# Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model
## 5 Analyses of the Settlement Trough
### Results and Interpretation of the Analyses  
#### 5.2.1 Modelling of the Excavation of the West Tube  
A particular feature of the analyses is the modelling of the high percentage of volume loss recorded during the excavation of the tunnel, which was 3.3% for the west tube and 2.9% for the east tube. This was a much higher volume loss than expected, which on average for London clay is between 1.0 and 2.0% [58], where a 2% is regarded a conservative estimate.  
The results of modelling of the excavation of the west tube using all four kinematic hardening models are shown in Figure 14 and the annotated field data was taken from [27]. All the graphs are shown relative to the axis of the west tube, which was excavated first. It can be seen in the figure that the largest settlements of 11.2 mm are predicted by the M3-SKH \"previous soft\" model. The SA_BRICK model predicts settlements of 10 mm while the BRICK model predicts those of 8.9 mm. However, the maximum measured settlement [20], labelled as field data, was for the west tube in excess of 20 mm, which was much higher than expected. [PERSON] and [PERSON] [27] attributed the causes of excessive volume loss to the fact that up to 1.9 m of unsupported tunnel heading was often advanced ahead of the shield, and as a result, about 50% of the measured volume loss occurred in front of the shield. They also commented that this division of the London clay contained sand and silt partings, giving potential for loosening and softening above the tunnel and well ahead of the shield. As indicated by [PERSON] at al. [59], instabilities in the shield excavation  
Figure 13: Initial \(K_{0}\) profiles for different constitutive models used in the analyses with empirical correlation of [PERSON] and Kulhawy [57] as a reference.  
can be also significantly affected by the anisotropy of soil strength on ultimate supporting force, which can be also a cause of increased volume loss.  
In terms of the accuracy of the prediction, the normalized graphs give a better representation of the narrowness of the settlement trough, which is the critical parameter for the possible impact of the tunnel excavation on the structures on the surface [60]. The normalized curves are, in practice, compared with the Gaussian distribution, which is widely accepted as a reference empirical curve [61], giving a fairly accurate general representation of the magnitude and lateral extent for the settlement trough.  
The vertical movements, normalized by the maximum settlement of the individual analysis are shown in Figure 15 together with the Gaussian distribution and the normalised settlement measured on the site. It can be seen in the figure that the Gaussian curve is the most approximate, with the prediction of SA_BRICK and M3-SKH as \"previous soft\", but both still deviate from the field models measurement. It should be noted that the SA_BRICK model was calibrated against \"new data\" which illustrate a much stiffer behaviour and not \"previous soft\" as M3-SKH in this case.  
There is also a distinctive difference between the prediction of the BRICK and SA_BRICK models, in which the SA_BRICK model gives a much narrower settlement trough. This result substantiates the appropriate choice of parameters and adequate implementation of both structure and anisotropy in the SA_BRICK model. Apart from that, it can be observed that the field data give a much narrower settlement trough than the Gaussian distribution curve. As already discussed, this fact is attributed by [PERSON] and [PERSON] [27] to an unexpectedly high volume loss at this section of the tunnel.