# Model Test on Grouting Properties of Alluvial Filler Soil
## 6 Engineering Characteristic Analysis of Grouting Soil
### Soil Strength Analysis
In order to facilitate the calculation of soil strength growth after grouting, the proposed approach is based on the following assumptions: (1) The area of slurry diffusion is uniform; (2) The hydration and hydrolysis of the slurry are neglected. The mechanical properties of the soil after grouting are shared by the slurry and the soil. Therefore, the variation in the maximum shear stress of the grouting soil depends on the volume ratio of the injected slurry to the soil and the maximum shear stress of the slurry veins. Moreover, the increasing cohesion and internal friction angle of the soil are directly related to the volume of grouting and the injection rate of the slurry (\(\eta\)). When grouting is completed, the internal friction angle and cohesiveness of the soil can be expressed as follows:  
\[ \begin{array}{l}\phi_{ag}=\frac{\eta}{1+\eta}\phi_{g}+\frac{1}{1+\eta}\phi_ {s}\\ c_{ag}=\frac{\eta}{1+\eta}c_{g}+\frac{1}{1+\eta}c_{s}\end{array}  \tag{8}\]  
where \(c_{g},c_{s}(c_{s}=c_{0})\) are the cohesive forces of the slurry and the soil, respectively, \(\phi_{g},\phi_{s}\) (\(\phi_{s}=\phi_{0}\)) and are the internal friction angles of the slurry and the soil, respectively. According to Equation (8), when grouting is completed, the increment of the internal friction angle and cohesion of the grouting soil can be expressed as follows:  
\[ \begin{array}{l}\Delta\phi_{ag}=\phi_{ag}-\phi_{s}=\frac{\eta}{1+\eta}\big{(} \phi_{g}-\phi_{s}\big{)}\\ \Delta c_{ag}=c_{ag}-c_{s}=\frac{\eta}{1+\eta}\big{(}c_{g}-c_{s}\big{)}\end{array}  \tag{9}\]  
Equation (8) defines the cohesion \(c\) and internal friction angle \(\Phi\) of the grouting soil after the grouting process. The cohesion \(c\) is the sum of the initial cohesion (\(c_{0}\)) of the soil before grouting and the incremental cohesion (\(\Delta c\)) due to grouting. Similarly, the internal friction angle (\(\Phi\)) is the sum of the initial internal friction angle (\(\Phi_{0}\)) of the soil before grouting and the incremental internal friction angle (\(\Delta\Phi\)) due to grouting. Equation (9) calculates the incremental values of cohesion (\(\Delta c\)) and internal friction angle (\(\Delta\Phi\)) of the grouting soil based on the properties of the grout (cohesion of slurry and internal friction angle of slurry) and the coefficient of variation. These coefficients account for the interaction between the soil and the grout during the grouting process. The importance of Equations (4)-(9) lies in their ability to predict the changes in the shear strength of the soil due to grouting. By estimating the incremental shear strength values, the effectiveness of the grouting process can be assessed, and engineers can make informed decisions regarding geotechnical reinforcement and stability in underground engineering projects. According to the mechanism of grouting, it is assumed that the coefficients of variation of cohesive force and internal friction angle are \(k_{c},k_{\Phi}\), it is caused by the interaction between soil and grout, and the two coefficients can be obtained by means of laboratory tests. Thus, when grouting is completed, the increment value of cohesive force and the internal friction angle can be obtained as follows:  
\[ \begin{array}{l}\Delta\phi=\frac{\eta}{1+\eta}\big{(}\phi_{g}-\phi_{s}\big{)} k_{\Phi}\\ \Delta c=\frac{\eta}{1+\eta}\big{(}c_{g}-c_{s}\big{)}k_{c}\end{array}  \tag{10}\]