## 4 Analysis of Test Results  
### Pile Top Load-Top Displacement Curve  
The curve depicting the pile top load (\(Q\)) against its corresponding top displacement (\(s\)) provides a clear and intuitive illustration of the pile foundation's bearing capacity and deformation behavior [15]. It serves as a crucial reference for engineering inspectors to assess the safety and stability of the test piles. The results obtained from the self-balancing test were converted into equivalent top load-top displacement curves, which correspond to those derived from traditional static load tests. These conversions yield the equivalent top load (\(Q\)) versus top displacement (\(s\)) curves for test piles TP1 and TP2, as illustrated in Figure 3.  
Figure 2: Schematic diagram of self-balancing test with double-level O-cells. As depicted in Figure 3, the curves of both test piles exhibit notable steep drop points prior to grouting, whereas the curves after grouting display a gradual change, indicating a significant enhancement in the single-pile bearing characteristics. Under low loading conditions, the variation in pile top displacement prior to and subsequent to grouting is comparatively negligible, as the primary support for the pile top load originates from the lateral resistance of the pile, and the strengthening influence of the grout has yet to manifest itself. However, as the load gradually increases, a significant disparity emerges between the \(Q\)-\(s\) curves before and after grouting. During this phase, the pile top load is distributed along the pile shaft down to the pile tip, with the pile's lateral resistance gradually nearing its ultimate capacity, while the contribution of the pile tip resistance starts to increase progressively. Prior to grouting, soil damage occurs upon reaching the ultimate bearing capacity, resulting in a steep decline in the load-displacement curve. Conversely, following the combined grouting procedure, the grout injected into both the pile sides and pile tip significantly improves the mud layer on the pile sides and the slag accumulation at the pile tip, respectively. This reinforcement leads to an improvement in the performance of both the side and tip resistance as the load at the pile top increases. Throughout this process, the grout applied to the pile sides notably boosts the bearing capacity of the individual pile under moderate loads while also reducing the pile top displacement. As the load further increases, the reinforcing effect of the grout at the pile tip becomes increasingly prominent, significantly augmenting the bearing capacity of the individual pile under heavier loads. Notably, upon reaching the ultimate bearing capacity post-grouting, there is no abrupt, steep decline observed. At a particular loading stage, the \(Q\)-\(s\) curve manifests a distinct point of inflection, signaling that the pile under test has attained its vertical ultimate bearing capacity. The load value recorded at the stage preceding this inflection point can be considered the pile's ultimate bearing capacity [16,17]. According to this criterion, the ultimate bearing capacities of test piles TP1 and TP2 before grouting are 27,644 kN and 26,560 kN, respectively. However, the curves of the test piles after grouting do not display any obvious inflection points; thus, the ultimate bearing capacity is taken as the last applied load, which is 36,765 kN for both TP1 and TP2. The ultimate bearing capacities of the test piles in different phases along with their corresponding pile top displacements are presented in Table 3. The ultimate bearing capacities of test piles TP1 and TP2 increase by 32.99% and 38.42%, respectively, after undergoing combined grouting. This underscores the profound  
Figure 3: Equivalent conversion \(Q\)-\(s\) curves of test piles: (**a**) TP1; (**b**) TP2. influence of combined post-grouting on the load-carrying capacity of individual piles.