## 3 Consideration of Dynamic Loads in Axle Load Spectra  
### Pavement Profiles and Vehicle Models  
Quarter-car models, two-freedom systems consisting of the wheel, suspension system, and a quarter of vehicle mass, have been widely adopted to simulate vehicle behavior and investigate the influence of pavement evenness on dynamic tire forces [3; 17; 18; 19]. Taking advantage of advanced software (such as MATLAB), multibody dynamic truck models were developed to simulate dynamic characters of vehicles considering comprehensive vehicle system components [4; 20]. TruckSim, a multi-body dynamic model with multiple freedoms, is capable of simulating dynamic behaviors of various truck configurations. Multiple bodies can be simulated on the basis of the database embedded for a truck, including the steering system, suspension system, power train, and sprung mass [21; 22]. Previous research has used TruckSim to simulate dynamic tire forces of moving vehicles with various truck configurations, considering a wide range of vehicle speeds and pavement roughness levels [23; 24].  
The dynamic tire forces of different axle configurations excited by pavement surface profiles at specific operational speeds were calculated using the TruckSim software. Figure 1 illustrates the axle configuration of Class 5, Class 7, and Class 9 trucks used in the study. The dynamic tire forces under single, tandem, and tridem axles were evaluated using the selected representative truck configurations. The spring rates of the tires were computed according to static load deflection measurements and applied in the previous study related to vehicle dynamics simulation [25]. For the steering axle (Axle 1), a single tire was equipped. The tire width was 275 mm, with a spring rate of 932 N/mm. For the drive axles (Axle 2, 3, 4, and 5), a dual tire assembly was equipped. The tire width was 275 mm, with a spring rate of 829 N/mm.  
Figure 1: _Cont._  
The Long-Term Pavement Performance (LTPP) program was founded to collect pavement performance data by the Strategic Highway Research Program (SHRP). The LTPP program consisted of two fundamental categories of studies, and some smaller studies to quantify specific pavement-related details that have significant influence on pavement performance. The two categories of studies are the General Pavement Study (GPS) and Specific Pavement Studies (SPS). Pavement profile data of select pavement sections in New Jersey were extracted from the LTPP database [27]. The moving average window of profile measurements was 0.3 m (0.98 ft), and the pavement surface elevation data were recorded at an interval of 0.15 m (0.49 ft). The total length of the individual pavement segment was 152.4 m (500 ft), and it consisted of 1017 surveyed points. Totally, 13 pavement profiles of five pavement sections (SHRP_ID = 341003, 341030, 341031, 341033, and 341034) on minor highways and 11 pavement profiles of five pavement sections (SHRP_ID = 340501, 340502, 340503, 340506, and 340560) on major (Interstate) highways were extracted. The measurements were conducted through 1997-2007 on the pavement sections of GPS-65, GPS-2, and SPS-5. Figure 2 illustrates the profiles of the select pavement sections with average IRI values measured in different years. The range of IRI values of the selected major routes was 0.73-2.78 m/km (46-176 inch/mile). A wide range of IRI values from 0.73 m/km (46 inch/mile) to 4.73 m/km (300 inch/mile) was considered for minor routes. The pavement sections with similar IRI values might have totally different surface profiles, such as pavement sections of 340503, 340507, and 340560. In the pavement management system, the IRI values of 1.50 m/km (95 inch/mile) and 2.68 m/km (170 inch/mile) were usually set as the thresholds of pavement conditions ranging from fair to good and poor to fair ratings, respectively [28].  
Figure 1: Illustration of axle configurations (schematic indication) for (**a**) Class 5; (**b**) Class 7; and (**c**) Class 9 trucks [26].