## 4 Model Comparison and Validation
### Comparison Results of the Proposed Models
It showed better fitting results for type B test data under low normal stress and types A test data (Figure 9(A-1)). As a whole, the scale parameter \(u_{0}\) of Weibull decreased with the increase of softening degree, and the shape parameter \(m\) increases with the increase of softening degree;
2. The fitting correlation coefficients (\(R^{2}\)) of Logistic-constitutive model for type A curves were 0.821, 0.792, and 0.892 (Figure 11a). For type B curves, the fitting correlation coefficient increased from 0.831 to 0.978 as the normal stress increased (Figure 11b), which is better than that of type A curves. Parameter \(a\) increased with the increase of softening degree, but the influence of softening degree on parameter \(b\) was not clear;
3. In the fitting result of the Normal-constitutive model, the peak displacement of model curves of type A in various normal stress and type B under low normal stress was greater than that of test data (Figure 9(A-3) and Figure 10(B-3)). The fitting result of  
Figure 11: Correlation coefficient analysis of shear constitutive models. (**a**,**b**) Present the correlation coefficients of various shear constitutive models based on different distribution functions for Huangtopo landslide slip zone soil representing weak softening type, and for Shizibao landslide slip zone soil representing strong softening type, respectively. (1) Weibull-constitutive model; (2) logistic-constitutive model; (3) normal-constitutive model; (4) lognormal-constitutive model; (5) exponential-constitutive model; (6) Gamma-constitutive model; (7) hyperbolic-constitutive model; (8) Gumbel-constitutive model. type B curve was better under high normal stress (400 kPa, 500 kPa), with correlation coefficients of 0.945 and 0.952 (Figure 11b);
4. The fitting result of the Lognormal-constitutive model (Figure 10(B-4)) for type B curves shows that the peak displacement of simulated curves deviated to the left and the peak stress were higher compared with the test data. In general, the fitting results for type A (Figure 9(A-4)) were better than those for type B (Figure 10(B-4));
5. The fitting result of the Exponential-constitutive model (Figures 9(A-5) and 10(B-5)) was similar to that of the Normal distribution, but the average fitting correlation coefficients of the two types of curves (\(R^{2}\) were 0.838 and 0.930, respectively in Figure 11) were higher than those of the Normal-constitutive model (\(R^{2}\) are 0.807 and 0.883, respectively in Figure 11). Parameters \(a\) and \(b\) decreased with the decrease of softening degree;
6. The average fitting correlation coefficients (\(R^{2}\)) of the Gamma-constitutive model for type A and type B curves were 0.861 and 0.974, respectively (Figure 11), which were the highest among the eight models, and the standard error was small. It indicates that Gamma-constitutive model was the best choice for describing both two types of shear curves of the slip zone soil among the introduced models;
7. Among the Hyperbolic-constitutive model, the fitting result of type A under normal stress 100 kPa was better, and the correlation coefficient was 0.936 (Figure 11a), but the characteristics of the model curves for type A under high normal stress and the model curves for type B (Figures 9(A-7) and 10(B-7)) were similar to the Lognormal-constitutive model;
8. The fitting result of Gumbel-constitutive model shows that the peak displacement of the model for type B was greater than the actual peak displacement (Figure 10(B-8)). The fitting correlation coefficient increases from 0.717 to 0.928 as the normal stress increased (Figure 11b). The peak displacement of model curves for type A was also larger than the actual peak displacement (Figure 9(A-8)), but the peak displacement offset increased with the increase of normal stress. The type A curves are the weak softening curves with the weak softening degree and even show hardening characteristics under the normal stress of 400 kPa. It can be seen from Figure 11a, the applicability of various constitutive models for weak softening curves.