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This study presents a three-dimensional numerical analysis of multiple fracture growth leading to spalling around nuclear waste deposition boreholes. Mechanical spalling due to stress amplification after drilling is simulated using a finite element-based fracture growth simulator. Fractures initiate in tension based on a damage criterion and grow by evaluating stress intensity factors at each fracture tip. Tip propagation is multi-modal, resulting in final fracture patterns that are representative of both tensile and shear failure. Their geometries are represented by smooth parametric surfaces, which evolve during growth using lofting. The corresponding surface and volumetric meshes are updated at every growth step to accommodate the evolving fracture geometries. The numerical model is validated by comparing simulated fracture patterns against those observed in the AECL Underground Rock Laboratory Mine-By Experiment. It is subsequently calibrated to simulate fracture initiation and growth around boreholes drilled in the Forsmark granodiorite, subjected to a far-field anisotropic triaxial stress that corresponds to the in situ stress model from the Swedish Forsmark site. The deposition tunnel is implicitly simulated by attaching the deposition borehole to a free domain boundary. Several geomechanical cases are investigated, in which fracture growth is numerically evaluated as a function of in situ stress state, tunnel orientation, borehole geometry, total number of boreholes and borehole spacing. Numerical results show that spalling occurs in all cases, given the underground conditions at Forsmark, with borehole geometry, spacing and stresses affecting the extent of fracture nucleation and growth patterns. The uncertainty in underground stress conditions is evaluated through varying stress magnitudes and orientations relative to the tunnel floor. Whereas tunnel orientation influences the relative locations where fractures initiate with respect to the tunnel floor, fracture growth and its final extent is determined by the relative magnitudes of the in situ stresses. Higher stress differential causes higher spalling depths, but in all cases, failure extent is localised to the borehole vicinity, not exceeding one borehole radius. The cylindrical borehole is modified at the top to provide an access ramp for the spent fuel canisters and fracture growth around several deposition boreholes is simulated for borehole tops having cylindrical, conical, and wedge shapes. The enlargement of the borehole top induces higher stress concentrations at the borehole–tunnel junction, increasing the severity of spalling closer to the tunnel floor. Massive failure occurs when a multiple borehole model is considered and the inter-borehole distance is small enough that adjacent “spalled” areas interact. At Forsmark, through-going fractures are predicted to develop when the borehole spacing is less than 4 m. The effect of spalling on the structural integrity of the deposition boreholes is illustrated for each test case and quantified in terms of maximum spalling depth, spalling width and total fractured surface area.

This paper presents a unified approach through which the influence of the elastic and strength anisotropy on wellbore instability can be thoroughly examined. The stresses at the wellbore wall are first calculated using the Lekhnitskii-Amadei solution, which accounts for elastic anisotropy. Then, shear failure is treated by combining the Mogi-Coulomb criterion for intact rock, with the Jaeger plane of weakness concept. The developed model accounts for all three principal stresses in predicting the onset of shear failure. The results of the specific case investigated show that rock elastic anisotropy induce higher stress concentrations. The difference, compared with the stresses found using the isotropic elastic model, could reach as high as 25% for the highest degree of anisotropy that might be expected for rocks of practical interest. The strengthening effect of the intermediate stress, as reflected in the Mogi-Coulomb criterion, reduces the required mud weight density by approximately 1.0 pounds-per-gallon (ppg). Furthermore, it is demonstrated that the risk posed by bedding slippage, for a wellbore with an inclination between 15° and 50° from the vertical, is masked when an isotropic elastic stress model is used. In contrast, the fully anisotropic model shows that an extra mud weight of approximately 4.5 ppg would be required, in order to avoid bedding plane slippage for the case under investigation. Although these results apply for a particular choice of strength properties and elastic properties, they give an indication of the implications of fully accounting for anisotropy and the effect of the intermediate stress when doing borehole stability analysis.

A fully coupled three-dimensional finite-element model for hydraulic fracturing in permeable rocks is utilised to investigate the interaction between multiple simultaneous and sequential hydraulic fractures. Fractures are modelled as surface discontinuities within a three-dimensional matrix. This model simultaneously accounts for laminar flow within the fracture, Darcy flow within the rock matrix, poroelastic deformation of the rock, and the propagation of fractures using a linear elastic fracture mechanics framework. The leakoff of fracturing fluid into the surrounding rocks is defined as a function of the pressure gradient at the fracture surface, the fluid viscosity, and the matrix permeability. The coupled equations are solved numerically using the finite element method. Quadratic tetrahedral and triangle elements are used for spatial discretisation of volumes and surfaces, respectively. The model is validated against various analytical solutions for plane-strain and penny-shaped hydraulic fractures. Several cases of simultaneous fracturing of multiple hydraulic fractures are simulated in which the effects of the various parameters (the in situ stresses, the distance between fractures, the permeability of the matrix, the Biot poroelastic coefficient, and the number of the fractures in a group) are investigated. The results show that the stress induced by the opening of the fractures, and the stress induced by the fluid leakoff, each have the effect of locally altering the magnitudes and orientations of the principal stresses, hence altering the propagation direction of the fractures. Opening of a fracture induces excessive compression (also known as the “stress shadow”) that causes adjacent fractures to curve away from each other. This excessive compression competes against the differential in situ stresses, which tend to cause the fracture to grow in the plane normal to the minimum in situ stress. The stress shadow effect is reduced by increasing the distance between fractures, and is increased by increasing the leakoff, which may be due to increased permeability of the rock, or an increase in the Biot coefficient.

Blast-induced fractures are simulated by a novel gas-solid interaction model, which combines an immersed-body method and a cohesive zone fracture model. The approach employs a finite element fluid model and a combined finite-discrete element solid model. This model is fully coupled and simulates the whole blasting process including gas pressure impulse, shock wave propagation, gas expansion, fragmentation and burden movement phases. In the fluid model, the John-Wilkins-Lee equation of state is introduced to resolve the relationship between pressure and density of the highly compressible gas in blasts and explosions. A Q-scheme is used to stabilise the model when solving extremely high pressure situations. Two benchmark tests, blasting cylinder and projectile fire, are used to validate this coupled model. The results of these tests are in good agreement with experimental data. To demonstrate the potential of the proposed method, a blasting engineering simulation with shock waves, fracture propagation, gas-solid interaction and flying fragments is simulated.

This paper aims to examine the validity of the discrete fracture network (DFN) method in representing a realistic two-dimensional fractured rock in terms of their geomechanical response to in-situ stresses and hydraulic behaviour in a steady state fluid field. First, a real fracture network is extracted from the geological map of an actual rock outcrop, which is termed the analogue fracture network (AFN). Multiple DFN realisations are created using the statistics of the analogue pattern. A conductivity parameter that was found to have a linear relationship with the conductivity of 2D fracture networks is included to further enhance network similarity. A series of numerical experiments are designed with far-field stresses applied at a range of angles to the rock domains and their geomechanical response is modelled using the combined finite-discrete element method (FEMDEM). A geomechanical comparison between the AFN and its DFN equivalents is made based on phenomena such as heterogeneity of fracture-dependent stress contours, sliding between pre-existing fracture walls, coalescence of propagating fractures and variability of aperture distribution. Furthermore, an indirect hydro-mechanical (HM) coupling is applied and the hydraulic behaviour of the porous rock models is investigated using the hybrid finite element-finite volume method (FEFVM). A further comparison is conducted focusing on the hydraulic behaviour of the AFN and DFNs under the effects of geomechanical changes. The results show that although DFNs may represent an AFN quite well for fixed mechanical conditions, such a representation may not be dependable if mechanical changes occur.

The cascading failure of underground pillar sections poses a risk to miners and surface structures. Assessing the risk of underground mining panels contributes to the prevention and control of the catastrophic failure. To resolve the challenge in quantifying the effect of failure of a single pillar on the risk of an entire pillar section, a new risk assessment model incorporating the stability of individual pillars and the load transfer between pillars was proposed to investigate the cascading failure of pillar sections. The load transfer process from failed pillars to adjacent ones was effectively quantified by the relationship between transferred incremental load and transferring distance. The influence of uncertainties of pillar strength, caused either by intrinsic strength variability of a single pillar (quantified by coefficient of variation COV) or the non-uniform deterioration process of pillar sections (quantified by correlation coefficient ρ), was investigated on the probability of cascading failure. Risk mapping was also performed on two representative historical collapsed pillar sections using the risk evaluation method proposed to illustrate the risk level of each pillar to trigger cascading failure. The proposed model could represent realistic load transfer process and provide reliable risk assessment results for pillar sections. The results showed that the reliability of pillar sections is significantly influenced by both intrinsic variability in pillar strength and intercorrelation of strength between pillars. The probability of cascading failure increases with increasing COV, which verifies that geological uncertainties increase the risk of collapse in pillar sections. The impact of COV on probability gradually decreases to negligible levels as ρ increases to 1, which means that the synchronous variation of pillar strength among a pillar section can significantly compensate for the impact of COV. The proposed approach provides a distinct perspective on understanding sudden failure of high-risk pillars and contributing to the risk control for abandoned pillar sections.