## 4 Conclusions  
In this paper, laboratory tests of simulated penetration grouting were carried out for soil around piles. The macro mechanical behavior and microstructural characteristics of grouting soil were investigated. The conclusions are as follows:  
1. The shear stress of the soil around piles was found to be obviously affected by permeation grouting. With the increase of grouting cement content, the peak shear stress of the soil around the pile increases significantly, and the corresponding shear displacement decreases gradually. For the permeation grouting muddy clay, the variation rules of shear stress-shear displacement can be divided into a rapid growth stage (\(0<\delta<1\) mm), peak stress stage (\(1<\delta<3\) mm), and stabilization stage (\(3<\delta<7\) mm).
2. For the permeation grouting silty clay, the curve of shear stress and shear displacement shows hardening development when the cement content is less than 15%. The shear stress and shear displacement curve increase approximately linearly first when the cement content is 15%, and the shear stress decreases gradually after reaching the peak, tending to a stable finally. The cement content of the slurry could change the failure mode of silty clay, and the original elastic-plastic failure gradually changed to brittle failure after grouting.
3. The shear failure of the soil around piles with permeation grouting obeys the Mohr-Coulomb criterion of failure, the shear strength of which increases with the normal stress and cement content, and has positive linear correlations with the normal stress. When the cement content increased from 0 to 15%, the cohesion of muddy clay increased from 9.7 kPa without grouting to 60.91 kPa, and the internal friction angle increased from 5.0\({}^{\circ}\) to 16.3\({}^{\circ}\).
4. A composite exponential model was established to describe the silty clay with permeation grouting. This model included the main mechanical parameters such as shear stress, normal stress, friction angle, cohesion, cement content, and shear displacement. The variation in the shear stress of permeation grouting silty clay with the shear displacement can be well simulated.
5. The variations in the structural characteristic parameters of the two types of soil around piles are different, and the structural connectivity of the muddy clay is slightly worse than that of the silty clay. Permeation grouting makes the particle structure denser, which limits changes in pore arrangement and distribution. This makes the particle skeleton arranged more closely, thus improving the shear strength. During on-site construction, the grouting parameters can be adjusted appropriately according to different soft soils to achieve the best strengthening effect.  
Due to the limited experimental conditions, some factors cannot be considered. This study only analyzed the change of soil sample microstructure characteristic parameters at the mesoscopic level, which can be further investigated through SEM testing in the future. In addition, more interesting and important conclusions can be obtained by improving test methods or conducting field tests.  
Conceptualization, B.H. and G.W; methodology, X.L.; software, G.W.; validation, D.S., Z.S. and Y.Y.; formal analysis, G.W.; investigation, Y.Y.; resources, B.H.; data curation, X.L.; writing--original draft preparation, G.W.; writing--review and editing, G.W.; visualization, Z.S.; supervision, D.S.; project administration, B.H.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was sponsored by the National Natural Science Foundation of China (Grant No. 51609071).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors' gratitude goes to the reviewers for their helpful comments and constructive suggestions in improving this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.