# Experimental Study on Shear Creep and Long-Term Strength of Clay-Type Muddy Interlayer
## 3 Results and Discussion
### Variation Law of Shear Creep Rate  
From Figure 7, the corresponding slopes of creep curves at different shear stress levels are calculated, and the average and steady-state shear creep rates of muddy interlayers under different stress states are obtained. As there are many data results, the creep results of normal stress 100 kPa and 400 kPa are listed in Table 3.  
It can be seen from Table 3 that under the constant normal stress level, the shear creep of each sample increases with the increase in the shear stress level, and the average creep rate of the muddy sandwich specimen is basically one- to three-times that of the stable creep rate. It shows that the initial attenuation creep stage of the specimen under all levels of stress has small deformation, short duration and long stable creep duration, and the creep of muddy interlayer is very significant. The stable creep rate basically remains constant at the constant stress level, and the steady creep rate at the lower shear stress level is a constant greater than 0, indicating that the muddy interlayer produces significant creep deformation at the lower stress level. According to the analysis results of Table 3, the curves of the relationship between average creep rate and shear stress under different normal stress levels were fitted. At the \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Normal Stress/kPa** & **Shearing Stress/kPa** & \(u_{0}\)**/mm** & \(A\) & \(B\) & \(C\) & \(n\) & \(R^{2}\) \\ \hline \multirow{8}{*}{200} & 9 & 0.001 & 0.0099 & 0.8480 & 0.0047 & 0.2019 & 0.99 \\  & 18 & 0.001 & 0.0078 & 0.7980 & 0.0060 & 0.2581 & 0.99 \\  & 27 & 0.001 & 0.0043 & 2.1471 & 0.0067 & 0.3353 & 0.99 \\  & 36 & 0.0015 & 0.0021 & 1.8468 & 0.009 & 0.3153 & 0.99 \\  & 45 & 0.0042 & 0.0089 & 1.4434 & 0.0032 & 0.5252 & 0.99 \\  & 54 & 0.0033 & 0.0096 & 1.2755 & 0.0029 & 0.5622 & 0.99 \\  & 63 & 0.0031 & 0.0077 & 1.8629 & 0.0036 & 0.5597 & 0.99 \\  & 72 & 0.0040 & 0.0076 & 2.4687 & 0.0034 & 0.6133 & 0.99 \\  & 81 & 0.0041 & 0.0101 & 1.9092 & 0.0022 & 0.7456 & 0.99 \\  & 90 & 0.0043 & 0.0130 & 1.2354 & 0.0016 & 0.8343 & 0.99 \\  & 99 & 0.004 & \(-\)52.2502 & 0.0016 & 0.0969 & 0.9556 & 0.91 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c} \hline
**Normal Stress/kPa** & **Shearing Stress/kPa** & **Average Creep Rate/(10\({}^{-2}\) mm\(\cdot\)h\({}^{-1}\))** & **Steady Creep Rate (10\({}^{-2}\) mm\(\cdot\)h\({}^{-1}\))** \\ \hline \multirow{8}{*}{100} & 7 & 0.0125 & 0.0084 \\  & 14 & 0.0214 & 0.0168 \\  & 18 & 0.0351 & 0.0287 \\  & 21 & 0.0583 & 0.0509 \\  & 35 & 0.0988 & 0.0892 \\ \hline \multirow{8}{*}{400} & 12 & 0.0107 & 0.006 \\  & 24 & 0.0125 & 0.0077 \\  & 36 & 0.0167 & 0.0119 \\  & 48 & 0.0202 & 0.0155 \\  & 60 & 0.0238 & 0.0179 \\  & 72 & 0.0244 & 0.0185 \\  & 84 & 0.0268 & 0.0214 \\  & 96 & 0.0303 & 0.0250 \\  & 108 & 0.0333 & 0.0274 \\  & 120 & 0.0393 & 0.0328 \\  & 132 & 0.0452 & 0.0387 \\  & 144 & 0.0512 & 0.0441 \\  & 156 & 0.06 & 0.0488 \\ \hline \end{tabular}
\end{table} 
Table 3: Analysis of shear creep rate. same normal stress level, the relationship between average creep rate and shear stress can be expressed as an exponential function:  
\[u_{a}=ae^{b\tau} \tag{2}\]  
In the formula: a and b are the material parameters of the muddy interlayer, as shown in Table 4. The curve of the relationship between average creep rate and shear stress is shown in Figure 10a. The fitting curve in the graph closely aligns with the data points, demonstrating a strong agreement. The range of the correlation coefficient \(R^{2}\) for the fitting parameters varies from 0.91 to 0.99, indicating a high level of fitting performance. The average creep rate at different normal stress levels increases exponentially with the increase in shear stress. As the main part of the shear creep of muddy interlayer, the stable creep stage lasts a long time and has a significant impact on the stability of the slope.