## 3 Test Results and Analysis
### Effect of Biopolymer on Compressive Strength
#### 3.1.3. Toughness Index  
To better understand and quantify the toughening characteristics in the post peak region, the load axis of the load deformation diagram was normalized with respect to the peak load. To focus only on the post peak behavior, a dimensionless split tensile toughness index value (_TI_ value) is defined as follows:  
\[TI=\frac{A_{d}-A_{p}}{d/d_{p}-1} \tag{1}\]  
where \(d_{p}\) = deformation at peak load \(P_{\text{max}}\); \(d\) = any deformation that is greater than the \(d_{p}\) value; \(A_{p}\) = area under the normalized curve up to the peak; and \(A_{d}\) = area under the normalized curve up to the deformation ratio \(d/d_{p}\). This study investigates the toughening effect of biopolymers on GRS using the _TI_ value, which is calculated based on the equal strain values derived from the stress-strain curve [37], as shown in Figure 10. The results reveal that the addition of biopolymers significantly enhances the toughness of GRS, with the _TI_ value exhibiting relatively stable changes over time as the curing period progresses. Soil treated with XG showed a substantial increase in _TI_ value on day 0, and the value continued to rise as curing time increased. The toughening effect of XG intensified with its  
Figure 9: Elastic modulus of biopolymer-treated GRS: (**a**) XG; (**b**) LBG; and (**c**) GG.  
increasing content, but when the XG content surpassed 1.5%, the _TI_ value experienced a slight decrease.  
The toughening effect of LBG follows a similar pattern to that of XG, but LBG is less sensitive to variations in curing time. When the content of LBG exceeds 1.5%, the _TI_ value significantly decreases. At 1.0% LBG, the growth rate of the _TI_ value noticeably slows compared to 0.5%, though the index still shows an upward trend. At 1.5%, the _TI_ value reaches a local peak, suggesting that the soil structure is nearing the limit of optimization achievable by LBG. When the LBG content exceeds 1.5%, excessive usage leads to a substantial decline in the _TI_ value. This result indicates that, to optimize the toughening effect of LBG, its content should be carefully controlled, as overuse can have detrimental effects. A content range of 0.5% to 1.5% appears to be the optimal choice for enhancing soil toughness while avoiding the negative effects associated with excessive LBG usage.  
For soils treated with GG, no significant difference in the _TI_ value was observed at day 0 compared to the untreated GRS. This suggests that GG did not significantly enhance the soil's toughness in the initial stage. However, as curing time progressed, the situation changed. After 3 days of curing, the _TI_ value of the GG-treated soil significantly increased,  
Figure 10: Toughness index of biopolymer-treated GRS: (**a**) XG; (**b**) LBG; and (**c**) GG.  
As the GG content increased, the _TI_ value of the soil also steadily improved, with the toughness performance remaining relatively stable and not easily influenced by the curing time. This characteristic makes GG advantageous in applications where curing time is not a major concern.  
Overall, GG exhibits a distinct pattern in enhancing the toughness of GRS. At low concentrations, GG has a minimal impact on increasing the _TI_ value. However, once the concentration reaches 1%, the _TI_ value begins to rise significantly. As the curing time extends, the _TI_ value of the GG-treated soil continues to grow steadily, without the slight or pronounced decrease in _TI_ value seen with higher concentrations of XG and LBG.