# 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
When \(Q_{\rm P}\)\({}^{\prime}\) increases to a certain extent, slip failure occurs at the bonding  
Figure 11: Equivalent model of the post-side-grouted pile subjected to axial loading: (**a**) MP1; (**b**) MP2. (**c**) MP3. surface. At this time, the bonding surface becomes the contact interface. The model pile and cement-stabilized mass become two independent units and no longer bear the load together. The axial bearing capacity, \(Q_{2}\), of the annular point grouted pile at this stage can be expressed as:  
\[Q_{2}=Q_{\rm s}+Q_{\rm P}=u\Sigma q_{\rm si}l_{i}+uq_{\rm s}^{\prime}l_{\rm s}+ q_{\rm P}A_{\rm P} \tag{5}\]  
where \(q_{\rm s}^{\prime}\) is the unit shaft resistance at the interface between the model pile and the cement-stabilized mass, and \(l_{\rm s}\) is the height of the bonding surface between the cement-stabilized mass and the pile shaft. For the ideal-geometry grouted pile (Figure 11c), the bonding area between the model pile and the cement-stabilized mass is relatively large. After the cement-stabilized mass is excavated at the end of the loading, it is found that there is no relative slip between the cement-stabilized mass and the model pile, so the two can be regarded as a whole. Figure 11 shows that, different from the annular point grouted pile, the cement-stabilized mass of the ideal-geometry grouted pile is equivalent to increasing the diameter of a section of pile, and there is a large shaft resistance, \(Q_{\rm f}\), between the cement-stabilized mass and the soil layer. The total shaft resistance, \(Q_{\rm s}\), of the ideal-geometry grouted pile includes the shaft resistance along the pile shaft, \(Q_{\rm f}\), which is provided by the pile shaft without the cement-stabilized mass, the shaft resistance along the pile shaft, \(Q_{\rm f}\), which is provided by the pile shaft with the cement-stabilized mass and the vertical bearing capacity \(Q_{\rm P}\)\({}^{\prime}\) provided by the cement-stabilized mass, i.e., \(Q_{\rm s}=Q_{\rm f}+Q_{\rm f}\)\({}^{\prime}+Q_{\rm P}\)\({}^{\prime}\). The axial bearing capacity, \(Q_{\rm s}\), can be expressed as:  
\[Q_{\rm 3}=Q_{\rm s}+Q_{\rm P}=Q_{\rm f}+Q_{\rm f}\)\({}^{\prime}+Q_{\rm P}\)\({}^{\prime}+Q_{\rm P}=u\Sigma q_{\rm s}l_{i}+u^{\prime}\Sigma q^{\prime}_{\rm si }l^{\prime}_{i}+q_{\rm ps}A_{\rm s}+q_{\rm p}A_{\rm p} \tag{6}\]  
where \(u^{\prime}\) is the perimeter of the cement-stabilized mass; \(q_{\rm si}\)\({}^{\prime}\) is the friction stress between layer soil \(i\) around the pile and the cement-stabilized mass; \(l_{i}\)\({}^{\prime}\) is the thickness of layer soil \(i\) outside the cement-stabilized mass. Combined with the distribution of the unit shaft resistance along the pile shaft, shown in Figure 6, the cement-stabilized mass of the annular point grouted pile and ideal-geometry grouted pile can provide great axial bearing capacity. The major portion of the load is supported by the cement-stabilized mass of the annular point grouted pile and ideal-geometry grouted pile during the initial load, and the settlement of the pile is very small; thus, the shaft resistance of the lower pile section of the cement-stabilized mass is small. With increasing axial load, the cement-stabilized mass of the annular point grouted pile and ideal-geometry grouted pile begins to settle with the pile shaft, and the shaft resistance of the lower pile section of the cement-stabilized mass gradually increases. In addition, the protruding cement-stabilized mass has a certain compaction effect on the lower soil layer during loading, which increases the normal stress at the pile-soil interface of the lower pile section. Hence, the lower pile section of the annular point grouted pile and ideal-geometry grouted pile have greater shaft resistance than the ungrouted pile. The cement-stabilized mass of the ideal-geometry grouted pile is firmly bonded to the pile shaft of the model pile. The test shows that the pile-soil system forms a close cooperative system, which is the most ideal effect of post-grouting on the side of the pile.