## 2 Ground Profile Characterization Based on a Probabilistic Approach
### Measuring Method Uncertainty  
If the site investigation comprises more than one type of test, as per example CPT and SPT, the comparison of both can be used to correct the dispersion due to the method of measurement.  
The concept used for this is that of the minimum statistical variance. It is well known that SPT and CPT tests measure different parameters, but also that there is a proportionality between them. This relationship can be obtained by comparing the outputs for the same soil condition, i.e., material type and stress level. But the aspect that is of interest at the moment is the dispersion presented by both. It could be said that the lowest dispersion of them is, at least, an upper limit of the dispersion of the statistic variable representing the soil strength. Thus, the test with higher dispersion can be corrected to a dispersion similar to the test with less dispersion. This correction is a way to eliminate uncertainty in the result introduced by the method of measurement.  
The dispersion of several tests can be compared through the relative standard deviation (Equation (1)).  
\[v=\frac{\textit{standard deviation}}{\textit{average}} \tag{1}\]  
Following Figure 1 shows an example from a soil investigation carried out with SPT and CPT. It is noted that:* The dispersion--or relative standard deviation--of the SPT outputs is greater than that of the CPT test, at least in the first 16 m. Its value is between 0.4 to 0.7, while in the CPT test it is around 0.2.
* In the last four meters, the dispersion of both tests is similar. Its value is in the range of 0.4 to 0.7.  
From the figure, it can be said that dispersion due to the SPT measurement method is at least the difference between the blue and the red line.  
This observation makes it possible to look at the original values of the SPT test in a somewhat more critical way. It is noted that the dispersion of the soil strength should be below the parameter \(\upsilon=0.2\). Therefore, all SPT outputs above or below the average (\(\mu\)) plus/minus twice the standard deviation have a probability of occurring less than 5%, calculated as follows Equation (2).  
\[/N_{SPT}-\mu/>2\times\mu\times\upsilon \tag{2}\]  
Values that exceed this quantity can be removed from the sample and the average and deviation are recalculated.  
The following Figure 2 represents the parameters calculated after correcting the SPT data, along with the previously obtained ones. It is noted that on this occasion the dispersion of the CPT and SPT tests are comparable.  
Different authors and codes [5; 6; 7; 8; 9] indicate what the typically expected variation of a geotechnical parameter is. In this case, both SPT and CPT outputs can be understood as a parameter since they feed empirical formulation for design prediction. It can be observed that for the CPT and SPT test typical values are about 0.15.  
Thus, in that particular case, the correction made in the SPT test thanks to the comparison with the CPT almost entirely allows reducing the uncertainty introduced by the measurement equipment. However, it does not provide information about the statistical uncertainty of the test.  
Figure 1: Dispersion on Standard Penetration Test (SPT) and Cone Penetration Test (CPT) before any statistical correction.