# Economic Impact Analysis of the Application of Different
## 2 Deterioration Models and Model Evaluation
### Deterioration Equations Derived from Measurements on the APT Facility  
The principle of accelerated pavement testing is an application of artificially induced load applied in a short period of time on an experimentally built road section. Such facility simulates a real load on the real pavement while providing great control during the experiment, this allows researchers to evaluate different factors of road deterioration throughout the pavement life cycle [19; 20].  
APT is essentially a laboratory test (Figure 1) at a scale of 1:1, during which a load unit (in our case, a semi-axle of a heavy vehicle) is used to induce a load at a frequency that simulates road performance in a relatively short time, which would otherwise be distributed throughout its whole life cycle [20].  
The degradation characteristics obtained experimentally were derived from data collected at the APT facility; the construction and operation parameters of the facility are presented in detail by [PERSON] et al. [21]. Derived functions from APT were already partly presented in several studies [21; 22]. This paper presents the deterioration of the pavement performance index--the rut depth (_RUT_). International roughness index (IRI), bearing capacity, and fatigue of selected asphalt layers and their evaluation were previously presented in [22; 23; 24]. The _RUT_ parameter is selected as a critical deterioration parameter for pavements with unmodified asphalt concrete surfacing.  
Two deterioration models were derived from the presented APT facility. The first function was derived after 700,000 cycles of heavy vehicle simulation using Equation (1) and the second after 900,000 cycles using Equation (2). Subsequently, they were compared with other functions in order to present a total difference in economic parameters, which can arise after only 200,000 loading cycles.  
The first function derived from the APT is defined by Equation (1) as follows:  
\[RUT=-0.0535\Big{(}\frac{n}{N}\Big{)}^{2}-0.9208\Big{(}\frac{n}{N}\Big{)}+1 \tag{1}\]  
The second function derived from the APT is defined by Equation (2) as follows:  
\[RUT=-3.8013\Big{(}\frac{n}{N}\Big{)}^{3}+5.5617\Big{(}\frac{n}{N}\Big{)}^{2}-2. 7629\Big{(}\frac{n}{N}\Big{)}+1 \tag{2}\]  
In both Equations, _RUT_ is degradation parameter (a relative value of selected deterioration of _RUT_ depth parameter, in the range from 0% to 100% deterioration); \(n\) is the number of loading at the time of evaluation; \(N\) is the number of loading when the end-of-life limit is reached.  
These deterioration equations were derived from collected data by measurement with three different measurement methods [25; 26]. These three measurement methods were as follows:  
* A 3D scanning method by total station Leica;
* A 3D scanning method by 3D portable scanner Bibus;
* Measurement of selected profiles via leveling measurement and the straightedge method [27].  
At 900,000 cycles, there are no cracks on the pavement surfacing. The first parameter that met the warning level of deterioration was the _RUT_ depth; therefore, this paper focused on _RUT_ evolution equations.  
Figure 1: APT facility (**left**); rutting on the pavement test section under the APT facility (**right**).