# Correlation of Pavement Distress and Roughness Measurement
## 5 Raveling vs. IRI
### Distresses Density and the IRI Model  
In this section, the regression method was chosen to create models that related IRI with the density of different distresses. The linear regression model would be in the form:  
\[\text{IRI}=\text{b}_{0}+\text{b}_{1}\text{ distress(1)}+\text{b}_{2}\text{ distress(2)}+\text{b}_{3}\text{ distress(3)}\ldots+\text{b}_{n}\text{ distress(n)}; \tag{2}\]  
where; \(\text{b}_{0},\text{b}_{1},\ldots,\text{b}_{n}\): regression coefficients  
For each street category, two regression models were generated. The first model looked at how different types of distress impacted pavement roughness (IRI). The previous results in detecting ride quality types of distress were then confirmed using this model. The second model was created to find the best match between IRI and the different types of ride quality distress. The two models were checked and analyzed using a variety of statistical tests. The \(t\)-test was used to evaluate the relationship between the two regression coefficients (\(\text{b}_{0}\), \(\text{b}_{1}\)) and the dependent variable at the 95% confidence level. Analysis of variance was used to determine the regression line's quality, or if the variation in IRI is dependent on the distress data. Finally, the correlation coefficient (R2) was used to show how well the regression model was fitted to the data. * The influence of pavement roughness on six different types of distress in the main street sections in Riyadh city was studied and analyzed. The study developed and tested two regression models; the first model attempted to link the IRI index to all types of distress in main street samples. The second regression model was developed to connect the IRI index to different types of distress that have been identified as ride quality distresses. The linear regression looked like this: \[\text{IRI}=\text{b}_{0}+\text{b}_{1}\text{ Cr}+\text{b}_{2}\text{ Pa}+\text{b}_{3}\text{ Po}+\text{b}_{4}\text{ Dr}+\text{b}_{5}\text{ Ru}+\text{b}_{6}\text{ Ra};\] (3) where; \(\text{b}_{0}\), \(\text{b}_{1}\), \(\text{b}_{2}\), \(\text{b}_{3}\), \(\text{b}_{4}\), \(\text{b}_{5}\), \(\text{b}_{6}\) are regression coefficients; Cr = crack distress density; Pa = patching distress density; Po = potholes distress density; Dr = depression distress density; Ru = rutting distress density; Ra = raveling distress density. 1. Model-1--connects IRI to all observable distresses: \[\text{IRI}=2.09+0.00265\text{ Cr}+0.00554\text{ Pa}+0.00906\text{ Po}+0.0193\text{ Dr}+0.00531\text{ Ru}+0.00317\text{ Ra}\] (4) Summary of the model parameters is presented in Table 2.  
The \(p\)-values for most regression coefficients are zero, meaning that there is a significant correlation between the types of distress and the estimated value of IRI. The \(p\)-values of the potholes (Po) and rutting (Ra) coefficients, on the other hand, are more than the 0.05 level of significance. As a result, there is sufficient evidence to exclude potholes and rutting in estimating the roughness index. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Predictor** & **Coef.** & **St.Dev.** & **T** & \(\boldsymbol{p}\) \\ \hline Constant & 2.09494 & 0.01593 & 131.54 & 0 \\ Cr & 0.0026529 & 0.0002124 & 12.49 & 0 \\ Pa & 0.0055395 & 0.000327 & 16.94 & 0 \\ Po & 0.009056 & 0.00501 & 1.81 & 0.071 \\ Dr & 0.019317 & 0.002978 & 6.49 & 0 \\ Ru & 0.005306 & 0.00176 & 3.01 & 0.063 \\ Ra & 0.0031703 & 0.0003066 & 10.34 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of \(t\)-tests for main streets (Model-1). Analysis of Variance \begin{tabular}{l l l l l l} Source & DF & SS & MS & F & \(p\) \\ Regression & 6 & 203.339 & 33.890 & 132.26 & 0.000 \\ Residual Error & 1610 & 412.547 & 0.256 & & \\ Total & 616 & 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. 3.