# Influence of Type of Sleeper–Ballast Interface on the Shear Behaviour of Railway Ballast: An Experimental and Numerical Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Test Materials

^{3}and 2.69, respectively. Sieve analysis was carried out to separate ballast aggregates into 4 different size groups, 19–25, 25–37.5, 37.5–50, and 50–63 mm. The test samples were prepared by mixing each sieved size of ballast aggregates according to the defined particle size distribution (PSD), as depicted in Figure 1a, which lies between the upper and lower limits of Indian standard gradation of ballast, widely adopted by the Department of Railways, Sri Lanka. Figure 1b shows the percentages of each sieved size group in a prepared test sample.

#### 2.2. Large-Scale Direct Shear Apparatus

#### 2.3. Test Procedure

#### 2.4. Experimental Results

#### 2.4.1. Shear Behaviour

#### 2.4.2. Compression/Dilation Behaviour

#### 2.4.3. Ballast Breakage

## 3. Numerical Study

#### 3.1. Discrete Element Modelling (DEM) of Ballast

_{B}denotes the radius of the finite-sized glue bonds. The criterion for bond breakage based on the normal and tangential shear stresses (σ

_{max}and τ

_{max}, respectively) is given by the following equations:

#### 3.2. Simulation of Ballast Particles

#### 3.3. Simulation and Validation of Large-Scale Direct Shear Test

#### 3.4. Parametric Study and Results

## 4. Conclusions

- The results of large-scale direct shear tests conducted under 60 kPa normal stress revealed that the ballast–ballast interface had the highest shear stress variation compared to the ballast–sleeper interface, regardless of the type of sleeper used in the railway tracks. In addition, when compared to timber and concrete sleeper interfaces, all three types of USPs employed in this study (including raw rubber USP and recycled rubber USP) improved the peak shear stress by 29% and 101%, respectively. Furthermore, because of its softer surface, the timber sleeper showed a 56% greater peak shear stress than the concrete sleeper. Moreover, as expected, the shear stress reduced when the normal stress decreased from 60 kPa to 30 kPa at the ballast–ballast interface.
- Based on the experimental data under 60 kPa normal stress, the ballast–ballast sample exhibited the greatest dilation behaviour, followed by the ballast–USP_Raw, ballast–concrete, ballast–USP_RCL#2, ballast–USP_RCL#1, and ballast–timber interface samples, respectively. Relatively softer USPs allowed ballast particles to embed into the USP surface and enhanced particle rolling at the ballast–USP interface, encouraging dilation. Because of its relatively soft and smooth surface, the timber sleeper promoted particle sliding, minimizing particle rolling as compared to the concrete sleeper. Additionally, the dilatation of the ballast–ballast sample at 30 kPa normal stress was greater than that at 60 kPa normal stress.
- Ballast particle breakage was quantified based on the ballast breakage index (BBI). The results under 60 kPa normal stress confirmed that the ballast–ballast interface had the highest BBI, followed by the ballast–concrete and ballast–timber interfaces. All three types of USPs used in this study exhibited the lowest BBI values, confirming their ability to reduce ballast degradation while enhancing the shear stress. Furthermore, as expected the ballast–ballast interface exhibited a lower BBI at 30 kPa normal stress compared to 60 kPa normal stress.
- The parametric study results of DEM simulation on the shear behaviour of each interface under different normal stresses revealed that when the normal stress increased, the shear stress also increased. For all normal stresses, the ballast–ballast interface showed the highest shear stress variation, followed by the ballast–USP_RCL#2, ballast–timber, and ballast–concrete interfaces, respectively.
- Based on the DEM results, the non-linear Mohr–Coulomb failure envelopes were developed for each interface. As expected, the ballast–ballast interface had the greatest variation in normalized shear stress, whereas the ballast–concrete interface exhibited the least variation. The apparent friction angle values for each interface were calculated under each normal stress. The friction angle value for ballast–ballast, ballast–USP, ballast–timber, and ballast–concrete interfaces varied between 53° to 76°, 43° to 58°, 30° to 53°, and 29° to 44°, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Particle size distribution of ballast with limits of Indian standard gradation [18] and (

**b**) percentages of each sieved size group of ballast.

**Figure 2.**Different sleeper arrangements: (

**a**) timber sleeper; (

**b**) concrete sleeper; (

**c**) concrete sleeper with USP_Raw; (

**d**) concrete sleeper with USP_RCL#1; (

**e**) concrete sleeper with USP_RCL#2.

**Figure 4.**Different interface test configurations: (

**a**) ballast–ballast; (

**b**) ballast–timber; (

**c**) ballast–concrete; (

**d**) ballast–USP attached to concrete (USP is USP_Raw, USP_RCL#1, or USP_RCL#2).

**Figure 6.**Shear area for calculating shear stress (after Olson and Lai [21]).

**Figure 11.**Developed DEM models: (

**a**) ballast–ballast interface, (

**b**) ballast–timber interface, (

**c**) ballast–concrete interface, and (

**d**) ballast–USP_RCL#2 interface.

**Figure 12.**Comparison of stress–strain variation of experimental and numerical results for four different interfaces.

**Figure 13.**Variation of shear stress against shear strain under different normal stresses for (

**a**) ballast–ballast, (

**b**) ballast–timber, (

**c**) ballast–concrete, and (

**d**) ballast–USP_RCL#2 interfaces.

Property | USP_Raw | USP_RCL#1 | USP_RCL#2 |
---|---|---|---|

Thickness | 10 mm | 10 mm | 10 mm |

Density | 420 kg/m^{3} | 920 kg/m^{3} | 970 kg/m^{3} |

Static bedding modulus (DIN 45673-1) | 0.22 N/mm^{3} | 0.20 N/mm^{3} | 0.19 N/mm^{3} |

Young’s modulus | 6.00 MPa | 6.12 MPa | 6.15 MPa |

Property Type | Parameter | Value |
---|---|---|

Material properties | Solid density | 2950 kg/m^{3} |

Shear modulus | 50 MPa | |

Poisson’s ratio | 0.25 | |

Particle-to-particle interaction properties | Coefficient of restitution | 0.2 |

Coefficient of static friction | 0.5 | |

Coefficient of rolling friction | 0.01 | |

Bond strength properties | Normal/shear stiffness per unit area | 6.84 × 10^{9} N/m^{3} |

Normal/shear strength | 6 MPa | |

Bond disc scale | 0.5 |

Parameter | Steel | Timber | Concrete | USP_RCL#2 |
---|---|---|---|---|

Solid density (kg/m^{3}) | 7850 | 890 | 2400 | 970 |

Shear modulus (MPa) | 8.0 × 10^{4} | 3.93 × 10^{3} | 1.5 × 10^{4} | 2.03 |

Poisson’s ratio | 0.3 | 0.25 | 0.2 | 0.48 |

Interface | ballast–steel wall | ballast–timber | ballast–concrete | ballast–USP |

Coefficient of restitution | 0.7 | 0.4 | 0.6 | 0.3 |

Coefficient of static friction | 0.7 | 0.85 | 0.75 | 1.5 |

Coefficient of rolling friction | 0.05 | 0.04 | 0.01 | 0.08 |

**Table 4.**Comparison of numerical and experimental results using mean absolute percentage error (MAPE) and percentage variation in peak shear.

Interface | MAPE (%) | Variation in Peak Shear (%) |
---|---|---|

Ballast–Ballast (60 kPa) | 1.6 | 1.4 |

Ballast–Timber (60 kPa) | 1.0 | 5.7 |

Ballast–Concrete (60 kPa) | 10.1 | 8.5 |

Ballast–USP_RCL#2 (60 kPa) | 6.7 | 4.4 |

Ballast–Ballast (30 kPa) | 9.1 | 9.8 |

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**MDPI and ACS Style**

Navaratnarajah, S.K.; Mayuranga, H.G.S.; Venuja, S.
Influence of Type of Sleeper–Ballast Interface on the Shear Behaviour of Railway Ballast: An Experimental and Numerical Study. *Sustainability* **2022**, *14*, 16384.
https://doi.org/10.3390/su142416384

**AMA Style**

Navaratnarajah SK, Mayuranga HGS, Venuja S.
Influence of Type of Sleeper–Ballast Interface on the Shear Behaviour of Railway Ballast: An Experimental and Numerical Study. *Sustainability*. 2022; 14(24):16384.
https://doi.org/10.3390/su142416384

**Chicago/Turabian Style**

Navaratnarajah, Sinniah Karuppiah, Henpita Gamage Sushan Mayuranga, and Somasundaraiyer Venuja.
2022. "Influence of Type of Sleeper–Ballast Interface on the Shear Behaviour of Railway Ballast: An Experimental and Numerical Study" *Sustainability* 14, no. 24: 16384.
https://doi.org/10.3390/su142416384