3D Distinct Element Method Research Articles

Modelling the Influence of Geological Structures in Paleo Rock Avalanche Failures Using Field and Remote Sensing Data

This paper focuses on the back analysis of an ancient, catastrophic rock avalanche located in the small city of Lettopalena (Chieti, Italy). The integrated use of various investigation methods was employed for landslide analysis, including the use of traditional manual surveys and remote sensing (RS) mapping for the identification of geological structures. The outputs of the manual and RS surveys were then utilised to numerically model the landslide using a 2D distinct element method. A series of numerical simulations were undertaken to perform a sensitivity analysis to investigate the uncertainty of discontinuity properties on the slope stability analysis and provide further insight into the landslide failure mechanism. Both numerical modelling and field investigations indicate that the landslide was controlled by translational sliding along a folded bedding plane, with toe removal because of river erosion. This generated daylighting of the bedding plane, creating kinematic freedom for the landslide. The formation of lateral and rear release surfaces was influenced by the orientation of the discrete fracture network. Due to the presence of an anticline, the landslide region was constrained in the middle-lower section of the slope, where the higher inclination of the bedding plane was detected. The landslide is characterized by a step-path slip surface at the toe of the slope, which was observed both in the modelling and the field. This paper highlights the combined use of a geological model and numerical modelling to provide an improved understanding of the origin and development of rock avalanches under the influence of river erosion, anticline structures, and related faults and fractures.

Evaluation of the Effects of Yielding Rockbolts on Controlling Self-Initiated Strainbursts: A Numerical Study

In this paper, a 2D distinct element method (DEM) model of a deep tunnel in an underground coal mine is built to thoroughly evaluate the effects of yielding (D-bolt and Roofex) and the traditional rockbolt (fully resin-grouted rebar) on controlling self-initiated strainbursts. The occurrence of self-initiated strainbursts is judged based on the stiffness difference between the loading system and rock masses for the first time. The results suggest that the total deformations of the tunnel supported with Roofex and resin-grouted rebar are 1.53 and 2.09 times that of D-bolts (1411 mm). The average velocities of detached rock blocks in the tunnel supported with Roofex and resin-grouted rebar are 3.22 and 3.97 m/s, respectively, which are much higher than that of D-bolts (0.34 m/s). 13 resin-grouted rebar bolts are broken during the strainburst, while D-bolts and Roofex survive. Compared with Roofex (295.16 kJ) and resin-grouted rebar (125.19 kJ), the D-bolt can reduce the most kinetic energy (469.30 kJ). D-bolt and resin-grouted rebar can maintain high axial force levels (214.87 and 151.05 kN) during strainbursts. Both Roofex and resin-grouted rebar fail to control strainbursts. The bolt number significantly influences the control effects of yielding rockbolts on strainbursts. 9 and 12 D-bolts cannot control the strainburst, while 15 and 18 D-bolts can make the tunnel stable. In addition, the detachment and ejection of rocks between rockbolts can be well restrained using surface retain elements, e.g., steel arch. This study highlights the usage of numerical modeling methods in assessing the performance of yielding rockbolts, which can be served as a promising tool to improve and optimize the design of rock supporting in burst-prone grounds.

Modelling discontinuity control on the development of Hell\u2019s Mouth landslide

This paper focuses on numerical modelling and back analysis of the Hell’s Mouth landslide to provide improved understanding of the evolution of a section of the north coast of Cornwall, UK. Discontinuity control is highlighted through the formation of a ‘zawn’ or inlet, the occurrence of two successive landslides and evidence of ongoing instability through opening of tension cracks behind the cliff top. Several integrated remote sensing (RS) techniques have been utilised for data acquisition to characterise the slope geometry, landslide features and tension crack extent and development. In view of the structural control on the rock slope failures, a 3D distinct element method (DEM) code incorporating a discrete fracture network and rigid blocks has been adopted for the stability analysis. The onset and opening of tension cracks behind the modelled slope failure zones has also been studied by analysing the displacements of two adjoining landslide blocks, between which, a joint-related tension crack developed. In addition, a sensitivity analysis has been undertaken to provide further insight into the influence of key discontinuity parameters (i.e. dip, dip direction, persistence and friction angle) on the stability of this section of the coastline. Numerical modelling and field observations indicate that block removal and preferential erosion along a fault resulted in the formation of the inlet. The development of the inlet provides daylighting conditions for discontinuities exposed on the inlet slope wall, triggering the initial landslide which occurred on 23rd September 2011. Numerical modelling, and evidence from a video of the initial landslide, suggests that the cliff instability is characterised by a combination of planar sliding, wedge sliding and toppling modes of failure controlled by the discrete fracture network geometry.

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.

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.

Do the normal compression lines of cemented and uncemented geomaterials run parallel or converge to each other after yielding?

Whether the normal compression lines (NCLs) of cemented and uncemented materials run parallel or converge to each other after yielding is a fundamental yet controversial issue in the study of compression behaviour of geomaterials. An effort is made here to clarify the question by means of the distinct element method (DEM) combined with available experimental observations. In the DEM simulations, the effects of cement content, void ratio, bond elastic modulus, bond strength and bond distribution on the compression curves are considered. In addition, the microscopic mechanical responses, including bond breakage events, deviatoric fabric and stress shared by bonded part or unbonded part, are investigated. The DEM simulations show that the NCLs for all the cemented specimens run parallel with the NCL for the uncemented specimen within the range of stresses adopted in the study, which is not influenced by the aforementioned factors. Through comparing the DEM results in this study, previous 3D DEM data and experimental observations, it can be preliminarily concluded that the interactions between cement breakage and particle crushing determine the convergence or non-convergence of NCLs. The NCLs of the cemented and uncemented sands run parallel for the strong-particle case, while those tend to converge for the fragile-particle case.

Numerical modeling of rock mechanical behavior and fracture propagation by a new bond contact model

This paper presents a numerical investigation into mechanical behavior and rock fracture using the distinct element method (DEM). Based on a series of laboratory tests on the bonded granules idealized by two glued aluminum rods, a normal force dependent bond contact model was proposed and implemented into a two-dimensional (2D) DEM code. This 2D DEM code was used to carry out a series of numerical simulations, including uniaxial and biaxial compression tests, direct tension and Brazilian tension tests, whose results were compared with experimental data to calibrate the proposed model and identify the microscopic deformability and strength parameters. In addition, the validated model was then used to simulate crack propagation and rock fracture in single-flawed and double-flawed samples with different flaw inclinations, and the simulations were then compared with experimental observations. The numerical results demonstrate that the proposed bond model incorporated into the distinct element method is able to capture the main mechanical behaviors of crystalline rocks (Lac du Bonnet granite and Hwangdeung granite). The limitations associated to a low strength envelope angle and high ratio between tensile strength and compressive strength frequently formed in DEM simulations of rock behaviors are solved. In addition, five distinct stages of the stress–strain curve and the marked stresses can be clearly identified by lateral strain, volumetric response and the cumulative number of bond failures. The mechanical behavior and rock fracture patterns obtained from DEM simulations are in good agreement with experimental observations and the model captures both the geometrical control and the general strength value for crystalline rocks.

Evolution of the surface deformation profile and subsurface distortion zone during reverse faulting through overburden sand

The 2D distinct element method was used to investigate the propagation of fault rupture traces through overlying sand during reverse faulting along a range of dip angles and at different vertical throws. Calibrated micromechanical material parameters were used in the numerical simulations, which were validated through a comparison of the simulation results with those obtained from a centrifuge experiment involving acceleration at 80g. The Gompertz sigmoid function with three parameters provided the best fit to the normalized surface deformation profiles obtained both from the numerical simulation and from centrifuge experiments. The three parameters that characterized the Gompertz sigmoid function were the normalized scarp height, the maximum slope on the scarp, and the location of the reverse fault outcropping. A surface deformation profile slope of 1/150 was used as the setback criterion. The normalized affected width and fault outcrop relative to the fault tip were determined for reverse faults having a variety of dips and throws. The dip angle significantly affected the kinematic mechanism underlying reverse faulting. At a given vertical throw, the scarp height increased as the dip angle decreased in the cases of α<45°, and the scarp maintained a relatively constant height in the cases of α>45°. As the dip angle decreased, the location of the fault outcropping shifted toward the footwall and the maximum slope on the scarp increased. The horizontal displacement played a significant role at low dip thrusts (α=22.5°, 30°, 37.5°), a back-thrust fault developed, and an inverted triangle wedge formed in the subsurface.

Back analysis of a natural jointed rock slope based on the photogrammetry method

In 2013, a potentially unstable jointed rock slope above a road in the Gold Coast area, Australia, partially failed after a rainfall event. In this study, the rock failure was back analyzed to evaluate the presence of key blocks through block analysis based on photogrammetry surveys. Friction angles of the joint sets at the point of failure were also investigated by means of a parametric study using a 3D distinct element method (DEM). The photogrammetry method was employed to obtain measurements of the orientation of the joint sets of the slope and the shape and size of rock blocks at the inaccessible slope. The joint roughness coefficient (JRC) obtained from the 3D photogrammetry model was utilized to estimate friction angles and the strength of the joint set. Safety factors of the rock mass were computed by both analytical and numerical approaches. Parametric analyses, using a DEM model, assessed the critical friction angle of the joint sets and also demonstrated the failure mechanism of the blocks. The result of this study indicates that the obtained safety factors are in agreement with the block analysis and the results from the numerical analysis performed by the distinct element code “3DEC.”

New insights into the 1963 Vajont slide using 2D and 3D distinct-element method analyses

The 1963 Vajont rock slide is studied using the distinct-element method (DEM). Two-dimensional (2D) and three-dimensional (3D) DEM models were constructed based on information published in the literature. In this study, a strength reduction approach was used to calculate the slide surface friction angles required for stability. The influence of several parameters was investigated in 2D, namely the reservoir water level, the shear stiffness of the slide surface, the rock mass strength, the rock mass deformability and rock joint patterns. Of the parameters which have been investigated, the most important parameter was found to be the reservoir water level. The rock mass deformability, which is neglected by other investigators, is also found to be important. From the 3D analyses, the failure friction angle was found to be sensitive to the assumptions made on the eastern boundary, and could affect the failure friction angle by approximately 3°. The slope was found to exhibit signs of failure beginning from φslide_surface = 26° before complete loss of resistance at φslide_surface = 18°. It also emerges that, although the eastern end of the slope is the first to exhibit signs of movement, the displacements at the western end of the slope become larger than the ones at the eastern end as the stability of the slope reduces. Finally, this study showcases some useful numerical techniques developed ad hoc for DEM analyses to investigate the stability of large-scale slopes.

3D DEM investigation of granular column collapse: Evaluation of debris motion and its destructive power

This paper presents a numerical investigation of the behaviour of dry granular flows generated by the collapse of prismatic columns via 3D Distinct Element Method (DEM) simulations in plane strain conditions. Firstly, by means of dimensional analysis, the governing parameters of the problem are identified, and variables are clustered into dimensionless independent and dependent groups.Secondly, the results of the DEM simulations are illustrated. Different regimes of granular motion were observed depending on the initial column aspect ratio. The profiles observed at different times for columns of various aspect ratios show to be in good agreement with available experimental results.Thirdly, a detailed analysis of the way energy is dissipated by the granular flows was performed. It emerges that most of the energy of the columns is dissipated by inter-particle friction, with frictional dissipation increasing with the column aspect ratio. Also, the translational and rotational components of the kinetic energy of the flows, associated to particle rotational and translational motions respectively, were monitored during the run-out process. It is found that the rotational component is negligible in comparison with the translational one; hence in order to calculate the destructive power of a granular flow slide, only the translational contribution of the kinetic energy is relevant.Finally, a methodology is presented to calculate the flux of kinetic energy over time carried by the granular flow through any vertical section of interest. This can be related to the energy released by landslide induced granular flows impacting against engineering structures under the simplifying assumption of neglecting all structure-flow interactions. This represents the first step towards achieving a computational tool quantitatively predicting the destructive power of a given flow at any location of interest along its path. This can be useful for the design of engineering works for natural hazard mitigation. To this end, also the distribution of the linear momentum of the flow over depth was calculated. It emerges that the distribution is initially bilinear, due to the presence of an uppermost layer of particles in an agitated loose state, but after some time becomes linear.This type of analysis showcases the potential of the Distinct Element Method to investigate the phenomenology of dry granular flows and to gather unique information currently unachievable by experimentation.

시멘트 혼합토 및 복합지반의 강도, 변형 특성 및 수치해석

In this research, the composite grounds including original clay and soil-cement were constructed for conducting uniaxial compression test. Strength and deformation properties were analysed using results of laboratory tests with variations of water content of clay, replacement ratio and cement content. Numerical simulation using 3D distinct element method was conducted for soil cement. For strength of composite ground that contains more than cement contents of 15 %, it is more effective to increase cement content than increase of replacement ratio. Strength and elastic modulus of composite ground could be predicted by regression equations using uniaxial compression strength of clay, cement content of soil cement and replacement ratio. For strength and elastic modulus of soil cement, which is most important things for predicting final strength and elastic modulus of composite ground, numerical simulation using the distinct element method adapted bonding model could be used to verify laboratory test, and predict strength and elastic modulus.

3DEC을 이용한 일정수직하중 조건에서의 전단강도에 관한 연구

암반 구조물의 안정성에 결정적인 영향을 미치는 절리의 특성을 파악하기 위해서는 일반적으로 직접전단시험을 통한 연구가 수행되고 있으나, 본 연구에서는 3차원 개별요소법에 근거한 3DEC을 사용하여 직접전단시험을 수치해석적으로 수행하였다. 톱니각과 강도가 상이한 인공 절리시험편에 대해 수직하중을 4단계로 변화시켜가며 일정수직하중 조건에서 실험실 직접전단시험으로 최대전단강도를 측정하였다. 그리고 실내시험을 통해 얻은 시험편의 역학적 물성으로 수치해석 모델링을 수행하였고, 획득한 전단강도를 실험실 직접전단시험으로 수행한 전단강도와 비교 분석하였다. 그 결과 개별요소법에 의한 수치해석은 암반의 전단거동을 잘 모사할 수 있을 것으로 사료된다. Direct shear tests have been initiated to understand the characteristics of joints which crucially affect the stability of rock mass. In this research, numerical approach in direct shear tests has been initiated using 3DEC on the basis of 3D distinct element method. Normal loads were altered in four different levels on artificial joint tests depending on the sawtooth angle and strengths on constant normal stress conditions, measuring the peak shear strength according to the direct shear tests under laboratory condition. Also results obtained from mechanical properties through laboratory test were used to perform numerical modeling, and shear strength obtained from the modeling was used to compare with laboratory direct shear test. As a result numerical analysis from distinct element method can simulate well on the shear behavior of rockmass.

Study of mechanical behavior and strain localization of methane hydrate bearing sediments with different saturations by a new DEM model

This paper presents a numerical investigation into mechanical behavior and strain localization in methane hydrate (MH) bearing sediments using the distinct element method (DEM). Based on the results of a series of laboratory tests on the bonded granules idealized by two glued aluminum rods and the available experimental data of methane hydrate samples, a pressure and temperature dependent bond contact model was proposed and implemented into a two-dimensional (2D) DEM code. This 2D DEM code was then used to numerically carry out a series of biaxial compression tests on the MH samples with different methane hydrate saturations, whose results were then compared with the experimental data obtained by Masui et al. [9]. In addition, stress, strain, void ratio and velocity fields, the distributions of bond breakage and averaged pure rotation rate (APR) as well as the evolution of strain localization were examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The numerical results show that: (1) the shear strength increases as methane hydrate saturation SMH increases, which is in good agreement with the experimental observation; (2) the strain localization in all the DEM MH samples develops with onset of inhomogeneity of void ratio, velocity, strain, APR, and distortion of stress fields and contact force chains; and (3) the methane hydrate saturation affects the type of strain localization, with one shear band developed in the case of 40.9% and 67.8% methane saturation samples, and two shear bands formed for 50.1% methane saturation sample.

An evaluation on the degradation evolutions in three constitutive models for bonded geomaterials by DEM analyses

This paper presents a numerical evaluation on the degradation evolutions in three well-known constitutive models for bonded geomaterials using the Distinct Element Method (DEM). A series of isotropic, constant stress ratio and biaxial compression tests on the bonded geomaterials were carried out by a two-dimensional (2D) DEM code, NS2D, for this purpose. The constitutive models examined are the disturbed state constitutive model (DSC model), the superloading yield surface model and Nova’s model. First, a microscopic interpretation of the degradation variable, which is used to describe the degradation evolution in the models, was presented based on the micromechanics theory to compare the degradation evolutions used by the models with the DEM results. Then, the macromechanical responses of the numerical specimens in the DEM tests were examined in comparison with the experimental data on the artificially bonded sands. Finally, the degradation evolutions observed in the DEM tests were compared with the results predicted by the constitutive models. The study shows that the DEM results are able to capture the main features of the artificially bonded sands. The degradation evolutions used in the three constitutive models are all overally in agreement with the DEM results. In addition, two simple evolution equations for the degradation variable, which can well describe the degradation evolution observed in the DEM tests, were presented and discussed.

Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in Äspö Pillar Stability Experiment (APSE)

In this paper, the coupled thermo-mechanical (TM) processes in the Äspö Pillar Stability Experiment (APSE) carried out by the Swedish Nuclear Fuel and Waste Management Company (SKB) were simulated using both continuum and discontinuum based numerical methods. Two-dimensional (2D) and three-dimensional (3D) finite element method (FEM) and 2D distinct element method (DEM) with particles were used. The main objective for the large scale in situ experiment is to investigate the yielding strength of crystalline rock and the formation of the excavation disturbed/damaged zone (EDZ) during excavation of two boreholes, pressurizing of one of the boreholes and heating. For the DEM simulations, the heat flow algorithm was newly introduced into the original code. The calculated stress, displacement and temperature distributions were compared with the ones obtained from in situ measurements and FEM simulations. A parametric study for initial microcracks was also performed to reproduce the spalling phenomena observed in the APSE.

Dynamic response of reinforced masonry columns in classical monuments

From the mechanical point of view, the particularity of masonry structures stems from the fact that the structural system is hard to be modeled by the classical Continuum Mechanics approach. The problem gets more complicated when imperfections, such as cracks are present. An example of a single multi-drum column, with fractured drums, is studied herein, using the Distinct Element Method (DEM). The purpose of the research is the investigation of the impact of the fractures to the overall stability of the structure. The 3D DEM numerical results are explained on the basis of simple 2D analytical considerations. The shear and normal crack deformation is monitored and the minimum required strength of the crack interface is quantified. An experimental program of direct shear tests is set in order to estimate the strength of the marble–cement interface. The experimental values are compared to the minimum required from the numerical analysis.

Analysis of Filling Characteristics of Granular Particles into Small Die Cavity Using Powder Simulation

Filling characteristics of granular particles into a small die cavity were investigated by experiment using model die filling system and 3D distinct element method (DEM) simulation. The influences of particle properties including flowability and speed of die shoe on filling fraction of granules, which is the ratio of the volume of filling particle to the volume of die cavity, were investigated experimentally, and it is shown that the filling fraction depends on the flow behavior of granular particles and geometry of die cavity. Three dimensional, large scale DEM simulation has been constructed to obtain detailed insights into complicated filling phenomena and apply to design of filling process. The determination method of simulation parameters in DEM model was discussed to get quantitative design parameters of filling operation by the simulation. Simulation results agreed well with experimental ones and DEM simulation can give detailed information of filling behavior of granular particles into small die cavity. Particle size-induced segregation generated in a moving shoe leads to non-uniformity of particle packing structure in the die cavity. There is optimum filling condition to minimize the segregation during die filling.

Electrostatic Transport of Lunar Soil for In Situ Resource Utilization

To realize a long-term lunar exploration, it is essential to develop a technology for transporting lunar soil for in situ resource utilization. We are developing a particle transport system that utilizes electrostatic traveling waves. The conveyer consists of parallel electrodes printed on a plastic substrate. Four-phase rectangular voltage is applied to the electrodes to transport particles on the conveyer. Mechanical vibration was applied to the conveyer to transport particles more efficiently. The results of our investigation are as follows: (1) The observed transport rate in air was 13.5 g/min for a conveyer with a width of 100 mm. By performing numerical calculations on the basis of the 3D distinct element method, we predicted that the system performance would improve in the high-vacuum and low-gravity environment on the moon. (2) Power consumption in this system is much less. It was only 10 W for a conveyer with an area of 1.0 m2 . (3) We demonstrated an inclined and curved transport path as well ...