## 5 Conclusions  
This study conducted a series of resonant column tests and unconfined compressive tests to evaluate the static strength and dynamic characteristics of MICP-treated calcareous sand. It investigated the effect of the treatment time and confining stress on the shear modulus degradation and damping ratio. The relationship between the unconfined compressive strength and the initial shear modulus was also analyzed. The correlation between the relative shear strain, treatment time, and confining stress was discussed. The conclusions can be stated as follows:  
1. The initial dynamic shear modulus and the unconfined compressive strength rose significantly after MICP treatment, indicating that MICP treatment improves the dynamic properties and strength of calcareous sand. The treated calcareous sand sample showed a higher strain sensitivity (strain-dependent) than that of untreated sands, and the strain sensitivity increased with the increase in treatment duration, demonstrating that the brittleness of the MICP-treated calcareous sands grew during treatment. The Hardin-Drnevich model can describe the \(G/G_{0}\) attenuation law of MICP-treated calcareous sand. The shear modulus of the MICP-treated sand eventually approached that of the untreated calcareous sand when the shear strain was approximately 0.03%. 2. The difference between the shear modulus of the treated sand and the at of untreated sand became more evident as the confining stress increased because of the reduced pore volume of samples and the increase in the contact between the particles. The MICP-cemented calcareous sand improved significantly in the initial dynamic shear modulus \(G_{0}\). The relationship between \(G_{0}\) and the confining pressure \(\sigma_{\rm c}\), as well as between \(G_{0}\) and the unconfined compressive strength \(q_{\rm u}\), can be described by a power function. 3. The variation in the reference shear strain \(\gamma_{\rm r}\) under various confining pressures dropped gradually with increasing treatment time, indicating that the influence of the confining pressure on the attenuation curve of the dynamic shear modulus of the MICP-treated calcareous sand decreased during the treatment process. The power function \(\gamma_{\rm r}=1/(a+b\cdot t^{\rm c})\) and the linear function \(\gamma_{\rm r}=\alpha\cdot\sigma_{\rm c}+\beta\) can describe the relationship between \(\gamma_{\rm r}\), \(t\), and \(\sigma_{\rm c}\). The confining stress substantially impacted the response of the damping ratio in the treated sample. The threshold calcium carbonate content was about 7%. However, the relationship between \(\gamma_{\rm r}\) and treatment duration or confining stress is provided in this manuscript. Nevertheless, the experimental data analyzed in this study are limited, and further efforts are needed to demonstrate the empirical formulas and their applicability to other types of liquefiable soils and treatment conditions. In addition, the empirical formulations between \(\gamma_{\rm r}\) and other physical properties such as relative density should be conducted in further work. Figure 12: Relationships between normalized \(G_{0}\) and \(C_{\rm C}\), and \(q_{\rm u}\) and \(C_{\rm C}\). **Author Contributions:** Conceptualization, X.Z. and Y.C. ; Methodology, X.Z. and H.G. ; Validation, J.G. and R.Y. ; Formal analysis, Y.C. and Y.H. ; Investigation, J.G. ; Resources, H.G. and H.L. ; Data curation, J.G. and R.Y. ; Writing--original draft, X.Z. and Z.S. ; Writing--review & editing, L.L. ; Visualization, J.G. All authors have read and agreed to the published version of the manuscript.