# Creep Properties and Creep Modelling of Guilin Red Clay
## 3 The Burgers Creep Model
### Derivation of Model Parameters  
As can be seen from Figure 8, all the above parameters can be determined from the test curve. Below is an example of the creep curve at 100 kPa cell pressure, which is used to illustrate the method of parameter determination. (1) Elastic modulus \(E_{1}\)  
As can be seen from the above, \(\varepsilon_{1}\), the deformation produced during the eccentric stress application stage, corresponds to the strain at the start of the creep curve in Figure 7. The relationship between deviator stress and axial strain at each stage is shown in Figure 9, and the relationship between deviator stress and axial strain is linear. From this empirical formula, the elastic modulus \(E_{1}\) can be derived as follows:  
\[E_{1}=\frac{\mathrm{q}}{A\times\mathrm{q}+\mathrm{B}} \tag{6}\]  
where \(A\) and \(\mathrm{B}\) are fitting coefficients and \(\mathrm{q}\) is the deviator stress. Figure 9: Relationship between axial strain and deviatoric stress \(\mathrm{q}\). (2) Elastic modulus \(E_{2}\)  
According to the above analysis, the strain produced with the Kelvin model \(\varepsilon_{3}\) approaches a constant value with increasing time under the action of the deviatoric stress, and the strain \(\varepsilon_{2}\) produced with the Kelvin model can be obtained by removing \(\varepsilon_{3}\) the creep strain at steady state. The strain produced with the Kelvin model corresponding to each deviatoric stress \(\varepsilon_{3}\) is shown in Table 4. It can be seen from Equation (4) that the elastic modulus \(E_{2}\) is the ratio of deviator stress to strain \(\varepsilon_{3}\), and the relationship between the elastic modulus \(E_{2}\) and deviator stress q is approximately an exponential function, as shown in Figure 10. The empirical relationship can be obtained by fitting it to Equation (7). \[E_{2}=C\times\exp(-D\times\text{q}) \tag{7}\]  
In the formula, \(C\), \(D\) is the fitting coefficient and q is the deviator stress. (3) Coefficient of sticky pot \(\eta_{1}\)  
As can be seen from Figure 8, when the Kelvin model decays to a constant value, the sample enters a steady creep phase, at which time the creep rate remains unchanged, and the slope of the curve is \(k_{1}\). When \(t>100\) min, the creep curve is approximately a straight line, and the sample enters the steady creep phase. The steady state creep rates at various deviator stresses are shown in Table 5. The relationship between deviator stress and a steady creep rate is shown in Figure 11, which shows a linear functional relationship. An empirical relationship can be established by fitting it with Equation (8). \[\eta_{1}=E\times\text{q}-\text{F} \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Deviatoric stress q/kPa & 143 & 172 & 201 & 229 & 258 \\ \hline Axial strain \(\varepsilon_{3}\)/\% & 4.392 & 4.447 & 4.517 & 4.603 & 4.769 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Axial strain under different deviatoric stresses. Figure 10: Relation \(E_{2}\) curve between elastic modulus and deviatoric stress q. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Deviatoric stress q/kPa & 143 & 172 & 201 & 229 & 258 \\ \hline Stabilisation of creep rate/min\({}^{-1}\) & 4.9254 \(\times\) 10\({}^{-5}\) & 9.7015 \(\times\) 10\({}^{-5}\) & 16.5672 \(\times\) 10\({}^{-5}\) & 25.8209 \(\times\) 10\({}^{-5}\) & 38.6567 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Stable creep rates corresponding to different deviatoric stresses. (4) Coefficient of sticky pot \(\eta_{2}\)  
From Equations (3)-(5), it can be seen that the slope of the initial phase curve of yield creep is \(k_{2}\). The relationship between the initial creep rate (as shown in Table 6) and the deviator stress is shown in Figure 12, and the relationship between them is linear. By fitting it with a linear function, it can be seen that the slope of the linear function is \(1/\eta_{2}\).