## 3 Experimental Results  
### Dynamic Shear Modulus of MICP-Treated Calcareous Sands  
Significant nonlinearity in soil stress-strain behavior is presented by two parameters of the shear modulus \(G\) and damping ratio \(D\), which change with shear strain amplitude. Figure 5a illustrates the variation in \(G\) with the shear strain \(\gamma\) ranging from \(10^{-4}\) to \(4\times 10^{-2}\%\). The shear modulus of the clean sands used in this investigation oscillated from \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**Treatment Time (Hours)**} & \multicolumn{2}{c}{**Effective Confining Stress \(\sigma_{c}\) (kPa)**} & \multirow{2}{*}{\(D_{\text{r}}\) (\%)**} & \multirow{2}{*}{\(m\) (g)} & \multirow{2}{*}{\(e_{0}\)} & \multirow{2}{*}{\(\Delta m\) (g)} & \multirow{2}{*}{\(C_{\text{C}}\) (\%)} \\  & & & & & & & & & \\ \hline \multirow{3}{*}{Group  UN} & UN1 & RCT & / & 25 & 41.3 & 236.4 & 1.27 & / & / \\  & UN2 & RCT & / & 50 & 39.2 & 235.5 & 1.28 & / & / \\  & UN3 & RCT & / & 100 & 40.5 & 236.0 & 1.27 & / & / \\ \hline \multirow{6}{*}{Group  M-A} & M11 & RCT & 6 & 25 & 40.1 & 235.9 & 1.27 & 5.28 & 2.24 \\  & M12 & RCT & 6 & 50 & 38.6 & 235.2 & 1.28 & 5.02 & 2.13 \\  & M13 & RCT & 6 & 100 & 42.3 & 236.8 & 1.26 & 4.98 & 2.10 \\  & M21 & RCT & 12 & 25 & 39.5 & 235.6 & 1.27 & 8.56 & 3.63 \\  & M22 & RCT & 12 & 50 & 40.9 & 236.2 & 1.27 & 8.67 & 3.67 \\  & M23 & RCT & 12 & 100 & 41.1 & 236.3 & 1.27 & 8.21 & 3.47 \\  & M31 & RCT & 18 & 25 & 39.5 & 235.6 & 1.27 & 11.42 & 4.85 \\  & M32 & RCT & 18 & 50 & 39.9 & 235.8 & 1.27 & 12.61 & 5.35 \\  & M33 & RCT & 18 & 100 & 40.2 & 235.9 & 1.27 & 11.89 & 5.04 \\  & M41 & RCT & 24 & 25 & 41.8 & 236.6 & 1.26 & 17.67 & 7.47 \\  & M42 & RCT & 24 & 50 & 39.8 & 235.7 & 1.27 & 16.93 & 7.18 \\  & M43 & RCT & 24 & 100 & 40.8 & 236.2 & 1.27 & 17.24 & 7.30 \\  & M51 & RCT & 48 & 25 & 40.2 & 235.9 & 1.27 & 25.24 & 10.70 \\  & M52 & RCT & 48 & 50 & 37.9 & 234.9 & 1.28 & 26.96 & 11.48 \\  & M53 & RCT & 48 & 100 & 39.4 & 235.5 & 1.27 & 26.68 & 11.33 \\ \hline \multirow{6}{*}{Group  M-B} & M1 & UCT & 6 & / & 42.1 & 236.7 & 1.26 & 5.98 & 2.53 \\  & M2 & UCT & 12 & / & 40.8 & 236.2 & 1.27 & 8.65 & 3.66 \\ \cline{1-1}  & M3 & UCT & 18 & / & 42.5 & 236.9 & 1.26 & 13.54 & 5.72 \\ \cline{1-1}  & M4 & UCT & 24 & / & 41.1 & 236.3 & 1.27 & 17.65 & 7.47 \\ \cline{1-1}  & M5 & UCT & 48 & / & 39.5 & 235.6 & 1.27 & 27.16 & 11.53 \\ \hline \end{tabular} Note: UN means an untreated condition; M means MICP-treated condition; RCT means resonant column test; UCT means unconfined compressive test.  
\end{table} 
Table 3: Summary of the conducted experiments and CaCO\({}_{3}\) generation. 58 MPa to 20 MPa, 63 MPa to 23 MPa, and 95 MPa to 50 MPa at confining stress of 25 kPa, 50 kPa, and 100 kPa, respectively. The dynamic shear modulus of the soil after treatment was not significantly increased at a low confining stress of 25 kPa when the treatment duration was less than 18 h. Because the amount of precipitated calcium carbonate in specimens with a low treated level is limited, and the stiffness of these cementations is low, a higher CaCO\({}_{3}\) content is required for the loose and porous calcareous sands to form an effective bonding network. The treated sands have a higher shear modulus than the untreated sands at a small shear strain under the same loading conditions. As the shear strain increases, the shear modulus of the MICP-treated sand gradually decreases and eventually approaches that of the untreated calcareous sand at approximately 0.03% shear strain. This observation indicates that when the shear strain exceeds 0.03%, the beneficial effect of calcite bonding between sand particles induced by MICP treatment disappears. [PERSON] et al. (2018) discovered comparable outcomes in their study of cemented sand.