# Study on Creep Behavior of Silty Clay Based on Fractal Derivative
## 4 Model Verification and Parametric Sensitivity Analysis
### Model Comparison  
The component models that are widely used to describe the elastoplastic creep characteristics of soft soil mainly include Merchant, traditional Burgers, five-element generalized Kelvin, and fractional Burgers models [26], which are composed of the most basic components connected by different connection methods, as shown in Figures 12 and 14, where \(E\) and \(\eta\) are Young's modulus and the viscosity coefficient, and the subscripts 0, 1 and 2 represent Hooke spring, the first Kelvin element and the second Kelvin element in a fractal form, respectively. To compare and analyze the fitting accuracy of different models, the fitting analyses of the test data using the corresponding constitutive models are shown in Figure 15. From the comparison, it can be seen that in the case of the same type of basic components, the greater the number of model components is, the higher the accuracy of the model fit, but the greater the computational workload. A comparison of the fractal Burgers and traditional Burgers models suggests that replacing the Newton dashpot with the fractal dashpot will achieve a higher fitting accuracy in the case of an equal number of components, and the calculation process is easy to implement.  
Figure 13: Comparison of test data with fractal Burgers and fractional Burgers models: (**a**) q = 117 kPa; (**b**) q = 220 kPa; (**c**) q = 330 kPa; (**d**) q = 459 kPa.  
Figure 15 also shows that the model fitting accuracy mainly depends on the curve slope and inflection point. This test involves only two stages of creep deformation: the initial curve slope determines the initial creep deformation, the final curve slope determines the long-term creep deformation value, and the inflection point determines the turning point of creep from one stage to another. Comparing the Merchant model and the Burgers model, it can be found that the Abel dashpot in the Maxwell model has a significant impact on the curve inflection point and slope. The Merchant model has an obvious inflection point delay, and the slope tends to zero with time going on, while the Burgers model exhibits the opposite phenomenon, which is not obvious in a short period but will become more pronounced in long-term observations. Comparing the traditional Burgers model with the fractal Burgers model, it can be found that the existence of derivative order \(\beta\) mainly plays a role in reducing the slope of the final curve. In general, the fitting laws of all the above models tend to be consistent with the test data, and the difference lies in the  
Figure 14: Schematic of different models: (**a**) Merchant model; (**b**) five-element generalized Kelvin model.  
Figure 15: Comparison of test data and the fitting curves of different models: (**a**) q = 117 kPa; (b) q = 220 kPa; (c) q = 330 kPa; (d) q = 459 kPa.  
degree of fitting coincidence. For low-stress soil, increasing the number of components can improve the fitting accuracy, while for high-stress soil, the fractional derivative and fractal derivative methods can effectively improve the fitting accuracy.