# Viscoelastic Strains of Palaeozoic Shales under the Burger's Model Description
## 4 Theoretical Basics of Rock Rheology in Triaxial Test Conditions for the Burger's Model
### Parameters of Burger's Model for the Paleozoic Shales from the Baltic Basin
For each creep test, the coefficient of determination R\({}^{2}\) was calculated (Table 1), determining the quality of estimation of the parameters of the [PERSON]'s model equations and the correctness of matching the model to the experimental test results. The obtained R\({}^{2}\) values indicate a good fit of the model to the creep results. For comparison of shale creep from the Baltic Basin with literature data as on Barnett, Haynesville, and Eagleford shale [27], as well as on Posidonia shale [24] we used a power law model proposed by [PERSON] and [PERSON] [27; 45]:  
\[\varepsilon_{creep}=Bt^{n} \tag{21}\]  
where \(B\) and \(n\) are constant. The analyses were performed for the load level of samples corresponding to approximately \((\sigma_{1}-\sigma_{3})/(\sigma_{1}-\sigma_{3})_{max}=0.5\), similar to the data of comparative literature tests. The results are given in Table 2. The literature data that were accepted for comparison, only horizontally oriented samples (bedding parallel) compared to those tested in this article, are presented in Table 3. From the Baltic Basin, the average values of parameters \(B\) and \(n\) were taken for comparison (Table 3, Figure 8). In Figure 8, the power law model parameter values determined for American shales [27] are shown in the appropriate ranges consistent with the data in Table 3.  
Considering that \(B\) essentially reflects the instantaneous elastic property of the rock [27], and that \(n\) determines the relative contribution of the time-dependent deformation to the total strain, a similar creep behavior of the compared shales can be observed. It is worth emphasizing that the testing conditions for the shales presented in our article were not exactly the same due to the different \(p_{c}\), and \(T\) conditions. When comparing the results, differences resulting from the mineralogical composition of individual formations should also be taken into account. Figure 8: Comparison of literature [24; 27] and this study power-law constitutive parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & **Sample** & \(\boldsymbol{(\sigma_{1}-\sigma_{3})}\) & \(\boldsymbol{B}\) & \(\boldsymbol{n}\) & \(\boldsymbol{\mathbf{R}^{2}}\) \\ \hline
**Location** & **Number** & \(\boldsymbol{\overline{(\sigma_{1}-\sigma_{3})}}_{max}\) & \(\boldsymbol{\mathrm{[MPa^{-1}]}\times 10^{-5}}\) & **[-]** & \\ \hline  & B-211-A & 0.65 & 1.6 & 0.043 & 0.93 \\  & M-30-B & 0.52 & 2.0 & 0.044 & 0.94 \\ Pelplin & W-260-A & 0.46 & 1.6 & 0.037 & 0.97 \\  & W-260-B & 0.52 & 1.7 & 0.045 & 0.97 \\  & W-264-A & 0.55 & 1.8 & 0.044 & 0.93 \\ \hline Average & & & 1.7 & 0.043 & \\ Standard dev. & & & 0.11 & \(4.4\times 10^{-5}\) & \\ \hline  & B-236-A & 0.41 & 1.7 & 0.023 & 0.94 \\ Paslek & W-277-B & 0.46 & 1.8 & 0.029 & 0.98 \\  & W-278-A & 0.56 & 1.9 & 0.032 & 0.98 \\  & W-278-B & 0.69 & 1.6 & 0.048 & 0.98 \\ \hline Average & & & 1.8 & 0.033 & \\ Standard dev. & & & 0.06 & \(3.4\times 10^{-4}\) & \\ \hline  & B-275-B & 0.52 & 2.6 & 0.040 & 0.99 \\  & B-279-D & 0.46 & 1.8 & 0.039 & 0.99 \\ Jantar & M-43B-B & 0.46 & 2.0 & 0.036 & 0.97 \\  & W-305-A & 0.49 & 2.0 & 0.048 & 0.76 \\  & W-306-A & 0.52 & 2.0 & 0.046 & 0.93 \\ \hline Average & & & 2.1 & 0.042 & \\ Standard dev. & & & 0.37 & \(1.1\times 10^{-4}\) & \\ \hline  & M-60-B & 0.60 & 1.9 & 0.036 & 0.96 \\ Sasino & M-62-A & 0.48 & 1.8 & 0.020 & 0.91 \\  & W-320-B & 0.42 & 2.4 & 0.027 & 0.82 \\ \hline Average & & & 2.0 & 0.028 & \\ Standard dev. & & & 0.17 & \(1.3\times 10^{-4}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Constant of the power law model for shales in the Baltic Basin. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Shale** & **Ref. ** & \(\boldsymbol{ \begin{array}{c}\boldsymbol{B}\\ \boldsymbol{\mathrm{[MPa^{-1}]}\times 10^{-5}}\end{array}