## 4 Results and Discussion
### Discussion  
(1) The SCS group foundation has obvious advantages. First, after the target layer of a certain thickness is reinforced, all the foundation piles are connected in a specified depth, which avoids the gradual failure of a single pile after loading. Second, this technology leverages the in situ reinforcement potential of sandy soil or gravel soil and makes it possible to increase the strength of the target reinforcement layer at a lower cost. As a result, the purpose of shortening pile length, reducing cost and settlement is achieved. This system can address high or ultra-high bearing capacity demands of group pile foundations in limited areas cost-effectively, such as for bridges, wind turbines, oil platforms, and other large or ultra-large foundations. However, there are some constraints. The SCS group pile foundation is only suitable for deep soft ground conditions, particularly for soft soil and sandy soil interlayer foundations. To ensure the reliable connection between the solidified part and the pile, the solidified part is required to have a certain strength and thickness. (2) According to the technical specification for building pile foundation [38], the theoretical formula for the ultimate bearing capacity of the new pile type is derived by introducing the coefficient of the number of foundation piles and considering the coefficient of the size effect of the end resistance of the large-diameter pile:  
\[Q_{u}=(tu_{1}+u_{2}){\sum}q_{sik}l_{i}+\Psi_{p}q_{pk}A_{p}\]  
where \(t\) is the number of foundation piles; \(u_{2}\) is the perimeter of the continuously solidified part (unit: m); \(u_{1}\) is the perimeter of the foundation pile body (unit: m); \(q_{sik}\) is the standardized value of ultimate lateral resistance of layer i soil on the side of the pile (unit: kPa); \(l_{i}\) is the thickness of layer i soil around the pile (unit: m); \(\Psi_{p}\) is the size effect coefficient of end resistance for large-diameter piles; \(q_{pk}\) is the standard value of ultimate end resistance (unit: kPa); and \(A_{p}\) is the area of the pile end (unit: m\({}^{2}\)), i.e., the area of the solidified part section. Figure 16: The 6D pile spacing foundation soil failure model. The model piles used for this test were scaled-down models of 1/20 th of the real bored piles, and the model piles with the greatest depth of solidified part were selected. According to the size of the model pile and its test data, the ultimate bearing capacity is scaled up to obtain the test value of the ultimate bearing capacity of the bored pile, which is compared with the calculated value using the theoretical formula, and the relationship between the calculated value and the model test value can be obtained, as shown in Figure 17 (note: the figure contains additional experimental data not listed in this paper for space limitations, which will be published in another paper.) The correlation coefficient between the experimental and calculated values can be calculated according to the [PERSON]'s correlation coefficient formula, which is defined as:  
\[r=\frac{\sum{(x-\overline{x})(y-\overline{y})}}{\sqrt{\sum(x-\overline{x})^{2 }\sum(y-\overline{y})^{2}}}\]  
where \(r\) is the correlation coefficient, \(x\) is the calculated value, \(y\) is the test value, \(\overline{x}\) is the average of the calculated values, and \(\overline{y}\) is the average of the test values. The equation calculated \(0.9<r=0.962<1\), which signifies an extreme correlation, verifying the accuracy of the present ultimate bearing capacity equation. (3) The bearing capacity of the SCS group pile foundation as a whole increases with the increase in continuously solidified part burial depth; this is due to the fact that when the group pile reaches its ultimate bearing capacity, the stress concentration will appear at the bottom of the solidified part.