## 2 Materials and Methods
### Equipment and Testing Procedure  
The experiments related to the MICP-treated calcareous sand were conducted using the resonant column apparatus TSH-100 developed by GCTS, as shown in Figure 4a. The shear modulus can be calculated by combining the frequency-response curve data, specimen size, and physical characteristics of the resonant column test apparatus. The configuration of the resonant column apparatus is bottom-fixed and top-free, and it can be modified according to the size of prepared soil specimens. The maximum pressure of the air-filled cell is 1 MPa, and there is an internal high-resolution LVDT for measuring the deformation of specimens. The specimen and vibration generator were enclosed together within the pressure chamber. The specimen's resonant frequency was determined by changing the excitation frequency and force applied to the bottom of the specimens. The shear modulus \(G\) was calculated using the theory of elastic wave propagation as follows:  
\[G=\rho V_{S}^{2} \tag{1}\]  
\[V_{S}=\frac{2\pi f_{n}l}{\beta} \tag{2}\]  
where \(V_{S}\) is shear wave velocity, \(\rho\) is density, and \(f_{n}\) is the natural frequency of the system. \(\beta\) is a function of the mass polar moment of inertia of both specimen \(I\) and the mass attached at the free end of the specimen \(I_{0}\), as determined by:  
\[\beta\tan(\beta)=1/I_{0} \tag{3}\]  
Figure 3: Schematics of MICP treatment device for **(a)** schematic diagram of mold for MICP-treated cylindrical specimens, **(b)** schematic of MICP-treated calcareous sand, and **(c)** sketch of MICP treatment procedure. (a. Bacterial liquid/cementation solution; b. peristaltic pump; c. sand sample; d. filter fabric; e. aspirating hole; f. PVC split mold; g. PVC pedestal; h. rubber membrane; i. effluent; j. plastic tube). In this study, the damping ratio is determined from the frequency-response curve, which can be calculated using:  
\[D=\left(\frac{f_{2}-f_{1}}{2f_{n}}\right)\times 100 \tag{4}\]  
where \(f_{1}\) and \(f_{2}\) are the frequencies at \(A=A_{\text{max}}/\sqrt{2}\), in which \(A\) is the acceleration of resonant frequency, and \(A_{\text{max}}\) is the maximum acceleration. The test procedure can be divided into four steps. First, the prepared sample was installed on the base, and the top of the sample was connected to a vibration generator. Second, the back-pressure saturated method was applied to ensure that the specimens were saturated and the back pressure was 400 kPa. In this study, a \(B\)-value of more than 0.97 was reached for all the specimens. The effective confining stress was then increased to the target value and maintained. When the average strain rate of the sample was less than \(1\times 10^{-3}\%/\text{min}\), the consolidation step was completed. Finally, the resonant frequency was determined by changing the excitation frequency and force applied to the bottom of the specimens, and the values of the dynamic shear strain, shear wave velocity, and dynamic shear modulus were recorded. A series of unconfined compressive tests were performed to analyze the relationship between the static strength and the dynamic properties of the MICP-treated calcareous sand. The unconfined compressive strength of the MICP-treated samples was measured using a YSH-2 type of unconfined compression apparatus (Figure 4b). The upper and lower surfaces of the samples were leveled and placed on the unconfined compressive apparatus. The unconfined compression strength of the soil samples was measured with a loading speed of 1 mm/min. Figure 4: This study’s experimental equipment consists of (**a**) a resonant column device and (**b**) an unconfined compression test.