# A Calculation Model of Grout Migration Height for Post-Grouting Technology
## 3 Results and Discussion
### Model Validation  
To verify the obtained solution of slurry migration height, a field test at the Dukiapu bridge, Zhejiang province, China was conducted. The post-grouted method is adopted to improve the bearing capacity of bored piles in this project. The geological parameters of test pile and layout of grouting pipes are shown in Figure 4. The Silty clay serves as the bearing stratum for the bored piles. The pile is 42.5 m in length and 800 mm in diameter. Both base and shaft grouting are adopted to reinforce the bored piles at the same time, where the shaft grouting point locates in the medium sand. A total of 3 tons of cement slurry with cement ratio of 0.5 were consumed, of which 1 ton is for shaft grouting and the rest 2 tons are for base grouting. The grouting pressure was set as 2.0 MPa in this application. After 30 days curing, the foundation pit was excavated at a depth of 14 m. During the excavation process, the detailed information of the solidified cement slurry on 5 piles were clearly obtained. The firstly observed depth values of solidified cement slurry are shown in Table 2. According to these measured depth values, the slurry migration height can be easily calculated by subtracting from the depth of shaft grouting outlet (21.5 m in this study). Therefore, the actual migration height ranges from 10.69 m to 11.44 m for these five piles. Figure 3: Correlations of cement slurry migration height with: (**a**) pile embedment depth; (**b**) pile diameter; and (**c**) grouting pressure. Figure 5 shows the photos of observed solidified cement slurry on piles, where the actual rising height of grouting varies in different directions. Based on the field conditions motioned above, the pile radius is \(\tau_{0}\) = 0.4 m, depth of shaft grouting outlet is \(H\) = 21.5 m, unit weight of grout is \(\tau_{c}\) = 18 kN/m\({}^{3}\), and gage pressure of shaft grouting is \(p_{1}\) = 1.8 MPa. Since the lateral earth pressure coefficient and unit weight of each soil layer are different, the weighted average method is employed in the calculation. The weighted average lateral earth pressure coefficient is \(k_{0}\) = 0.43, and the weighted average unit weight of soil is \(\gamma\) = 19.65 kN/m\({}^{3}\). In addition, five grout samples were tested in the laboratory, and the yield shear strength of cement slurry is determined as \(\tau_{0}\) = 6 Pa. The average thickness of weak layer measured on 5 piles is \(b\) = 0.05 m. \begin{table}
\begin{tabular}{c c c} \hline \hline
**File Number** & **Observed Depth (m)** & **Actual Migration Height (m)** \\ \hline
1 & 10.06 & 11.44 \\
2 & 10.58 & 10.92 \\
3 & 10.36 & 11.14 \\
4 & 11.23 & 10.27 \\
5 & 10.81 & 10.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: First observed depth of cement slurry for 5 bored piles. Figure 4: Formation of construction site and layout of grouting pipes. Figure 5: Photos of the bored pile after excavation: (**a**) solidified cement slurry and (**b**) thickness measurement. According to the Equations (17) and (18), the outlet pressure \(p_{0}\) can be calculated:  
\[p_{0}=p_{1}+p_{2}-\Delta p=1800+21.5\times 19.65-0.037\times 21.5=1427\;\text{ kPa}\]  
Parameter \(c_{1}\) can be derived by Equation (10):  
\[c_{1}=\frac{\tau_{0}R_{H}}{\ln(1+R_{H})-\frac{2R_{H}}{2+R_{H}}}=\frac{-0.006 \times 0.075}{\ln(1+0.075)-\frac{2\times 0.075}{2+0.075}}=-8.3\;\text{ kPa}\cdot\text{m}\]  
Then parameter \(m\) can be derived by:  
\[m=\frac{2c_{1}}{\left(r_{0}+\frac{b}{2}\right)^{2}}-\gamma_{c}=\frac{2\times- 8.3}{\left(0.4+\frac{0.03}{2}\right)^{2}}-19.65=-114\;\text{kN}/\text{m}^{3}\]  
Finally, the migration height of cement slurry can be obtained by Equation (16):  
\[z=\frac{p_{0}-k_{0}\gamma H}{-m-k_{0}\gamma}=\frac{1427-0.43\times 19.65\times 2 1.5}{84.3-0.43\times 19.65}=11.90\;\text{m}\]  
Compared with the actual migration height of 10.69 m\(\sim\)11.44 m, the calculated value of 11.90 m is slightly overestimated but fully acceptable from a viewpoint of engineering design.