# Study on Creep Behavior of Silty Clay Based on Fractal Derivative
## 4 Model Verification and Parametric Sensitivity Analysis
### Fractal Burgers Model Parametric Sensitivity Analysis  
The above analysis shows that the fractal Burgers model is suitable for describing the creep characteristics of soft soil. As seen from Equation (10), the parameters affecting the creep characteristics mainly include [PERSON]'s modulus E, the viscosity coefficient \(\eta\) of the dashpot, the order of the fractal derivative \(\beta\), and the stress level \(\sigma\). To better analyze the influence of model parameters, according to the results of the abovementioned test and the fractal Burgers model fitting, taking 200 kPa confining pressure and 220 kPa deviatoric stress as an example, the fitting parameters of the proposed model are shown in Table 5, and the parameter sensitivity analysis is carried out for the creep model to clarify the influence mechanism of each parameter. First, by changing Young's modulus of the Maxwell and Kelvin elements, the influence of [PERSON]'s modulus on the creep curve is analyzed. As Figure 16a indicates, E\({}_{\rm m}\) has a negative linear correlation with the creep strain, which affects the initial transient elastic deformation, and E\({}_{\rm k}\) has a negative nonlinear correlation with the creep strain, affecting the creep rate and inflection point, and the effect is particularly pronounced when the creep strain is small. Figure 16: Sensitivity of the creep strain to different parameters: (**a**) [PERSON]’s modulus; (**b**) derivative order; (**c**) viscosity coefficient. The fractal Burgers model is characterized by the use of fractal derivative theory to solve the nonlinear creep problem, and the influence of the derivative order on the creep characteristics is significant. Leaving the other parameters unchanged and only changing the derivative order of the model, the rheological curves corresponding to the different derivative orders can be obtained, as shown in Figure 16b. The derivative order is positively correlated with the creep value and deformation rate, of which \(\beta_{\rm m}\) significantly affects the creep rate, and \(\beta_{\rm k}\) has an obvious impact on the inflection point of the creep curve. The presence of a derivative order causes the slope of the curve to appear to be linear. To study the influence law of the viscosity coefficient parameters, creep curves can be obtained by changing the viscosity coefficient, as shown in Figure 16c. The viscosity coefficient is negatively correlated with the value and deformation rate of the creep, where \(\eta_{\rm m}\) significantly affects the creep rate and \(\eta_{\rm k}\) has a more significant influence on the inflection point of the creep curve; that is to say, \(\eta_{\rm k}\) represents the speed rate when the deformation tends to be in steady state during the creep stage. A larger value of \(\eta_{\rm k}\) indicates that the soil would take longer to reach the steady state. In addition, the presence of a viscosity coefficient makes the curve nonlinear. The effect of the stress level \(\sigma\) can be directly observed from the test result in Figure 6, and the influence of the stress level on creep characteristics is significant. At the low-stress level, the creep deformation is mainly determined by the transient deformation value, while at the high-stress level, it is the result of the combination of transient creep values and steady-state strain rates. The higher the stress level is, the greater the creep deformation value. According to the sensitivity analysis of the above key parameters, the creep rate is largely limited by the derivative order; the viscosity coefficient mainly affects the morphology of the curve, and Young's modulus and the stress level significantly affect the deformation value of the soil. For the two model elements in the fractal Burgers model, the Maxwell component-related parameters mainly affect the initial creep value and rate, and the Kelvin component mainly affects the creep curve inflection point and morphology.