# Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model
## 1 Introduction
At the Terminal 5 site, the clay was of high to very high plasticity, in which the plasticity index (_PI_) averaged around 40% (minimum of 33% and maximum of 49%), while the liquid limit (_LL_) was between 65 and 70%. The same lithological unit at St. James's Park had similar index properties, with an average mass water content of 20% to 25% and a unit weight varying between 20 kN/m\({}^{3}\) and 22 kN/m\({}^{3}\)[27]. The coefficient of permeability of London clay typically varies between \(k=1\times 10^{-9}\) m/s and \(k=1\times 10^{-10}\) m/s. In terms of the strength effective stress parameters, the apparent cohesion is characteristically taken as \(c^{\prime}=0\), while the angle of shear resistance ranges from a peak of \(\Phi^{\prime}=25^{\circ}\), to a large strain of \(\Phi^{\prime}=20^{\circ}\), and to residual values of \(\Phi^{\prime}=12^{\circ}\)[26]. Following progressive digitalisation of the test control and instrumentation in the laboratory, further research highlighted the importance of structure in governing the behaviour of London clay [18; 28]. In this context, the role of anisotropy at small and large strain levels [29; 30] and the influence of recent stress history, creep and rates of loading on stiffness at small strains [28; 31] were extensively studied. A comprehensive overview of the role of structure in the behaviour of London clay at different observed scales was given by [PERSON] and [PERSON] [32]. They highlighted that unfissured samples were found to be considerably stronger than equivalent reconstituted samples at similar void ratios and stress levels, while this effect was less pronounced in terms of stiffness, in particular at small strains. Using scanning electron micrographs (SEMs), [PERSON] et al. [28] showed significant differences in the micro-fabric between natural and reconstituted samples, so that a denser and more orientated packing of natural samples was found at greater depths. An increase in the anisotropy of stiffness with depth was found to be dependent on the increased stress level and the change in the sub-unit. This was manifested as an increase in the ratio of anisotropy (defined in terms of the ratio of the horizontal to the vertical Young's modulus; \(\rm E_{h}/E_{v}\)), starting from slightly less than 2 at the top of strata to nearly 3 at 30 m depth. Additionally, the ratio of shear moduli remains nearly constant at around 1.5 at all depths, as previously observed by [PERSON] et al. [33]. In terms of the macro-fabric, the natural fissures are found within the London clay at all depths and present principal manifestation of a noticeable anisotropy of strength [30]. It was also shown that the presence of fissures can significantly lower the peak strength of a sample, when compared to samples which fail due to strain localisation. [PERSON] et al. [18] found that structure has a pronounced effect on the compressibility and strength of London clay, and a significant effect on the anisotropy of stiffness and strength. These effects were observed to be relatively stable and do not break down rapidly with straining, particularly in compression [34]. The 3 SKH (three-surface kinematic hardening) model of [PERSON] [7] (Figure 1) was also used to model natural London clay. Apart from the yield surface and bounding surface, the third history surface is defined as an envelope of points where the stiffness no longer depends on the previous loading history. Both the BRICK and 3 SKH models were used effectively to model the behaviour of London clay, notwithstanding that neither of the two models expressly account for the effects of anisotropy and structure. The 3 SKH model was improved by [PERSON] et al. [35], further referred to as the M3-SKH model, for the generalised three-dimensional (3D) stress state. The improvement contained a different hardening modulus, to model a smooth elastic-plastic transition, compared to the original 3 SKH formulation, in which a marked drop in stiffness occurred once plasticity was engaged.