Distinct Element Method Model Research Articles

Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM)

In recent years, an international consortium of research organizations conducted investigations at the Chicxulub Crater in Yucatan, Mexico, to better understand the crater’s formation mechanisms and the effects produced by the impact of the asteroid that is hypothesized to have caused one of the major life extinctions on Earth. This study aims to reproduce the asteroid’s impact mechanics by matching computer simulations obtained with the use of the distinct element method (DEM) against the latest topographic data observed across the crater footprint. A 2D model was formulated using ITASCA’s PFC2D software to reproduce the asteroid’s impact on Earth. The model ground conditions prior to impact were replicated based on available geological and geophysical field information. Also, the proposed DEM model configuration was designed to reproduce a far-field effect to ascertain the energy dissipation of the asteroid’s impact at the model’s boundaries. Impact conditions of the asteroid were defined based on previous asteroid impact investigations. A parametric analysis including the asteroid’s impact angle and the asteroid’s impact velocity was conducted to assess their influence on the crater formation process. Results of the simulations included the final crater topography and stratigraphy, stress profiles, contact force chains, and velocity fields. Numerical simulations showed that both the asteroid velocity and impact inclination play a major role in the crater formation process, and that the use of DEM provides interesting insights into impact crater formation.

Effects of intermediate stress on deep rock strainbursts under true triaxial stresses

The effect of intermediate stress (in situ tunnel axial) on a strainburst is studied with a three-dimensional (3D) bonded block distinct element method (DEM). A series of simulations of strainbursts under true triaxial in situ stress conditions (i.e. high tangential stress, moderate intermediate stress and low radial stress) of near-boundary rock masses are performed. Compared with the experimental results, the DEM model is able to capture the stress-strain response, failure pattern and energy balance of strainbursts. The fracturing processes of strainbursts are also numerically reproduced. Numerical results show that, as the intermediate stress increases: (1) The peak strain of strainbursts increases, the yield stress increases, the rock strength increases linearly, and the ratio of yield stress to rock strength decreases, indicating that the precursory information on strainbursts is enhanced; (2) Tensile and shear cracks increase significantly, and slabbing and bending of rock plates are more pronounced; and (3) The stored elastic strain energy and dissipated energy increase linearly, whereas the kinetic energy of the ejected rock fragments increases approximately exponentially, implying an increase in strainburst intensity. By comparing the experimental and numerical results, the effect of intermediate stress on the rock strength of strainbursts is discussed in order to address three key issues. Then, the Mogi criterion is applied to construct new strength criteria for strainbursts by converting the one-face free true triaxial stress state of a strainburst to its equivalent true triaxial stress state. In summary, the effect of intermediate stress on strainbursts is a double-edged sword that can enhance the rock strength and the precursory information of a strainburst, but also increase its intensity. ©2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

3D DEM investigation of the resistance of ice and frozen granular soils

Frozen soils are mixtures of ice and solid grains. Since the mechanical properties of ice and dry granular soils are completely different, the behaviour of the ice-soil mixture is highly dependent on the ice content. In this paper, a 3D model based on the distinct element method (DEM) is introduced and used for evaluating the resistance of frozen soil. In the DEM model, two groups of elements are used for representing soil particles and ice. The modelling of granular soils by DEM has been widely treated in the literature. However, few researches are available regarding DEM modelling of ice, and no DEM simulations have been published regarding soil-ice mixtures. For these reasons, preliminary simulations are performed to calibrate the DEM ice model and assess the relationship between the micromechanical parameters and the macroscopic behaviour. Then, several specimens are built by mixing different proportions of the two constituents to reproduce different ice contents, and appropriate parameters for the ice-soil interface are introduced. A series of triaxial compression and shear simulations are performed and analysed. The obtained macroscopic behaviour of the ice-soil mixtures is qualitatively and quantitatively described, and compared to existing experimental data in terms of resistance parameters.

Discrete Element Modelling of Rock Creep in Deep Tunnels using Rate Process Theory

Rock creep behaviour is a key aspect of many engineering projects, such as deep tunnels in which squeezing problems could occur. Many theories have been published in the literature to reproduce rock creep behaviour; however, most of them are not able to capture the last phase of creep (i.e., tertiary creep, or the accelerating strains that occur prior to failure). In this work, the Distinct-Element Method (DEM) approach is employed, in conjunction with Rate Process Theory (RPT), to simulate the effect of rock creep in deep tunnels. To do that, the DEM models are constructed using particles, whose interactions are simulated with a hybrid mixture of the Flat Joint Contact Model (FJCM) and the Linear Model (LM) contact models; the RPT is implemented into DEM models using a Visual C++ function. Results show that the DEM plus RPT combination can suitably reproduce the tunnel convergences due to rock creep.

A DEM-Based Factor to Design Rock-Socketed Piles Considering Socket Roughness

The Distinct Element Method (DEM) has gained recent attention to study geotechnical designs with rock-concrete or rock–rock interfaces, such as rock-socketed piles. In this work, 3D DEM models with non-standard contacts laws (the Smooth-Joint and Flat-Joint contact models) are proposed to analyze the response of axially loaded rock-socketed piles with different sockets roughness, since socket roughness is a key factor affecting their side shear resistance that is not usually considered for pile design. DEM models are calibrated using experimental data, and the consequences of applying 2D models for calibration, to be subsequently used in a 3D analysis, are studied. Numerical results suggest that such DEM models can be employed to reproduce key aspects of the behavior of rock-socketed piles, such as their load and global stiffness-settlement response, their side shear resistance, and the damage at the rock-pile interface. Finally, an empirical factor $${\alpha }_{RF,1\%D}$$ is proposed to estimate the side shear resistance of rock-socketed piles considering the socket roughness and the uniaxial compressive strength (UCS) of the weaker material (rock or pile) at the interface.

Influence of radial stress on strainbursts under true triaxial conditions: Insights from a distinct element modelling

The radial (minimum) stress of the near-boundary rockmass in deep excavations plays a key role in inducing rock failures such as spalling and strainbursts. In this study, a strainburst is treated as a structural failure of the near-boundary rockmass. The influence of the radial stress acting asymmetrically on one boundary surface of the burst volume on strainbursts is numerically investigated using a 3D bonded block distinct element method (DEM). The 3D DEM model for simulating the overall process of strainbursts is introduced and its effectiveness is verified by comparing with the analogous true triaxial experiments. Then based on the simulation results, the influence of radial stress on strainbursts is studied from the perspectives of deformation and strength characteristics, fracturing process, crack development, failure mode and energy balance. In addition, discussions of the mechanisms of the influence of radial stress on strainbursts are presented from the perspectives of fracture mechanics and a graphical explanation. Results show that, as the radial stress increases, the strength of the strainburst sample exhibits a quadratic law that increases first and then decreases, the number of shear cracks increases remarkably, the degree of accumulated rock damage precedes burst is getting higher and higher, the failure mode of strainbursts transforms gradually from a tensile-type to a shear-type, and the kinetic energy is getting higher and higher. The fundamental influence of radial stress on strainbursts is concluded as its suppression effect on the tensile failure mechanism of brittle rocks.

Failure mechanism of TRSS mode in landslides induced by earthquake

Investigation of the slopes in the Wenchuan earthquake shows that tension failures appear in the upper part in many landslides. The typical failure mode can be generalized as “tensile-rupture and sheared-sliding” (TRSS). In this paper, the distinct element method (DEM) is employed to simulate the gradual failure process of the Tangjiashan landslide under the excitation of the Wenchuan earthquake. It is found that the first failure is the appearance of deep tension cracks on the top, and then shearing slip along the bottom. The posterior fracture is deep, steep, and rough, and the bottom shear slip surface has a relatively gently dip. The simulation shows the failure mode of TRSS in the slope can be well reproduced, and the geological and mechanical mechanisms can be revealed in the DEM model.

Discrete element modelling of rock creep behaviour using rate process theory

Rock creep behaviour is crucial in many rock engineering projects. Different approaches have been proposed to model rock creep behaviour; however, many cannot reproduce tertiary creep (i.e., accelerating strain rates leading to rock failure). In this work, the distinct element method (DEM) is employed, in conjunction with the rate process theory (RPT) of M.R. Kuhn and J.K. Mitchell (published in 1992) to simulate rock creep. The DEM numerical sample is built using a mixture of contact models between particles that combines the Flat Joint Contact Model and the Linear Model. Laboratory uniaxial compression creep tests conducted on intact slate samples are used as a benchmark to validate the methodology. Results demonstrate that, when properly calibrated, DEM models combined with the RPT can reproduce all creep stages observed in slate rock samples in the laboratory, including tertiary creep, without using constitutive models that incorporate an explicit dependence of strain rate on time. The DEM results also suggest that creep is associated with damage in the samples during the laboratory tests, due to new microcracks that appear when the load is applied and maintained constant at each loading stage.

Static and dynamic analysis on slope stability using a DFN-DEM approach on the right abutment of the Karun 4 dam

Uncertainty in input fracture geometric parameters during analysis of the stability of jointed rock slopes is inevitable and therefore the stochastic discrete fracture network (DFN) — distinct element method (DEM) is an efficient modeling tool. In this research, potentially unstable conditions are detected in the right abutment of the Karun 4 dam and downstream of the dam body as a case study. Two extreme states with small and relatively large block sizes are selected and a series of numerical DEM models are generated using a number of validated DFN models. Stability of the rock slope is assessed in both static and dynamic loading states. Based on the design basis earthquake (DBE) and maximum credible earthquake (MCE) expected in the dam site, histories of seismic waves are applied to analyze the stability of the slope in dynamic earthquake conditions. The results indicate that a MCE is likely to trigger sliding of rock blocks on the rock slope major joint. Furthermore, the dynamic analysis also shows a local block failure by the DBE, which can consequently lead to slope instability over the long term. According to the seismic behavior of the two models, larger blocks are prone to greater instability and are less safe against earthquakes.

Granular soils: from DEM simulation to constitutive modeling

In this study, the distinct element method (DEM) was employed to numerically explore the mechanical responses of granular soils and to extract key components for an elastoplastic constitutive model for them. Considering the irregular shapes of real particles, a contact model considering rolling and twisting resistances was used in the DEM simulations. It is shown that this contact model can successfully capture the density-dependent, pressure-dependent behavior of granular soils as well as stress–dilatancy behavior. A critical state-based, double yielding surface constitutive model was used to describe the mechanical behavior of the DEM numerical material. A marked feature of the proposed constitutive model is the incorporation of a flow rule that defines the relationship between the stress Lode angle and strain Lode angle in the deviatoric plane. The model parameters were completely determined from DEM simulation results. The agreement between the DEM simulation results and the constitutive model prediction indicates that realistic complex mechanical behavior of granular soils in generalized loading paths can be reproduced well in both discrete and continuum ways. This will allow effective coupling of discrete–continuum modeling (such as DEM–FEM) in solving geotechnical boundary value problems with large deformation, where a consistent representative of soil is required for the near-field DEM modeling and far-field FEM modeling.

Investigating Earth Reaction to Pull-Out Process of Frictional Rock Bolts Using Distinct Element Method

The reaction of earth to pull-out process of frictional rock bolts was here modeled by the distinct element method (DEM). Ten frictional bolts were prepared; the expanding shells of five bolts included convex edges and the others had the shells with concave bits. The strength of bolts was measured by applying a standard pull-out test; the results confirmed that the strength of shells with convex edges was remarkably more than the strength of other shells. Furthermore, a two-dimensional DEM model of the test was developed by a particle flow code; the obtained results showed that the reaction of rock particles to the contacts occurring between the convex edges and earth was considerably more than those of the concave bits. In the other words, the convex edges transferred the pull-out force into a large area of the surrounded rock, causing these bolts to have the highest resistance against earth movements.

On the homogenization and up-scaling of a discrete element method model

A Distinct Element Method (DEM) up-scaling framework is presented that estimates the parameters of a continuum constitutive model that best captures the salient features of naturally fractured rock (NFR) behaviour. Up-scaling is achieved using homogenized DEM stress–strain curves and a particle swarm optimization algorithm followed by a Levenberg–Marquardt algorithm. The effectiveness of the framework is demonstrated by up-scaling a DEM model of a NFR to a Drucker–Prager damage-plasticity model. The up-scaled continuum model is shown to compare well (<5% error) with direct numerical simulation in a slope stability analysis and requires two orders of magnitude less computational effort.

Distinct element geomechanical modelling of the formation of sinkhole clusters within large-scale karstic depressions

Abstract. The 2-D distinct element method (DEM) code (PFC2D_V5) is used here to simulate the evolution of subsidence-related karst landforms, such as single and clustered sinkholes, and associated larger-scale depressions. Subsurface material in the DEM model is removed progressively to produce an array of cavities; this simulates a network of subsurface groundwater conduits growing by chemical/mechanical erosion. The growth of the cavity array is coupled mechanically to the gravitationally loaded surroundings, such that cavities can grow also in part by material failure at their margins, which in the limit can produce individual collapse sinkholes. Two end-member growth scenarios of the cavity array and their impact on surface subsidence were examined in the models: (1) cavity growth at the same depth level and growth rate; (2) cavity growth at progressively deepening levels with varying growth rates. These growth scenarios are characterised by differing stress patterns across the cavity array and its overburden, which are in turn an important factor for the formation of sinkholes and uvala-like depressions. For growth scenario (1), a stable compression arch is established around the entire cavity array, hindering sinkhole collapse into individual cavities and favouring block-wise, relatively even subsidence across the whole cavity array. In contrast, for growth scenario (2), the stress system is more heterogeneous, such that local stress concentrations exist around individual cavities, leading to stress interactions and local wall/overburden fractures. Consequently, sinkhole collapses occur in individual cavities, which results in uneven, differential subsidence within a larger-scale depression. Depending on material properties of the cavity-hosting material and the overburden, the larger-scale depression forms either by sinkhole coalescence or by widespread subsidence linked geometrically to the entire cavity array. The results from models with growth scenario (2) are in close agreement with surface morphological and subsurface geophysical observations from an evaporite karst area on the eastern shore of the Dead Sea.

Evaluation of the Effect of Fault on the Stability of Underground Workings of Coal Mine through DEM and Statistical Analysis

The rock mass around an excavation is generally traversed by different geological discontinuities such as faults, folds, slips, joints, etc. Fault is one of the major geological discontinuities which creates lot of difficulties during underground winning of coal. Entire stress regime and ground conditions in the formation are altered in and around the faults. Faults also impose detrimental effects by introducing impurities, including clay and various forms of mineral matter into the coal seams; opening of pathways for the influx of water and gas into the underground workings; displacing the coal seams upward/downwards making the coal seams difficult or sometimes impractical to mine. Appropriate evaluation of the effect of the fault on the stability of the underground workings is a requisite for safe design of the underground mining structures. In this paper, a study has been carried out to assess the effect of the fault on the stability of underground coal mines by numerical simulation with distinct element method (DEM). On the calibrated DEM model, parametric study has been performed by varying the selected parameters, the dip and the friction angles of the fault. The analysis of variance (ANOVA) shows that both the factors have statistically significant effect on the strength of the coal pillar. Similarly, the displacement of the immediate roof and the height of the disturbed strata are evaluated by the DEM modelling and statistical analysis when the fault passes through the middle of the gallery. The results of ANOVA for both cases indicate that the both factors have significant effect on the displacement of the immediate roof and the height of the disturbed strata. It is obtained from the study that the low angle fault causes high instability in the immediate roof. The paper has been supplemented with the field observations where instability in underground roadways of a coal mine in India is caused by the fault. It was observed in VK-7 incline mine of Singareni Collieries Company Limited, India that there was sudden failure of immediate roof of a roadway where a low angle fault crosses the middle of the roadway. The findings of the paper help to understand the behaviour of the coal pillar and the surrounding rock mass in the presence of the fault. The study would also help to take appropriate decisions about the unstable regions of the working safeguarding safety in underground coal mines.

The emergence of asymmetric normal fault systems under symmetric boundary conditions

Many normal fault systems and, on a smaller scale, fracture boudinage often exhibit asymmetry with one fault dip direction dominating. It is a common belief that the formation of domino and shear band boudinage with a monoclinic symmetry requires a component of layer parallel shearing. Moreover, domains of parallel faults are frequently used to infer the presence of a décollement. Using Distinct Element Method (DEM) modelling we show, that asymmetric fault systems can emerge under symmetric boundary conditions. A statistical analysis of DEM models suggests that the fault dip directions and system polarities can be explained using a random process if the strength contrast between the brittle layer and the surrounding material is high. The models indicate that domino and shear band boudinage are unreliable shear-sense indicators. Moreover, the presence of a décollement should not be inferred on the basis of a domain of parallel faults alone.

Reaction-induced grain boundary cracking and anisotropic fluid flow during prograde devolatilization reactions within subduction zones

Devolatilization reactions during prograde metamorphism are a key control on the fluid distribution within subduction zones. Garnets in Mn-rich quartz schist within the Sanbagawa metamorphic belt of Japan are characterized by skeletal structures containing abundant quartz inclusions. Each quartz inclusion was angular-shaped, and showed random crystallographic orientations, suggesting that these quartz inclusions were trapped via grain boundary cracking during garnet growth. Such skeletal garnet within the quartz schist formed related to decarbonation reactions with a positive total volume change (∆V t > 0), whereas the euhedral garnet within the pelitic schists formed as a result of dehydration reaction with negative ∆V t values. Coupled hydrological–chemical–mechanical processes during metamorphic devolatilization reactions were investigated by a distinct element method (DEM) numerical simulation on a foliated rock that contained reactive minerals and non-reactive matrix minerals. Negative ∆V t reactions cause a decrease in fluid pressure and do not produce fractures within the matrix. In contrast, a fluid pressure increase by positive ∆V t reactions results in hydrofracturing of the matrix. This fracturing preferentially occurs along grain boundaries and causes episodic fluid pulses associated with the development of the fracture network. The precipitation of garnet within grain boundary fractures could explain the formation of the skeletal garnet. Our DEM model also suggests a strong influence of reaction-induced fracturing on anisotropic fluid flow, meaning that dominant fluid flow directions could easily change in response to changes in stress configuration and the magnitude of differential stress during prograde metamorphism within a subduction zone.

Numerical analysis on mining-induced fracture development around river valleys

ABSTRACTThis paper presents a detailed study of the mechanisms contributing to fracture development around river valleys associated with mining operations. Due to the geology and geomorphology of the Southern Coalfield of New South Wales, Australia, non-conventional subsidence effects usually occur. The influences associated with valley closure and upsidence are principally tensile and shear fracturing/cracking of the river and underlying strata, which act as underground flow paths for surface water. This paper explicitly simulates the mining-induced fracture development around the valley structure, utilising a distinct element method modelling technique with Voronoi tessellation. The fracture propagations within intact rock as well as along existing discontinuities are simulated in this study. It is demonstrated that the presence of natural geological discontinuities and the mining-induced stress field play an important role in determining the extent and pattern of fracture propagation. Analysis of the mining-induced explicit fracturing system in the vicinity of valley provides an improved understanding of the near-surface hydrological cycle and enables effective remediation of the mining-induced adverse impacts on river valleys.

Three-dimensional Distinct Element Method modelling of the growth of normal faults in layered sequences

AbstractThe growth of normal faults in mechanically layered sequences is numerically modelled using three-dimensional Distinct Element Method (DEM) models, in which rock comprises an assemblage of bonded spherical particles. Faulting is induced by movement on a pre-defined normal fault at the model base whilst a constant confining pressure is maintained by applying forces to particles lying at the model top. The structure of the modelled fault zones and its dependency on confining pressure, sequence (net:gross) and fault obliquity are assessed using various new techniques that allow (a) visualization of faulted horizons, (b) quantification of throw partitioning and (c) determination of the fault zone throw beyond which theoretical juxtaposition sealing occurs along the entire zone length. The results indicate that fault zones become better localized with increasing throw and confinement. The mechanical stratigraphy has a profound impact on fault zone structure and localization: both low and high net:gross sequences lead to wide and relatively poorly localized faults. Fault strands developing above oblique-slip normal faults form, on average, normal to the greatest infinitesimal stretching direction in transtensional zones. The model results are consistent with field observations and results from physical experiments.

Discrete element modeling of shielding and size effects during single particle crushing

In granular assemblies such as soil, ballast, cementitious aggregates, food and medical products, particle fragmentation and crushing alter material properties. The goal of this research work is to better understand the microstructure parameters that control the triggering of fragmentation, and to predict how microstructure evolution consequent to crushing can actually enhance or reduce material properties. We focused on size and shielding effects, which respectively refer to the decrease of particle strength with increasing particle size, and to the increase of particle strength with the redistribution of stress towards hydrostatic stress conditions upon crushing of neighboring particles. We calibrated the parameters of a Distinct Element Method (DEM) cluster model of crushable particle so as to match the displacement and axial force obtained experimentally at the first particle fragmentation. In order to study the influence of the coordination number on particle crushing, we modeled the mechanical confinement effect of neighboring particles by placing rigid walls around the DEM cluster. In order to understand why larger particles have lower tensile strength, we studied size effects on the crushing process of clusters with and without internal flaws. We found that for clusters with a porosity ranging between 0% and 30%, tensile strength only depends on porosity and not on flaw size. Overall results show that particle strength depends: (1) linearly on particle coordination number; (2) quadratically on particle porosity. Theoretical and DEM modeling of particle crushing will advance the fundamental understanding of energy transfer in particulate media.

DEM assessment of scaling laws capturing the grain size dependence of yielding in granular soils

Experimental evidences show that the pressure at which granular soils exhibit a sharp increase of their compressibility depends on the size of the particles that constitute their skeleton, thus reflecting the role of micro-scale fracture events on the macroscopic compression of granular systems. In this paper, the distinct element method (DEM) is used to test the validity of scaling laws relating the macroscopic energy at which the grains of a soil matrix crush collectively to the energy at which individual grains subjected to diametrical compression undergo tensile fracture. Oedometric compression tests on uniformly graded specimens with different values of particle size have been simulated by considering two deterministic fracture models and a probabilistic criterion based on the Weibull weakest link theory. It has been shown that the constants of proportionality between grain-scale and assembly-scale crushing thresholds depend considerably on the statistical variability of the particle strength, and that a larger variability exacerbates the departure between the scaling constants pertaining to deterministic and probabilistic models. Nevertheless, for the chosen set of initial conditions and loading paths, the simulations have suggested the applicability of a proportional scaling between the energy stored in the assembly at the moment of yielding and that required to fracture a single grain. In particular, the simulations revealed that the scaling constants relating the microscopic and macroscopic energy thresholds fall within a rather narrow range and do not depend significantly on the grain size. The Breakage Mechanics theory has been used to further explore such connection between length scales, finding a good agreement between the DEM simulations and the yielding stress computed by the theory whenever its parameters were defined on the basis of the scaling constants computed from the DEM model. These results confirm the interplay between the statistical variability of the particle strength and the grain size dependence of the yielding pressure, stressing at the same time the usefulness of energy scaling arguments in incorporating the effect of micro-scale fracture events into continuum models.