# Numerical Implementation of the Barcelona Basic Model Based on Return-Mapping Integration
## 3 Numerical Implementation
### Result Analysis  
Experimental results and numerical simulation results are shown in Figure 6. It can be seen from Figure 6 that the four groups of samples show obvious plastic processes during compression and recovery. The yield stress of samples SO-01\(\sim\)04 increased gradually, indicating that the water absorption process reduced the yield stress of the material. According to the fitted compression parameters during the compression process, the compression parameters of bentonite decreased gradually during the water absorption process. It can be seen from the elastic parameters fitted during the recovery process that the absorption of bentonite reduces the linear elastic modulus of the material.  
\begin{table}
\begin{tabular}{c c c c c c} \hline Paramter & **Unit** & **SP01** & **SP02** & **SP03** & **SP04** \\ \hline M & - & 1.07 & 1.07 & 1.07 & 1.07 \\ \(P_{08}\) (-) & MPa & 0.67 & 1.052 & 1.052 & 1.052 \\ \(P_{c}\) (-) & MPa & 0.01 & 0.01 & 0.01 & 0.01 \\ \(\lambda_{0}\) & - & 0.1352 & 0.104 & 0.106 & 0.12 \\ \(Kappa\) & - & 0.0687 & 0.034 & 0.0308 & 0.024 \\ \(Kappa_{s}\) & - & 0.03 & - & - & - \\ r & - & 0.75 & 0.75 & 0.75 & 0.75 \\ \(\beta\) & - & \(0.25\times 10^{-6}\) & \(0.25\times 10^{-6}\) & \(0.25\times 10^{-6}\) & \(0.25\times 10^{-6}\) \\ \(\epsilon_{o}\) & - & 0.97 & 0.75 & 0.73 & 0.69 \\ \(k_{s}\) & - & 0.1 & 0.1 & 0.1 & 0.1 \\ \(\sigma_{x}\) & MPa & \(-1.52\) & \(-1.68\) & \(-1.443\) & \(-1.22\) \\ \(\sigma_{y}\) & MPa & \(-1.52\) & \(-1.68\) & \(-1.443\) & \(-1.22\) \\ \hline \end{tabular}
\end{table}
Table 3: Numerical parameters in suction controlled compression.  
Figure 6: Experimental and numerical void ratio vs. vertical stress of suction controlled compression. (**a–d**) corresponding to samples SO-01 to 04.  
Figures 7 and 8 show the displacement diagram of samples SO-01 and SO-02 respectively. As can be seen from Figures 7 and 8, the axial displacement of the model in the numerical calculation is small within the compression pressure of 0.5 MPa. When the compression load reaches 10 MPa, the model has significant displacement change and reaches the maximum displacement at the compression load of 50 MPa, and the model is mainly manifested as the deformation of the upper part of the model under compression. Then the displacement of the upper part of the sample decreases gradually with axial pressure decreasing. By comparing Figures 7 and 8, it can be found that the sample with smaller suction has a larger axial displacement, indicating that the water absorption process reduces the stiffness of the bentonite sample.  
Figures 9 and 10 reflect the strain cloud diagrams of samples SO-02 and SO-03 under six different compression pressures, respectively. It can be seen from Figure 10 that the strain generated by the model at 0.5 MPa is very small, and when the compression stress reaches 2.5 MPa, obvious strain occurs in the area near the symmetry axis at the upper end of the model. When the compression load reaches 10 MPa, the strain in the upper part of the model near the symmetry axis is large, while the strain in the bottom part of the model is close to 0. In the process of gradually unloading the compression load, the position near the symmetry axis at the bottom of the sample has obvious deformation. When the compressive stress is released to 0.5 MPa, sample SO-03 still maintains a large strain in the  
Figure 8: Displacement contour of SO-02 at (**a**) 0.5 MPa, (**b**) 2.5 MPa, (**c**) 10 MPa, and (**d**) 50 MPa in compression, and (**e**) 25 MPa and (**f**) 0.5 MPa in recovery.  
Figure 7: Displacement contour of SO-01 at (**a**) 0.5 MPa, (**b**) 2.5 MPa, (**c**) 10 MPa, and (**d**) 50 MPa in compression, and (**e**) 25 MPa and (**f**) 0.5 MPa in recovery.  
center area at the bottom, indicating that the model has a large stiffness under the condition of a large suction force.