# Correlation of Pavement Distress and Roughness Measurement
## 6 Rutting vs. IRI  
Figure 2f shows the correlation between IRI and rutting density. The graph shows that rutting density and IRI values have a positive relationship. there is no clear choice about the relationship's linearity. The correlation coefficient is 0.357, meaning that the linear relationship only affected 35.7 percent of the IRI and rutting density observations. There is insufficient evidence of a link between IRI and rutting density since the \(p\)-value is 0.045, which is extremely near to the 0.05 level of significance.  
* Secondary Street Sections  
There are six distress types included in secondary pavements of the Riyadh street network. The cracking distresses Block Cracking (code D2) and Longitudinal and Transverse Cracking (code D3) have been aggregated to one group called cracking distress. After grouping the distress types were reduced to five. The total distress groups in the second section are Cracking (codes D2 and D3) Patching (code D4); Potholes (code D5); Depressing (code D6) and Raveling (code D11).  
The relation between IRI and each group of distress types in secondary Streets is discussed in the subsequent paragraphs.  
1. Cracks vs. IRI  
The graph in Figure 3a shows the relationship between IRI and crack density. The correlation coefficient is 0.28, which indicates that the linear relationship only affected 28 percent of the IRI and crack density observations. There is insufficient evidence of a link between IRI and crack density since the \(p\)-Value of the hypothesis test is zero. The positive sign means a positive correlation between IRI and crack density, the low relationship factor indicates insignificant linearity relation between crack density and IRI.  
2. Patching vs. IRI  
The relation between IRI and patching distress density is seen in Figure 3b. The graphic shows that patching density and IRI have a positive relationship. The coefficient of correlation is 0.514. The positive sign indicates that patching density and IRI have a positive relationship. Furthermore, the correlation factor indicates that the linear relationship distinguished around 51.4 percent of the IRI and patching density data. The p-value for the hypothesis test is zero. As a result, the relation between IRI and patching density has sufficient evidence at a 95 percent confidence level.  
3. Potholes vs. IRI  
Figure 3c shows the relationship between IRI and pothole distress density. The correlation factor is 0.322 indicating low linearity of the relationship. The \(p\)-value is 0.208 which is greater than the 0.05 level of significance; so, there is insufficient evidence of the relation between the value of IRI and pothole density. This result could be because potholes are usually avoided during roughness measurements.  
Depression vs. IRI  
The correlation between IRI and depression distress density is presented in Figure 3d. The graph shows that patching density and IRI have a positive relationship. When the density of depressions in the pavement sample is high, the IRI value increases. The linear relationship distinguished about 43.6 percent of the IRI and depression density data, on the basis of the correlation factor value. The hypothesis test gave a \(p\)-value of 0.004, which is less than the 0.05 level of significance, showing that there is sufficient relation between IRI and depression density at the 95 percent confidence level.