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The paper presents a description of the methods used to model rock as discontinuous media. The objective of the work is to bring to the geomechanics community recent advances in numerical modeling in the field of rock mechanics. The following methods are included: 1 the distinct element method; 2 the discontinuous deformation analysis method; and 3...
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... slope stability Hatzor and Benary 1998;Hatzor et al. 2004;Sitar et al. 2005;Yeung et al. 2006;Yeung andWong 2007, tunneling in discontinuous rock masses Shi 1993;Yeung et al. 1994;Ke 1997;Hatzor and Benary 1998;Kim et al. 1999;Wu et al. 2004;Hatzor 2006 andblasting Mortazavi andKatsabanis 2001. Additional case studies are pre- sented in Lu 2003. Fig. 6 shows an example to illustrate the use of DDA. The case analyzed involves a concrete dam, 30 m high, on a blocky rock foundation see Fig. 6a. The rock mass is characterized by two sets of discontinuities, one highly persistent and dipping away from the reservoir and the second one, nonpersistent dipping to- ward the reservoir. The ...
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... rock masses Shi 1993;Yeung et al. 1994;Ke 1997;Hatzor and Benary 1998;Kim et al. 1999;Wu et al. 2004;Hatzor 2006 andblasting Mortazavi andKatsabanis 2001. Additional case studies are pre- sented in Lu 2003. Fig. 6 shows an example to illustrate the use of DDA. The case analyzed involves a concrete dam, 30 m high, on a blocky rock foundation see Fig. 6a. The rock mass is characterized by two sets of discontinuities, one highly persistent and dipping away from the reservoir and the second one, nonpersistent dipping to- ward the reservoir. The stability of the dam is evaluated when the reservoir is full. In the analysis, it is assumed that static water pressure also exists along joint ...
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... have the same friction angle. The results show that displacements remain small and fairly constant while the friction angle of the joints is larger than 5.5°. Such small displacements are due to elastic de- formations. For smaller friction angles, the displacements along the dam foundation increase significantly. The failure mechanism is shown in Fig. 6b and it is caused by slip along the nonper- sistent joints. The slip causes a horizontal translation of the dam and heave of both the dam and of the rock downstream. The failure in this case is simple enough such that it could also be analyzed using classical limit equilibrium analysis; however as the complexity of the problem ...
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Citations
... Pressure tunnels are a vital component for water conveyance in pumped storage hydropower, and they are often concrete lined for achieving cost-effectiveness and long-term reliability (Pachoud et al. 2017;Zhou et al. 2017;Karami et al. 2019). These tunnels are commonly subjected to internal water pressure as high as 3-8 MPa during operation, hence inevitably inducing cracking of the concrete linings (Bobet et al. 2009;Bian et al. 2016;Huang et al. 2019;Zhang et al. 2019aZhang et al. , 2021. Consequently, almost full of the water pressure will be directly exerted on the excavation surface of the surrounding rocks. ...
Concrete-lined pressure tunnels have been widely used for water conveyance in pumped storage hydropower. With increasing internal water pressure, the tunnels are at higher risk of leakage, and the flow regime in the surrounding rocks is likely to transition from laminar to non-Darcian. Grouting has been considered as a cost-effective technique for controlling leakage in pressure tunnels, and an optimization design is usually needed to save the cost. This study proposes to use the Forchheimer’s law-based model for design optimization of grouting for a concrete-lined tunnel in hard rocks subjected to 8 MPa internal water pressure. The hydraulic conductivity K of the surrounding rocks is determined from packer tests, and the excavation-induced K variation is characterized by an equivalent elasto-plastic model. The non-Darcian coefficient β is estimated from K with a calibrated power-law scaling. It is proposed that a proper design of grouting should be able to limit the region with significant non-Darcian effect within the grouted zone, in addition to other commonly-used criteria for leakage, seepage erosion and fracturing failure in the surrounding rocks. It is found that when the quality of grouting is controlled to a standard of K = 6 × 10⁻⁸ m/s, the optimal depth of grouting is 6 m in fractured rocks and 12 m in fault zones. Hydraulic tests and seepage measurements confirm that this design scheme has been well implemented at the site, and is effective in controlling pore pressure and leakage to the level predicted by the Forchheimer’s law-based simulation.
... Because rock masses have inherent discontinuities which make it difficult to understand their actual rock behaviour (Bobet et al. 2009). To a large extent, numerical modelling tools for analysing rockmass behaviour are employed to comprehend and solve complex geotechnical issues. ...
Backfilling in goaf after pillar extraction seems to be a promising technology to help exploit these standing pillars. This paper presents the assessment of the impact of sand-stowing-based backfill on the peak strength and post-failure behavior of coal pillars. Rectangular coal samples were prepared and tested with different proportions of sand stowing, and a 3D finite-difference code was used for the numerical simulation to achieve the objective of the study. In laboratory experiments, the proportion of sand stowing was set at 0%, 60%, 70%, 80%, 90%, and 100% and tested in a servo-controlled machine, whereas, in numerical simulation, the percentage of sand stowing varied from 9 to 91% along with the coal pillar width-to-height ratios ranging from 1.5 to 5. The experimental and numerical results demonstrated that the average pillar strength increased as the proportion of stowing increased. The overall strength increased by 22% in the experimental study and about 28% to 32% in numerical simulation. The load vs. displacement characteristic changed from brittle to ductile as the sand proportion increases and the width-to-height ratio increased.
... Estimating the hydraulic from the mechanical aperture necessitates consideration of flow processes. Numerical simulations have become popular in the last decades due to their cost-and time-effectiveness as well as their wide range of applicability compared to experimental methods (Berre et al. 2019;Bobet et al. 2009;Viswanathan et al. 2022). However, same as with the determination of the mechanical aperture, numerical simulations require an exact representation of the fracture surface geometry as an input (Tatone and Grasselli 2012). ...
Knowledge of fracture properties and associated flow processes is important for geoscience applications such as nuclear waste disposal, geothermal energy and hydrocarbons. An important tool established in recent years are hydro-mechanical models which provide a useful alternative to experimental methods determining single fracture parameters such as hydraulic aperture. A crucial issue for meaningful numerical modeling is precise imaging of the fracture surfaces to capture geometrical information. Hence, we apply and compare three distinct fracture surface imaging methods: (1) handheld laser scanner (HLS), (2) mounted laser scanner (MLS) and (3) Structure from Motion (SfM) to a bedding plane fracture of sandstone. The imaging reveals that the resolution of the fracture surface obtained from handheld laser scanner (HLS) is insufficient for any numerical simulations, which was therefore rejected. The remaining surfaces are subsequently matched and the resulting fracture dataset is used for detailed fracture flow simulations. The resulting hydraulic aperture is calibrated with laboratory measurements using a handheld air permeameter. The air permeameter data provide a hydraulic aperture of 81 ± 1 µm. For calibration, mechanical aperture fields are calculated using stepwise increasing contact areas up to 15%. At 5% contact area, the average hydraulic aperture obtained by MLS (85 µm) is close to the measurement. For SfM, the measurements are fitted at 7% contact area (83 µm). The flow simulations reveal preferential flow through major channels that are structurally and geometrically predefined. Thus, this study illustrates that resolution and accuracy of the imaging device strongly affect the quality of fluid flow simulations and that SfM provides a promising low-cost method for fracture imaging on cores or even outcrops.
... While well-designed splitting rules may produce realistic results [58], these techniques are fundamentally limited to slow strain rates as they assume a separation in timescales between the external loading of a grain and the dynamics of fracture. Another approach is to represent a grain using a collection of particles linked by a network of attractive bonds [24,[59][60][61][62][63][64][65][66]. Fracture is modeled by allowing bonds to break. ...
A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a new model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a non-trivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean squared grain mass across rates and system sizes. Consistent scaling persists across all material properties studied although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses.
... In contrast, discontinuum and hybrid continuum-discontinuum approaches explicitly simulate rock damage development under various loading conditions without using pre-defined macroscopic constitutive models (Lisjak and Grasselli 2014;Zhang and Wong 2018;Wang and Cai 2019). Detailed descriptions of these approaches can be found in the literature (Jing and Hudson 2002;Jing 2003;Jing and Stephansson 2007;Bobet et al. 2009) and are beyond the scope of the current study. ...
This study aims to numerically investigate how various common simplifications of grain structure representation in bonded block models affect simulations of rock mechanical behavior. Specimens of Wausau granite were characterized mechanically through Brazilian tensile strength tests for this work. The samples were also characterized petrographically using thin section microscopy, scanning electron microscopy-based automated mineralogy, and visual inspection. Four types of representations of the Wausau granite samples were developed, including 6 detailed manually developed deterministic models, 6 semi-deterministic models, and 120 randomly generated representations (Voronoi models). First, a calibrated set of micro-properties was determined using the deterministic representations to simulate the Brazilian tensile strength measurements. Next, the study examined the ability of different Voronoi tessellations to adequately represent the grain structure for the purposes of accurate tensile strength simulation. This was evaluated by comparing Voronoi model results to the deterministic grain structure model results and laboratory test results. The findings of the study show that the four types of models used in this study can all provide realistic representations of the mechanical behavior of rock. The study confirms that standard Voronoi approximations of grain structures can be reasonably used in lieu of less practical, manually developed representations of the grain structure. Specifically, Voronoi models can properly replicate the geometric heterogeneity within the grain structure, even though they simplify some of its geometric attributes.
... The DEM enables no deformation coordination constraint between blocks, discretizes discontinuities into multilateral bodies, and allows discontinuities and deformations between variable and rigid bodies to be discontinuous (Jiang et al. 2018;Liu et al. 2020a;Gong et al. 2021;Deng et al. 2022). The DEM can be used for solving discontinuities in rock masses and is mainly used to simulate the actual instability evolution of slopes, so it has been widely applied to study the kinematic and sliding behavior characteristics of landslides (Bobet et al. 2009;Huang et al. 2015). ...
Because of the complexity of geological conditions and disturbance of external factors, the process of instability of open-pit landslides is very complicated. To illustrate this complex process, taking an open-pit coal mine landslide as an example, an accurate landslide geological section was established via detailed field investigation, remote sensing image interpretation, and field borehole data, in this study. A two-dimensional discrete-element model was established by the Fast CPU Matrix Computing of Discrete-Element Method (MatDEM, Version 1.60). The failure evolution of the landslide was investigated; then, the deformation behavior and dynamic characteristics of the landslide were systematically studied. The analyses of the failure process, velocity, displacement, and heat showed that the evolution of the landslide could be divided into the stages of initial deformation, accelerated deformation, and deceleration and stabilization. During the movement of the landslide, the gravitational potential energy of the landslide gradually converted into kinetic energy, heat, and elastic potential energy. The kinetic energy in the initial stage was small but rapidly increased and occupied the dominant position in the second stage. The kinetic energy gradually decreased and tended to be stable in the third stage. The final geometry and accumulation characteristics of the landslide obtained by numerical simulation were consistent with the corresponding field investigation and remote sensing interpretation. This work can provide a reference for the study of the evolution and prevention of open-pit mine landslides.
... The opening and shear in coal are described in virtue of traction-separation laws such as the cohesive zone models (CDMs). These models are usually utilized to investigate the failure problems in geo-materials (Bobet et al. 2009;Li et al. 2015;Lisjak and Grasselli 2014;Bazant and Planas 1997;Borst 2002). ...
We investigate the tensile failure processes of coal specimens under loading conditions by using both laboratory experiments and the 3D cohesive zone model (CZM) combined with the continuous-discontinuous method (CDM). Specifically, uniaxial, Brazilian, and triaxial tests were conducted in the laboratory to obtain the mechanical and strength properties of the coal such as Young’s modulus, Poisson’s ratio, fracture energy, cohesive strength, friction angle, uniaxial compression and shear strength. These properties were carefully calibrated prior to being taken as input parameters for the CDM modeling. The nucleation, growth and propagation of cracks in the coal were described by the CZMs, while the potential contact detection and interaction of fractured solids were treated via the penalty method. Furthermore, the parallel computation in Abaqus was employed to accelerate the calculations. All the results of our simulation were fairly consistent with the one obtained from the tensile tests in the laboratory. This study demonstrates that the CZM and CDM technique can be utilized together to obtain powerful insights into the failure mechanism of coal, which is also a powerful tool to clarify the collapse mechanism of coal block caving in the mining engineering design and scheme optimization.
... Anisotropy of rock is manifested as the directional response of physical and mechanical behaviours, especially in sedimentary and metamorphic rocks (Bobet et al. 2009). Typical geological movements change the structural characteristics of rock masses and the arrangement of mineral grains, introducing weaknesses and defects along specific directions (Nara 2015). ...
The engineering behaviour of rock is strongly associated with the anisotropy, which exists at different scales for construction safety and evaluation of rock properties. It is also well known that the anisotropy of the drilling mechanical characteristics in the rock cutting process has an essential effect on the drilling efficiency and cost. For this purpose, an effort was made to characterize the anisotropy of the drilling mechanical characteristics of rocks in the rock drilling process. The drilling strength and specific energy at the cutting point are considered to characterize the drilling process in three different directions according to the drilling response model. A drilling characteristic-based index is proposed to evaluate the anisotropy of rock. Drilling tests were conducted in three directions for six types of rock to study the anisotropy variation along the borehole depth. The anisotropy evolution result along the borehole suggested that this critical point is identified as the cutting point, dividing the drilling process into two stages of cutting and frictional contact. The cutting point also shows anisotropic features. The anisotropic ranking of tested rocks was obtained. Based on how the drilling parameters depend on the unconfined compressive strength, the reliability of the proposed anisotropy index is examined by comparison with the strength anisotropy index. The comparative result demonstrates that the proposed method can provide a reliable determination for rock anisotropy by using the drilling strength. The work performed in this paper provides a very useful approach for evaluating the anisotropy of rock and provides a good understanding of the drilling mechanical characteristics in rock drilling.
... Crack growth from stress concentrations can ultimately trigger dynamic failure in the form of landslides, earthquake ruptures, and volcanic eruptions in the crust. [1][2][3][4] Furthermore, it is thought that seismic events associated with landslides, earthquakes, and volcanic eruptions are commonly caused by the sudden failure of sub-critically stressed crustal rocks that have deformed slowly over long timescales. [5][6][7][8][9] The sub-critical crack growth mechanism considered to be responsible for time-dependent brittle deformation of rocks under upper crustal conditions is stress corrosion cracking; a process that involves fluid-rock interactions between pore fluids and stressed crack-tip bonds. ...
Time-dependent cracking and brittle creep of rock is fundamental to understanding the long-term evolution and dynamic failure in underground rock engineering. In the present paper, we present a systematic laboratory investigation into the control of single open macrofractures of differing orientations on time-dependent cracking and brittle creep in sandstone using digital image correlation (DIC). For a given macrofracture inclination angle β, we find that the failure of macrofractured sandstone under a constant stress is accompanied by the generation of more tensile fractures (wing cracks and secondary cracks) than in our constant strain rate experiments. This result differs from experiments performed on intact sandstones, for which macroscopic failure under a constant stress and constant strain rate were essentially identical. The nucleation site for the wing cracks is β-dependent. As β is increased, the crack nucleation position gradually moves from the center of the fracture towards the fracture tip with a decreasing speed. The kink angle of the secondary crack (k1) increases quasi-linearly with the increase of fracture angle γ. With the increase of the secondary crack angle θ, the kink angle of the tail crack (k2) shows different increasing trends for the left-lateral and right-lateral shear. The secondary crack could be inclined at a maximum of 26° (θ) to the maximum principal stress direction. Creep bursts—transient accelerations in deformation—are more easily triggered in macrofractured rock than in initially intact rock, and coincide in time with the coalescence of secondary cracks. The likelihood of occurrence of a creep burst was found to be higher for lower values of β. Finally, we present a secondary crack location map that defines the swing interval and identifies the fracture mechanism. The influence of a macrofracture, and its orientation, on damage evolution and the likelihood of creep bursts during interseismic periods provides crucial information for those tasked with monitoring hazards associated with the dynamic failure of crustal rocks.
... Contact resolution includes determining the geometric features among the particles including the point of contact, the amount of overlapping between particles and contact normal (Lai et al., 2021;Williams and O'Connor, 1999). As such, spherical particles are popular in DEM codes since their shape is simple and friendly for contact resolution (Bobet et al., 2009). More complex particle shapes can be realized by clumping several spherical particles into a rigid body or adapting polyhedral-shaped particles (Barreto and Leak, 2020). ...
... More complex particle shapes can be realized by clumping several spherical particles into a rigid body or adapting polyhedral-shaped particles (Barreto and Leak, 2020). A common plane approach among spherical contacts was proposed by Cundall(1988) to simplify contact resolution (Bobet et al., 2009), and simultaneously allow polyhedral-like geometry among the particles. A flat-joint (FJ) contact model is one such example. ...
Discrete-element-method (DEM) codes were developed in the field of rock mechanics. Compared to continuum codes, it has many advantages such as allowing larger grain displacements, detachment of grains, and simulation of discrete fractures. However, the disadvantage of DEM codes in the simulation of higher confining pressure triaxial tests were not previously discussed. In this study, we explored how the non-Dirac-delta distribution of contact forces controls the fault rupture initiation, and its impact on fault rupture propagation under high confining pressure. Based on the above study, a novel local dynamic weakening model was proposed and incorporated into the smooth-joint (SJ) contact model. The dynamic weakening model is tested with simulations of experiments conducted under high confining pressures. It is shown to be successful at reproducing realistic fault rupture behaviors, and the synthetic acoustic emission (AE) characteristics including magnitude-frequency relationships and fractal dimensions match those in the experiment.
