# Optimization of Bituminous Road Surfacing Rehabilitations Based on Optimization of Road Asset Value
## 4 Residual Service Life and Pavement Performance Model
### Pavement Performance Models  
PPM are a key part of determining the value of road assets. PPM are used to predict the development of pavement serviceability, which is the main factor influencing road user costs and socio-economic value of an asset. Pavement degradation occurs during the pavement life-cycle due to traffic load and climatic conditions.  
PPM can be deterministic or stochastic. The deterministic models include primary response, structural and function performance, and damage models. The stochastic models are represented by the Markov transition process based on transition probability matrices.  
Most deterministic models work as traffic-related or time-related mathematic functions which produce degradation curves of individual pavement performance parameters [59]. The general shape of the degradation curves expresses the dependence of the relative value of the monitored parameter on time or the number of load repetitions as is shown in Equation (13). The generalized shape expressed mathematically is an exponential function in which the exponent changes the shape of the curve. This makes them simple to calibrate by regression analysis of measured data, with two coefficients A and B:  
\[\begin{split} P_{t}&=1-A*\left(\frac{t}{T}\right) ^{B}\\ P_{n}&=1-A*\left(\frac{n}{N}\right)^{B}\end{split} \tag{13}\]  
where:  
\(P_{t}\): relative value of performance parameter in relation to time t,  
\(t\): time from the beginning of the life-cycle [years],  
\(T\): predicted life expectancy of the pavement in terms of the performance parameter [years],  
\(P_{n}\): relative value of performance parameter in relation to traffic load,  
\(n\): standard axle load cycles from the beginning of the life cycle [SAL],  
\(N\): predicted life expectancy of the pavement in terms of the performance parameter [SAL],  
\(A\): coefficient of pavement class and paving materials \(0<A\leq 1\),  
\(B\): coefficient of degradation shape of performance parameter \(0.2<B\leq 6.0\).  
Figure 4 is a regression analysis of measured data, collected on APT facility pavement, and it shows a relationship between traffic load and pavement parameter RUT. The PPM is a polynomic-shaped curve and equation describing this relationship. On the right side of Figure 4 is again a regression analysis, but in this case, the PPM is created with a limited data source and a large part is only a prediction. On this chart, the parameter is defined within an interval 1-0, where 1 is the perfect condition and 0 is the limit value of pavement failure. The traffic load is described as a ratio of loading cycles (n) and loading capacity (N). This general expression of PPM makes its application easier between different pavements (but of the same type).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **Complex Modulus** & **Strength** & **Poisson Number** & **Layer Thickness** \\ \hline Surface course AC 11 & 7577 & 3.2 MPa & 0.33 & 40 mm \\ Base course AC 16 & 9967 & 2.4 MPa & 0.33 & 80 mm \\ Mechanically bound aggregate, 31,5 & 586 & 0.1 MPa & 0.30 & 180 mm \\ Gravel Sub-base, 31,5 & 365 & 0.07 MPa & 0.30 & 200 mm \\ Sub-grade & 100 & - & 0.35 & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pavement construction parameters.