# Practical Application of Sustainable Road Structure: Mechanical and Environmental Approach
## 4 Mechanical Analysis
### Loading Testing on Test Sections  
On the basis of the FWD deflections and knowing the thickness of the structural layers, calculations of elastic modulus of layers with the back-calculation method were conducted using the ELMOD 6 software [24]. The structure was divided into a packet of bituminous layers, the sub-base and the sub-grade and the elastic moduli were marked as E1, E2 and E3, respectively. The modulus of the bituminous layers packet has been designed at 13 \({}^{\circ}\)C, which is the equivalent temperature used in the design of the pavements in Poland [25]. The results of the calculations are shown in Figure 6. A common feature of all pairs of measurements from the two years is the increase in stiffness after a year of service life of the road. This dependence can be justified by the extremely different rain conditions discussed above. While the increase in the sub-grade elastic modulus or mineral sub-base can be associated with differences in the moisture content of the layers, this is no longer so obvious in terms of the stiffness of the asphalt binder packet. This may be due to some shortcomings in the back-calculation method for determination of moduli. It is also worth noting that in the case of the APSE structure, the increase in stiffness is much greater, at about 40%, which can proof the longevity of the processes occurring in the mixture with the BIO-additive. The measurement in 2017 showed significantly higher stiffness of the asphalt binder packet in the reference section, while in 2018, the results remained at the same level. The comparison of the stiffness of the individual layers of the APSE structure and the reference structure does not allow for the indication of an unambiguous relationship. Taking into account the scattering of the results, it can be concluded that the differences are generally not statistically significant and thus the structures are comparable in terms of the stiffness of the layers. Further parts of the study included an analysis of the fatigue life of the structure using mechanistic method. Mechanistic method of pavement designing stands on the evaluation of the pavement fatigue life on the basis of stress and strain field analysis. Pavement is considered as an elastic multilayer structure with defined thicknesses laying on an infinite half space. Each layer is described by: thickness, stiffness modulus and Poisson ratio. Horizontal elastic tensile strain in the bottom of asphalt layers and vertical compressive elastic strain at the top layer of the soil base were calculated. Evaluations of the strain field in pavement structure were conducted with NOAH 2.0 software with the following assumptions: single wheel load of 50 kN, contact pressure: \(q\) = 850 kPa and equivalent temperature: 13 \({}^{\circ}\)C. Evaluations of asphalt layers fatigue life (\(N\)) were conducted using the AASHTO 2004 law:  
\[N_{asf}=7.3557*\left(10^{-6}\right)\cdot C\cdot k_{1}^{\prime}\cdot\left( \varepsilon_{t}^{-3.9492}\right)\cdot E^{-1.281} \tag{2}\]  
where:  
\[C=10^{M} \tag{3}\]  
\[M=4.84*\left(\frac{V_{b}}{V_{a}+V_{b}}-0.69\right) \tag{4}\]  
\(N_{asf}\)--fatigue life, (number of equivalent standard axles),  
\(\varepsilon_{t}\)--tensile strain, (um/m),  
\(E\)--stiffness modulus, (MPa),  
\(V_{b}\)--asphal content by volume, (%_v_/_v_),  
\(V_{a}\)--air voids, (%_v_/_v_),  
\(h_{ac}\)--total thickness of bituminous layers, (cm)  
\(k_{1}^{\prime}\)--parameter according to the formula:Figure 6: Elastic modulus of pavement structure layers at the years 2017 and 2018: **(a)** E1—Asphalt layers, **(b)** E2—Sub-base, (c)** E3—Sub-grade. \[k_{1}^{\prime}=\frac{1}{0.000398+\frac{0.003602}{1+e^{(1.01-3.74\,k_{\rm{acc}})}}} \tag{5}\]  
The criterion of subgrade strain according to the equation of the Asphalt Institute:  
\[\varepsilon_{P}=0.0105\cdot Ngr^{-0.223} \tag{6}\]  
where:  
\(N_{gv}\)--life, (number of equivalent standard axles),  
\(\varepsilon_{P}\)--subgrade strain, (um/m). The structure fatigue life \(N_{min}\) is the lowest of the \(N_{asf}\) and \(N_{gr}\) values.