# Assessment of Spatial Variability in Ground Models Using Mini-Cone Penetration Testing
## 4 Discussion of the Results
### CL Analysis
#### 4.3.2 Vertical _Cl_  
Figure 6 shows the vertical correlation lengths of two points as a representative example for Case 1 silica sand ground and Figure 6c shows the _CL_s for all measured points. The vertical _CL_s for each point were calculated with a spacing of 1 mm, and the results for each location are presented in Figure 6c.  
Figure 5: Horizontal correlation length: (**a**) Case 1 silica sand layer; (**b**) Case 2 silica sand layer; (**c**) and Case 2 weathered soil layer.  
Each fitted vertical _CL_ was found to be 97.76 mm on average for the Markovian model and 134.60 mm for the Gaussian model. Furthermore, the vertical _CL_s were calculated within a range of 96.61 to 98.74 mm for the Markovian model and 133.24 to 135.62 mm for the Gaussian model. The _CV_ for each model was 0.68% and 0.59%, respectively, indicating that the _CL_s at each point were very consistent.  
These minor differences can be attributed to the homogeneity of the ground models, as mentioned in Section 3.3. Therefore, it is considered that these vertical _CL_ results enhance the reliability of the _CL_ calculations performed on the ground models in this study.  
Figure 7 shows the vertical _CL_s for Case 2. Similar to the calculation of horizontal _CL_s, calculations were conducted separately for the silica sand layer and the weathered soil layer. Figure 7c,f display the vertical _CL_s for each location.  
Figure 7a,b represent the vertical _CL_s for representative points in the silica sand layer, and Figure 7c shows the _CL_s for all measured points. Based on the results from 18 penetration points, the vertical _CL_s in the sand layer were calculated to be an average of 26.09 mm for the Markovian model and an average of 35.55 mm for the Gaussian model. They varied within the ranges of 23.01 to 28.72 cm and 28.36 to 37.93 cm, respectively, with coefficients of variation measuring 1.18% and 1.14%. It was observed that the variability was very low.  
Figure 7c,d represent the vertical _CL_s for representative points in the weathered soil layer, and Figure 7f shows the _CL_s for all measured points. The vertical _CL_s in the weathered soil layer were calculated to be an average of 14.49 cm for the Markovian model and an average of 18.64 cm for the Gaussian model based on natural conditions. They varied within the ranges of 5.05 to 19.5 cm and 5.33 to 26.11 cm, respectively, with _CV_ measuring 29.46% and 33.63%. This higher variability is attributed to the natural state of the weathered  
Figure 6: Case 1 vertical correlation length: (**a**) representative point 1; (**b**) representative point 2; and (c) Case 1 vertical correlation length.  
soil layer, which exhibits variations in particle sizes and pore structure compared to the artificially homogenized structure of the silica sand layer.  
Figure 7: Case 2 vertical correlation length: (**a**) silica layer representative point 1; (**b**) silica layer representative point 2; (**c**) silica layer vertical correlation length; (**d**) weathered soil layer representative point 1; (**e**) weathered soil layer representative point 2; and (**f**) weathered soil layer vertical correlation length.