Multiple underground excavations for various purposes including transportation tunnels, repositories for nuclear waste disposal and other types of waste, facilities for oil and gas storage, mining, etc., are under development at a global level. Moreover, the increasing demand in underground development has pushed the frontiers of the tunnelling field, with numerous projects taking place at great depths and under high magnitude stresses. Numerical modelling and its relevant advances have proven to be a valuable tool in the engineer’s arsenal by providing useful insights in the material response during an excavation.
However, and especially at great depths, the employed numerical technique lays heavily on the in situ stress regime and the in situ material properties, such as strength and deformability, that control the ground behaviour during an excavation. Previous and current research at the Queen’s Geomechanics Group and the Royal Military College of Canada focuses on the modelling of such diverse tunnelling conditions with a view to address potential implications and the integration of the appropriate numerical modelling technique into the design process.
NUMERICAL MODELLING
Over the last decades a number of different numerical approaches have been developed to address different problems within the engineering field. More specifically for the simulation of rockmasses continuum approaches such as the finite element method (FEM) and the finite difference method (FDM) have been widely used for the simulation of tunnel excavations, followed by discontinuum mechanics numerical techniques such as the distinct element method (DEM), coupled numerical models utilizing both discrete and finite element techniques (coupled FEM-DEM), and hybrid methods such as the finite-discrete element method (FDEM) that utilizes the use of finite elements and discrete modelling algorithms.
Each modelling technique is aiming for the simulation of specific rockmass conditions given the strength of the intact rock, the degree of jointing, the strength of joints and other material properties, with the modelling results depending on these parameters and the as accuracy of their estimation. Especially for rock materials in nature, these parameters can be highly variable as they cover a wide range of materials including massive rockmasses with no or few joints, jointed rocks with non-persistent joints, moderately jointed materials with persistent joints forming complete blocks, heavily jointed rockmasses, highly weathered jointed rocks that resemble soils, etc. Therefore, this may rise significant challenges in their simulation.
SIMULATING EXCAVATIONS IN WEAK, SOFT ROCKS
The response of weak, soft rockmasses (fractured, soft rockmasses with persistent joints, moderately to heavily fractured materials, weathered rocks) during an underground excavation is the result of the combined effect of the properties of the intact rock and the rockmass structure, the effects of which are incorporated together to create an “equivalent” continuum medium by assuming that is homogeneous and isotropic.
For very blocky rockmasses that is a valid assumption given the fact that no specific joints control the rockmass behaviour, hence no specific plane of weakness can be identified, and the material behaviour is controlled by the overall rockmass shear strength. In such cases, the rockmass can be safely assumed to be a material with an elasto-plastic behaviour and continuum analyses can provide good estimates. A characteristic example is the extensive work conducted by Vlachopoulos (2009) at the Driskos Tunnel in Northern Greece (Figure 1), which was excavated in flysch, a material mainly consisting of thin to medium bedded alternations of siltstones and sandstones (Figure 2).
The combined effect of a low rockmass strength with a relatively high overburden (approximately 220m) led to highly squeezing conditions successfully captured by elasto-plastic continuum models (Figure 3). Further work by Vlachopoulos and Diederichs (2009) utilized elasto-plastic continuum models in 2D and 3D to associate the development of the plastic zone surrounding an excavation, as a result of shear failure, and the expected convergence in a tunnel with the advancement of the excavation face, better known as the Longitudinal Displacement Profile (LDP) approach (Figure 4).
NUMERICAL SIMULATION OF HARD ROCK EXCAVATIONS
Shear failure based models capture relatively well the behaviour of weak, soft rockmasses in tunnelling environments. However, within hard highly interlocked rockmasses with non-persistent joints shear failure based criteria integrated into continuum codes cannot capture the fracturing mechanisms.
Fracturing triggered by the loss of confinement in high magnitude in situ stress regimes during the tunnel advancement and brittle rock failure are better captured by using discontinuum based approaches. Research conducted at Queen’s Geomechanics Group using the finite-discrete element method (FDEM) showed how such an approach can capture the brittle response of a hard rock excavation.
More specifically, by using field observations from the Underground Research Laboratory (URL) Test Tunnel in Manitoba (Diederichs 2007) (overburden 420m), a tunnel scale model created in Irazu (Geomechanica 2017) was calibrated to capture the fracturing mechanisms and the replication of the “v-shaped” notch failure observed at the URL Test Tunnel (Figure 5) which was excavated within a massive, “fracture-free” granite. The numerical model was able to capture the rockmass failure in extension due to the high compressive stresses at the crown and the floor of the tunnel. Recorded stress paths from the numerical model are in a good agreement with proposed rockmass strength models for brittle fracturing, hence showing the great potential of the method (Figure 6).
SIMULATION OF DISCONTINUITIES
For the successful modelling of a tunnel project within a rockmass it is critical to incorporate the discontinuities observed in the material in a fashion that is going to be both mechanically and computationally efficient. Weak, highly fractured rockmasses simulated using continuum based modelling are usually not explicitly incorporating rock joints. The effect of the discontinuities in such cases is integrated in the model by appropriately reducing the shear strength of the rockmass based on the degree of jointing and the joint condition. Work by Vlachopoulos (2009) utilized the Geological Strength Index (GSI) (Marinos and Hoek 2000) estimated at the Driskos Tunnel in order to achieve the required rockmass strength reduction by using the Hoek-Brown criterion (Hoek et al. 2002) in 2D and 3D numerical models. On the contrary, hard rockmasses with nonpersistent joints require the explicit simulation of them within the numerical model to capture the material response during an underground excavation.
Furthermore, non-persistent joint systems in nature can have variable geometries depending the in situ conditions. In order to capture this variability, discrete fracture network (DFN) modelling may be employed.
Research by Vazaios et al. (2017) focused on acquiring discontinuity geometrical data from an unsupported railway tunnel in Brockville, Ontario using LiDAR (Light Detection and Ranging) and used DFN modelling in order to replicate the joint network geometry for that given rockmass. The simulated joints can then be extracted and imported into discontinuum codes in order to replicate the fracture conditions of a specific site (Figure 7).
ASSESSING THE EXCAVATION DAMAGE ZONE (EDZ)
By adopting the appropriate numerical method, tunnel scale excavations can be successfully simulated and provide a great insight of the expected rockmass response that can assist and optimize the engineering design.
Numerical models that can capture the failure mechanisms in a realistic manner can provide reasonable estimates of the extent of the stress induced damage as a result of an underground excavation and the subsequent stress redistributions. That is of great importance as excavation induced damage changes the properties of the surrounding ground, with the extent of this altered material depending on the initial rockmass strength and field stresses. Especially for underground excavations, and given specific site conditions and project requirements, estimating relatively accurately that damage extent is critical.
Within weak rockmasses twin tunnelling for instance is a rather characteristic example. Excavation induced damage due the excavation of the first branch alters the rockmass properties and affects the second boring if the damage extent exceeds that of the pillar between the two tunnels (Figure 8). Regarding hard rock excavations, the interaction of stress induced fractures and pre-existing, non-persistent joints is a significant issue that may rise–especially in cases where the underground development is for the purpose of storage of substances that are required to stay in isolation from the ground surface, such as nuclear waste for instance. In such cases the numerical model has to be able to capture the fracture mechanics of the intact rock bridges between the pre-existing joints and reasonably predict their interaction (Figure 9).
CONCLUSIONS
Numerical modelling for deep excavations can be a great asset in the design toolbox of a tunnel engineer. Given that the appropriate method for specific site conditions and project specifications is adopted, numerical models can provide a great insight of the rockmass response during an excavation, assist in the design process, and be an integral part of the observational tunnelling approach in which numerical models and field observations are coupled to provide solutions and optimize the project’s design. Numerical models developed with caution and by making reasonable assumptions can estimate excavation induced damage extents and help with determining the support system required for a given project. However, they are subjected to limitations.
Employed methods, determination of the required input parameters, constitutive assumptions, required computational time, and level of realism achieved from the model are only some of the factors that need to be taken into account for the development of a numerical model that is going to be representative and correspond to the in situ conditions (Figure 10).
A tunnel model that is not obeying in the field conditions it is meant for can result in significant misinterpretations, hence misleading the engineer and resulting in a design that is not appropriate for the specific ground conditions.
