HYBRID DESIGN ROCK SUPPORT | GROUND SUPPORT


stresses is primarily related to shear and bending, the analyses then focused on the stability analysis of these parameters. By further evaluation and comparison of the


distribution and size of the support loading and factor of safety (FS) in each of the pair models A1–A2 and B1–B2, it was possible to assess design optimisation possibilities.


7 SET UP OF THE NUMERICAL MODELS The UDEC models are built in plane-strain conditions, with elasto-plastic Mohr–Coulomb material, and the non-linear Barton-Bandis joint model (Barton and Bandis 1990). Such a combination of material and joint models is intended to be representative of the studied rock mass conditions where rock displacements are not only related to shear translations through existing joints but also to buckling failure of rock when subject to loading. The individual rock blocks were subdivided into a


mesh of finite-difference elements, the size of the mesh established on the basis of the rock mass conditions, the dominant failure mechanisms, and the size of the excavation. As such, the maximum element length was set to not exceed a value of 1m in the UDEC models, in line with modelling recommendations given by, among others, Lorig and Varona (2013) and Itasca (2011). Boundary conditions were set first by an external


geometry or box of 100m × 100m that contains the geological model and the tunnel in its centre. The external boundaries were constrained to zero- horizontal movement in the vertical walls of the box, and zero-vertical movement in the horizontal (top and bottom) sides of the box, to prevent the model rotating. Both in-plane and out-of-plane in-situ stresses were also applied. The modelled tunnel geometry was based on a D-shaped, 12.5m span tunnel, and updated to match the actual excavation profiles. Jointing in the models was simulated to replicate


the actual rock mass structure. However, some simplifications - typically one of the approaches Chen et al. (2001) - were included since the presence of joint contacts in UDEC modelling normally occupy a relatively large computational memory. The four models were calibrated before performing


the analyses. Tunnel deformations registered in monitoring were utilised as a basis for back-


Table 5: Model Profile


A1 A2 B1 B2 3+162 3+162 2+227 2+227


calculations. Rock and joint properties obtained from field and lab investigations were adjusted through an iterative process until consistent with measured behaviour. Bulk modulus (K) and shear modulus (G) of rock were also for the UDEC models. Calibration of numerical models performed on the


basis of deformation monitoring in hard rock tunnels is a widely used procedure in rock engineering. As pointed out by Sakurai (2017), it provides a rather useful posteriori rock engineering indicator reflecting the true response of a set of rock mass properties to tunnel excavation. However, the same author along with Walton and Sinha (2022) advises that the use of such a back-analysis process normally involves limitations and assumptions. For the two studied tunnel sections, the main


assumptions and considerations for the modelling and calibration processes were: ● Constitutive are assumed to capture the behaviour of layered hard rock and distinct joints subject to low levels of horizontal stress confinement;


● Field and laboratory investigations are representative of the ground conditions;


● No evidence of time-dependent or creep deformations;


● Displacements registered in the four MPBX and from several tunnel were assumed representative and measurements reliable;


● UDEC calculations are performed in computational steps or stages, which provide a representative simulation of the sequential installation of support.


● Material properties of the rock support elements are not subject to calibration;


● It is assumed that rock displacement is the parameter that best defines the behaviour of layered and hard rock subject to relatively low stresses. However, various combinations of input parameters used in the back-analyses can also yield a similar response.


As noted by Walton and Sinha (2022), however, there can always be remaining possibilities for reliability improvement since every parameter added to the back- analyses intrinsically adds a source of uncertainty. Due to the limitations of the methodologies (i.e., rock testing, in-situ testing, rock mass classification and mapping, numerical method) involved in the study, uncertainty and subjectivity can still remain. In that sense, we


Description of design stage Rock support design before tunnel failure Hybrid design Rock support design after tunnel failure Hybrid design


Design approach Empirical


Hybrid Empirical, numerical Hybrid


Face mapping at the face, rock mass classification with Q-system


Performed rock mass investigations Engineering geological report for tendering.


Face mapping at the face, core holes at failure area, lab testing, in-situ stress measurements, deformation monitoring


Investigations as for Model A1. Core holes at failure area


Face mapping at the face, core holes at failure area, lab testing, in-situ stress measurements, deformation monitoring


Above, table 5: Model description in relation to the design stage, design approach and performed investigations September 2025 | 27


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