# Axial Bearing Mechanism of Post-Grouted Piles in Calcareous Sand
## 4 Analysis of Grout Distribution and Bearing Mechanism of a Post-Grouted Single Pile
### Analysis of Axial Bearing Mechanism of Post-Side-Grouted Pile  
According to the comparative analysis of the test results, the post-side-grouted pile has significantly greater axial bearing capacity than the ungrouted pile, and the ideal-geometry grouted pile has greater axial bearing capacity than that of the annular point grouted pile. Combined with the morphological characteristics of the cement-stabilized mass, the contact interface between the cement-stabilized mass of the annular point grouted pile and the model pile is much smaller than that of the ideal-geometry grouted pile, and the annular point grouted pile and model pile show a separation state after loading. Therefore, it can be considered that, under the continuous increase in vertical load, the contact interface between the cement-stabilized mass of the annular point grouted pile and the pile shaft cannot provide sufficient cohesive force. At a certain axial load, the bonding surface slips, so the cement-stabilized mass and model pile fail to bear together, which seriously affects the bearing capacity of the grouted pile. Based on the above analysis, the force diagram of the three pile types is drawn, as shown in Figure 11, and the axial bearing mechanism of the post-side-grouted pile is analyzed. Figure 10: Pull-out force-slip curves for the cement grout and pile shaft: (**a**) calcareous sand; (**b**) siliceous sand. It can be seen from the foregoing that the axial load of the model pile is supported by the tip resistance, \(Q_{\rm P}\), and the total shaft resistance, \(Q_{\rm s}\), that is, \(Q=Q_{\rm P}+Q_{\rm s}\). 1. For the ungrouted pile (Figure 11a), the total shaft resistance is equivalent to the shaft resistance along the pile shaft, \(Q_{\rm f}\), i.e., \(Q_{\rm s}=Q_{\rm f}\). The axial bearing capacity, \(Q_{1}\), can be calculated as follows: \[Q_{1}=Q_{\rm s}+Q_{\rm P}=u\Sigma q_{\rm ss}i_{l}+q_{\rm P}A_{\rm P}\] (3) where \(u\) is the perimeter of the cross section of the model pile; \(q_{\rm ss}\) is the unit shaft resistance between the pile and layer soil \(i\) around the pile, which is related to the compactness of the soil and the normal stress of the pile-soil interface; \(l_{i}\) is the thickness of layer soil \(i\) around the pile; \(q_{\rm P}\) is the pile tip stress; \(A_{\rm P}\) is the pile tip area. 2. For annular point grouted piles (Figure 11b), the model pile and cement-stabilized mass form a common interaction. The radial dimension of the cement-stabilized mass is larger, the longitudinal dimension is smaller, the bonding surface between the model pile and the cement-stabilized mass is small, and it easily slips when the load is large. The bearing mechanism of the annular point grouted pile is different before and after the relative slip between the model pile and the cement-stabilized mass. Before the slip failure of the bonding surface, the annular point grouted pile can be considered a special-shaped pile. The total shaft resistance, \(Q_{\rm s}\), includes the shaft resistance along the pile shaft, \(Q_{\rm f}\), and axial bearing capacity, \(Q_{\rm P}\)\({}^{\prime}\), which is provided by the cement-stabilized mass, i.e., \(Q_{\rm s}=Q_{\rm f}+Q_{\rm P}\)\({}^{\prime}\). The axial bearing capacity, \(Q_{2}\), of the annular point grouted pile, in this stage, can be expressed as:  
\[Q_{2}=Q_{\rm s}+Q_{\rm P}=Q_{\rm f}+Q_{\rm P}\)\({}^{\prime}+Q_{\rm P}=u\Sigma q_{\rm ss}i_{l}+q_{\rm PS}A_{\rm s}+q_{\rm P}A_{\rm P} \tag{4}\]  
where \(q_{\rm PS}\) is the vertical stress at the bottom of the cement-stabilized mass, and \(A_{\rm s}\) is the equivalent area of the cement-stabilized mass. The vertical bearing capacity, \(Q_{\rm P}\)\({}^{\prime}\), provided by the cement-stabilized mass is transferred to the model pile through the bonding surface. As the increase in the applied load, \(Q_{\rm P}\)\({}^{\prime}\) also increases.