## 5 Discussion of Results  
To evaluate the performance of the new formula in comparison to existing ones, a comparative analysis was conducted using the comprehensive Database B.  
Comparing the predicted results with the objective reality can intuitively demonstrate the accuracy of the new method given in Equation (27). The liquefaction evaluation results under various probability contours and fines contents are presented in Figures 8 and 9.  
Figure 8 demonstrates that the new formula achieves an overall accuracy exceeding 60% across all the probability contours, reaching the highest accuracy at the 60% probability contour. The new formula maintains a leading overall accuracy across all the probability profiles compared to the other formulae. At a conservative probability level of 20%, the overall accuracy of the new formula is comparable to the best-performing formulae (e.g., Formula (8)), exceeding the accuracy of the other formulae by approximately 3%. At a balanced probability level of 50%, the overall accuracy of the proposed formula is approximately 3% higher than all the other formulae. Specifically, the non-liquefaction accuracy is 3% to 7% higher than that of the other formulae, while the liquefaction accuracy is 3.8% lower than that of Formula (8). However, the total accuracy and non-liquefaction accuracy of the new formula are both higher than those of Formula (8).  
Figure 9 compares the accuracy of the new formula with the other formulae under varying fines contents. The new formula exhibits a clear advantage in balance across various fines contents. Its liquefaction evaluation accuracy ranges between 87% and 75%, comparable to the best performance of the existing formulae. Moreover, its non-liquefaction evaluation accuracy never falls below 50%, significantly higher than that of all the other formulae, demonstrating the new formula's balance within these intervals. Similarly, in the \(FC>35\%\) interval, although Formula (8) outperforms the new formula by 7% in liquefaction accuracy, its non-liquefaction accuracy is significantly lower by 14%.  
Figure 8: Accuracy of evaluation under different probability contours for new formula and existing formulae: (**a**) Equation (27), (**b**) Equation (7), (**c**) Equation (8), (**d**) Equation (11), and (**e**) Equation (18).  
Additionally, when \(FC>35\%\), all formulae except the new one show a slight increase in the liquefaction accuracy and a significant decrease in the non-liquefaction accuracy. In this range, the overall non-liquefaction accuracy of the existing formulae is around 40%, while the new formula maintains at least 60%, which is, on average, 11% higher. This demonstrates that the new formula better addresses the impact of fines content changes on the liquefaction probability evaluation, reflecting the performance improvement from the fines content optimization during the new method's construction. Thus, the new formula  
Figure 9: Evaluation accuracy under different fines contents for new formula and existing formulae: (**a**) Equation (27), (**b**) Equation (7), (**c**) Equation (8), (**d**) Equation (11), and (**e**) Equation (18).  
exhibits a good balance across different fines contents, especially in the non-liquefaction evaluation, significantly outperforming the other formulae and adapting well to the changes in fines content.