# Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model
## 5 Analyses of the Settlement Trough
### Modelling of the Excavation of the Jubilee Line Tunnels at St. James's Park
The aim was to determine the parameters that most adequately describe the stiffness degradation obtained in the laboratory. It should be noted here that the existing experimental data did not include stress paths that would allow the calculation of the parameter T (ratio of the size of the history surface relative to the size of the bounding surface), so it was determined based on values given by [PERSON] [51]. Due to this uncertainty, two sets of input data were used to encompass a range of reliable input data. These were named \"previous soft\" and \"new data\" to retain the same notation as in [52]. It should be noted that \"previously soft\" data refer to a softer response of laboratory samples and that exclusively \"new data\" were used for validation of the SA_BRICK model. For comparison purposes, we provide the full set of input parameters for M2-SKH and M3-SKH models that were used in ICFEP analyses in Table 4[52]. The programs PLAXIS and ICFEP differ in the form of the elements that can be generated in the finite element mesh. To achieve comparability of the number of Gaussian points in both programs, the triangular finite elements with 15 Gaussian points were used for calculation in the PLAXIS program. The input parameters for the BRICK and SA_BRICK models are given in Tables 1 and 3, respectively. To initiate the models, it was necessary to determine initial stresses and states by calculating the positions of strings and tension states of bricks prior to the excavation of the tunnel. These were determined using the single-element NAPgeo program by simulating the geological history up to the point of sedimentation for the same input parameters. State values, string position and the stress states were further copied to a separate file which was used as an input to start the PLAXIS analysis. The geologic history was further modelled assuming an additional thickness of 175 m of London clay above the existing profile, which was removed gradually, so that up to 20 m of clay was removed in each step to mode erosion. Apart from the mesh generation, the PLAXIS and ICFEP programs also differ in the method of modelling the excavation tunnel and lining placement. However, the program PLAXIS enables automatic modelling of the installation of the lining after a previously determined percentage of volume reduction, which is an equivalent procedure the \"volume loss\" method. In both PLAXIS and ICFEP analyses, made ground and gravel deposits (terrace gravel) were modelled using the Mohr-Coulomb model and the input parameters given in Table 5.  
Apart from the effect of anisotropy [42; 53; 54], the prediction of deformations in over-consolidated soils, such as London clay, is highly dependent on the initial horizontal pressure at rest \(K_{0}\), as highlighted in previous numerical studies (e.g., [55; 56]). It was,  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline _Model_ & \(N\) & \(\lambda^{\bullet}\) & \(\kappa^{\star}\) & \(A\) & \(n\) & \(m\) & \(\varphi^{\prime}\)  
therefore, necessary to check the predictions of the \(K_{0}\) profile for all the models used prior to the modelling of tunnel excavation. The predicted \(K_{0}\) profiles for the models BRICK and SA_BRICK are shown in Figure 13 along the prediction curves of M2-SKH and M3-SKH obtained for the same profile [51]. As a reference, the prediction based on empirical correlation of Mayne and Kulhawy [57] for overconsolidated clays is also presented in the same figure. It can be seen in Figure 13 that despite different approaches, the \(K_{0}\) profiles are in good agreement for all four models used. It should be observed that at the depths of tunnel excavations (e.g., between 20 m and 30 m), the values for \(K_{0}\) are close to 1.0 for all model predictions, including the empirical approach.