# A Modified Plastic Burgers Model for the Non-Decaying Creep of Frozen Soils
## 5 Model Verification and Analysis  
To demonstrate the validity of the plastic Burgers model deformation parameter calibration method at first, the creep strain of the tested results and calculated results without a plastic part (Formula (9)) under different temperatures are shown in Figure 7. It can be seen from the tested results that the onset time of the non-decaying creep stage, i.e., the time on the creep curve that the slope of the creep strain vs. time changes from essentially constant to quickly increasing, is inversely proportional to the stress level. This is due to the decay of the compression strength (Formula (17) and Figure 6). When the current applied stress is higher than the compression strength, plastic flow happens, and the creep strain rate increases sharply (Figures 6 and 7a). This is the so-called non-decaying creep process. Obviously, a higher applied stress corresponds to a shorter time with the onset of the non-decaying creep process. When the current applied stress is lower than the compression strength, the creep strain curve shows the development process with only a creep strain rate decrease at first which then becomes essentially constant (Figures 6 and 7a). This is the so-called decaying creep process. In other words, for these curves with relatively lower stress levels in Figure 7, the observation time is not long enough for the compression strength to decrease lower than the current applied stress, and subsequently, only the decaying creep process can be observed. \begin{table}
\begin{tabular}{c c c} \hline
**Temperature/\({}^{\circ}\)C** & \(m\)**/MPa\(\cdot\)s\({}^{-1}\)** & \(m/-\) \\ \hline \(-5.0\) & \(2.43\) & \(-0.0919\) \\ \(-10.0\) & \(4.23\) & \(-0.0907\) \\ \(-15.0\) & \(5.92\) & \(-0.0946\) \\ \hline \end{tabular}
\end{table} 
Table 4: Measured strength decay function parameters under different temperatures. Figure 7: _Cont._By comparing the tested and calculated results in Figure 7, it can be seen that Formula (9) generally has a good predictive performance when the non-decaying creep stage is not involved. It can be seen in Figure 7 that the calculated results of the initial instantaneous strain, creep strain rate decrease section and essentially constant creep strain rate section generally have good agreement with the tested results under different stress levels. This indicates that the plastic Burgers model deformation parameter calibration method proposed in Section 4.1 is valid under different axial stress levels and temperatures. The deformation parameter calibration method can be further applied in practical engineering calculations. Figure 8 is the comparison of the tested results and calculated results taking the plastic strain into account (Formula (1)). As can be seen in Figure 8, when the cohesion decay function (Formula (8)) was incorporated into the plastic Burgers model, the continuous development process from the decaying to non-decaying creep stage could be reasonably described under different temperatures and axial stress levels. This indicates that the modification of the plastic Burgers model with the cohesion decay function is valid for describing the creep process when non-decay is involved. Figure 7: Tested creep strains and calculated results without a non-decaying creep stage at temperatures of (**a**) \(-5.0\)\({}^{\circ}\)C; (**b**) \(-10.0\)\({}^{\circ}\)C; and (**c**) \(-15.0\)\({}^{\circ}\)C.  
Figure 8: Tested creep strains and calculated results with cohesion decay taken into account at temperatures of (**a**) \(-5.0\) \({}^{\circ}\)C; (**b**) \(-10.0\) \({}^{\circ}\)C; and (**c**) \(-15.0\) \({}^{\circ}\)C.  
From the above analysis, it can be concluded that the frozen soil creep process with only a decaying creep stage can be well described by the plastic Burgers model with the proposed deformation parameter calibration method; when the non-decaying creep stage is involved, the cohesion decay function must be incorporated into the plastic Burgers model to describe the whole creep process reasonably.