Simulations have been conducted on ABAQUS using a dload subroutine where speed of the class A40 truck is kept constant at 90 Km/h on a 20 meters long pavement section. Simulations correspond to 5000 average annual truck passes for a design life of 15 years. Screenshots are taken from the simulations for the positioning of tire foootprints at different locations.
Figure 5 shows the stress values exerted under each tire foootprint 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. Highest stress accumulation within the truck axles ia observed under the driving axle and along the middle axle of the trailer.
Figure 6 shows the cut section view of the stresses under the middle axle of the trailer, where the highest amounts of stresses are exerted along the pavement. For the calculation of vertical and horizontal strains, the functions E in the ABAQUS were used to determine fatigue and rut life of the pavement.
Futhermore, the stresses were recorded under the tires at various lateral positions of axles. Figure 7 shows the screenshot taken when the lateral positioning of the truck was at extreme left of the lane during a uniform wander mode.
Even during the selection of uniform wander mode, due to the geometric configuration of dual wheels on the driving axle of the tractor, the majority of load concentration is along the central part of the pavement lane as shown in Fig. 8. The effected area is overlapped by truck passes when a uniform wander mode is due to geometric configuration lateral dimensions of drive axles..
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. 9. As observed with the total length of the section being 20 m. The highest magnitude of strains are recorded along the middle axle of the trailer at 350 microns, followed by the front and back axles of the trailer at 286 microns. The minimum amount of strain occurs under the steering axle of the truck at 136 microns.
3.1 LEF and ESALs Calculation
The damage accumulated from each axle corresponding to design life of 15 years was then converted into equivalent damage to a standard 80 kN single axle load using load equivalency factor (LEF) 20. A standard formula in which a standard single axle load of 80 kN (18,000lbs) is divided to a designated axle load and the ratio is powered to four as shown below in Eq. (8).
$$LEF={\left(\frac{designated axle load\left(kN\right)}{standard axle load\left(kN\right)}\right)}^{4}$$
8
Correspoonding LEF values for each axle in the truck are shown in Table 4.
Table 4
Calculated LEF for each axle group.
Axle Type
|
LEF
|
Damage effect compared to standard axle load
|
Steering axle
|
0.48
|
Less than 2 times
|
Drive axle
|
3.03
|
More than 3 times
|
Front rear axle
|
0.79
|
Equivalent
|
Middle rear axle
|
0.79
|
Equivalent
|
Back rear axle
|
0.79
|
Equivalent
|
The LEF for a standard 80 kN single axle load is 1.00. A steering axle load of 66.75 kN would do less than two times the damage as that of an 80 kN standard axle load. A drive axle usually has a higher axle load of about 105.61 kN, hence the damage accumulated by this axle is three times that of damage accumulated by an 80 kN standard axle load. For the three single axles on the trailer, the damage from each axle was found to be equivalent to the standard axle load of 80 kN 21. Hence, a total equivalent single axle to truck (ESAL/Truck) ratio of 1.55 was obtained and was calculated using the following Eq. (9).
$$Truck Category Esals in Construction Year=load factor*Lane AADT*3.65$$
9
Table 5 shows the calculation of a construction year design ESALs.
Table 5
Truck Category
|
Load Factor (ESALs/Truck)
|
Lane Average Annual Daily Traffic
|
ESALs in construction Year
|
5 Axles
|
5.88
|
5000
|
29,400
|
Finally, total design ESALs very calculated using the following Eq. (10).
$$Total design ESALs=total construciton year ESALs*\frac{{(1+{i}_{B to D})}^{n}-1}{{i}_{B to D}}$$
10
Where \(n\) is base year of construction and \({i}_{B to D}\) is growth rate from base year to final year of design period. With a growth rate of 3.5%, a toal ESALs of 1,300,000 were obtained. Hence the caculated ESALs were used to obtain vertical stress and strains for zero wander mode as shown in figure below
Using the E (Strain) values from the ABAQUS results, strains were calculated under each tire and each axle based on their orientations such as vertical strain on top of subgrade and horizontal strains on bottom of asphalt layer for calculation of rutting and fatigue cracking respectively. Using the equivalent damage calculation, all the measured strains from the axles for a specific number of passes were then combined into accumulated damage by a single axle 80 kN equivalency factor.
Maximum magnitude of equivalent values of strains was calculated to be at 350 microns for a zero wander mode. Magnitudes of microstrain values observed under a zero wander mode for the remaining axles are shown in the Table 6.
Table 6
Oberved vertical strain under each axle
Axle type
|
Strain (Microns)
|
Steering Axle
|
136
|
Driving Axle
|
227
|
Front Trailer Axle
|
286
|
Middle Trailer Axle
|
350
|
Back Trailer Axle
|
286
|
Maximum magnitude of vertical strains under a zero wander ode have been recorded under the middle axle of the trailer tire, which is around 80% more than the remaining two axles of the trailer. The steering axle exerts the minim amount of vertical strain at 136 microns.
During the moving load simulations along the 20 meter long crossection, when the uniform wander mode was used, with lateral acceleration of the truck kept around 1.84 m/s2. It was observed that 90% of the highest loaded elements in the model were subjected to 40% less damage in terms of stresses as compared to the elements that were loaded under a zero wander mode. Hence, the calculated vertical strain values under the top of subgrade were eventually reduced to a corresponding amount and shown in Fig. 10.
Furthermore, along the lateral section of the truck axle, strains were recorded at the bottom of the asphalt layer. Load equivalency factor was used to calculate the equivalent magnitude of strain observed under the tires, corresponding to the axle load of 80 kN. Accumulation of strains on the bottom of the asphalt layer for a lateral cross-section are shown in Fig. 11.
The middle trailer axle exerts the maximum amount of strain with a magnitude of 80 microns, followed by the strains values of 60.4 microns under remaining trailer axles. The difference between the strain values observed along the lateral cross-section if high at higher magnitudes of strains in case of a middle trailer axle and driving axle of the truck. The difference in strains of about 145% is observed for the zero wander and uniform wander mode under the middle trailer axle as shown in Fig. 12.
3.2 Rutting and Fatigue Cracking Evaluation
Using the equivalent values of microstrains observed with a projected traffic of 1.3 million ESALs for a design life of 15 years, number of loading cycles to rutting and fatigue cracking were calculated from the distress prediction models developed by Asphalt Institute. Two of the fatigue and rutting prediction models respectively given by Asphalt Institute are presented below in Eq. (11) and Eq. (12) respectively 22.
$${N}_{f}=0.0796* {\epsilon }_{t}^{-3.291}*{E}^{-0.854}$$
11
$${N}_{d}=1.365*{10}^{-9}*{\epsilon }_{t}^{-4.477}$$
12
Where, where \({N}_{f}\) is the allowable number of load repetitions to prevent fatigue cracking and \({N}_{d}\) is the allowable number of load repetitions to prevent permanent deformation (rutting), \(E\) is the elastic modulus of asphalt concrete layer, \({\epsilon }_{t}\)is tensile horizontal strain under HMA layer and \({\epsilon }_{c}\) is vertical compressive strain on top of the subgrade.
Microstrains obtained from FE modelling are used to calculate permanent plastic strain \({\epsilon }_{p}\) as per following Eq. (13),23.
$${\epsilon }_{p}={\epsilon }_{r}*{a}_{1}*{N}^{{a}_{2}}*{T}^{{a}_{3}}$$
13
Where, \({\epsilon }_{p}\) is permanent strain \({\epsilon }_{r}\) is resilient strain \(N\) is number of load repetitions \(T\) is temperature and \({a}_{1},{a}_{2},{a}_{3}\) are regression coefficients with values 1.69, 1.85, 0.275 respectively taken from (40). Finally, the rut depth occurring in asphalt layer can then be computed using the following Eq. (14), 24.
$$RD=\sum _{I=1}^{N}{\epsilon }_{P}^{I}{h}^{i}$$
14
where \(RD\) is the total rut depth in the asphalt concrete layer; \(N\) is the number of sublayers, \({\epsilon }_{P}^{I}\) is the plastic strain in the ith sublayer; and \({h}^{i}\) is the thickness of the i-th sublayer. However, in this research asphalt layer was not divided into subseueant sublayers, rather the accumulation of plastic strains at bottom of the asphalt layer and vertical strains on top of subgrade layer were used to calculate the rut depth.
Maximum amount of reduced number of passes occurs under a zero wander mode with 527,000 number of reduced passes by the end of lifetime of the pavement as shown in Fig. 13, and it translates to the decrease in fatigue life of around 1.2 years if the zero wander mode is used. On the other hand, the decrease in number of passes reduced by fatigue damage is only limited to 239,000 passes, corresponding the decrease in fatigue life of only 4 months when a uniform wander mode is used.
Asphalt pavement must be rehabilitated as it reached its terminal serviceability when the rut depth of 6 mm occurs on the pavement surface. Figure 14 compares the number of passes under each wander mode to reach a rut depth of 6 mm. Under a zero wander mode, the pavement only needs 735,286 number of passes to reach rut depth of 6 mm, however when uniform wander mode is used, the number of required passes to reach 6 mm increases to 1,205,380 which makes upto a 38% increase in number of passes. When a uniform wander mode is used, the pavement can sustain its serviceability until the end of its predicted lifetime for the same amount of traffic growth and number of passes.
Rut depth was obtained using equation and also compared from the (U) deformation results in ABAQUS results section and presented in Fig. 15. 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. On the other hand, for the uniform wander mode, the rut depth remains at 6.2 mm at the end of the pavement's services life. The decrease in rut depth is around 1.5 times when a uniform wander mode is used. Magnitude of rut depth under a uniform wander mode provides the effectiveness of uniform wander mode in prolonging the service life of pavement as compared to the projected zero wander mode.