# Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model
## 2 Development of the BRICK Model  
### Original BRICK Model Formulation  
Different versions of the BRICK model have been developed, so far giving satisfactory numerical predictions for various geotechnical problems. The original BRICK model in plane strain was developed [8] specifically to model natural London clay, although not accounting for structure. The BRICK model was originally developed to model the recent stress history effect [6] using an analogy of a man dragging a series of bricks on strings behind him in a strain space at different lengths (Figure 2). As the man changes his direction of movement, the various strings become loose until the bricks re-engage, so that the strings fall into line behind the man again and become tight. The model is formulated so that the movement of each brick directly represents the development of plastic strain for a specified proportion of the material. This means that the model behaviour is fully elastic when all strings are loose. In contrast, the behaviour is fully plastic when all strings are tight, so that the bricks are lined up behind the man and are normal to the volumetric strain axis. It is assumed that only elastic strains cause stress changes. The effect of recent stress history is,  
Figure 1: The 3 SKH model surfaces in the \(q-^{\prime}\) plane (after [7]). therefore, modelled by the disposition of memory points defining the approach loading path [8], so that the stiffness decay curve is essentially a model parameter (as each brick corresponds to plastic strain for a specified proportion of the material, the string lengths define the shape of the stiffness decay curve). The important feature of the model is that if the tangent shear modulus \(G_{tun}\) is normalised by the mean stress, \(s^{\prime}=(\sigma_{x}{}^{\prime}+\sigma_{y}{}^{\prime})/2\), and then plotted against the shear strain, \(\gamma\), the area under the curve is equal to \(sin\,\phi^{\prime}\). The original BRICK parameters used to model the London clay are presented in Table 1. The string lengths are defined against normalised shear modulus \((G/G_{max})\) to cover the full range of shear strains. The parameters \(\lambda^{*}\) and \(\kappa^{*}\) are the gradients of the compression and swelling lines in the \(\varepsilon_{v}-\ln\,p^{\prime}\) plane. The parameter \(\iota\) defines the ratio of elastic stiffness to mean effective stress \(p^{\prime}\), and \(\
u\) is the Poisson's ratio. The BRICK model adopts a linear relationship between the logarithm of the overconsolidation ratio (OCR) and stiffness, whereas the original parameter \(\beta\) is divided into two components, \(\beta^{G}\) and \(\beta^{\phi}\), to separate the influence of overconsolidation on the stiffness and strength, respectively. The original formulation of the BRICK model was successfully used to evaluate the deformation and stability response of the platform in the North Sea [36], which was founded on heavily overconsolidated and structured clays. The effect of structure was accounted for by a careful calibration of the artificial degree of consolidation, which was needed to accurately model undrained shear strength of a structured stiff clay. \begin{table}
\begin{tabular}{c c} \hline
**String Length** & \(G/G_{max}\) \\ \hline \(8.3\times 10^{-5}\) & 0.92 \\ \(2.1\times 10^{-4}\) & 0.75 \\ \(4.1\times 10^{-4}\) & 0.53 \\ \(8.3\times 10^{-4}\) & 0.29 \\ \(2.2\times 10^{-4}\) & 0.13 \\ \(4.1\times 10^{-4}\) & 0.075 \\ \(8.2\times 10^{-3}\) & 0.044 \\ \(2.1\times 10^{-2}\) & 0.017 \\ \(4.1\times 10^{-2}\) & 0.0035 \\ \(8.0\times 10^{-2}\) & 0 \\ \(\lambda^{*}=0.1\), \(\kappa^{*}=0.02\), \(\iota=0.0041\), \(\upsilon=0.2\), \(\beta^{G}=4.0\), \(\beta^{\phi}=4.0\), \(n=1\) \\ \hline \end{tabular}
\end{table} 
Table 1: BRICK soil model input parameters for the modelling of London clay (after [PERSON], [8]).