## 3 Parameter Identification
### Permeability  
Laboratory tests and field tests were carried out on the samples, which were the falling head permeability test and ring inflitrometer test, respectively. For a ring inflitrometer test, one ring is rammed into the ground and is filled with water. Water is added until \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{c^{\prime}}\) **(kN/m2)** & \(\mathbf{\varphi^{\prime}}\) **(c)** \\ \hline
5\% fractile & 12.5 & 18.1 \\
95\% fractile & 45.8 & 20.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Limits for the shear parameters as 5% and 95% fractiles of the shear strength of the upper layer. Figure 8: Mohr’s circles of soil samples and resulting shear strengths of Mohr-Coulomb. (**a**) Samples MG, G1, and G2 (in total 9 stress levels) for the upper glacial deposit layer; (**b**) sample M (in total 3 stress levels) for the lower marl layer. Figure 9: Result of the Bayesian approach based on experimental data of samples MG, G1, and G2. The stress range used for linearization is depicted by vertical blue dashed lines. \(\sigma_{2}\) is the lateral stress given by the confining pressure in the consolidated drained triaxial test, and \(\sigma_{1}\) is the axial stress by measurement in the CD test. reaching a quasi-stationary flow to keep the water level steady. The hydraulic conductivity is backcalculated by monitoring the time and the amount of added water [60]. The resulting coefficients of permeability for different layers are listed in Table 5.  
For the upper layer, the soil experienced long travel distances in its emergence. Therefore, no predominant discontinuities were expected or observed during the field campaign. Reconstituted samples on homogeneous material should reveal realistic values for the permeability. There are also many empirical relations available for determining the permeability coefficient based on the particle size data, e.g., Kozeny-Carman formula, Breyer formula, Terzaghi formula, etc. [61; 62; 63; 64; 65; 66; 67; 68; 69; 70] which can be used for validation. These empirical formulas have limitations. The \(d_{10}\) (10% of the weight of the soil sample is finer than this grain diameter) of our samples in the upper layer was very small and the uniformity coefficient was relatively large, so the conditions for most empirical relations were not fulfilled. However, the Kozeny-Carman (KC) equation for estimating the soil permeability was appropriate for this case and utilized for the validation to ensure the plausibility of the experimental data:  
\[k=\frac{g}{\
u}\times 8.3\times 10^{-3}\left[\frac{n^{3}}{(1-n)^{2}}\right]d_{10} ^{2} \tag{1}\]  
Therein, \(k\) is the permeability; g is the acceleration due to gravity; \(\
u\) is the kinematic viscosity, which can be obtained from the dynamic viscosity (\(\mu\)) and fluid (water) density (\(\rho\)):  
\[\
u=\frac{\mu}{\rho} \tag{2}\]  
The porosity \(n\) can be derived from the empirical relationship [63]:  
\[n=0.255(1+0.83^{C_{\mathrm{u}}}) \tag{3}\]  
The coefficient of uniformity \(C_{\mathrm{u}}\) is given by: \(C_{\mathrm{u}}=d_{60}/d_{10}\) (\(d_{60}\) and \(d_{10}\) are the grain diameters for which 60% and 10% (by weight) of the sample is finer, respectively). According to the data from the particle size distribution test, the permeability coefficients of different samples in the upper layer could be derived by the Kozeny-Carman equation with the temperature of \(0^{\circ}\) or \(10^{\circ}\), for example, as shown in Table 6.  
The permeability coefficients of the samples MG, G1, and G2 calculated by the Kozeny-Carman equation were of the same order of magnitude and very close to each other (Table 6). These values were also close to the experimentally obtained permeability coefficients (Table 5), so it was considered reasonable to use 9 \(\times\)\(10^{-11}\) m/s as the coefficient of permeability for the upper layer in the calculation. Fractures, fissures, tension cracks, and other potential channels existed in the lower marl layer.