Three-dimensional Distinct Element Method Research Articles

Three-dimensional Distinct Element Method for stability analysis of marble quarries in the Apuan Alps (Italy)

The present article analyses and proposes an innovative dynamic planning methodology, supported by computer tools and in-situ measurements, for the optimization of the planning techniques of underground marble quarries. The abovementioned planning methodology has been implemented in ‘Cava Piastreta’, an underground marble quarry located in the Apuan Alps, Italy. The entire excavation area has been characterized with tridimensional topographic surveys, geotechnical traditional surveys, and radar surveys, as well as stress-level measurement campaigns through a CSIRO cell. When an underground excavation project concerning stone material is designed, it is mandatory to have an instrument allowing a forecast of the stress-strain behavior of the rock mass. To this end, the rocky outcrop can also be represented by different mathematical models to schematize the geomechanical behavior. The accuracy and reliability of the simulation of the mechanical response of the fractured mass depend on the exactness with which the rocky outcrop is defined. Therefore, the geometric modeling phase acquires prominent importance. To better address the discontinuous nature of the studied rocky mass, the distinct element method has been used in modeling the mechanical behavior of the mass itself. Given the peculiar geometrical characteristics of the excavation site in question, the deterministic approach has been chosen to simulate as closely as possible the position of the major discontinuities identified in-situ. The present article thus aims to briefly describe a study that has been developed over the last years intended to deepen the analysis of the geostructural characterization of the excavation site, as well as to compare the obtained results through the geometrical tridimensional modeling with the values measured in-situ.

Performance of mechanical agitation type of ground-improvement by CAE system using 3-D DEM

Ground-improvement technology, aimed at ensuring the stability of the ground, can achieve the desired ground strength and other geological conditions by artificially improving soft grounds. Although many ground-improvement technologies have been proposed, there are few ways to confirm whether the target ground improvement has actually been carried out, and a method to visually evaluate these ground-improvement technologies is necessary. In this research, focusing on the relative stirring type of deep mixing method, which is one of the ground-improvement methods, a computer aided engineering (CAE) analysis, based on the three-dimensional distinct element method (DEM), is performed. Then, the behavior of the ground is evaluated and the characteristics of the relative stirring type of deep mixing method are verified. From the results, the behavior of the soil particles and the stirring characteristics of the relative type of stirring blade can be grasped, and it is shown that the ground-improvement method can be visually evaluated.

Investigation and modeling of direct toppling using a three-dimensional distinct element approach with incorporation of point cloud geometry

Block toppling instability can be a common problem in natural rock masses, especially in mining environments where excavation activity may trigger discontinuity-controlled instability by modifying the natural slope geometry. Traditional investigations of block toppling failure consider classic kinematic analyses and simplified two-dimensional limit equilibrium methods. This approach is still the most commonly adopted, but the simple two-dimensional conceptual model may often oversimplify the instability mechanisms, ignoring potential critical factors specifically related to the three-dimensional geometry. This paper uses a three-dimensional distinct element method approach applied to an example case study, identifying the critical parameters that influence direct toppling instability in an open pit environment. Terrestrial laser scanning was used to obtain detailed three-dimensional geometrical information of the slope face geometry for subsequent stability analyses. A series of sensitivity analyses on critical parameters such as friction angle, discontinuity shear and normal stiffness, discontinuity spacing, and orientation was performed, using simple conceptual three-dimensional numerical modeling. Results of the analyses revealed the importance of undertaking three-dimensional analyses for direct toppling investigations that allow identification of critical parameters. A three-dimensional distinct element analysis was then performed using a more realistic complex volumetric mesh model of the case study slope which confirmed the previous modeling results but also identified unstable blocks in high slope angle areas, providing useful information for life of mine design. The paper highlights the importance of slope geometry and fracture network orientation on potential slope instability mechanisms.

Slip perturbation during fault reactivation by a fluid injection

Slip orientation inferred from fault striae or focal mechanism datasets is commonly used in stress inversion methods based on the Wallace-Bott hypothesis. The hypothesis postulates that slip on a fault plane is collinear with the orientation of the resolved shear stress. It is valid for a single planar fault subjected to a homogeneous far-field stress. However, the experimental displacement data from an induced fault reactivation experiment, conducted in the Mont Terri rock laboratory, Switzerland, indicated multiple triggered slip orientations, thereby preventing application of the above inversion method. We present numerical and analytical results of slip on a reactivated fracture with a non-uniform fluid pressure distribution. Using these models, we evaluate the reasons for the inconsistency of our observations and the traditional Wallace-Bott hypothesis and test the physical effects of various parameters on fault slip. In the fully coupled hydromechanical numerical model (three-dimensional distinct element method), fluid pressure at a point on the fault surface is increased stepwise (assumed planar and singular) until shear reactivation of the fault is induced. We studied two different models with high and low fault plane stiffness to represent hard and soft rock masses, respectively. The model shows that high fault stiffness preserves the planarity of the fault plane, while low fault stiffness permits dilation and morphological changes of the fracture related to fluid pressure diffusion. The highest slip perturbation was observed in the low stiffness model due to the change of the fracture shape, controlled by the non-uniform pressure distribution. The Eshelby analytical solution confirmed that the more the fracture is dilated, the more the corresponding resolved shear stress is perturbed. Additionally, when compared to dilation and fault aperture, the friction angle has the most influence on the angular difference between geomechanical slip vectors and resolved shear stress.

Evaluation of load-carrying capacity of full-scale falling protection net using distinct element method

This article presents a simulation of a full-scale falling protection net using three-dimensional distinct element method. First, an application of distinct element method utilized cylinder rigid body element for collision response analysis of a flexible structure that has a long and slender shape similar to wire rope. Second, contact spring normally obtain contact force between the cylindrical element and spherical element in the case of distinct element method. However, connect spring that expresses axial stiffness like tension or compression and bending stiffness of the flexible structure was indicated as a fresh approach of the analysis method. Third, it is suggested to simulate large deformation program using connect spring of three-dimensional distinct element method and examine the application of reproducibility to analyze a full-scale falling protection net. Finally, the analysis result evaluated the performance of falling protection net using distinct element method which utilized connect spring and cylindrical model.

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.

Assessment of roof stability in a room and pillar coal mine in the U.S. using three-dimensional distinct element method

This paper examines the effect of different geological and mining factors on roof stability in underground coal mines by combining field observations, laboratory testing, and numerical modeling. An underground coal mine in western Pennsylvania is selected as a case study mine to investigate the underlying causes of roof falls in this mine. Three-dimensional distinct element analyses were performed to evaluate the effect of different parameters, such as the variation of immediate roof rock mass strength properties, variation of discontinuity mechanical properties, orientations and magnitudes of the horizontal in-situ stresses, and the size of pillars and excavations on stability of the immediate roof. The research conducted in this paper showed that the bedding planes play an important role on the geo-mechanical behavior of roofs in underground excavations. Therefore, an appropriate numerical modeling technique which incorporates the effect of discontinuities should be employed to simulate the realistic behavior of the discontinuous rock masses such as the layered materials in roof strata of the underground coal mines. The three-dimensional distinct element method used in this research showed the capability of this technique in capturing the important geo-mechanical behavior around underground excavations.

Evolution of the internal structure of fault zones in three-dimensional numerical models of normal faults

Fault zone internal structure is characterised by heterogeneous distributions of both continuous (drag, lens rotation) and discontinuous (joints, faults) deformation which cannot be easily modelled using continuum numerical methods. Distinct element method (DEM) models, that exhibit bulk rheologies comparable to rock, demonstrate emergent behaviours that make them ideal for modelling both the nucleation and growth of fault zones. The ability to model fault zones numerically allows extant conceptual models for fault zone evolution based on outcrop studies to be tested, and controls on fault zone structure to be analysed. Three-dimensional DEM models of faults zones in mechanically layered sequences demonstrate that internal fault zone structure is predominantly controlled by the geometry of the initial fault. Whether the initial fault is a segmented array or an irregular surface determines the complexity of structure it will develop as displacement increases. Confining pressure at the time of faulting determines the irregularity of the initial fault array and also the efficiency with which irregularities are incorporated into a fault and subsequently comminuted, leading to a relationship whereby brittle faulting at high confining pressure results in less complex internal fault zone structure than at low confining pressure.

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.

Resonant Column Apparatus Tests on Intact and Jointed Rock Specimens with Numerical Modelling Validation

The determination of rock mass dynamic parameters including the influence of joints/discontinuities on wave propagation is of interest for solving problems in geophysics, rock protective engineering, rock dynamics and earthquake engineering. This topic is covered in this paper by means of laboratory tests on intact and jointed rock specimens performed with the resonant column apparatus (RCA). Attention is dedicated to the determination, with this equipment, generally used for testing soils, of the shear modulus at small strain and the damping ratio of intact and jointed rock specimens. A correction procedure based on the RCA tests performed on aluminium specimens is described. The results of the tests performed are analysed in detail. Three-dimensional distinct element method modelling is used to evaluate the applicability of the RCA and the correctness of the laboratory tests performed. A comparison with the results obtained using the scattering matrix method is also presented.

DISTINCT ELEMENT METHOD SIMULATION ON DEFORMATION MODE AND STRESS STATE FOR SPECIMEN SHAPE IN DIRECT SHEAR TEST

In order to examine the deformation mode and the stress state according to the specimen shape in the direct shear test (DST), a series of the three-dimensional DEM (distinct element method) simulations of the DST for sandy soils were carried out with the circular and the rectangular specimens. From the obtained results, the deformation mode of the rectangular specimen was under the plane strain condition, while the deformation mode of the circular specimen could not be explained as a plane strain condition. In addition, the principal stress states around the potential shear plane were analyzed and discussed by means of the analysis of the soil particle level.

DEM simulation of collapse behaviours of unsaturated granular materials under general stress states

In this study, a numerical simulation of true triaxial tests was conducted using the three-dimensional distinct element method (DEM) in order to examine how unsaturated granular materials collapse under general stress states. The collapse process was simulated by reducing the intergranular adhesive forces corresponding to the effect of the capillary suction during the isotropic compression and the shearing processes under general stress states. Based on the relationship between the void ratio and the mean principal stress after collapsing, it was found that the initially soaked compression line obtained with an inundation test may be used to predict the collapse of granular materials under a general stress state. From the analysis for the fabric tensor in the particle aggregate after collapsing, the skeleton structures became identical to those in which no intergranular adhesive force was applied. Furthermore, even though the collapse process was simulated under a plane strain condition, the shear band inside the sample did not occur clearly, and the slippage between particles was instead induced randomly during collapsing.

Failure process of masonry buildings during earthquake and associated casualty risk evaluation

Collapse of masonry structures during an earthquake is analyzed using the three-dimensional distinct element method (3D-DEM) code developed by the first author. The DEM is a numerical analysis technique, in which positions of elements are calculated by solving equations of motion step by step. Both individual and group behavior can be simulated. The structure is modeled as an assembly of distinct elements connected by virtual springs and dashpots, where elements come into contact. First, the validity of the developed 3D-DEM code is confirmed by comparing analytical results with static experimental results of masonry walls. Second, failure process of masonry buildings due to earthquake is investigated using DEM. Effects of reinforcing methods are also examined. Finally, injury to human bodies in the collapsing masonry buildings is also calculated. Assuming that occupants lie down on the floor, two types of casualty criteria are introduced and assessed.

Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images

The objective of this study is to predict the dynamic modulus of asphalt mixture using both two-dimensional (2D) and three-dimensional (3D) Distinct Element Method (DEM) generated from the X-ray computed tomography (X-ray CT) images. The 3D internal microstructure of the asphalt mixtures (i.e., spatial distribution of aggregate, sand mastic and air voids) was obtained using the X-ray CT. The X-ray CT images provided exact locations of aggregate, sand mastic and air voids to develop 2D and 3D models. An experimental program was developed with a uniaxial compression test to measure the dynamic modulus of sand mastic and asphalt mixtures at different temperatures and loading frequencies. In the DEM simulation, the mastic dynamic modulus and aggregate elastic modulus were used as input parameters to predict the asphalt mixture dynamic modulus. Three replicates of a 3D DEM and six replicates of a 2D DEM were used in the simulation. The strain response of the asphalt concrete under a compressive load was monitored, and the dynamic modulus was computed. The moduli of the 3D DEM and 2D DEM were then compared with both the experimental measurements results. It was revealed that the 3D discrete element models successfully predicted the asphalt mixture dynamic modulus over a range of temperatures and loading frequencies. It was found that 2D discrete element models under predicted the asphalt mixture dynamic modulus.

On Impact Penetration Analysis and Evaluation of Laminated Glass Plate Using Three-Dimensional DEM

It is important to know the impact fracture behaviors in the safety design of the laminated glass plate. However, the three-dimension analysis for the impact fracture behaviors of the laminated glass plate is not done over the current. In this research, the impact penetration fracture when the impact body collides with the center of the laminated glass plate is analyzed by PFC3D. It is the general three-dimensional program that uses the Distinct Element Method (DEM). DEM is suitable for the analysis of the fracture behavior of the non-individual body and the break-up body. The analytical results are compared with the experimental one and the validity of analytical results are checked. By this research, it is obvious that the penetration speed and the loss energy increase as the impact velocity, radius and mass of the impact body increase. Moreover, the relations between the parameters of impact body and fracture behavior are clarified.

Improvement of contact detection in 'approaching faces' method for use in three-dimensional discontinuous deformation analysis

One of the most efficient procedures of contact detection in three-dimensional distinct element method (3D DEM) is detection of contact patterns between approaching faces of two neighbouring convex blocks, however some modifications should be done on this method to make it usable in 3D discontinuous deformation analysis (DDA). In many occasions two blocks having more than one pair of approaching face come close to each other. Consequently, more than one contact pattern may be detected which results in multicalculation of some contact points and following incorrect calculation of contact forces in 3D DDA. By applying the algorithm of 'dominant contact detection' presented in the present paper, only one contact type which includes all contact points is found among all detected contact patterns. The proposed algorithm was programmed using VC++ and verified by an illustrative example.

NUMERICAL SIMULATION FOR LANDSLIDE WITH FALLEN TREES USING 3D DISTINCT ELEMENT METHOD

To reduce damages of recurrent disasters of landslide in moutainside towns, a constant awareness of the disaster prevention is important. A dynamic and visual representation of a disaster would play an effective role to explain a danger of a landslide disaster. In the present study, numerical simulation of a landslide was performed using the three-dimensional Distinct Element Method, and an eloquent performance of this kind of simulator was represented by showing various angle of snapshots. Especially, a landslide considered with fallen trees modeled by the passively-moving-solid model was simulated because a usual landslide disaster contains fallen trees, and the simulation result showed a good agreement with an actual landslide in a tendency of accumulation form.

Morphologies of three-dimensional shear bands in granular media

We present numerical results on spontaneous symmetry breaking strain localization in axisymmetric triaxial shear tests of granular materials. We simulated shear band formation using the three-dimensional distinct element method with spherical particles. We demonstrate that the local shear intensity, the angular velocity of the grains, the coordination number, and the local void ratio are correlated and any of them can be used to identify shear bands; however, the latter two are less sensitive. The calculated shear band morphologies are in good agreement with those found experimentally. We show that boundary conditions play an important role. We discuss the formation mechanism of shear bands in the light of our observations and compare the results with experiments. At large strains, with enforced symmetry, we found strain hardening.

Rotation Response of a Rigid Body under Seismic Excitation

After the 1994 Sanriku-Haruka-Oki, Japan, earthquake, rotation of tombstones along the vertical axis occurred in a graveyard about 34m from the Japan Meteorological Agency Hachinohe Observatory where strong motion was recorded. The properties of seismic motion that make a rigid rectangular solid body rotate are discussed. Shaking table tests were conducted to reproduce the rotation response of Japanese-style tombstones which typically consist of several stone blocks whose shapes are rectangular solids. Data obtained from those tests were used to calibrate a numerical model by the three-dimensional distinct element method. Results of the shaking tests and numerical analyses showed that rotation of a rigid rectangular solid body may be caused by the combination of the rocking of the body and particle motion of the input acceleration. Rotation behavior of an actual tombstone was simulated based on the observed accelerogram. Findings show that one or two cycles of particle motion near peak acceleration caused the rotation.

Three-dimensional numerical simulation method for gas–solid injector

A three-dimensional turbulent gas–solid two-phase flow model for a gas–solid injector is developed in the present study. Time-averaged conservation equation for mass and momentum and a two-equation k– ɛ closure are used to model the carried fluid phase. The solid phase is simulated by using a Lagrangian approach. In this model, the drag and lift forces on particles, the multi-body collisions among particles and the mutual interaction between gas and particles were taken into account. Interparticle interactions and particle–wall collisions are emulated by using the three-dimensional distinct element method (DEM). A new correlation, β ( δ ⁡ v p ⁢ δ ⁡ v p ― − δ ⁡ u ⁢ δ ⁡ v p ― ) = − 2 ⁢ β ⁢ K ( 1 − τ L τ L + τ d ) τ L τ L + τ d , which represents the transfer of kinetic energy of the particle motion to kinetic energy of the carrier fluid, is introduced in the additional source term S d ɛ of the transport equation of turbulence kinetic energy, K. The calculated pressure distributions along the axis in the different parts of gas–solid injectors using pressured pneumatic conveying system under different driving jet velocities, pressures and values of angle of convergent section ( α) are found to be in agreement with the experimental results. The axial mean velocity of particles and the behavior of gas and particles in the gas–solid injector are calculated, their results reasonably explaining actual phenomenon observed in experiment.