Hybrid Finite-discrete Element Research Articles

Mechanical analysis and interpretation of excavation damage zone formation around deep tunnels within massive rock masses using hybrid finite–discrete element approach: case of Atomic Energy of Canada Limited (AECL) Underground Research Laboratory (URL) test tunnel

The construction of an underground opening leads to changes in the in situ stress regime surrounding the excavation. The opening influences the rock mass owing to the redistribution of the stresses and results in the disturbance of the surrounding ground. At great depths, massive to slightly or moderately fractured rock masses are usually encountered, and under high stresses, they are more likely to behave in a brittle manner during an excavation. While constitutive models have been developed and proposed for the numerical simulation of such excavations using continuum mechanics, this brittle response cannot be simulated accurately enough, since the material behaviour is governed by fracture initiation and propagation. On the contrary, discontinuum approaches are more suitable in such cases. For the purposes of this paper, the brittle behaviour of hard, massive rock masses and the associated spalling failure mechanisms were simulated by employing a finite–discrete element method (FDEM) approach using Irazu software. The generated numerical model was utilized to replicate field conditions based on the observations at the Atomic Energy of Canada Limited (AECL) Underground Research Laboratory (URL) test tunnel located in Pinawa, Manitoba, Canada. The model results are compared with field observation data to explicitly demonstrate the suitability of the method.

A numerical study of stress variability in heterogeneous fractured rocks

We conduct numerical simulations to investigate the variability of local stresses in heterogeneous fractured rocks subjected to different far-field stress conditions. A realistic fracture network is constructed based on a real outcrop mapped at the Hornelen Basin in Norway. The heterogeneity of the rock material is modelled using a Weibull distribution of Young's modulus characterised by a homogeneity index m. As m decreases, the rock material becomes less homogeneous. The distribution of local stresses in the fractured rock under far-field stress loading is derived from a hybrid finite-discrete element model, and the stress variability is further analysed using a tensor-based formalism that faithfully honours the tensorial nature of stress data. The local stress perturbation is quantified using the Euclidean distance of each local stress tensor to the mean stress tensor, and the overall stress dispersion is measured using the effective variance of the entire stress tensor field. We show that the local stress field is significantly perturbed when the far-field stresses are associated with a high stress ratio and imposed at a critical direction in favour of intense sliding along preferentially-oriented fractures. The strong correlation between fracture sliding and local stress variability are further revealed from a scanline sampling analysis through the domain. Furthermore, larger perturbation of local stresses can be induced as the inhomogeneity of the rock materials increases (i.e. m decreases). Whether the stress field is dominated by fractures or matrix depends on the far-field stress state, material inhomogeneity, and fracture properties. If the rock material is highly heterogeneous, stress variability is controlled by the matrix when the far-field stress ratio is low; however, the stress distribution becomes more affected by fractures as the stress ratio increases. If the rock material is more homogeneous, the system tends to be more dominated by fractures even under a relatively low stress ratio.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method (FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations. Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network (DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

The Numerical Simulation of Hard Rocks for Tunnelling Purposes at Great Depths: A Comparison between the Hybrid FDEM Method and Continuous Techniques

Tunnelling processes lead to stress changes surrounding an underground opening resulting in the disturbance and potential damage of the surrounding ground. Especially, when it comes to hard rocks at great depths, the rockmass is more likely to respond in a brittle manner during the excavation. Continuum numerical modelling and discontinuum techniques have been employed in order to capture the complex nature of fracture initiation and propagation at low‐confinement conditions surrounding an underground opening. In the present study, the hybrid finite‐discrete element method (FDEM) is used and compared to techniques using the finite element method (FEM), in order to investigate the efficiency of these methods in simulating brittle fracturing. The numerical models are calibrated based on data and observations from the Underground Research Laboratory (URL) Test Tunnel, located in Manitoba, Canada. Following the comparison of these models, additional analyses are performed by integrating discrete fracture network (DFN) geometries in order to examine the effect of the explicit simulation of joints in brittle rockmasses. The results show that in both cases, the FDEM method is more capable of capturing the highly damaged zone (HDZ) and the excavation damaged zone (EDZ) compared to results of continuum numerical techniques in such excavations.

Role of natural fractures in damage evolution around tunnel excavation in fractured rocks

This paper studies the role of pre-existing fractures in the damage evolution around tunnel excavation in fractured rocks. The length distribution of natural fractures can be described by a power law model, whose exponent a defines the relative proportion of large and small fractures in the system. The larger a is, the higher proportion of small fractures is. A series of two-dimensional discrete fracture networks (DFNs) associated with different length exponent a and fracture intensity P21 is generated to represent various scenarios of distributed pre-existing fractures in the rock. The geomechanical behaviour of the fractured rock embedded with DFN geometry in response to isotropic/anisotropic in-situ stress conditions and excavation-induced perturbations is simulated using the hybrid finite-discrete element method (FEMDEM), which can capture the deformation of intact rocks, the interaction of matrix blocks, the displacement of natural fractures, and the propagation of new cracks. An excavation damaged zone (EDZ) develops around the man-made opening as a result of reactivation of pre-existing fractures and propagation of wing cracks. The simulation results show that when a is small, the system which is dominated by large fractures can remain stable after excavation given that P21 is not very high; however, intensive structurally-governed kinematic instability can occur if P21 is sufficiently high and the fracture spacing is much smaller than the tunnel size. With the increase of a, the system becomes more dominated by small fractures, and the EDZ is mainly created by the coalescence of small fractures near the tunnel boundary. The results of this study have important implications for designing stable underground openings for radioactive waste repositories as well as other engineering facilities that are intended to generate minimal damage in the host rock mass.

HYBRID FINITE-DISCRETE ELEMENT MODELLING OF BLAST-INDUCED EXCAVATION DAMAGED ZONE IN THE TOP-HEADING OF DEEP TUNNELS

A hybrid finite-discrete element method (FEM/DEM) is introduced to model the excavation damage zone induced by blast in a deep tunnel. The key components of the hybrid finite-discrete element method, i.e. transition from continuum to discontinuum through fracture and fragmentation, and detonation-induced gas expansion and flow through fracturing rock, are introduced in detail. The stress and crack initiation and propagation of an uniaxial compression test is then modelled by the proposed method and compared with those well documented in literature to calibrate the hybrid FEM/DEM. The modelled stress-loading displacement curve presents a typical failure process of brittle materials. The calibrated method is then used to model the stress and crack initiation and propagation induced by blast for the last step of excavation in a deep tunnel. A separation contour, which connects the borehole through the radial cracks from each borehole, is observed during the excavation process. The newly formed tunnel wall is produced and the main components of excavation damage zone (EDZ) are obtained. Therefore, the proposed treatment has the capabilities of modelling blast-induced EDZ and rock failure process. It is concluded that the hybrid FEM/DEM is a valuable numerical tool for studying excavation damage zone in terms of crack initiation and propagation and stress distribution.

Role of Brittle Behaviour of Soft Calcarenites Under Low Confinement: Laboratory Observations and Numerical Investigation

The strength decay that occurs in the post-peak stage, under low confinement stress, represents a key factor of the stress–strain behaviour of rocks. However, for soft rocks this issue is generally underestimated or even neglected in the solution of boundary value problems, as for example those concerning the stability of underground cavities or rocky cliffs. In these cases, the constitutive models frequently used in limit equilibrium analyses or more sophisticated numerical calculations are, respectively, rigid-plastic or elastic–perfectly plastic. In particular, most of commercial continuum-based numerical codes propose a variety of constitutive models, including elasticity, elasto-plasticity, strain-softening and elasto-viscoplasticity, which are not exhaustive in simulating the progressive failure mechanisms affecting brittle rock materials, these being characterized by material detachment and crack opening and propagation. As a consequence, a numerical coupling with mechanical joint propagation is needed to cope with fracture mechanics. Therefore, continuum-based applications that treat the simulation of the failure processes of intact rock masses at low stress levels may need the adoption of numerical techniques capable of implementing fracture mechanics and rock brittleness concepts, as it is shown in this paper. This work is aimed at highlighting, for some applications of rock mechanics, the essential role of post-peak brittleness of soft rocks by means of the application of a hybrid finite–discrete element method. This method allows for a proper simulation of the brittle rock behaviour and the related mechanism of fracture propagation. In particular, the paper presents two ideal problems, represented by a shallow underground cave and a vertical cliff, for which the evolution of the stability conditions is investigated by comparing the solutions obtained implementing different brittle material responses with those resulting from the assumption of perfectly plastic behaviour. To this purpose, a series of petrophysical and mechanical tests were conducted on samples of soft calcarenite belonging to the Calcarenite di Gravina Fm. (Apulia, Southern Italy), focusing specific attention on the post-peak behaviour of the material under three types of loading (compression, indirect tension and shear). Typical geometrical features representative of real rock engineering problems observed in Southern Italy were assumed in the problems examined. The numerical results indicate the impact of soft rock brittleness in the assessment of stability and highlight the need for the adoption of innovative numerical techniques to analyse these types of problems properly.

Hybrid finite-discrete element modelling of dynamic fracture and resultant fragment casting and muck-piling by rock blast

A state-of-the-art review is conducted to highlight the fracture mechanism in rock blast and advantages and limitations of various methods in modelling it. A hybrid finite-discrete element method (FEM-DEM) is implemented to simulate rock fracture and resultant fragment muck-piling in various blasting scenarios. The modelled crushed, cracked and long radial crack zones are compared with those in literatures to calibrate the hybrid FEM-DEM. Moreover, the hybrid modelling reproduces the rock fragmentation process during blasting. It is concluded that the hybrid FEM-DEM is superior to continuous and discontinuous methods in terms of modelling dynamic fracture of rock under blast-induced impact load.

Hybrid finite-discrete element modelling of asperity degradation and gouge grinding during direct shearing of rough rock joints

A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.

Hybrid Finite-Discrete Element Simulation of the EDZ Formation and Mechanical Sealing Process Around a Microtunnel in Opalinus Clay

The analysis and prediction of the rock mass disturbance around underground excavations are critical components of the performance and safety assessment of deep geological repositories for nuclear waste. In the short term, an excavation damaged zone (EDZ) tends to develop due to the redistribution of stresses around the underground openings. The EDZ is associated with an increase in hydraulic conductivity of several orders of magnitude. In argillaceous rocks, sealing mechanisms ultimately lead to a partial reduction in the effective hydraulic conductivity of the EDZ with time. The goal of this study is to strengthen the understanding of the phenomena involved in the EDZ formation and sealing in Opalinus Clay, an indurated claystone currently being assessed as a host rock for a geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are performed. With its explicit consideration of fracturing processes, FDEM modeling is applied to the HG-A experiment, an in situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. A quantitative simulation of the EDZ formation process around the microtunnel is first carried out, and the numerical results are compared with field observations. Then, the re-compression of the EDZ under the effect of a purely mechanical loading, capturing the increase of swelling pressure from the backfill onto the rock, is considered. The simulation results highlight distinctive rock failure kinematics due to the bedded structure of the rock mass. Also, fracture termination is simulated at the intersection with a pre-existing discontinuity, representing a fault plane oblique to the bedding orientation. Simulation of the EDZ re-compression indicates an overall reduction of the total fracture area as a function of the applied pressure, with locations of ineffective sealing associated with self-propping of fractures. These results are consistent with hydraulic testing data revealing a negative correlation between pressure values and an increase in the EDZ transmissivity.

A calibration procedure for two-dimensional laboratory-scale hybrid finite–discrete element simulations

In recent years, Bonded-Discrete element methods (Bonded-DEM) and hybrid finite–discrete element methods (FDEM) have become widely employed to model brittle fracturing processing in geomaterials. These approaches possess the ability to explicitly simulate fracture and fragmentation, but necessitate a large number of input parameters to be specified. Many of these parameters cannot be directly measured or characterized via laboratory tests and therefore must be estimated via calibration procedures to attain reliable results. In this work, a prescriptive procedure to arrive at a combination of input parameters for the newly developed Y-Geo FDEM code is developed. The proposed procedure is applicable for laboratory-scale simulations where some laboratory testing data for the material to be simulated is available. It uses a combination of the known elastic parameters, uniaxial compressive strength, and Brazilian disc strength of a material as calibration targets and limits the over-determined nature of the calibration problem by considering the similitude of the resulting fracture patterns. The development of this procedure represents a major step forward in obtaining reliable and consistent results using an FDEM approach.

The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus Clay): Short-term rock mass response and FDEM numerical analysis

The Opalinus Clay formation is currently being investigated as a potential host rock for the deep geological disposal of radioactive waste in Switzerland. Recently, a test tunnel was excavated at the Mont Terri underground rock laboratory (URL) as part of a long-term research project (“Full-scale Emplacement (FE) experiment”) aimed at studying the thermo-hydro-mechanical (THM) effects induced by the presence of an underground repository. The objective of this paper is twofold. Firstly, the results of the rock mass monitoring programme carried out during the construction of the 3m diameter, 50m long FE tunnel are presented, with particular focus on the short-term deformation response. The deformation measurements, including geodetic monitoring of tunnel wall displacements, radial extensometers and longitudinal inclinometers, indicate a strong directionality in the excavation response. Secondly, the deformational behaviour observed in the field is analyzed using a hybrid finite-discrete element (FDEM) analysis to obtain further insights into the formation of the excavation damaged zone (EDZ). The FDEM simulation using the Y-Geo code is calibrated based on the average short-term response observed in the field. Deformation and strength anisotropy are captured using a transversely isotropic, linear elastic constitutive law and cohesive elements with orientation-dependent strength parameters. Overall, a good agreement is obtained between convergences measured in the field and numerical results. The simulated EDZ formation process highlights the importance of bedding planes in controlling the failure mechanisms around the underground opening. Specifically, failure initiates due to shearing of bedding planes critically oriented with respect to the compressive circumferential stress induced around the tunnel. Slippage-induced rock mass deconfinement then promotes extensional fracturing in the direction perpendicular to the bedding orientation. The simulated fracture pattern is consistent with previous experimental evidence from the Mont Terri URL.

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional (3D) hybrid finite-discrete element method (FDEM) to investigate the development of an excavation damaged zone (EDZ) around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibrated against standard laboratory experiments, including Brazilian disc test and uniaxial compression test. The effect of increasing confining pressure on the mechanical response and fracture propagation of the rock was quantified under triaxial compression tests. Polyaxial (or true triaxial) simulations highlighted the effect of the intermediate principal stress (σ2) on fracture directions in the model: as the intermediate principal stress increased, fractures tended to align in the direction parallel to the plane defined by the major and intermediate principal stresses. The peak strength was also shown to vary with changing σ2.

Fracture development around deep underground excavations: Insights from FDEM modelling

Over the past twenty years, there has been a growing interest in the development of numerical models that can realistically capture the progressive failure of rock masses. In particular, the investigation of damage development around underground excavations represents a key issue in several rock engineering applications, including tunnelling, mining, drilling, hydroelectric power generation, and the deep geological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finite-discrete element method (FDEM) code to simulate the fracturing mechanisms associated with the excavation of underground openings in brittle rock formations. A brief review of the current state-of-the-art modelling approaches is initially provided, including the description of selecting continuum- and discontinuum-based techniques. Then, the influence of a number of factors, including mechanical and in situ stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for three different geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropic rock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy on the development of an excavation damaged zone (EDZ) around a tunnel excavated in a layered rock formation is considered. Finally, the interaction mechanisms between two large caverns of an underground hydroelectric power station are investigated, with particular emphasis on the rock mass response sensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEM simulations can provide unique geomechanical insights in cases where an explicit consideration of fracture and fragmentation processes is of paramount importance.

Modelling of blast-induced damage in tunnels using a hybrid finite-discrete numerical approach

This paper presents the application of a hybrid finite-discrete element method to study blast-induced damage in circular tunnels. An extensive database of field tests of underground explosions above tunnels is used for calibrating and validating the proposed numerical method; the numerical results are shown to be in good agreement with published data for large-scale physical experiments. The method is then used to investigate the influence of rock strength properties on tunnel durability to withstand blast loads. The presented analysis considers blast damage in tunnels excavated through relatively weak (sandstone) and strong (granite) rock materials. It was found that higher rock strength will increase the tunnel resistance to the load on one hand, but decrease attenuation on the other hand. Thus, under certain conditions, results for weak and strong rock masses are similar.

Hybrid finite–discrete element modeling of geomaterials fracture and fragment muck-piling

The essential components of hybrid finite–discrete element methods (FEM/DEMs) available in literature are reviewed in this paper first, which include contact detection and interaction between individual bodies, deformability, and transition from continuum to discontinuum through fracture and fragmentation, and temporal integration scheme. Among them, the transition from continuum to discontinuum through fracture and fragmentation is introduced in detail since it is regarded as the key component and makes the hybrid FEM/DEM superior to the continuum-based finite element method (FEM) and the discontinuum-based discrete element method (DEM). An integrated development environment (IDE) is then developed for a hybrid FEM/DEM using C++ and OpenGL on the basis of the authors' enriched FEM-based codes and the open-source combined FEM/DEM libraries available in open-source repositories. The proposed IDE not only simplifies the use of the hybrid FEM/DEM through graphically building numerical models and visually displaying calculated results in real time but also provides a platform for further developing the hybrid method. The proposed development is then used to model the quasi-static failure of rock in uniaxial compression tests and dynamic fracture of rock in impact tests, which are well documented in literatures, to calibrate the hybrid method. Finally, several engineering problems are modeled to demonstrate the application of the hybrid method in geotechnical engineering. The models of particle flow through a draw point and rock-falling along a staged slope demonstrates the benefits of the proposed development in dealing with the discrete systems in 2D and 3D, respectively. Compared with DEM, the hybrid method is more versatile in dealing with deformable, irregular-shaped and breakable discrete particles. The modeling of rock fragmentation by blast and resultant fragment muck-piling demonstrates the key feature of the hybrid method in dealing with the transition from continuum to discontinuum through fracture and fragmentation. Compared with FEM, the hybrid methods are more robust and efficient in dealing with rock fragmentation after the rock fracture occurs, especially in modeling resultant fragment movement, tertiary fracture, and fragment muck-piling.

Hybrid Finite-Discrete Element Modelling of Dynamic Fracture of Rocks with Various Geometries

The hybrid finite-discrete element method Y-2D/3D IDE is applied to model the dynamic fracture of rock specimens with various geometries during impacting a fixed rigid surface. It is found that the modelled primary fractures are highly dependent on the rock geometry determining the weakest plane for a given impact, which agrees well with others' experimental and SPH numerical results. Compared with others' SPH results, Y-2D/3D IDE better simulates the actinomorphic pattern of primary fractures around the impact area and the secondary & tertiary fractures observed in the dynamic fracture experiments. It is concluded that the proposed Y-2D/3D IDE is a valuable tool to model rock dynamic fracture compared with FEM and DEM.

Hybrid Finite-Discrete Element Simulation of Crack Propagation under Mixed Mode Loading Condition

This paper describes the numerical modeling based on combination of finite element method (FEM) and discrete element method (DEM) has been employed to simulate crack propagation under mixed mode loading. The work demonstrates the ability of combination finitediscrete element method to simulate the crack propagation that is usually performed through, what is termed, transition from continua to discontinua process. Crack propagation trajectory under selected loading angles (30o & 60o) are presented. The result obtained using the proposed model compare well with experimental result.