# Correlation of Pavement Distress and Roughness Measurement
## 5 Findings  
The influence of all of the distress types that are present in the study area, on the IRI measurement was analyzed in order to study the riding quality-related types of distress. From the main street sections, six distress groups exist in the Riyadh network samples. While the secondary streets involve five distresses groups. Tables 6 and 7 conclude the final analysis of the relationship between the roughness evaluation index (IRI) and the pavement \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Predictor** & **Coef.** & **St.Dev** & **T** & \(p\) \\ \hline Constant & 2.5889 & 0.1321 & 19.6 & 0 \\ Cr & 0.043121 & 0.008927 & 4.83 & 0 \\ Pa & 0.04366 & 0.01249 & 3.49 & 0.001 \\ Dr & 1.3193 & 0.4077 & 3.24 & 0.002 \\ Ra & 0.010589 & 0.005002 & 2.12 & 0.036 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of t-tests for main streets (Modal-2). distress density for both main and secondary streets, sequentially. The correlation between the value of IRI and distress types has been investigated by two important statistical tests:  
1. Testing the individual correlation hypothesis between the value of IRI and each type of distress. 2. The regression coefficients were used to evaluate the overall regression model that links the IRI value with the different types of distress. Tables 6 and 7 show that \(p\)-values for cracking, depression, patching, and traveling in both main and secondary streets are near zero, indicating a significant relationship between these distress types and IRI. As a result, the findings of the research in both the main and secondary street categories suggests that there is a significant relationship between IRI and cracking, patching, depression, and traveling with a 95% confidence level. Statistical testing on the overall model between IRI and distress types confirmed these findings. The \(p\)-values for each regression coefficient were obtained in the regression coefficients test. In both the major and subsidiary streets, the regression coefficients for cracking, depression, patching, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distress Type** & **Correlation Factor** & **Correlation Hypothesis Test** \\ \hline Cracks & r = 0.167 & \(p\) = 0.000 \\ Patching & r = 0.471 & \(p\) = 0.000 \\ Potholes & r = 0.123 & \(p\) = 0.390 \\ Depression & r = 0.342 & \(p\) = 0.011 \\ Rutting & r = 0.357 & \(p\) = 0.045 \\ Raveling & r = 0.399 & \(p\) = 0.000 \\ \hline \hline \multicolumn{3}{c}{Regression Model Equation: IRI = 2.10 + 0.00267 Cr + 0.00553 Pa + 0.0195 Dr + 0.00316 Ra} \\ \hline \hline \multicolumn{3}{c}{Regression Coefficients Test (\(t\)-test)} \\ \hline Distress Type & Hypothesis Test \\ \hline Cracks & \(p\) = 0.000 \\ Patching & \(p\) = 0.000 \\ Potholes & \(p\) = 0.071 \\ Depression & \(p\) = 0.000 \\ Putting & \(p\) = 0.003 \\ Raveling & \(p\) = 0.000 \\ \hline \hline \multicolumn{3}{c}{Analysis Of Variance \(p\) = 0} \\ \hline \hline \multicolumn{3}{c}{Regression Model Adequacy R2 = 32.8\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of correlation factors and regression models in main street sections. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distress Type** & **Correlation Factor** & **Correlation Hypothesis Test** \\ \hline Cracks & r = 0.280 & \(p\) = 0.000 \\ Patching & r = 0.541 & \(p\) = 0.000 \\ Potholes & r = 0.322 & \(p\) = 0.208 \\ Depression & r = 0.436 & \(p\) = 0.004 \\ Raveling & r = 0.327 & \(p\) = 0.006 \\ \hline \hline \multicolumn{3}{c}{Regression Model Equation: IRI = 2.10 + 0.00267 Cr + 0.00553 Pa + 0.0195 Dr + 0.00316 Ra} \\ \hline \hline \multicolumn{3}{c}{Regression Coefficients Test (T-test)} \\ \hline Cracks & 0.280 & \(p\) = 0.000 \\ Patching & 0.514 & \(p\) = 0.000 \\ Potholes & 0.322 & \(p\) = 0.168 \\ Depression & 0.436 & \(p\) = 0.001 \\ Raveling & 0.387 & \(p\) = 0.036 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of correlation factors and regression models in secondary street sections.