## 2 Experimental Studies
### Three-Dimensional Spatial Diffusion Morphology Model
The effect of grouting pressure on it is relatively small, so the effect of grouting pressure on the diffusion morphology of gravel soil infiltration grouting is not considered in this paper. Referring to the elliptical flatness theory, this study defines the deviation rate of the three-dimensional spatial diffusion morphology of cement grout in gravel soil to quantify = the effect of the coupling effect of porosity and cement grout weight on the diffusion morphology of infiltration grouting in gravel soil:  
\[\alpha=\frac{a-\min(b,c)}{a} \tag{3}\]  
where \(\min\) (\(b,c\)) is the smaller of the \(x\) semi-axis and \(y\) semi-axis lengths of the ellipsoidal form of cement grout diffusion in gravel soil, and the other meanings are the same as above. From the experimental results and theoretical analysis, it is known that the deviation rate \(\alpha\) can be taken in the range of \(0\leq\alpha<1\):  
1. When \(\alpha=0\), the diffusion of cement grout in gravel soil is spherical, and the three-dimensional spatial morphology is a standard sphere. This indicates that porosity and cement grout weight coupling effect have no influence on the diffusion morphology of penetration grouting in gravel soil, which is the assumption of cement penetration grouting diffusion theory in gravel soil and does not exist in actual grouting penetration diffusion. 2. When \(0\leq\alpha<1\), the coupling effect of porosity and cement grout weight has an effect on the diffusion morphology of penetration grouting in gravel soil, and the penetration grouting in gravel soil is ellipsoidal diffusion, and the three-dimensional spatial morphology is approximately ellipsoidal, which is consistent with the actual penetration grouting diffusion; the larger indicates that the effect of coupling effect of porosity and cement grout weight on the diffusion morphology of penetration grouting in gravel soil is also greater. Based on Equation (3), the deviation rate of the approximated ellipsoidal morphology of porosity and cement grout weight coupling effect on the penetration grouting diffusion of gravel soil can be calculated and shown in Table 3 and Figure 5.  
From the practical investigation, it is known that most of the gravelly soil layers have porosity distribution in the range of 0.35-0.55, and according to the three-dimensional spatial diffusion morphology of cement in gravelly soil, the porosity of gravelly soil can be divided into \(\phi\leq\) 0.4, 0.4 \(<\phi<\) 0.5 and \(\phi\geq\) 0.5, and the deviation rate \(\alpha\) of diffusion morphology of approximate ellipsoid can also be divided into \(\alpha\leq\) 5% (indicating insignificant effect), 5% \(<\alpha\leq\) 15% (indicating significant effect), 15% \(<\alpha\leq\) 25% (indicating significant effect) and \(\alpha\geq\) 25% (indicating more significant effect) to analyze the effect of the coupling effect of porosity and cement grout weight on the diffusion morphology of gravel soil infiltration grouting. The effect of porosity and cement grout weight coupling effect on the three-dimensional spatial diffusion laws of gravel soil infiltration grouting is shown in Table 4.  
Figure 5: Morphological deviation rate of the approximate ellipsoid of the coupling effect between gravel soil porosity and cement grout weight on cement grouts into the gravel soil by penetration grouting.