## 1 Introduction  
There are several major factors that lead to the deterioration of asphalt pavement, and traffic loads are among the most important. These loads significantly affect pavement performance due to their repetition over time [1,2]. Traffic loads, their frequency, and the resulting stresses are pivotal in determining the performance and longevity of the pavement. When vehicles pass, they generate different stresses that can cause various types of damage, depending on the type and weight of the load. As the weight of the load increases, the likelihood of pavement damage also increases, leading to deformation, cracking, and fatigue. Pavements are designed to withstand a certain number of load repetitions throughout their service life; however, excessive repetition of heavy loads can exceed the structural capacity of the pavement [3, 4, 5]. Each time a vehicle passes over the pavement, it generatesstress that accumulates over time, which can lead to fatigue failure, especially in areas with heavy traffic. Moreover, determining the stresses generated by vehicles in pavements poses a significant challenge for designers. This process involves understanding how different types of vehicles, loads, and traffic patterns affect pavement performance. Therefore, understanding and addressing these factors is essential for maintaining the safety and longevity of asphalt pavements [6; 7; 8]. The impact of traffic and vehicles on pavement design can be classified into three main categories: fixed traffic, fixed vehicle, and variable vehicle and traffic. In fixed traffic scenarios, pavement thickness is determined based on the load of a single wheel, disregarding the number of load repetitions [9; 10]. However, in situations involving different types of wheels, such as heavy wheel loads on highway pavements, they need to be converted to an equivalent single-wheel load (ESWL). Conversely, the fixed vehicle method considers the number of load repetitions of a standard axle, typically a single axle with dual tires and a load of 18 kips (80 kN). For pavements exposed to various axle types, like tandem or tridem axles, they are converted to an equivalent axle load factor (EALF) to achieve an equivalent effect based on an 18 kip (80 kN) single-axle load [11; 12]. The variable traffic and vehicles method treats vehicles and traffic separately, eliminating the need to assign equivalent factors for different axles. This method evaluates strains and deflections for each load individually. Several methods have been developed to determine the equivalent single-wheel load (ESWL), including the equal vertical stress criterion, equal vertical deflection criterion, equal tensile strain criterion, criterion based on equal contact pressure, and criterion based on equivalent contact radius. The semi-rational equal vertical stress criterion, introduced by [PERSON] and [PERSON] [10; 13], calculates the produced stress (ESWL) based on pavement layer thickness. However, safety concerns arose from accelerated traffic tests, leading to the equal vertical deflection criterion by [PERSON] and [PERSON] [10; 14]. This method assumes a homogeneous half-space pavement layer and determines the developed vertical deflection at the top of the subgrade layer using Boussinesq solutions. [PERSON], 1969 [15], suggested that this method still poses safety risks, as some pavement thicknesses exceed those obtained by the Boyd and Foster method. Other methods, such as the criterion based on equal contact pressure and the criterion based on equivalent contact radius, have been developed to address these challenges. Previous methods are ineffective in explaining the stress concentration generated by tire contact overlap in tandem and tridem axles, resulting in an incomplete understanding of stress distribution. However, the thickness of pavement layers plays a crucial role in load distribution; thicker layers help minimize stress on underlying layers and enhance the ability to support loads.