## Abstract

Effects of autonomous trucks' different lateral wander modes have been analyzed in this research using a dload subroutine. Two lateral wander modes, a zero-wander mode in which a truck is programmed to follow a predetermined wheel path without any lateral movement and a uniform wander mode, where the truck uniformly distributes itself along the lateral width of the lane, are used. European class A40 truck has been modeled in ABAQUS code. Results show that fatigue life of pavement increases by 1.45 times if a uniform wander mode is used, which corresponds to a decrease in fatigue life of 14 months if a zero-wander mode is used. In case of rutting progression, 40% acceleration of rutting happens under a zero-wander mode. In case of uniform wander mode, rut depth decreases by 1.25 times against the zero-wander mode.

## 1 Introduction

Autonomous Trucks (ATs) are bound to be integrated into the current transport infrastructure system, however for the initial period; ATs would be integrated with the current human driven truck traffic. Full segregation and coverage of autonomous trucks on highways requires a lot of refinement and training of artificial intelligence related to its behavior with the surrounding environment and vehicles. Effect of ATs on pavement structure requires in depth research since it is presumed that ATs will use the minimum width of lane without any lateral wander with the help of onboard sensors to increase fuel efficiency and traffic safety. However, under these zero lateral wander scenarios, an extensive amount of channelized loading can accelerate pavement distress and prematurely damage the pavement. In these research two lateral wander modes, a zero wander and a uniform wander mode are compared based on accumulated rutting by AT traffic.

Simulating the field conditions on asphalt pavement response requires using adequate modeling techniques. Pavement distress in terms of rutting induced by autonomous truck traffic can be measured using static and part dynamic loading scenarios as provided in ABAQUS code, however these methods are only limited to application where no lateral wander is considered in by traffic. Moreover, in another concept the moving load can be simulated by shifting the load and its amplitude over a loading path step by step until one wheel pass is completed [1, 2]. A dload subroutine written on FORTRAN code, on the other hand can be used to define position, time, element number and load integration point number being a function of distributed load magnitude. A dload subroutine can be used to define position, time and speed of applied load [3, 4].

Application of programmed scripts and dload subroutine integrated into ABAQUS has been evaluated in previous research. Si et al. [5] performed simulations of dynamic loading load on a pavement surface in a 3D model developed in ABAQUS by incorporating the dload subroutine written in FORTRAN. Results concluded with good capability of suggested framework for indicating the progression of bottom-up cracking in pavement by self-sensing surface sensors. Cao et al. [6] employed the use of dload and ultra-cloud subroutines to simulate the moving load on bridge deck. Cheng et al. [7] used viscoelastic FE model developed in ABAQUS and performed dynamic loading analysis using a dload subroutine. Results showed that plastic behavior did not have impact of rutting; however the viscous behavior was the most prevalent one in occurrence of rutting.

## 2 Research methodology

A typical four layered pavement structure has been selected consisting of an asphalt layer, aggregate base course, aggregate sub-base course, and a subgrade layer with presumed thickness of 2 m. Length of the pavement section to be analyzed is kept at 20 m and the width of the pavement section is kept at 3.5 m, simulating the width of truck traffic lane.

### 2.1 Pavement

Validated pavement layer properties to be used in ABAQUS have been taken from [8] as it shown in Table 1.

Pavement layer properties

Layer type | Thickness (cm) | Elastic modulus (kPa) | Poissions ratio |

Asphalt | 20 | 950,000 | 0.41 |

Base course | 40 | 500,000 | 0.35 |

Sub-base course | 20 | 350,000 | 0.35 |

Subgrade | - | 60,000 | 0.40 |

Prony series parameters

Elastic properties | |

Poisson's ratio | Instantaneous modulus (MPa) |

0.35 | 6,674 |

Prony constants | |

Prony series coefficient | Retardation time |

0.611947 | 0.000063 |

0.251542 | 0.012589 |

0.068537 | 1.258925 |

0.030080 | 12.589254 |

### 2.2 Loading

For the simulation of pavement loading, a typical European A40 type semi-truck with maximum allowable gross weight of 40 tones has been selected. Data from each axle has been obtained from [8] with axle configurations and axle loads is shown in Fig. 1

^{2});

Tire load, pressure, and dimensions

Tire type | 295/80R22.5 | 295/80R22.5 | 385/65R22.5 | 385/65R22.5 | 385/65R22.5 |

Twin vs. Single | Single | Twin | Single | Single | Single |

Axle load (Tons) | 6.70 | 10.60 | 7.57 | 7.57 | 7.57 |

Load per wheel (kN) | 32.85 | 25.98 | 37.00 | 37.00 | 37.00 |

Tire inflation pressure (kPa) | 690 | 690 | 690 | 690 | 690 |

Tire contact pressure (kPa) | 430 | 350 | 550 | 550 | 550 |

Contact patch Length/Width (mm) | 250/330 | 250/310 | 275/310 | 275/310 | 275/310 |

### 2.3 Finite element model

A 3D model has been developed with length of 20 m and width of 3.5 m. The total depth of the model is kept at 2.8 m and the bottom of the model has an interface of elastic foundation to simulate infinite thickness of natural soil foundation. Figure 2 shows the assembly of the model. Model type used is 8-node linear brick, reduced integration with hourglass control. Sensitivity analysis has been done for the element size selection based on the previous research conducted by [17]. Therefore, mesh of the model consisted of a total of 25,584 elements with an element size of 120 that has been validated.

The interaction of layers in the pavement was kept as a normal surface-to-surface contact with hard and frictionless characteristics. For the boundary conditions, nodes were free to move along the normal directions but were restricted in perpendicular horizontal directions as it is shown in Fig. 2.

## 3 Results and discussion

Simulations have been conducted on ABAQUS using a dload subroutine where speed of the class A40 truck is kept constant at 90 km h^{−1} on a 20 m long pavement section. Simulations correspond to 5,000 average annual truck passes for a design life of 15 years.

Figure 3 shows the stress values exerted under each tire footprint while a truck is moving along the middle of the lane corresponding to the zero-wander mode at a moving speed of 90 km h^{−1}, highest stress accumulation within the truck axles is observed under the driving axle and along the middle axle of the trailer.

Furthermore, the stresses were recorded under the tires at various lateral positions of axles. Figure 4 shows the screenshot taken when the lateral positioning of the truck was at extreme left of the lane during a uniform wander mode.

Magnitude of strain values were observed along the longitudinal profile under each axle and tire with raw data obtained from ABAQUS and are shown in Fig. 5. As observed with the total length of the section being 20 m. The highest magnitude of strains is recorded along the middle axle of the trailer at 350 μm, followed by the front and back axles of the trailer at 286 μm.

### 3.1 LEF and ESALs calculation

Table 4 shows the calculation of a construction year design ESALs.

Construction year ESALs

Truck Category | Load Factor (ESALs/Truck) | Lane Average Annual Daily Traffic | ESALs in construction Year |

5 Axles | 5.88 | 5,000 | 29,400 |

The calculated vertical strain values under the top of subgrade were eventually reduced to a corresponding amount and it is shown in Fig. 6.

### 3.2 Rutting and fatigue cracking evaluation

*i*-th sub-layer.

Rut depth was obtained using equation and also compared from the (*U*) deformation results in ABAQUS results section and presented in Fig. 7. With projected traffic of 1.3 million ESALs the pavement reaches a rut depth of 10.21 mm at the end of its service life.

## 4 Conclusions and findings

In this research, a fully loaded class A40 truck with maximum allowable weight of 40 kN has been used to analyze the effect of zero wander and uniform wander modes on resulting fatigue life and magnitude of rut depth in the flexible pavement. Moving load has been simulated by using the dload subroutine written in FORTRAN.

A difference in magnitude of rut depth is 1.5 times lower and fatigue life can increase by a factor of 40% if a uniform wander mode is used, making the uniform wander mode an ideal selection for lateral wander of autonomous trucks. In terms of limitations, effects of temperature and climatic conditions have not been taken into account. Therefore, pavement performance would be favorable for resistance against fatigue during lower temperatures and favorable against rutting during higher temperatures.

Following findings are obtained from this research.

Due to action of induced vertical strains, decrease in fatigue life is around 1.75 times more in case of a zero wander mode;

Fatigue life decreases by 14 months in case of a zero wander mode;

A rutting depth of 6 mm occurs under a uniform wander mode at about 1,105,380 number of passes which roughly translates to 8 percent advancement of rutting progression near the end of service life of pavement;

Overlap of wheel paths occurs in case of uniform wander mode, with the overlapping width of 1.5 m for an A40 type truck;

Acceleration for rut development in case of a zero wander is almost 2 times than that of a uniform wander mode;

After the end of service life of pavement, under zero wander mode, rut depth is around 10 mm.

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