Distinct Element Method Code Research Articles

Flowchart of DEM Modeling Stability Analysis of Large Underground Powerhouse Caverns

The power of the Distinct Element Method (DEM) in solving the stability of underground powerhouse caverns (UPC) is discovered, but when does the DEM need to be adopted? What problems can be solved? The flowchart is provided and applied to analyze the stability of UPC in this paper. With the guide of the flowchart, the damage index (Di) is used as a failure type (gravity‐controlled or stress‐induced) judgment indicator. Through the calculation of three typical engineering, the problems of random blocks stability, dynamic calculation, and support system evaluation are studied, respectively, with the help of the DEM code 3DEC. The method and results of this paper can give reference to engineering projects of its category.

Numerical models for planning landslide risk mitigation strategies in iconic but unstable landscapes: The case of Cinque Torri (Dolomites, Italy)

This study deals with the numerical modelling of large deep-seated instability processes affecting the Cinque Torri Group (Dolomites, Italy), which is a UNESCO World heritage site. The aim is to evaluate the role of intrinsic causal factors and to assess the failure mechanism proposed in previous investigations. The geological model is based on topographic, geological and geomechanical surveys, complemented with mineralogical, physical and geotechnical lab analyses for parameters determination. The numerical simulations have been carried out using a Distinct Element Method code on conceptual and site-specific slope models. A series of parametric analyses have been performed to characterize the role of the different predisposing factors potentially related with the ongoing rock spreading: i) load of the rocky pinnacles; ii) lithology, stratigraphy and attitude of the geological units; iii) discontinuity sets in the rock mass; iv) degradation of the mechanical properties. The results of this study suggest that the shear zone initiation is controlled by stress concentration due to the loading of the dolomitic pinnacles, whereas its shape appears to be structurally controlled by the dip-slope attitude of bedding in clay-rich mudstones. The interpretation of the modelling results has provided a better understanding of the ongoing deformation process, which can help in targeting effective and low-impact landslide risk mitigation strategies in this iconic landscape.

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.

Modeling failure of jointed rock slope with two main joint sets using a novel DEM bond contact model

In order to investigate the failure processes and mechanisms of jointed rock slopes, Distinct Element Method (DEM) was applied with a novel bond contact model. The bond contact model is validated by a series of numerical direct shear tests on jointed models and the comparisons to laboratory test results. DEM jointed rock slope models were then generated and two arrangements of joint sets and two types of slope surface were chosen to test the capabilities of the bond contact model. The slope models were destabilized progressively by the critical gravity approach, and both the failure onset and the slope collapse process were analyzed. Microscopic information reveals that the initiation of slope failure can be divided into three phases and is induced from stress concentration within the rock bridges, occurrence of tension cracks, and their propagation and coalescence. The slope surface properties reflected by different damping affect both post-failure configuration and propagation distance of the rock slope. The study demonstrates that the novel bond contact model implemented in the DEM code is able to tackle the fundamental problems of jointed rock slope failure and helps to better understand the slope failure mechanisms from a macroscopic and microscopic level.

Simulating the behaviour of fresh concrete with the Distinct Element Method – Deriving model parameters related to the yield stress

This article describes a numerical approach based on the Distinct Element Method (DEM) as a means of simulating fresh concrete during its different working processes. First, a rheological model for fresh concrete and its implementation into a DEM code are presented. Then the main focus is directed at establishing an algorithm to derive the model parameters related to yield stress according to the Bingham model. For this an analytical prediction of stress distribution at the beginning of the slump-flow test is used as reference for the corresponding numerical analysis. For the sake of validation, the analytical and numerical predictions of the final shape of the concrete cake in the slump-flow test are compared. The validation was performed for three different reference values of yield stress. Additionally, the numerical and analytical results of the so-called LCPC-box test were evaluated for the same sets of parameters. The results of the numerical analysis agreed well with the results predicted by analytical solutions for all parameter combinations. Therefore, the proposed algorithm was shown to be a sound procedure in linking yield stress of the simulated concrete to the bond strength, which is the main parameter of the model suggested.

A bond contact model for methane hydrate-bearing sediments with interparticle cementation

While methane hydrates (MHs) can be present in various forms in deep seabeds or permafrost regions, this paper deals with MH-bearing sediments (MHBS) where the MH has formed bonds between sand grains. A bond model based on experimentally validated contact laws for cemented granules is introduced to describe the mechanical behavior of the MH bonds. The model parameters were derived from measured values of temperature, water pressure and MH density. Bond width and thickness adopted for each bond of the MHBS were selected based on the degree of MH saturation. The model was implemented into a 2D distinct element method code. A series of numerical biaxial standard compression tests were carried out for various degrees of MH saturation. A comparison with available experimental data shows that the model can effectively capture the essential features of the mechanical behavior of MHBS for a wide range of levels of hydrate saturation under drained and undrained conditions. In addition, the analyses presented here shed light on the following: (1) the relationship between level of cementation and debonding mechanisms taking place at the microscopic level and the observed macro-mechanical behavior of MHBS and (2) the relationship between spatial distribution of bond breakages and contact force chains with the observed strength, dilatancy and deformability of the samples. Copyright © 2014 John Wiley & Sons, Ltd.

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.

Distinct element modeling for Class II behavior of rock and hydraulic fracturing

In this research, newly developed numerical approaches using the Distinct Element Method (DEM) were presented, and a series of DEM simulations were performed for better understanding the physical phenomena and mechanism for the following two fundamental issues in rock engineering field. The first issue is the Class II behavior of the brittle rocks under uniaxial compression. The radial strain control method for uniaxial compression tests was introduced in the DEM codes and the Class II behavior of rocks was simulated. The simulation results suggest that the DEM can reproduce the Class II behavior of the rock successfully and revealed that the loading condition of rocks (radial strain control) will play an important role for the Class II behavior. The second issue is the hydraulic fracturing behavior in rocks. A series of simulations for hydraulic fracturing in rock was performed by using the flow-coupled DEM code. Simulation results clearly show that the fluid infiltration behavior depends on the fluid viscosity. The fluid infiltrates into the fracture immediately, when a low viscosity fluid is used and the fluid infiltrates slowly into the cracks after the fracture generation and propagation, when a high viscosity fluid is used. Moreover, the tensile cracks are dominantly generated in the DEM simulations as expected in the conventional theory. However, the energy released from tensile cracks becomes smaller due to the fact that the tensile strength of rock is usually smaller than the compressive one. Such a small AE events is not distinguishable from noise and hard to recognize during laboratory experiments. Therefore, in AE measurements, shear type AE events with large energy are dominantly observed.

Simulation of Permanent Deformation of Unbound Granular Materials Under Repeated Loading by DEM

This paper presents a numerical investigation of permanent deformation of unbound granular materials under repeated loading using the distinct element method (DEM). Rigid walls are used as the boundaries in the simulation. Stress-controlled loading scheme is designed to perform biaxial compression testing using a commercial DEM code, Particle Flow Code (PFC2D). Three runs with different confining stress levels are conducted for simulation of the permanent deformation of randomly generated unbound granular materials. Simulation results show that both confining and cyclic axial stresses can be effectively applied to the testing sample. In addition, preliminary results of mechanical response imply that simulated permanent deformation trend of unbound granular materials is consistent with the classic results in real laboratories.

A simple distinct element modeling of the mechanical behavior of methane hydrate-bearing sediments in deep seabed

The study on the mechanical behavior of methane hydrate-bearing sediments (HBS) in deep seabed is of great significance for the safe exploitation of methane hydrate in the future. Recent studies have shown that the mechanical behavior of HBS is significantly influenced by methane hydrate since it leads to cementation among soil grains. For better understanding its microscopic mechanical mechanism, this paper presents a simple numerical model of HBS using the distinct element method (DEM). First, a set of tests on two bonded aluminum rods were performed under different loading paths with a specially designed apparatus. Then, a simple bond contact model was proposed based on the experimental data and implemented into our two-dimensional DEM code, NS2D. Finally, a series of drained biaxial compression tests under different confining stresses on HBS samples with different bond strengths, which are used to represent different methane hydrate saturations \((S_{\mathrm{MH}})\), were carried out with this code. By comparing the results of numerical simulations with the experimental data obtained from triaxial compression tests, the study shows that the DEM incorporating the new bond contact model is capable of capturing the main mechanical characteristics of HBS such as the strain softening and dilation. And it can also capture that (a) the peak shear strength increases as \(S_{\mathrm{MH}}\) or the confining stress increases, while the dilation increases as \(S_{\mathrm{MH}}\) increases or the confining stress decreases; (b) both the cohesion and friction angle increase with the increasing of \(S_{\mathrm{MH}}\), but the influence of \(S_{\mathrm{MH}}\) on the cohesion is much more significant than on the friction angle.

Numerical Simulations for Class II Behavior of Rocks under Uniaxial Compression using Distinct Element Method

The brittle fracture is the most studied process in rock mechanics fields, especially the post-failure behavior of rock is one of the key issues for rock mechanical problems. However, even at present, it is still difficult to obtain complete stress-strain curve of brittle rocks in the laboratory experiments. Therefore, a new Distinct Element Method (DEM) code for the uniaxial compression tests with radial strain control was developed and Class II behavior of rock was simulated. The simulation results show good agreement with the complete stress-strain curve obtained from the laboratory experiment with radial strain control. These imply that the DEM simulation may be a strong tool for the analyses of rock failure mechanisms such as class II behavior. The post-failure behavior of rock was discussed in detail by using a newly developed DEM code. The simulation results suggest that the loading control methods strongly affect the failure mechanisms and processes of rocks under uniaxial compression (Class I and II). Moreover, it is also found that the key to understand the Class II behavior of rock is the localized deformation, such as shear band. A clear shear band appears in the axial strain controlled uniaxial compression test, and a significant increase of the axial strain occurs with the crack surface slips along the shear band. As a result, complete stress-strain curve of the entire rock shows the Class I behavior. On the other hand, clear shear band does not appear in the radial strain controlled uniaxial compression tests, because formation of shear band does not grow due to the unloading in a critical state. Since clear shear band is not formed, most local small parts of the rock still keep elastic behavior, and as a result, the complete stress-strain curve of the entire rock shows Class II behavior.

A simple and efficient approach to capturing bonding effect in naturally microstructured sands by discrete element method

AbstractA discrete element modelling of naturally microstructured sands is very important to geomechanics. This paper presents a simple discrete element model for naturally microstructured sands with the aim to efficiently capture the effect of cementation between particles (bonds). First, a simple bond contact model was proposed by introducing a rigid‐plastic bond element into the conventional contact model for dry granular material. Second, efficient numerical techniques were investigated to implement this contact model into the distinct element method (DEM). Then, a two‐dimensional DEM code was developed to simulate a series of isotropic compression tests on the materials of different densities and bonding strengths. Finally, the DEM results were examined in comparison with the experimental data on artificially bonded sands obtained by Rotta et al. (Géotechnique 2003; 53(5):493–502). In addition, we discussed the yielding mechanism, the Coop and Willson criteria on weak/strong bonding (J. Geotech. Eng. (ASCE) 2003; 129(11):1010–1019) and the strong bonding phenomenon observed by Rotta et al. based on the DEM data. The study shows that the DEM model is able to capture the main features of naturally microstructured sands, such as variations of yielding and bulk modulus against bonding strength or material density. In addition, it is shown that the gross yielding (the yielding defined in terms of strains) is largely related to bond breakage; Coop and Willson criteria are generally reasonable; and the strong bonding in the experimental data obtained by Rotta et al. comes from that their bonded materials start at different points on the same compression line. Copyright © 2006 John Wiley & Sons, Ltd.

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two-dimensional (2-D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE-ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131(11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2-D distinct element method code, NS2D. Using the NS2D, a total of 86 1-D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first-yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.

NUMERICAL SIMULATION OF BLOCKING PROCESS OF GRID-TYPE DAM BY DEBRIS FLOW

A maximum diameter of sediment passing a grid is one of the most important condition of a design of grid-type dam. The model which can handle a collision and a contact between sediment particles is effective for a estimation of the blocking limit. Because a contact process of a grid and sediment shows remarkable three dimension characteristics, an introduction of 3D model is required. In this paper, a 3D distinct element method code is introduced to reproduce a blocking limit in previous experiments. A mechanism of a blocking is discussed from the viewpoint of a computational dynamics by estimating a spatial distribution of contact force between sediment particles.

Three-dimensional distinct element modelling of relay growth and breaching along normal faults

Three-dimensional numerical models of neutral (i.e. slip-parallel) relay zones on normal faults that cut massive sandstone host rocks have been constructed using the distinct element method code, Particle Flow Code in 3-D (PFC 3D). The models successfully reproduce the geometries, displacement profiles and strains observed in natural relay zones. In contrast to boundary element method simulations, the modelled relay ramps dip towards the hanging wall, consistent with observations of most natural relay zones. The modelling shows that relay zones are stable structures that ‘grow’ by progressive rotation of an approximately planar relay ramp without significant propagation of the relay-bounding faults prior to breaching. Stable growth is terminated when a breaching fault propagates across the top or bottom of the relay ramp. Breaching fault propagation is not instantaneous and the ramp continues to rotate, and therefore transfer displacement between the relay-bounding faults, until they become fully hard linked. Following hard linkage, displacement is accommodated by slip on the through-going fault surface. The modelling results confirm previous conceptual models of relay growth and breaching based on geometric and kinematic analysis of natural relay zones.

Application of distinct element method in dynamic analysis of high rock slopes and blocky structures

Comprehensive studies on the dynamic behaviours of a high rock slope of the Three Gorges shiplock and a blocky arch structure are performed using the distinct element method (DEM). Some additional functions have been incorporated into the current DEM code, including a scheme of non-uniform seismic input on the boundaries and an improved triangular mesh generator for deformable elements. Parameters from the field and laboratory tests of the project are used in the analysis of the shiplock slope. Comparisons between the DEM results and the field measurements under the excavation unloading process are made and the good agreement obtained demonstrates the effectiveness of the DEM for predicting the deformation process of the slope. The above examples of the high rock slope and the blocky arch demonstrate that the effects of different earthquake input, input mechanism and parameters on the dynamic response behaviours and collapse pattern of the systems are significant.

The effect of joint constitutive laws on the modelling of an underground excavation and comparison with in situ measurements

The paper discusses the results of a numerical study which examines the influence of joint constitutive models on the response of a specific jointed rock mass made up of an anisotropic rock (slate). It presents a comparison between predicted convergences and displacements of rock mass surrounding a pilot gallery, and those measured during field investigations. To perform this analysis, the two-dimensional Distinct Element Method code, UDEC, is used and three joint laws are compared. Based on field investigations for site characterisation, two models are constructed according to fracture density (MODEL A and MODEL B). For each of them, the influence of joint constitutive law on the stability of the gallery is examined, and comparisons between the investigations and predictions are made. Examination of the results shows that there is no noticeable change in stress magnitudes between laws. The displacement magnitudes depend on (1) the constitutive law, (2) the input model parameters and (3) the fracture density. A parametric study in the case of MODEL A indicates that a relatively good match between predicted and measured displacements around the gallery can be observed in certain areas.

Study of rock joints under cyclic loading conditions

A conceptual model for the behaviour of rock joints during cyclic shear and under constant normal stresses was proposed according to results from shear tests with 50 concrete replicas of rock joints. The shear strength and deformability of joint samples were found to be both anisotropic and stress dependent. Based on these experimental results, a two-dimensional constitutive model was developed for rock joints undergoing monotonic or cyclic loading sequences. The joint model was formulated in the framework of non-associated plasticity, coupled with empirical relations representing the surface roughness degradation, appearance of peak and residual shear stresses, different rates of dilatancy and contraction, variable normal stiffness with normal deformation, and dependence of shear strength and deformability on the normal stress. The second law of thermodynamics was represented by an inequality and used to restrict the values of some of the material parameters in the joint model. The new joint model was implemented into a two-dimensional Distinct Element Method Code, UDEC, and its predictions agreed well with some well-known test results.