# Correlation of Pavement Distress and Roughness Measurement
## 5 Raveling vs. IRI
### Distresses Density and the IRI Model
Squared multiple correlation coefficient (R2): R-Sq = 32.5% R-Sq(adj) = 32.3%  
The squared multiple correlation coefficient (R2) is 32.3 percent. This means that 32.3 percent of the IRI values can be reflected and described by the regression model. It also shows that while there are statistically significant relationships between IRI and some types of distress, the relationship isn't strong enough to use distress types as an accurate measure of roughness conditions. (a) Model-2--connects IRI to ride quality distresses:  
In this case, the types of distress that had a strong relationship with the IRI index are called ride quality types of distress. This distress includes cracks distress (Cr), patching distress (Pa), depression distress (Dr), and raveling distress (Ra). 1. The regression model developed is as follows:  
\[\text{IRI}=2.10+0.00267\text{ Cr}+0.00553\text{ Pa}+0.0195\text{ Dr}+0.00316\text{ Ra} \tag{5}\]  
A summary of the regression model is shown in Table 3.  
Since all the regression coefficients have \(p\)-values equal to zero, this indicates that there is a statistically significant link between the different types of ride quality distress and the expected levels of IRI. 2. Analysis of Variance \begin{tabular}{l l l l l l} Source & DF & SS & MS & F & \(p\) \\ Regression & 4 & 200.181 & 50.045 & 194.06 & 0.000 \\ Residual Error & 1612 & 415.705 & 0.258 & & \\ Total & 1616 & 615.886 & & & \\ \end{tabular}   
The \(p\)-values for the ANOVA-tests for the model are zero, meaning that there is no significant variation in the IRI predicted values caused by the regression model. The results show a strong connection between IRI and various types of distress. The F-value for model-2 is greater than that in model-1 meaning improvement of model-2 over model-1. 3. Squared multiple correlation coefficient (R2): R-Sq = 33.0% R-Sq(adj) = 32.8%  
The squared multiple correlation coefficient (R2) is 32.8 percent. This means that 32.8 percent of the IRI values can be reflected and described by the regression model. It also shows that while there are statistically significant relationships between IRI and some types of distress, the relationship isn't strong enough to use distress types as an accurate measure of roughness conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Predictor** & **Coef.** & **St.Dev.** & **T** & \(p\) \\ \hline Constant & 2.09875 & 0.01594 & 131.67 & 0 \\ Cr & 0.0026746 & 0.0002129 & 12.56 & 0 \\ Pa & 0.0055299 & 0.0003278 & 16.87 & 0 \\ Dr & 0.019547 & 0.002987 & 6.55 & 0 \\ Ra & 0.003156 & 0.0003075 & 10.26 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of \(t\)-tests (Model-2). * Secondary street sections  
The effect of the pavement roughness on five distress types in the section of the secondary streets in the Riyadh city network has been studied and analyzed. The study developed and tested two regression models; the first one was to relate the IRI index to all distresses in the secondary street samples, whereas the second model was to relate IRI index to ride quality distress types. The distresses included in the regression evaluations were, cracks distress (Cr), patching distress (Pa), potholes distress (Po), depression distress (Dr), and raveling distress (Ra). The linear regression model would be in the form:  
\[\text{IRI}=\text{b}_{0}+\text{b}_{1}\text{ Cr}+\text{b}_{2}\text{ Pa}+\text{b}_{3}\text{ Po}+\text{b}_{4}\text{ Dr}+\text{b}_{5}\text{ Ra}; \tag{6}\]  
where the number of regression coefficients equal 6. The distress in the secondary streets class chosen to be ride quality type distresses that showed a statistically significant association with the IRI were cracks distress (Cr), patching distress (Pa), depression distress (Dr), and raveling distress (Ra). The linear regression model would be in the form:  
\[\text{IRI}=\text{b}_{0}+\text{b}_{1}\text{ Cr}+\text{b}_{2}\text{ Pa}+\text{b}_{3}\text{ Dr}+\text{b}_{4}\text{ Ra}; \tag{7}\]  
where the number of regression coefficients equals 5.