# Study on Vertical Load-Carrying Capacity of Post-Grouting Bored Piles
## 4 Effect of Grouting on the Performance of Bored Pile
### Calculation Model for Post-Grouting Bored Pile  
As the cement slurry under pressure will have a permeating, compacting [13], and fracturing [14] effect on the soil around the pile, the soil on the side of the pile and the soil at the tip of the pile were reinforced to form a cement soil consolidation body around the pile and at the pile tip. During injection, the slurry is cemented within the diffusion range through each grouting hole, forming an approximate columnar reinforcement with the soil around the pile (as shown in Figure 4). Therefore, the cement soil consolidation body in the grouting segment combined with the original pile can be regarded as a composite pile segment of equal cross-section in the calculation.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{w_{b}}\) (mm) & 1.0 & 3.0 & 5.0 & 7.0 & 9.0 & 11.0 & 11.5 & 12.0 \\ \hline \(\mathbf{w_{0}}\) (mm) & 1.4 & 4.2 & 7.0 & 9.8 & 12.5 & 14.8 & 15.3 & 15.8 \\ \(\mathbf{P_{0}}\) (\(\mathbf{kN}\)) & 208 & 623 & 1038 & 1453 & 1747 & 1841 & 1854 & 1854 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculation of pile top settlement \(w_{0}\) and pile top load \(P_{0}\) under each pile tip settlement \(w_{b}\).  
Figure 3: Relationship between pile top load \(P_{0}\) and pile top settlement \(w_{0}\).  
The compression of the pile in the grouting segment is:  
\[\Delta_{i} =\frac{N_{i}}{E_{ci}A_{ci}+E_{pi}A_{pi}}l_{i} \tag{14}\] \[A_{p} =\frac{\pi}{4}[(d+2R)^{2}-d^{2}] \tag{15}\]  
where \(E_{pi}\) is the elastic modulus of the segment \(i\) of the cement soil consolidation body, \(A_{pi}\) is the cross-sectional area of the segment \(i\) of the cement soil consolidation body, and \(R\) is the diffusion radius after grouting.  
According to the diffusion theory of [PERSON] [15], the diffusion radius R after grouting is  
\[R=\sqrt[3]{\frac{3 kh_{0}r_{0}t}{\beta n}} \tag{16}\]  
where \(k\) is the soil permeability coefficient, \(h_{0}\) is the grouting pressure head, \(r_{0}\) is the grouting tube radius, \(t\) is the grouting time, \(\beta\) is the ratio of slurry viscosity to water viscosity, and \(n\) is the porosity of the soil  
Considering that in the actual grouting, if the diffusion radius is small, the enhancement effect on the pile is not obvious, if the diffusion radius is large, it is difficult to implement in the project, so this paper selects the diffusion radius \(R\) as 100 mm. Pre-embedding of 20 mm diameter grouting steel tube on the pile circumference surface was considered. The ratio of slurry viscosity to water viscosity \(\beta\) is 0.95. The soil permeability coefficient \(k\) and the porosity of the soil n are selected according to Equation (16) for different soil layers and the corresponding grouting pressure head h0 and grouting time t are selected according to the diffusion radius \(R\). As there are multiple layers of soil in the actual project and the properties of different soils vary, the amount of cement injected into the soil needs to be used to roughly predict the soil conditions in which the slurry will be located in order to adjust the grouting pressure and grouting time accordingly. After reinforcement by grouting, the grouting pile segment can be treated as a composite pile segment with a pile diameter of 700 mm.  
In order to ensure the effect of grouting, the cement soil consolidation body should have a certain strength, selected consolidation body strength of 5 MPa, and the corresponding mixing ratio 25% was obtained by taking soil samples from each layer of the site and conducting ratio tests in the laboratory. The cement soil test specimens were made according to the mixing ratios obtained from the tests and were subjected to compression  
Figure 4: Pile tip and pile side grouting abridged general view of bored pile.  
tests. The modulus \(E_{50}\) of the cement soil was measured to be 295-372 MPa. The calculation takes the modulus \(Ep\) of the cement soil consolidation body as 300 MPa.