# Assessing the Sustainability of Alternative Shaft Construction Methods
## 3 Numerical Model
### Calibration of the Dublin Boulder Clay Units  
The calibration of IC MAGE M06 [45; 48] followed a hierarchical approach, where each parameter was estimated sequentially and the order was set by its physical relevance and by its independency from other values [49; 50; 51]. The first aspect of the model to calibrate is determining the shear stiffness at very small strains (term (1) in Equation (3)). Using as a reference the results plotted in Figure 3a of different field tests (MASW, seismic refraction and cross-holes), performed at the WA2 shaft site and in other locations in Dublin with a similar profile [37; 52], the evolution with the depth of the shear stiffness at very small strains (\(G_{max}\)) was interpreted, allowing for the definition of parameters \(G_{ref}\) and \(m_{G}\) for all DBC units. Given the variability observed in the field tests, it was decided to adjust the parameters so that the average stiffness was reproduced. It should be noted that given the weathered nature of the UBrBC, and in agreement with the field tests results, a constant \(G_{ref}\) of 220 MPa was adopted for this unit (i.e., \(m_{G}=0\)).  
Based on the results of conventional triaxial compression and extension tests, and as suggested by [PERSON] and [PERSON] [37], a value \(\varphi^{\prime}=36^{\circ}\) was adopted for the strength at the critical state of all units. The parameters of the compression and swelling lines were adopted following the revisited analysis performed by [PERSON] et al. [41], where the authors defined a set of different values for Brown and Black Boulder Clay units, regardless of their position (Upper or Lower) in the ground profile. Finally, the Hvorslev surface (shape and potential) and the shear stiffness degradation (term (2) in Equation (3)) were calibrated against the triaxial data presented by [PERSON] and [PERSON] [37]. It is worth mentioning that since no test results were available to calibrate the LBkDC unit, it was assumed that its parameters were identical to those of the UBkBC unit, with the exception of \(G_{\textit{ref}}\), which had a higher value, reflecting the deeper position of that layer.  
Table 1 in Appendix A summarizes all parameters of the IC MAGE M06 model adopted for all the DBC units considered in the analysis. Moreover, numerical reproductions of the oedometer and triaxial (compression and extension) tests that were used to calibrate the constitutive model are also shown in Appendix A. The results demonstrate a very good agreement between the numerical and measured data for all units, validating the adopted calibration process.  
A final aspect required for the numerical simulation is related to the definition of the OCR profile at the WA2 shaft site. Unfortunately, there are no records of this state parameter available in the literature, and its estimation had to be performed indirectly based on the undrained shear strength (\(\mathrm{S_{u}}\)) profile. Figure 3b presents the \(\mathrm{S_{u}}\) values measured in triaxial compression and extension tests performed on DBC samples [37]. Although scatter and some discrepancies between compression and extension can be observed, the Irish practice usually considers an isotropic undrained shear strength defined by the profile presented by the solid black line [37]. A value of 60 kPa in the weathered UBrBC is generally assumed, and in the remaining units, a value of 300 kPa is commonly adopted. Based on this \(\mathrm{S_{u}}\) profile, an equivalent OCR profile was derived using the closed-form solution of IC MAGE M06 [45] and introduced into the model as an initial state condition.