## 3 Results and Discussion
### Mechanical Parameters
#### 3.2.2 Peak Strain Energy and Deformation Modulus  
The peak strain energy \(E_{\mathrm{u}}\) serves as a comprehensive indicator characterizing the toughness of the material, encompassing both the strength and ductility [46]. Figure 7 illustrates the variations in \(E_{\mathrm{u}}\) concerning the initial water content and cement content and curing ages. In Figure 7a, \(E_{\mathrm{u}}\) values exhibited a significant rise with the increasing cement content, ranging from 62.5 to 360.5 kJ/m\({}^{3}\). As shown in Figure 7b, the \(E_{\mathrm{u}}\) values showed a noticeable decline with the increasing initial water content, ranging from 17.1 to 116.0 kJ/m\({}^{3}\). Furthermore, there was a general upward trend in \(E_{\mathrm{u}}\) with the increasing curing time. Specifically, for the soil-based CLSM samples with a cement content of 25%, the \(E_{\mathrm{u}}\) values were approximately 2.6 times higher than those for the soil-based CLSM samples with a cement content of 8%. At a cement content of 8%, the introduction of PCE resulted in a reduction in \(E_{\mathrm{u}}\). This reduction is consistent with the effect of PCE on strength. The \(E_{\mathrm{u}}\) ranged from 50 to 350 kJ/m\({}^{3}\) because the samples of recycled concrete powder stabilized the dispersive soil, and \(E_{\mathrm{u}}\) was directly related to the strength improvement reported by [PERSON], et al. [47].  
Figure 6: The relationship of \(\varepsilon_{\mathrm{f}}\) and \(q_{\mathrm{u}}\).  
Figure 7: Peak strain energy under different (**a**) cement contents and (**b**) initial water contents.  
Figure 8 shows the change in the deformation modulus \(E_{50}\) under different cement contents, initial water contents, and curing time periods. As the cement content and curing time periods increased, a substantial enhancement in \(E_{50}\) values was observed in Figure 8a, indicating an improvement in specimen stiffness. The \(E_{50}\) values ranged from 60 to 360 MPa for different cement contents. However, a notable reduction in \(E_{50}\) values was evident with the rise in the initial water content, as shown in Figure 8b. Despite the extended curing time periods, there was a persistent increase in \(E_{50}\) values. The \(E_{50}\) values ranged from 15 to 120 MPa for different initial contents.  
As seen in Figure 9, the relationship between \(E_{50}\) and \(q_{\text{u}}\) closely follows the same trend observed in the relationship between \(E_{\text{u}}\) and \(q_{\text{u}}\). With a least-squares-fitting-based regression analysis, both \(E_{50}\) and \(E_{\text{u}}\) exhibited a robust linear correlation with the strength \(q_{\text{u}}\). The associations of \(E_{50}\) and \(E_{\text{u}}\) with \(q_{\text{u}}\) for the soil-based CLSM were effectively captured by the following linear functions: \(E_{50}=111.520\)\(q_{\text{u}}+1.658\) and \(E_{\text{u}}=90.989\)\(q_{\text{u}}+14.217\). Notably, the correlation coefficients \(R^{2}\) exceeded 0.95, indicating a strong relationship. [PERSON], et al. [48] revealed that the relationship between \(E_{50}\) and \(q_{\text{u}}\) for cement solidified dredged mud was expressed as \(E_{50}=75\)-200 \(q_{\text{u}}\). Interestingly, the relationship between \(E_{50}\) and \(q_{\text{u}}\) of the soil-based CLSM aligns consistently with that observed in cement solidified dredged mud.  
Figure 8: Deformation modulus \(E_{50}\) under different (**a**) cement contents and (**b**) initial water contents.  
Figure 9: Deformation modulus and peak strain energy in relationships with unconfined compressive strength.