# Creep Properties and Creep Modelling of Guilin Red Clay
## 3 The Burgers Creep Model  
### Model Introduction  
The Burgers model has high accuracy in describing the decay and stable creep stages of geotechnical bodies [26], so this paper establishes a Burgers creep model applicable to red clay in the Guilin area. The Burgers model is a four-component viscoelastic creep model consisting of the Maxwell model and the Kelvin model in tandem, and its structure is shown in Figure 8. The Maxwell model is a viscoelastic model composed of a Hooke's spring and a Newtonian clay pot connected in series, which can describe the characteristics of the soil body in the case of constant stress with an increase in strain with time (creep). The Kelvin model is a viscoelastic model composed of a Hooke's spring and a Newtonian clay pot connected in parallel, which is suitable for describing the attenuation creep characteristics of the soil body.  
The Burgers model equation is composed of the deformation of the Hooker spring in the Maxwell model \(\varepsilon_{1}\), the deformation of the Newton sticky pot corresponds to the constant velocity creep stage \(\varepsilon_{2}\), and the deformation corresponding to the Kelvin model \(\varepsilon_{3}\), as shown in Equation (1).  
\[\varepsilon=\varepsilon_{1}+\varepsilon_{2}+\varepsilon_{3}=\frac{\Delta \sigma}{E_{1}}+\frac{\Delta\sigma}{\eta_{1}}t+\frac{\Delta\sigma}{E_{2}}\bigg{(} 1-\exp\bigg{(}-\frac{E_{2}}{\eta_{2}}t\bigg{)}\bigg{)} \tag{1}\]  
where \(\Delta\sigma\) is the applied deviator stress; \(E_{1}\), \(E_{2}\) is the modulus of elasticity; \(\eta_{1}\), \(\eta_{2}\) is the sticky pot coefficient, and \(t\) is time.  
The relationship between strain rate and time \(t\) can be obtained from Equation (1) \(\varepsilon^{\prime}\):  
\[\varepsilon^{\prime}=\frac{\Delta\sigma}{\eta_{1}}+\frac{\Delta\sigma}{\eta_{ 2}}\bigg{[}\exp\bigg{(}-\frac{E_{2}}{\eta_{2}}\bigg{)}\bigg{]} \tag{2}\]  
Figure 8: Burgers model structure.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Cell Presure/kPa** & **Deviatoric Stress/kPa** & **Axial Strain/\%** & **Cell Presure/kPa** & **Deviatoric Stress/kPa** & **Axial Strain/\%** \\ \hline \multirow{4}{*}{100} & 143 & 4.458 & & 271 & 5.375 \\  & 172 & 4.577 & & 325 & 5.585 \\  & 201 & 4.740 & 300 & 379 & 5.944 \\  & 229 & 4.950 & & 433 & 6.484 \\  & 258 & 5.291 & & 488 & 7.422 \\ \hline \multirow{4}{*}{200} & 215 & 3.935 & & 331 & 5.886 \\  & 258 & 4.094 & & 397 & 6.142 \\ \cline{1-1}  & 301 & 4.327 & 400 & 463 & 6.853 \\ \cline{1-1}  & 345 & 4.711 & & 529 & 7.617 \\ \cline{1-1}  & 388 & 5.724 & & 596 & 9.997 \\ \hline \end{tabular}
\end{table}
Table 3: The axial strain value of the sample after loading under different cell pressures and different deviatoric stresses.  
When \(t=0\):  
\[\left\{\begin{array}{l}\varepsilon=\varepsilon_{1}=\frac{\Delta\sigma}{E_{1}}\\ \varepsilon^{\prime}=\frac{\Delta\sigma}{\eta_{1}}+\frac{1}{\eta_{2}}=k_{1}+k_ {2}\end{array}\right. \tag{3}\]  
When \(t\rightarrow\infty\), the strain produced by the Kelvin model tends to a constant value. Substituting Equations (2) and (3), we obtain:  
\[\left\{\begin{array}{l}\varepsilon_{3t\rightarrow\infty}=\frac{\Delta \sigma}{E_{2}}\\ \varepsilon^{\prime}_{t\rightarrow\infty}=\frac{\Delta\sigma}{\eta_{1}} \end{array}\right. \tag{4}\]  
The calculation equation of Burgers model parameters can be obtained by simultaneously using Equations (3) and (4) as follows:  
\[\left\{\begin{array}{l}E_{1}=\frac{\Delta\sigma}{E_{1}}\\ \eta_{1}=\frac{\Delta\sigma}{E_{1}}\\ E_{2}=\frac{\Delta\sigma}{\varepsilon_{3t\rightarrow\infty}}\\ \eta_{2}=\frac{\Delta\sigma}{k_{2}}\end{array}\right. \tag{5}\]  
where \(k_{1}\) is the initial creep rate; \(k_{2}\) is the stable creep rate; \(\varepsilon^{\prime}\) is the strain rate; and \(\varepsilon_{3t\rightarrow\infty}\) is the final value of strain is generated for the Kelvin model.