# Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model
## 4 Validation of the SA_BRICK Model
### Verification of the Modelling of Anisotropy
Calibration of the SA_BRICK Model against the Results of Laboratory Testing on the Samples of Natural London Clay  
As already mentioned, [PERSON] [45] did not use the string lengths suggested by [PERSON] [8] in discretizing the S-curve, but adapted them to fit the stiffness degradation curves determined for London clay by [PERSON] [47]. This was understandable, as there was no attempt to model the structure. In the formulation of the SA_BRICK model, a different approach was taken so that the string lengths determined by [PERSON] [8] were treated as model parameters and were not changed. Instead, the effect of structure on the stiffness degradation S-curve was implemented, using the parameter \(\alpha\) by [PERSON] and [PERSON] [16], as explained in the previous section. Table 3 provides basic input data for SA_BRICK model. Parameter values for anisotropy are taken according to [44] and did not change during the analysis. The parameters \(\lambda\) and \(\kappa\) for London clay were determined on the basis of oedometer tests [47]. The length of  
Figure 7: Validation of the SA_BRICK model against the A_BRICK model [44] on laboratory samples 10.1 UC and 10.2 DE: (**a**) \(q\)-\(p^{\prime}\) diagram; (**b**) \(q\)-\(e_{y}\) diagram; (**c**) \(u\)-\(e_{y}\) diagram; (**d**) \(\varepsilon_{y}\)-\(\varepsilon_{\text{vol}}\) diagram (only for sample 10.2 DE). the strings was modified by the factor _fSL_ = 0.8, which corresponds to a basic angle of shearing resistance of 20.5\({}^{\circ}\). To model the structure, the laboratory results were best characterized by the value \(\alpha\) = 1.2 for the strength, and by the value of \(\omega\) = 0.85 for the stiffness. Anisotropy parameters were accepted after [44], with parameter \(\upsilon_{hh}\) approximated as zero, as previously taken by other researchers [42,49]. Geological history was evaluated for the given site of Heathrow Airport Terminal 5 [26,47], from where the samples were taken. Generally, the modelling of geological history included the deposition of clay (sedimentation) and the erosion of 175 m of London clay, which was followed by the subsequent deposition of 6 m of gravel (Figure 8). Both structure and anisotropy were modelled after the end of sedimentation and before erosion, which was then followed by the deposition of gravel. Modelling of geological history was followed by the unloading caused by sampling, and after the establishment of the initial stress state through isotropic compression, the exact stress path (e.g., shearing in compression or extension) was modelled as in the triaxial test as used by [PERSON] [47]. In this research, the samples from lithological unit B2a were chosen for the analyses. The intention was to be compatible with the depth of excavation of the twin tunnels under St. James's Park, the modelling of which will be explained in the next section (the tunnel tubes are located at a depth of between 20 and 30 m). The validation results on samples from unit B2a are shown in Figures 9 and 10. Each figure contains three diagrams: \(q\)-\(p^{\prime}\) diagram, \(q\)-\(e_{a}\) diagram and \(G_{sec}\)-\(e_{s}\) diagram so that important aspects of mechanical behaviour can be evaluated. Figure 11 additionally contains a \(\Delta u\)-\(e_{a}\) diagram, since the measurements of pore pressure were available for this test. Figure 9 shows the validation results of the SA_BRICK model on samples 23 gUE (undrained extension),