical properties of concrete and prestresssing tendon in the models. For the post-cracking behavior of the UHPC, the direct stress onset of cracking was found to be 3.17 MPa, 6.52 MPa, and 5.58 MPa for the UHPC with steel fiber content 0.5%, 1.0%, and 1.5%, respectively, from the direct tension test. It is important to note that the direct stress onset of cracking of the UHPC with 1.0% steel fiber content is slightly higher than that of the UPHC with 1.5% steel fiber content. However, the ultimate strength of the UHPC with 1.5% steel fiber content is the highest (see Figure 1).

In this study, a 2D model with plane stress elements (four-node plane stress element) was adopted to describe the concrete body of a sleeper. The width of the sleeper is separately defined at the various regions; the width of 360 mm was assigned to the rail-seat area, and the width of 270 mm at the center section. The PS tendons were modeled as 1D truss model (two-node linear truss element) with a specific area (132.95 mm<sup>2</sup> = 2 × 66.48 mm2) at the specific heights. The prestressing tendons were fully embedded into the concrete body. Figure 3 shows the 2D numerical model developed in ABAQUS (ABAQUS 6.14, Dassault Systèmes Simulia Corp, Providence, RI, USA). The total number of the elements and the nodes were 1840 and 1985, respectively. Then, 69,000 N (1038 MPa) of the prestressing force was assigned to each tendon. A pin and roller boundary conditions were assigned at 197 mm and 697 mm nodes from the free end. A point load was applied at 447 mm from the free end on the top surface at the rail-seat section, similar to the experimental test. An explicit dynamics analysis was performed for a quasi-static process [23].


**Table 1.** Summary of the material properties.

**Figure 3.** The 2D numerical sleeper model (**a**), its mesh (**b**), and the boundary conditions (**c**).

#### **4. Comparisons with Experimental Data**

#### *4.1. Summary of the Testing at the Rail-Seat Section*

A quasi-static three-point bending test according to European standards [9], was conducted on three UHPC sleepers with 0.5% steel fiber contents, six sleepers with 1.0% steel fiber contents, and three sleepers with 1.5% steel fiber contents. The centerline of the actuator is placed at 447 mm away from the free end of the sleeper, and the supports were placed 500 mm away from each other. Figure 4 shows a testing setup of the static three-point bending test. The reference test load, Fro of 126.8 kN, was computed [17]. The force and crack-width relationship of each sleeper was obtained and compared to each other. Overall, the higher the steel fiber contents are, the higher load capacities become. The 1.5% UHPC sleepers showed the highest failure forces and were able to mitigate the crack propagation. In Section 4.2.2, the experimental force and crack-width relationships together with numerical results are presented. The detail of the experimental tests and results can be found in the previous study [8].

**Figure 4.** Static bending test setup at the rail-seat section.
