Distinct Element Simulation Research Articles

Assessment of discontinuity related instability potential in a surge pool cavern: kinematic and distinct element approach

Safe and economical subsurface excavation requires a holistic assessment of the ground. Possibilities of stress-induced and structural failures need thorough consideration before excavation. Over-supporting an excavation is uneconomical while under-supporting can lead to disastrous results. Thus, in this research, an attempt has been made to devise the most efficient and reliable support system. An under-construction underground surge pool cavern to store and lift water at the Indian state of Telangana was taken up as the research site. The methodology involved in-depth geological and geotechnical investigations to identify possible adverse features. Rock mass rating and Q-index, were implemented for rockmass characterization. The surge pool was constructed using the Norwegian Method of Tunnelling (NMT) and validated with BIS codes. The stability analysis and support design were carried out with the help of distinct element simulation and wedge analysis for the surge pool heading portion. A right crown portion was found to be most susceptible to failure, which was also confirmed by the both the analysis. A thorough examination led to the most robust and economical support design for long-term stability.

A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

AbstractDisplacement‐based methods contained in recent standards for seismic safety assessment require the determination of the full nonlinear pushover curve for local failure mechanisms in historic masonry structures. This curve should reflect both the initial elastic behavior and the rigid body behavior after the activation of rocking. In this work, a rigid block model is proposed for the displacement‐based seismic assessment of local collapse mechanisms of these structures. Masonry is modeled as an assemblage of two‐dimensional rigid blocks in contact through frictional interfaces. Two types of contact models are formulated to capture, respectively, the pre and postpeak branches of the pushover curve: a unilateral elastic contact model, capturing the initial nonlinear behavior up to the force capacity of the structure, corresponding to the activation of the collapse mechanism, and a rigid contact model with finite friction and compressive strength, which describes the rigid‐body rocking behavior up to the attainment of the displacement capacity of the structure. Tension‐only elements are also implemented to model strengthening interventions with tie‐rods. The contact problems associated with the elastic and rigid contact models are formulated using mathematical programming. For both models, a sequential solution procedure is implemented to capture the variation of the load multiplier with the increasing deformation of the structure (P–Δ effect). The accuracy of the modeling approach in reproducing the pushover curve of masonry panels subjected to horizontal seismic loads is evaluated on selected case studies. The solution is first tested against hand calculations, existing analytical models, and distinct element simulations. Then, comparisons against experimental tests follow. As a final application, the failure mechanism and pushover curve of a triumphal masonry arch are predicted by the model and its seismic assessment is performed according to codified force‐ and displacement‐based methods, demonstrating the adequacy of the proposed tool for practice.

The Tensile Strength of Loess in Northwest China by Unconfined Penetration Test and the Distinct Element Simulation

The unconfined penetration test (UP test) is one of the indirect methods to measure the tensile strength of soils. Through a series of UP tests of undisturbed and remolded loess, the split angle (α) of the wedge body which was shaped in the process of the experiment was discussed. And then, the particle movement, the force transfer, and the fracture development law of the sample were studied by the distinct element method (PFC2D). The experiment and numerical simulation results show the following: (1) the split angle (α) presents an exponential decrease with tensile strength (σt) and a linear decrease with internal friction angle (φ); (2) K that can be written as tan (2α + φ) is a coefficient to calculate tensile strength, which is equal to 2.00 for remolded loess and 1.50 for undisturbed loess; (3) the distinct element simulation shows that the resisting force by the UP test comes from both tensile stress and shear stress; (4) the tensile fractures and shear fractures appear at almost the same time when the tensile stress is approximately 70% of tensile strength.

Distinct Element Simulation of a Landslide Process

Abstract The paper presents a numerical simulation of the development of a catastrophic landslide in a sandstone quarry and methods of reconstructing the quarry to its previous condition from before the landslide. The important objective of the paper is to present the capabilities of the numerical method used in the analysis of the landslide process, namely the Distinct Element Method (DEM). This method is poorly known, though it is capable of solving important geotechnical problems in which massive displacements are modelled. The features of the method are presented on the basis of a case study. Therefore a numerical analysis is carried out to show the performance of DEM in generating a displacement of several dozen meters in the example of a catastrophic landslide that occurred some years ago in a sandstone quarry. This engineering problem makes it possible to describe and analyse the mechanisms, causes and consequences of the landslide.

A macro-micro study and distinct element simulation on large-scale shear test of coarse-grained soil

A macro-micro study and distinct element simulation on large-scale shear test of coarse-grained soil

Distinct Element Simulation of Mechanical Properties of Hypothetical CNT Nanofabrics

A universal framework for modeling composites and fabrics of micro- and nanofibers, such as carbon nanotubes, carbon fibers and amyloid fibrils, is presented. Within this framework, fibers are represented with chains of rigid bodies, linked with elastic bonds. Elasticity of the bonds utilizes recently developed enhanced vector model formalism. The type of interactions between fibers is determined by their nature and physical length scale of the simulation. The dynamics of fibers is computed using the modification of rigid particle dynamics module of the waLBerla multiphysics framework. Our modeling system demonstrates exceptionally high parallel performance combined with the physical accuracy of the modeling. The efficiency of our technique is demonstrated with an illustrative mechanical test on a hypothetical carbon nanotube textile. In this example, the elasticity of the fibers represents the coarse-grained covalent bond within CNT surface, whereas interfiber interactions represent coarse-grained van der Waals forces between cylindrical segments of nanotubes. Numerical simulation demonstrates stability and extremal strength of a hypothetical carbon nanotube fabric.

Simulation analysis of water resource damage feature and development degree of mining-induced fracture at ecologically fragile mining area

Mining-induced water damage has become one of wide concerned issues in contemporary society. Knowing the main causes to water resource damage (especially the superficial aquifer damage) as well as the damage mode is the basis for realizing water conservation. In this paper, the mining height and position of aquifuge are regarded as the main influencing factors in analyzing the change of aquifer. Taking the geological conditions of Yili No. 4 coal mine as an example, a total of 18 numerical analysis models with different mining heights (3, 5, 8, 10, 15, 20 m) and different positions of aquifuge (upper, middle and bottom) as changing conditions were established using universal distinct element code discrete element simulation software. The variation characteristics of water resources in aquifers after disturbance were studied. The variation of water pressure with mining height and position of aquifuge was analyzed. The variation of water pressure in aquifer was proposed as a novel criterion for distinguishing the development degree of mining-induced fracture. The criterion for determining the failure of aquifer was established based on the ratio of water pressure change and mining height (P/H), which is a pioneering research on the relationship between mining-induced fracture and aquifer failure. This study provides a reference for evaluating the development degree of mining-induced fracture and provides theoretical basis for analyzing the coupling relationship between mining and water resource change in aquifer and for water conservation at ecologically fragile mining area.

Distinct Element Simulations of Shear Rupture in Dilatant Granular Media

AbstractThe development of shear rupture in granular media due to boundary deformation was captured using the distinct element method (DEM). Assemblages of nonspherical, three-dimensional particles...

Distinct element simulations of earthquake fault rupture through materials of varying density

Surface manifestations of earthquake fault rupture are strongly affected by the dilatant response of the soil deposit overlying the bedrock fault displacement. The granular material’s in-situ void ratio and effective confining stress affect its dilatancy, and hence, its stress-strain response and ductility. Distinct element method (DEM) assemblages of 3D, non-spherical particles are prepared with different void ratio distributions, and their dilatancy is characterized using direct shear test simulations. DEM simulations capture the response of sand in centrifuge experiments of earthquake fault rupture propagation. Macro-scale mechanisms of ground deformation and micro-scale mechanisms of shear band formation during dip-slip fault rupture propagation are analyzed through particle rotations, homogenized strains, frictional dissipation, and particle displacements. The brittle and ductile responses of granular media undergoing fault rupture are related to changes in the coordination numbers in each particle assemblage. The deformational characteristics of a metastable fabric in the loosest particle assemblages and a stable fabric in the densest particle assemblages are revealed through the accumulation of energy dissipated through friction. The normalized strong contact forces are also greater in magnitude in the loosest particle assemblages and greater in number in the densest assemblages.

Performance comparisons of bonding box-based contact detection algorithms and a new improvement technique based on parallelization

Purpose – The purpose of this paper is to find a convenient contact detection algorithm in order to apply in distinct element simulation. Design/methodology/approach – Taking the most computation effort, the performance of the contact detection algorithm highly affects the running time. The algorithms investigated in this study consist of Incremental Sort-and-Update (ISU) and Double-Ended Spatial Sorting (DESS). These algorithms are based on bounding boxes, which makes the algorithm independent of blocks shapes. ISU and DESS algorithms contain sorting and updating phases. To compare the algorithms, they were implemented in identical examples of rock engineering problems with varying parameters. Findings – The results show that the ISU algorithm gives lower running time and shows better performance when blocks are unevenly distributed in both axes. The conventional ISU merges the sorting and updating phases in its naïve implementation. In this paper, a new computational technique is proposed based on parallelization in order to effectively improve the ISU algorithm and decrease the running time of numerical analysis in large-scale rock mass projects. Originality/value – In this approach, the sorting and updating phases are separated by minor changes in the algorithm. This tends to a minimal overhead of running time and a little extra memory usage and then the parallelization of phases can be applied. On the other hand, the time consumed by the updating phase of ISU algorithm is about 30 percent of the total time, which makes the parallelization justifiable. Here, according to the results for the large-scale problems, this improved technique can increase the performance of the ISU algorithm up to 20 percent.

A Combined Remote Sensing–Numerical Modelling Approach to the Stability Analysis of Delabole Slate Quarry, Cornwall, UK

Rock slope geometry and discontinuity properties are among the most important factors in realistic rock slope analysis yet they are often oversimplified in numerical simulations. This is primarily due to the difficulties in obtaining accurate structural and geometrical data as well as the stochastic representation of discontinuities. Recent improvements in both digital data acquisition and incorporation of discrete fracture network data into numerical modelling software have provided better tools to capture rock mass characteristics, slope geometries and digital terrain models allowing more effective modelling of rock slopes. Advantages of using improved data acquisition technology include safer and faster data collection, greater areal coverage, and accurate data geo-referencing far exceed limitations due to orientation bias and occlusion. A key benefit of a detailed point cloud dataset is the ability to measure and evaluate discontinuity characteristics such as orientation, spacing/intensity and persistence. This data can be used to develop a discrete fracture network which can be imported into the numerical simulations to study the influence of the stochastic nature of the discontinuities on the failure mechanism. We demonstrate the application of digital terrestrial photogrammetry in discontinuity characterization and distinct element simulations within a slate quarry. An accurately geo-referenced photogrammetry model is used to derive the slope geometry and to characterize geological structures. We first show how a discontinuity dataset, obtained from a photogrammetry model can be used to characterize discontinuities and to develop discrete fracture networks. A deterministic three-dimensional distinct element model is then used to investigate the effect of some key input parameters (friction angle, spacing and persistence) on the stability of the quarry slope model. Finally, adopting a stochastic approach, discrete fracture networks are used as input for 3D distinct element simulations to better understand the stochastic nature of the geological structure and its effect on the quarry slope failure mechanism. The numerical modelling results highlight the influence of discontinuity characteristics and kinematics on the slope failure mechanism and the variability in the size and shape of the failed blocks.

Back Analysis of the 2014 San Leo Landslide Using Combined Terrestrial Laser Scanning and 3D Distinct Element Modelling

Landslides of the lateral spreading type, involving brittle geological units overlying ductile terrains, are a common occurrence in the sandstone and limestone plateaux of the northern Apennines of Italy. The edges of these plateaux are often the location of rapid landslide phenomena, such as rock slides, rock falls and topples. In this paper, we present a back analysis of a recent landslide (February 2014), involving the north-eastern sector of the San Leo rock slab (northern Apennines, Emilia-Romagna Region) which is a representative example of this type of phenomena. The aquifer hosted in the fractured slab, due to its relatively higher secondary permeability in comparison to the lower clayey units leads to the development of perennial and ephemeral springs at the contact between the two units. The related piping erosion phenomena, together with slope processes in the clay-shales have led to the progressive undermining of the slab, eventually predisposing large-scale landslides. Stability analyses were conducted coupling terrestrial laser scanning (TLS) and distinct element methods (DEMs). TLS point clouds were analysed to determine the pre- and post-failure geometry, the extension of the detachment area and the joint network characteristics. The block dimensions in the landslide deposit were mapped and used to infer the spacing of the discontinuities for insertion into the numerical model. Three-dimensional distinct element simulations were conducted, with and without undermining of the rock slab. The analyses allowed an assessment of the role of the undermining, together with the presence of an almost vertical joint set, striking sub-parallel to the cliff orientation, on the development of the slope instability processes. Based on the TLS and on the numerical simulation results, an interpretation of the landslide mechanism is proposed.

A bond failure criterion for DEM simulations of cemented geomaterials considering variable bond thickness

SUMMARYA series of micromechanical tests were conducted to investigate the bond failure criterion of bonded granules considering the effect of bond thickness, with the aim of enhancing the bond contact model used in the distinct element simulations of cemented geomaterials. The granules were idealized in a two‐dimensional context as one pair of aluminum rods bonded by resin epoxy or cement. The mechanical responses of nearly 500 rod pairs were tested under different loading paths to attain the yield loads of bonded granules at variable bond thickness. This study leads to a generic bond failure criterion incorporating the effect of the bond thickness. The results show that the bond compressive resistance largely decreases with increasing bond thickness owing to the presence of the confinement at the bond‐particle interface. The strength envelopes obtained from the combined shear compression tests and combined torsion compression tests have identical functional form, and they decrease in size with increasing bond thickness but remain unchanged in shape. Given the same cementation material, the generic bond strength envelope in a three‐dimensional contact force space under different loading paths remains the same in shape but shrinks with the increase of bond thickness. Copyright © 2014 John Wiley & Sons, Ltd.

Distinct element simulation of lugged wheel performance under extraterrestrial environmental effects

Lunar regolith demonstrates a high angle of internal friction due to particle angularity and apparent cohesion due to interparticle short-range interaction in lunar environment. This paper investigates the mobility of lunar rovers under partial gravity. A high-efficient contact model of lunar regolith that fuses rolling resistance and van der Waals forces was employed in the distinct element analyses of model wheel tests. Soil behavior and wheel performance under an extraterrestrial environment were analyzed in comparison with that under a terrestrial environment. Results indicate that van der Waals forces enhance the macroscopic shear strength of lunar soils particularly under low confining pressures associated with microgravity conditions. In the extraterrestrial environment, the mobility of a lugged wheel becomes not as well as expected due to more slippage and sinkage than that in the terrestrial environment, while it moves more efficiently in view of tractive efficiency. Increased slip ratio and sinkage on the lunar surface are attributed to loosely packing of soil particles in microgravity conditions, where reduced wheel load plays only minor role in improving the mobility of the wheel. Van der Waals forces between soil grains are beneficial to the wheel performance due to increased strength in soils, while this contribution is overwhelmed by the effect of largely reduced confining pressure in soils due to partial gravity on the Moon.

Distinct element simulation of ultimate bearing capacity in jointed rock foundations

In this paper, distinct element method numerical modeling is applied to evaluate bearing capacity of strip footing rested on anisotropic discontinuous rock mass. As yet, a little work has been carried out to investigate the effect of joint set orientation on the bearing capacity of rock mass. Generally, the overall behavior of rock mass under loading is very complicated and such analysis should include deformation determination, sliding along discontinuities and failure of rock material. Failure mechanism of rock mass depended on both geometrical parameters of joint sets and strength parameters of rock mass. In this research, it is assumed that rock mass contains one joint set, and therefore the anisotropy in bearing capacity and rock behavior is only due to the existence and orientation of the joint set. In this study, by assuming constant strength parameters and using Mohr–Coulomb failure criterion for the single joint set and nonlinear Hoek–Brown failure criterion for rock material, variation of the bearing capacity values and the type of failure mechanism of rock mass with different joint set dips is investigated. The obtained results indicate that the ultimate bearing capacity of rock mass containing one joint set varies between 27 and 86 % of intact rock.

Thermomechanical state parameter models for sands

The granular structure of sands and other geomaterials makes them amongst the most difficult engineering materials to model. In this paper a recently developed thermomechanical procedure is used to derive constitutive models for sands undergoing triaxial deformations. The well-known geomechanical state parameter is given a new significance and is taken as the fundamental thermomechanical state parameter. The logarithm of the specific volume is shown to be the plastic volume strain, and its relationship to the logarithm of the effective pressure is shown to be fractal. In addition the shear-induced volume strains, characteristic of granular materials, are introduced via a workless constraint, and the resulting deformation is seen to exhibit ‘induced anisotropy' automatically. The associated reaction stress tensor is shown to be identical with the extant fabric tensor. The plastic flow rule is shown to be necessarily non-associated. Comparison with experimental data is made, together with some discussion of the model's relation to the predictions of distinct element simulations.

Development of characteristic volcanic debris avalanche deposit structures: New insight from distinct element simulations

Large-scale catastrophic collapse of volcanic edifices is a relatively common phenomenon in the geologic record. However, the processes that occur during debris avalanche emplacement remain poorly understood and must generally be inferred from analysis of avalanche deposits in the field, which are recognized to contain a suite of recurrent features, such as conical surface hummocks and toreva block ridges. This study uses the distinct element numerical modelling method to investigate debris avalanche emplacement processes, because it allows brittle deformation of the failure mass to be examined. After describing the material calibration and model setup necessary for modelling the geomechanical behaviour of a failed edifice flank, a sequence of emplacement snapshots is described. The simulated debris avalanche is seen to evolve from initial block sliding, through extension with horst and graben structures defined by propagation and offset of large-scale discontinuities, to a final stage in which the avalanche flows down-valley. The numerical model is consistent with emplacement theory in the literature and allows for a more precise view of the processes at work during failure and the deposits created thereby. For example, toreva blocks are formed in the medial and proximal sections of the failure through top-down propagation of normally offset discontinuities developed from upper surface tension. A mechanism for surface hummock formation is also recognized involving the retention of surface blocks. As these and other characteristic deposit features are formed from a flank with homogeneous material properties, brittle deformation of the initially listric-shaped failure mass and associated macroscopic structural evolution are recognized as important factors in failure evolution and subsequent deposit morphology.

Discrete modelling of granular materials and geotechnical problems

ABSTRACT Distinct Element (DEM) simulations are more and more used to solve selected real problems involving granular materials, both in the geotechnical engineering and chemical engineering fields. This approach involves a series of difficulties, which are related to the definition of the model itself and to the calibration of its micromechanical parameters. In this paper, the main features involved with DEM modelling of granular materials are reviewed, and a simple modelling approach is proposed. Under the light of existing literature, a series of modelling guidelines are given and the performance of the proposed approach tested by simulating the mechanical behaviour of sand.

Experimental validation of distinct element simulation for dynamic wheel–soil interaction

The deformation behaviour of the soil during dynamic wheel–soil interaction was studied by using the discontinuum modelling technique, distinct or discrete element method (DEM). The simulation model was developed using DEM for two types of soil, soil-A (coarse sand) and soil-B (medium sand). A transparent sided soil bin was used to observe the soil deformation. Three CCD video camera photographic images of the validation experiments were analyzed and compared with the simulation program results. This paper presents the simulation and validation results for two types of soil at three different vertical loadings of 4.9, 9.8 and 14.7 N. Wheel sinkage, vertical and horizontal draft force acting on the rigid wheel and the soil deformation images from the validation experiments were some of the data used to compare the simulation program results with the validation experiments. The simulation program was helpful to understand the complex deformation behaviour of the soils. The simulated results for the deformation behaviour of soil-B showed better correlation with the validation experiments than soil-A. The results obtained have also been compared with the previous work on DEM to explain phenomena such as the high simulated sinkage of the rigid wheel.

A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior

The discrete element method is a widely used particle orientated simulation approach for modeling granular systems. It is based on tracking each particle's movement and its interactions with the surroundings over time. The motion of a particle is given by a system of coupled ordinary differential equations which are solved numerically. Therefore, models for the forces acting between particles in contact need to be specified. In the past, detailed investigations dealing with the accuracy of tangential force–displacement models have been very limited, with sparse experimental data considered and the frequent restriction of including only fully elastic materials. In large scale discrete element simulations, on the other hand, viscoelastic or plastic material behavior is often assumed for normal contacts and combined with arbitrary tangential models. To address this situation a number of tangential force–displacement models are reviewed including linear models by Cundall and Strack [1979. A discrete numerical model for granular assemblies, Geotechnique 29, 47–65], Di Maio and Di Renzo [2004. Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model. Chemical Engineering Science 59(16), 3461–3475], Brendel and Dippel [1998. Lasting contacts in molecular dynamics simulations. In: Herrmann, H.J., Hovi, J.-P., Luding, S. (Eds.), Physics of Dry Granular Media, Dordrecht. Kluwer Academic Publishers, pp. 313], Walton and Braun [1986. Viscosity, granular temperature and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology 30, 949] and simple non-linear models by Brilliantov et al. [1996. Model for collisions in granular gases. Physical Review E 53(5), 5382–5392], Tsuji et al. [1992. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology 71, 239–250] and Di Renzo and Di Maio [2005. An improved integral non-linear model for the contact of particles in distinct element simulations. Chemical Engineering Science 60(5), 1303–1312]. Whereas for fully elastic materials the parameters of the tangential force–displacement models can be derived directly from mechanical properties a scaling approach is proposed for the estimation of the parameters in the non-elastic case. The effect of different normal force–displacement models is analyzed. For all model combinations macroscopic final collision properties are derived and compared to experimental results by Foerster et al. [1994. Measurements of the collision properties of small spheres. Physics of Fluids 6(3), 1108–1115], Lorenz et al. [1997. Measurements of impact properties of small, nearly spherical particles. Experimental Mechanics 37(3), 292–298], Gorham and Kharaz [2000. The measurement of particle rebound characteristics. Powder Technology 112(3), 193–202] and Dong and Moys [2003. Measurement of impact behaviour between balls and walls in grinding mills. Minerals Engineering 16(6), 543–550; 2006. Experimental study of oblique impacts with initial spin. Powder Technology 161(1), 22–31].