## 4 Model Test Verification
### Experiment Results and Analyses  
#### 4.3.1 Experiment Results  
(1) Loading and displacement of test piles  
Taking upward displacement as positive and downward as negative, the load displacement curves of the two soil model tests of traditional static pressure piles and self-balanced test piles can be seen in Figure 9. When the traditional static pressure pile was loaded to 1800 N, the pile top displacement reached 9.80 mm, and the increase of its displacement was significantly larger than the previous level. When the test load reaches 1680 N, the test pile fails, and this value can be determined as the maximum bearing capacity of the single pile. When loaded to 2 \(\times\) 750 N, the lower pile's downward displacement reached 6.51 mm, and it was damaged. At this time, the upper pile continues to be loaded to 800 N to reach the ultimate load and take the upper and lower piles' ultimate bearing capacity of 778 N and 725 N.  
(2) The axial analysis of pile  
To explore the bearing characteristics of the measured pile, the internal force of the self-balanced measure pile in the layered soils was analyzed. Equation (35) illustrates the connection between the strain calculation and the axial force of test value. \[N_{ij}=\epsilon_{ij}EA \tag{35}\]  
where \(N_{ij}\) is the axial force of the \(j\)-th unit pile under the \(i\)-th load; \(\epsilon_{ij}\) is the strain value of the \(j\)-th unit pile under the \(i\)-th load. \(A\) is the test pile's cross-sectional area, \(E\) is the pile's elastic modulus. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Soil** & **Type of Soil** & **Soil** & **Water** & **Force of** & **Internal** & **Elastic** & **Poisson** \\
**Layer** & **Layer** & **Thickness/mm** & **Content** & **Cohesion/kPa** & **Angle/\({}^{c}\)** & **/MPa** & **Ratio** \\ \hline
1 & Mealy sand & 150 & 18 & 5.5 & 36.4 & 14 & 0.35 \\
2 & Clayey silt & 150 & 18 & 7.2 & 25 & 23 & 0.35 \\
3 & Silty clay & 200 & 26 & 25 & 19.0 & 19.0 & 0.42 \\
4 & Clay & 450 & 26 & 59.6 & 18.0 & 28.0 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic physical mechanical properties of layered soils samples. Under the above-mentioned self-balanced loading conditions, the theoretical analysis of the loading values at each level of the load box was used to determine the axial force at each position of the corresponding pile. Taking 200 N, 400 N, 600 N, 725 N (lower pile bearing capacity), and 758 N (upper pile bearing capacity), respectively. The comparison between the measured value and the theoretical value of the pile axial force under different loads is shown in Figure 10. The self-balanced theoretical axial loading calculation in each of the pile body's points is relatively coincident with the measured data, and the maximum error of the bottom position of the pile does not exceed 5%. The load transfer law is gradually transferred from the loaded end to the far end. For the upper pile, the axial force curve bulges to the left. The load is transferred from bottom to top, and the closer the loading point is, the larger the axial force is, and it decays to the top of the pile. It can be seen from the linear density that the magnitude of the axial force gradually attenuates with the sparseness of the curve. The upper pile has a sparser curve from the loading point of 0 m to 0.15 m, and the attenuation is 46.67% to 60.85%, indicating that this part of the soil layer is subjected to higher loads. In addition, the upper and lower pile axial force curves at the same location far from the loading position overlap, indicating that the effect of the axial force has nothing to do with the loading direction. Figure 10: Distribution of axial force across the measure pile body at various loading levels. Figure 9: The test piles’ \(\mathbf{Q}\)-\(\mathbf{s}\) curves. (**a**) Traditional static pressure pile. (**b**) Self-balanced test pile.