# Mechanical-Empirical Pavement Design Guide Applied to Portuguese Pavement Structures
## Appendix A Appendix A Appendix A.1. _Pavement Performance Prediction Models_
#### a.1.4 International Roughness Index (IRI)  
\[IRI=IRI_{0}+0.0150(SF)+0.400(FC_{Total})+0.0080(TC)+40.0(RD) \tag{119}\]  
\[SF=Age[0.02003(PI+1)+0.007947(PR+1)+0.000636(FI+1)] \tag{120}\]  
where  
\(IRI_{0}\) is the initial IRI after construction (in/mi);  
\(SF\) is the site factor;  
\(FC_{Total}\) is the area of fatigue cracking (combined alligator, longitudinal, and reflection cracking in the wheel path), percent of total lane area; all load cracks are combined on an area basis--the length of cracks is multiplied by 1 ft to convert length into an area basis;  
\(TC\) is the length of transverse cracking, including the reflection of the transverse cracks in existing HMA pavements (ft/mi);  
\(RD\) is the average rut depth (in);  
\(Age\) is the pavement age (years);  
\(PI\) is the percent of the plasticity index of the soil;  
\(FI\) is the average annual freezing index (\({}^{\circ}\)F days);  
\(PR\) is the average annual precipitation or rainfall (in).  
Transverse cracking-thermal cracking  
\[\Delta C=A(\Delta K)^{n} \tag{121}\]  
\[A=10^{k_{i}\beta_{i}(4.389-2.52 Log(E_{HMA}\sigma_{m}n))} \tag{122}\]  
\[\eta=0.8\bigg{[}1+\frac{1}{m}\bigg{]} \tag{123}\]  
\[K=\sigma_{tip}\Big{[}0.45+1.99(C_{0})^{0.56}\bigg{]} \tag{124}\]  
\[TC=\beta_{t1}N\bigg{[}\frac{1}{\sigma_{d}}Log\bigg{(}\frac{C_{d}}{H_{HMA}} \bigg{)}\bigg{]} \tag{125}\]  
where  
\(\Delta C\) is the change in the crack depth due to a cooling cycle;  
\(\Delta K\) is the change in the stress intensity factor due to a cooling cycle;  
\(A,n\) are the fracture parameters for the HMA mixture;  
\(k_{i}\) is the coefficient determined through global calibration for each input level (level 1 = 5.0; level 2 = 1.5; and level 3 = 3.0);  
\(E_{HMA}\) is the HMA indirect tensile modulus (psi);  
\(\sigma_{m}\) is the mixture tensile strength (psi);  
\(m\) is the \(m\)-value derived from the indirect tensile creep compliance curve measured in the laboratory;\(\beta_{t}\) is the local or mixture calibration factor;  
\(\sigma_{tip}\) is the far-field stress from the pavement response model at the depth of the crack tip (psi);  
\(C_{0}\) is the current crack length (ft);  
\(TC\) is the observed amount of thermal cracking (ft/mi);  
\(\beta_{t1}\) is the regression coefficient determined through global calibration (400);  
\(N[z]\) is the standard normal distribution evaluated at \([z]\);  
\(\sigma_{d}\) is the standard deviation of the log of the depth of cracks in the pavement (0.769)  
(in);  
\(C_{d}\) is the crack depth (in);  
\(H_{HMA}\) is the thickness of the HMA Layers (in).  
Reflection cracking  
\[RC=\frac{100}{1+e^{a(c)+bt(d)}}\] (A26)  
\[a=3.5+0.75\times(H_{eff})\] (A27)  
\[b=-0.688684-3.37302\times(H_{eff})^{-0.915469}\] (A28)  
where  
\(RC\) is the percent of cracks reflected; the percent of the area of reflection cracking is output with the width of cracks being 1 ft;  
\(t\) is the time (years);  
\(a,b\) are regression fitting parameters defined through the calibration process;  
\(c,d\) are user-defined cracking progression parameters;  
\(H_{eff}\) is the thickness of HMA layers in new flexible pavements (in).