## 4 SLT Results  
The test results in Section 3.2 show that there is an obvious relationship between the dynamic stiffness and foundation constraint state. To quantitatively analyse the relationship between the foundation capacity and dynamic stiffness, SLTs were performed. Figure 17 illustrates the load-settlement curves (_P_-_s_ curve) for the three types of foundations. For each foundation type, the absolute value of the slope is smaller for foundation models with larger sizes and relatively greater design capacities. That is, under the same vertical load, the foundation models with larger sizes have stronger resistances to vertical settlement or higher static stiffnesses. In addition, the loading values corresponding to the inflection points in the _P_-_s_ curves of the spread and caisson foundations are higher than those of the grouped pile foundations. This indicates that the spread and caisson foundations have larger allowable bearing capacities, which is consistent with the design size of the model foundation and the actual situation.  
Figure 16: Dynamic stiffness changes for various pile buried depths for model P3: (**a**) \(K_{\text{d}}(f)\) function; and (**b**) \(K_{\text{d}}\) values at 10, 20, 30, 40, and 50 Hz.  
Figure 15: Dynamic stiffness changes for various pile buried depths for model P1: (**a**) \(K_{\text{d}}(f)\) function; and (**b**) \(K_{\text{d}}\) values at 10, 20, 30, 40, and 50 Hz.  
During the SLT, the \(P\)-\(s\) curve exhibits a linear relationship at the initial loading stage. Figure 18 illustrates the initial loading stages and corresponding linear fitting results of the three types of foundations. The correlation coefficients are greater than 0.99 for the spread and caisson foundations and exceed 0.97 for the grouped pile foundations. Then, the fitting results were used to calculate the static stiffnesses.  
Figure 17: SLT \(P\)–\(s\) curves of the (**a**) spread; (**b**) caisson; and (**c**) grouped pile foundations.  
Figure 18: _Cont_.  
Figure 19 illustrates the relationship between the dynamic and static stiffnesses of the three types of foundations. For the spread foundations, the static stiffness ratio of models S1 to S2 is 1.51, whereas the average dynamic stiffness ratio of models S1 to S2 is 1.64. For the caisson foundations, the static stiffness ratio of models C1 to C2 is 1.73, whereas the average dynamic stiffness ratio of models C1 to C2 is 1.55. The two groups of ratios are close to each other. For the grouped pile foundations, the average dynamic stiffness exhibit a logarithmic growth trend with increase in the static stiffness, showing that there is a strong correlation between the dynamic and static stiffnesses. Generally, the bearing capacities of foundations can be controlled by deformation or strength under different loading conditions. When the capacity is controlled by the vertical deformation, the capacity can be described by the static stiffness value. That is, the dynamic stiffness is a sensitive index that can be used to evaluate the foundation capacity.  
Figure 19: _Cont._  
Figure 18: Linear fittings of the static loading test _P_–_s_ curves during the initial loading stage: (a) spread foundation; (b) caisson foundation; and (c) grouped pile foundation.