# Estimating CPT Parameters at Unsampled Locations Based on Kriging Interpolation Method
## 4 Bearing Capacity Calculation  
In order to examine the reliability of the Kriging interpolation results and its applicability to solve practical engineering problems, we use the interpolated CPT data of F5 to calculate the bearing capacity of a driven procast pile. The length and diameter of the pile are 4.5 and 0.3 m, respectively. Based on previous studies, researchers held the point that the cone penetrometer can be considered as a mini-pile foundation, whereby the measured tip resistance (\(q_{\mathrm{c}}\)) and sleeve resistance (\(f_{\mathrm{s}}\)) correspond to the pile end bearing (\(q_{\mathrm{b}}\)) and the component of side friction (\(f_{\mathrm{p}}\)). So far, many CPT-based axial bearing capacity calculation methods of pile foundation have been proposed [20]. [PERSON] et al. [21] evaluated and graded 10 CPT-based methods by comparing the measured capacity from static load tests with the estimated result from different pile capacity prediction methods, and the results showed that the CPT-based methods had reliability and the Laboratoire Central des Ponts et Chausees method (LCPC, Bustamante and Gaineselli) [22] is one of the most accurate prediction methods. Another research conducted by [PERSON] and [PERSON] [1] obtained the same result that the LCPC method was relatively better when applied to predict the ultimate bearing capacity of square precast prestressed concrete (PPC) piles driven into Louisiana soils. Moreover, [PERSON] [7] also recommended LCPC methods as the best prediction method for the soil in Adelaide. For the LCPC method, the unit tip bearing capacity of the pile (\(q_{\mathrm{b}}\)) is predicted from the following equation:  
\[q_{\mathrm{b}}=k_{\mathrm{b}}q_{\mathrm{eq}} \tag{9}\]  
where \(k_{\mathrm{b}}=0.45\) for driven precast piles in clay or silt with \(q_{\mathrm{c}}\) values ranging from 1 to 5 MPa, \(q_{\mathrm{eq}}\) is equivalent average cone tip resistance from 1.5 D above the pile tip to 1.5 D below the pile tip as shown in Figure 10.  
Firstly, the average value \(q^{\prime}_{\mathrm{ca}}\) in the upper and lower 1.5 D range is determined. Then the values higher than 1.3 \(q^{\prime}_{\mathrm{ca}}\) or lower than 0.7 \(q^{\prime}_{\mathrm{ca}}\) are eliminated. After that, the \(q_{\mathrm{eq}}\) could be obtained by averaging the remained \(q_{\mathrm{c}}\) values over the same zone. In this study, due to data insufficiency and stability of \(q_{\mathrm{c}}\) values around the pile tip, as shown in Figure 9, \(q_{\mathrm{eq}}\) is determined by averaging the \(q_{\mathrm{c}}\) values from 1.5 D above the pile tip to the last available value, and the result of \(q_{\mathrm{b}}\) is 1.089 MPa. Now the end bearing capacity can be determined as:  
\[Q_{\mathrm{b}}=q_{\mathrm{b}}A_{\mathrm{b}} \tag{10}\]  
Figure 10: Calculation of the equivalent average tip resistance for the LCPC method. where: \(A_{\rm b}\) is the end area of the pile, and the calculation result is 77 kN. The pile unit skin friction is estimated by:  
\[f_{\rm p}=\frac{q_{\rm c}}{k_{\rm s}} \tag{11}\]  
where \(k_{\rm s}\) is the skin friction coefficient ranging from 30 to 150 and equals 40 for driven procast piles in moderately compact clay (\(q_{\rm c}\) range: 1 MPa-5 MPa). [PERSON] and [PERSON] [22] also imposed different upper limits for \(f_{\rm p}\) depending on pile and soil typology as well as installation methods. In this case, the upper limit is 35 kPa. According to Equation (11), the \(q_{\rm c}\) data is first transformed to \(f_{\rm p}\), and the data over 35 kPa is replaced with 35 kPa, then the data is used to calculate the total pile skin friction by Equation (12). \[Q_{\rm s}=\sum_{i=1}^{n}f_{\rm pi}A_{\rm si} \tag{12}\]  
where \(A_{\rm si}\) is the side area of the ith layer, and the \(Q_{\rm s}\) is calculated to be 148 kN. Finally, [PERSON] and [PERSON] [20] suggested that the allowable design load of the pile is defined by the following equation:  
\[Q_{u}=\frac{Q_{\rm b}}{3}+\frac{Q_{\rm s}}{2} \tag{13}\]  
Through Equation (13), the final allowable design load is 99.6 kN.