# Experimental Study on Shear Creep and Long-Term Strength of Clay-Type Muddy Interlayer
## 3 Results and Discussion
### Empirical Formula of Shear Creep  
According to the above analysis results of the characteristics of the shear-creep test curve, the following empirical formula was proposed to fit the graded shear-creep test curve:  
\[u=u_{0}+A(1-e^{-Bt})+Ct^{n} \tag{1}\]  
In the formula: \(u_{0}\) is instantaneous deformation, at constant stress level, \(A\), \(B\), and \(C\) are all constant; \(t\) is creep time; \(A(1-e^{-Bt})\) characterizes the attenuation creep deformation characteristics of muddy interlayer; and exponent \(n\) represents the creep deformation characteristics of muddy interlayer after attenuation creep at different shear stress levels.  
In view of the large number of data, Table 2 only gives the fitting parameters of the corresponding shear stress under the normal stress 100 kPa and 200 kPa obtained by empirical formula. The variation range of \(R^{2}\) is 0.90-0.99, which shows that the proposed empirical formula can well simulate shear creep. The curve is drawn according to the data sorted out by the fitting formula and compared with the experimental data, as shown in Figure 9. From Table 2 and Figure 9, it is evident that when the normal stress is 200 kPa, the empirical formula exhibits less-than-optimal fitting for the application of the final level of shear stress. In this case, the \(R^{2}\) value is 0.91. However, for all other normal  
Figure 8: Vertical compression displacement variation diagram under different normal.  
stress levels, the empirical formula shows good fitting results. This suggests that the empirical formula effectively captures the instantaneous deformation, initial creep and steady-state creep of muddy interlayer stratification but falls short in fitting the accelerated creep. Other researchers have also employed different empirical formulas. [PERSON] (2018) used a logarithmic function to fit the creep curve when investigating the creep characteristics of mud stratification. [PERSON] et al. (2019) utilized a power function to fit the changes in shear creep deformation over time in muddy layers, achieving good fitting results. Considering the stronger creep characteristics of cohesive mud stratification, these alternative empirical formulas may not be suitable for our study.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Normal Stress/kPa** & **Shearing Stress/kPa** & \(\mathbf{u_{0}/mm}\) & \(\mathbf{A}\) & \(\mathbf{B}\) & \(\mathbf{C}\) & \(\mathbf{n}\) & \(\mathbf{R^{2}}\) \\ \hline \multirow{6}{*}{100} & 7 & \(6.5750\times 10^{-4}\) & 0.0026 & 17.6874 & 0.0037 & 0.3265 & 0.99 \\  & 14 & 0.0022 & 0.0043 & 9.1325 & 0.0024 & 0.5170 & 0.99 \\  & 18 & 0.0040 & 0.0066 & 15.5837 & 0.0031 & 0.5658 & 0.99 \\  & 21 & 0.0066 & 0.0075 & 23.4534 & 0.0039 & 0.6226 & 0.99 \\  & 35 & 0.0086 & 0.0093 & 28.3479 & 0.0060 & 0.6357 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter fitting values of empirical formula.  
Figure 9: Comparison between the calculated value of empirical formula and the experimental value under different normal stress ((**a**) \(\sigma\) = 100 kPa, (**b**) \(\sigma\) = 200 kPa, (**c**) \(\sigma\) = 300 kPa, (**d**) \(\sigma\) = 400 kPa).