Distinct Element Method Research Articles

Mechanical behavior of clayey methane hydrate-bearing sediment: Effects of pore size and physicochemical characteristics using a novel DEM contact model

The mechanical behavior of Methane Hydrate-Bearing Sediment (MHBS) is essential for the safe exploitation of Methane Hydrate (MH). In particular, the pore size and physicochemical characteristics of MHBS significantly influence its mechanical behavior, especially in clayey grain-cementing type MHBS. This study employs the Distinct Element Method (DEM) to investigate both the macroscopic and microscopic mechanical behavior of clayey grain-cementing type MHBS, focusing on variations in pore size and physicochemical characteristics. To accomplish this, we propose a Thermo-Hydro-Mechanical-Chemical-Soil Characteristics (THMCS) DEM contact model that incorporates the effects of pore size and physicochemical characteristics on the strength and modulus of MH. This THMCS model is validated using experimental data available in the literature. Using the proposed contact model, we conducted a series of investigations to explore the mechanical behavior of MHBS under conventional loading paths, including isotropic and drained triaxial tests using the DEM. The numerical results indicate that smaller pore sizes and lower water content—key physicochemical characteristics resulting from variations in electrochemical properties and the intensity of the electric field—can lead to reduced shear strength and stiffness due to the increased breakage of aggregates and weakened cementation. Additionally, heating was found to further accelerate the process of structural damage in MHBS.

Debris Flow Modeling of the Chandmari and Sichey Landslides in Sikkim, India, Using the Distinct Element Method

Debris Flow Modeling of the Chandmari and Sichey Landslides in Sikkim, India, Using the Distinct Element Method

Comparative analysis between continuous and discontinuous methods for the assessment of a cultural heritage structure

AbstractIn an era marked by the urgent need to ensure the safety of existing buildings according to current standards, evaluating the stability of masonry structures against hazard events has become a significant challenge. Despite the versatility and durability of masonry, structural assessments are hampered by factors such as limited information on material properties, irregular geometries, and ageing. To address this issue, numerous modelling techniques have been developed, supported by extensive scientific literature. However, significant factors related to the case study replication, such as the geometric complexity, the mechanical behaviour of masonry, the loading applications, contribute to the challenges associated with modelling procedures, including computational time, discretization procedures, and step incrementation. This paper critically discusses the most innovative modelling approaches. Specifically, it aims to compare the efficiency of the Distinct Element (discontinuous) Methods and the Finite Element (continuous) Method, both applied to the numerical simulation of a case study structure severely damaged by the 2016 Central Italy earthquake under lateral loading conditions. The continuous method is analysed using Midas FEA NX©, while the discontinuous methods are studied using 3DEC© and LMGC90© software, each with different contact conditions. Finally, the investigation highlights the main advantages and disadvantages of each method. In particular, the discontinuous method demonstrates reliability in accurately replicating failure patterns, whereas the continuous method allows for a faster model setup, making it suitable for preliminary studies on structural dynamics.

Distinct Element macro-crack networks for expedited discontinuum seismic analysis of large-scale URM structures

Discontinuum analysis is a powerful tool for the detailed seismic assessment of unreinforced masonry (URM) structures, whose widespread use is however still mostly limited to small-scale assemblies or isolated components. Despite their unique capabilities, including the explicit simulation of separation phenomena, collapses and out-of-plane (OOP) failures that are hardly replicable using traditional continuum solutions, the high computational cost entailed by micro-to-meso-scale discontinuum modelling strategies, which are the standard approaches in applied research, presently prevent their employment for building-scale problems. The few available macro-scale discontinuum models specifically conceived for URM, on the other hand, rely on complex geometrical discretization processes that require costly manual work, as well as on less efficient deformable block formulations. In this paper, a new simplified discontinuum macro-model is presented and validated against full-scale laboratory test outcomes on walls, pier-spandrel systems and building specimens, in addition to various meso-scale numerical results, under either in-plane (IP) or OOP actions, and considering quasi-static (monotonic, cyclic) or dynamic loadings. The proposed simulation technique, implemented in a robust Distinct Element Method (DEM) framework, leverages a semi-automated Equivalent Frame discretization algorithm that idealizes masonry piers, spandrels and nodes as an assembly of interlocked rigid macro-blocks connected by a network of zero-thickness interface springs. The latter are herein demonstrated to effectively replicate URM damage at the component-level through fracture energy contact laws, providing macro-scale yet representative failure patterns, as well as adequate predictions of overall strength and deformation capacities. Results obtained show a good agreement between macro- and more sophisticated meso-scale predictions, as well as with experimental outcomes, albeit dissimilarities among measured and computed force-displacement responses – similarly to other simplified strategies – were detected as vertical overburden increases. Notably, for analogous levels of accuracy, the analysis time required by our new macro-models is up to 150 times lower than its meso-counterparts. The use of the proposed simplified strategy also enabled the satisfactory simulation of the quasi-static cyclic and seismic responses of full-scale building-scale specimens, prohibitive tasks using traditional detailed DEM models, while also being up to 10 times faster than previous deformable macro-models.

Optimized Dropping and Rolling and Virtual Surface Method for High Packing Fraction of Dispersed Fuel Particles in Annular Container

Because of their favorable thermal conductivity and commendable fuel performance, dispersed fuel elements have been widely adopted in research reactors. However, the geometric complexity resulting from the high packing density of dispersed fuel poses challenges to current geometric modeling methods. Various implicit and explicit modeling techniques have been implemented in Monte Carlo codes. Implicit methods struggle to achieve the correct packing fraction and, therefore, lack accuracy. In this paper, we introduce the Optimized Dropping and Rolling and Virtual Surface method for precise and efficient geometric modeling of such structures. Simultaneously, we apply this novel method to the packing process of an annular container. Test results across various packing fraction cases demonstrate that our modified Optimized Dropping and Rolling method significantly enhances packing efficiency, surpassing the Distinct Element Method hundreds of times.

Analysis of tensile failure mechanism in intact, foliated, and cracked rocks using distinct element method: Influence of anisotropy

A thorough numerical analysis was conducted to understand the failure mechanisms and behaviour in intact rocks, foliated rocks and rocks with pre-existing cracks using the Brazilian tensile strength tests. The dominant anisotropy in rocks, especially foliated rocks like phyllites, slates and schists, as well as sedimentary rocks like sandstone, limestones and shale, leads to complex failure mechanism. The presence of cracks leads to anisotropy causing different mechanisms of failure and variation in tensile strengths of rock mass. Numerical simulations were conducted based on experimental studies of foliated phyllite and dolomitic limestone from the Tejam Group, Lesser Himalaya. The variations in failure behaviour and strength of foliated rocks were studied for samples at different foliation angle using the particle distinct element model. The simulation results show that with increase in foliation angle to the loading direction (from 0° to 90°), the peak tensile strength of rocks remains almost same for specimens with θ = 0° to 30° and then increases linearly till 90°. The influence of cracks as anisotropy was also studied by changing crack length (from 5 mm to 30 mm) and angle (from 0° to 90°). The development of failure patterns in rocks with pre-existing cracks leads to a better understanding of the failure modes and makes it possible to interpret failure behavior, pattern, and strength parameters. With increase in crack length, the tensile strength of rocks decreases. Overall, this study depicts the influence of anisotropy and microparameters on failure modes and behavior in Brazilian tensile strength tests on foliated and pre-cracked rocks.

Seismic fragility analysis and reliability evaluation for ancient stone pagoda using distinct element method

This study presents an application of performance-based assessment to establish fragility functions and evaluate the seismic reliability of an ancient stone pagoda in Korea. The pagoda was constructed of stone elements which were stacked over each other in layers without bonding material. To account for the discrete nature of this kind of structural configuration, the distinct element method is used to perform the incremental dynamic analysis to develop fragility functions. Three performance levels are specified on the capacity curve which is established based on non-linear pushover analysis. The randomness in seismic demand generation was considered when exciting the pagoda by a set of 23 input ground motion records, which were scaled into different intensity levels. The seismic response of the pagoda under different ground motions at several peak ground acceleration levels shows that the predominant frequency of the excitation is closely related to the behavior of this kind of structure. Ground motions with lower predominant frequency values induce stronger distortion to the pagoda than the ones with higher predominant frequency. The fragility functions estimated by maximum likelihood method show that earthquakes with peak ground motion of 0.469 g have a 50% probability of causing a collapse on the pagoda in the most conservative assessment. The probability of the pagoda collapsing within 50 years is 1.65% for the most earthquake-vulnerable site among the sites considered in the study.

A contact-based constitutive model for the numerical analysis of masonry structures using the distinct element method

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

Distinct element modeling of hydraulic fracture propagation with discrete fracture network at Gonghe enhanced geothermal system site, northwest China

Accurate prediction of hydraulic fracture propagation is vital for Enhanced Geothermal System (EGS) design. We study the first hydraulic fracturing job at the GR1 well in the Gonghe Basin using field data, where the overall direction of hydraulic fractures does not show a delineated shape parallel to the maximum principal stress orientation. A field-scale numerical model based on the distinct element method is set up to carry out a fully coupled hydromechanical simulation, with the explicit representation of natural fractures via the discrete fracture network (DFN) approach. The effects of injection parameters and in situ stress on hydraulic fracture patterns are then quantitatively assessed. The study reveals that shear-induced deformation primarily governs the fracturing morphology in the GR1 well, driven by smaller injection rates and viscosities that promote massive activation of natural fractures, ultimately dominating the direction of hydraulic fracturing. Furthermore, the increase of in situ differential stress may promote shear damage of natural fracture surfaces, with the exact influence pattern depending on the combination of specific discontinuity properties and in situ stress state. Finally, we provide recommendations for EGS fracturing based on the influence characteristics of multiple parameters. This study can serve as an effective basis and reference for the design and optimization of EGS in the Gonghe basin and other sites.

Stochastic Rock Slope Stability Analysis: Open Pit Case Study with Adjacent Block Caving

In last decades, numerical modelling become a useful tool for solving complex geoengineering problems such as slope stability. On the other hand, probabilistic slope stability analyses are able to consider the variability of the rock mass properties in the decision making process. However, the application of probabilistic slope stability analysis with large three-dimensional numerical models is still limited due to the computational expenses of evaluating a substantial number of considered models. It is well-known that response surface methodology (RSM) couples the mathematical and statistical techniques to relate input variables to the response, allowing a reliable outcome and reasonable time of the analysis. Taking these advantages, this article presents an application of RSM in probabilistic slope stability analysis using three dimensional distinct element modelling. For this purpose, the most influencing factors including: uniaxial compressive strength, geological strength index (GSI), and shear strength of discontinuities, were taken into consideration to determine the probability of failure of an open pit slope located in vicinity of a block caving-induced subsidence crater. Numerical analysis of slope stability was conducted for an open pit slope using the Distinct Element Method code-3DEC. Probability distribution of the factor of safety (FS) was determined and possible slope failure mechanism was observed. In addition, the block caving-induced subsidence was investigated. The final outcomes indicate that Response Surface Methodology is applicable when couples with numerical modelling of complex issues, GSI is considered the most influential variable. The studied slope is considered stable due to the low value of the FS probability distribution (2.2%). This research is expected to provide a reference for slope stability analysis in case of transition from Open Pit to Underground Mining.

Wellbore breakouts in heavily fractured rocks: A coupled discrete fracture network-distinct element method analysis

Wellbore breakout is one of the critical issues in drilling due to the fact that the related problems result in additional costs and impact the drilling scheme severely. However, the majority of such wellbore breakout analyses were based on continuum mechanics. In addition to failure in intact rocks, wellbore breakouts can also be initiated along natural discontinuities, e.g. weak planes and fractures. Furthermore, the conventional models in wellbore breakouts with uniform distribution fractures could not reflect the real drilling situation. This paper presents a fully coupled hydro-mechanical model of the SB-X well in the Tarim Basin, China for evaluating wellbore breakouts in heavily fractured rocks under anisotropic stress states using the distinct element method (DEM) and the discrete fracture network (DFN). The developed model was validated against caliper log measurement, and its stability study was carried out by stress and displacement analyses. A parametric study was performed to investigate the effects of the characteristics of fracture distribution (orientation and length) on borehole stability by sensitivity studies. Simulation results demonstrate that the increase of the standard deviation of orientation when the fracture direction aligns parallel or perpendicular to the principal stress direction aggravates borehole instability. Moreover, an elevation in the average fracture length causes the borehole failure to change from the direction of the minimum in-situ horizontal principal stress (i.e. the direction of wellbore breakouts) towards alternative directions, ultimately leading to the whole wellbore failure. These findings provide theoretical insights for predicting wellbore breakouts in heavily fractured rocks.

A size‐dependent energy‐based strain burst criterion

AbstractThis paper presents a size‐dependent energy‐based strain burst criterion linking strength, elasticity, fracture energies and specimen size effect with stress state due to changes in boundary conditions. It proposes the concept of a ‘Burst Envelope’, a surface in three‐dimensional principal stress space derived based on energy storing and dissipation characteristics of a rock sample, taking into account the size of the specimen and potential localised failure pattern. A scalar burst index is also proposed to quantify the bursting scale. To illustrate and verify its functioning, a numerical modelling framework based on the distinct element method and employing a new cohesive‐frictional contact model is used to perform virtual strain burst experiments under different polyaxial loading‐unloading scenarios, mimicking various underground excavation scenarios. The obtained results are in good agreement with the theoretical prediction of burst occurrence. On that basis, the variation of burst possibility and magnitude are investigated with key factors, including confinement level and the material's elastic, strength and fracture properties. The effect of the specimen's aspect ratio and size on the rock burst potential is elaborated and verified using virtual strain burst experiments, facilitating the linking of the proposed theoretical framework with the evaluation of in‐situ strain bursts in rock masses around underground openings.

Fluctuations and failure in granular materials: theory and numerical simulations

We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model.Graphical Statistical representation of the aggregate: conditional average.

Modeling distribution and change of loess pore structure by two-dimensional distinct element method analyses

Modeling distribution and change of loess pore structure by two-dimensional distinct element method analyses

Distinct element method simulation of mechanical properties of material layer of pellet belt roasting machine

Distinct element method simulation of mechanical properties of material layer of pellet belt roasting machine

Distinct Element Method Analyses for Damage Assessment: The Northern Spur of Valverde Bulwark in the Venetian Fortress of Bergamo

ABSTRACT The 16th century Venetian Fortress, with more than 70,000 m2 of masonry wall facing, characterises the city landscape of Bergamo. Almost intact and well preserved, the defensive system was inscribed on the UNESCO World Heritage List in 2017. Today, the first causes of its deterioration are the vegetation growth and the lack of maintenance, which have led to instabilities and local failures, particularly in the northwest portion. Thus, in 2019 and 2020, survey campaigns were carried out to assess the safety of one of the most damaged sections, the Valverde bulwark. The survey combines on-site observations, laboratory tests, and photogrammetric and laser scanner surveys to describe the bulwark. Numerical simulations have been performed using a distinct element approach, i.e. assimilating the masonry to a system of discrete bodies consisting of blocks (usually rigid) interacting on their interfaces. A routine dedicated to defining a real-like geometrical model has been developed. The numerical analyses were run to assess the conditions of the Valverde bulwark under self-weight and earth pressure and considering seismic load. Through the detailed survey and its automatic digitisation, it is possible to fully recognise and analyse the state of health of these historic structures and their mechanical behaviour.

Numerical Investigation of Stratified Slope Failure Containing Rough Non-Persistent Joints Based on Distinct Element Method

To address the critical issue of slope stability in jointed rock masses with complex and rough structural planes, a rough joint network model using the Fourier transform was proposed and applied to the Shilu open pit mine. The on-site structural plane survey results were combined with MATLAB and PFC2D to establish numerical models for slope stability analysis considering both linear-jointed and rough-jointed rock slopes. By comparing the slip body and fracture distribution, it was found that the rough-jointed slope was stabler than the linear-jointed slope. In addition, the fracture patterns and slip displacement were significantly influenced by the inclination and undulation of the bedding planes. Slip failure patterns occurred when the angle of inclination was set at 60°. The joints played a crucial role in inducing the shear strength of slope rock masses, and the slide area was mainly observed in the shallow slope surface for inclination angles of 0° and 45°, and in the middle deep area for 60° and 90°. These results demonstrated the importance of considering rough non-persistent fractures when developing a new numerical model for slope failure modes.

Simultaneously improving ROP and maintaining wellbore stability in shale gas well: A case study of Luzhou shale gas reservoirs

The ROP (rate of penetration) within the horizontal section of shale gas wells in the Luzhou oil field is low, seriously delaying the exploration and development process. It is proved that reducing mud density mitigates the bottom-hole differential pressure (ΔP) and increases the ROP during overbalanced drilling. However, wellbore collapse may occur when wellbore pressure is excessively low. It is urgent to ascertain the optimal equilibrium point between improving ROP and maintaining wellbore stability. The safe mud weight window and the lower limit of mud density in the horizontal section of the Luzhou block are predicted using the piecewise fitting method based on conventional logging data. Then, the accuracy of the collapse pressure prediction was verified using the distinct element method (DEM), and the effect of wellbore pressure, in-situ stress, rock cohesion, and natural fracture density on borehole collapse was investigated. Finally, a fitting model of ΔP and ROP of the horizontal section in the Luzhou block is established to predict ROP promotion potential after mud density reduction. The field application of this approach, demonstrated in 8 horizontal wells in the Luzhou block, effectively validates the efficiency of reducing mud density for ROP improvement. This study provides a useful method for simultaneously improving ROP and maintaining wellbore stability and offers significant insights for petroleum engineers in the design of drilling parameters.

Wellbore instability in naturally fractured formations: Experimental study and 3D numerical investigation

Wellbore instability due to natural fractures is a significant issue impeding drilling operations in shale formations. However, most of the existing literature on wellbore stability analysis focuses on the coupled effects of fluid flow and deformation, and the impact of three-dimensional natural fracture characteristics on wellbore instability is not yet closely examined. This paper carried out a series of experiments to analyze the shale sample's fracture characteristics and shear strength. A fully coupled 3D hydro-mechanical model was then developed using the distinct element method (DEM) to investigate the wellbore instability. Finally, a comprehensive parametric study was performed to analyze the effects of characteristics of fractures (e.g., distribution density, fracture roughness and associated shear strength, dip angle, and seepage time) on wellbore stability under different in-situ stress states. The results show that the shear strength of shale increases with the increase in normal pressure (4 MPa, 6 MPa, and 8 MPa); the shear strength increases by 64.9% when the roughness is 0.325 mm (the largest increase among the three roughness cases). The maximum displacement around the wellbore is 1.3–1.5 times greater under the presence of weak planes than under no weak planes. Fracture roughness poses an important impact on wellbore stability because larger fracture roughness is associated with higher fracture shear strength. As the dip angle of the weak plane increases, the number of yield zones (shear failure) and maximum wellbore displacement increases and then decreases, and the peak occurs at the dip angle of 45°. The seepage time of drilling fluid is positively correlated with the number of yield zones around the wellbore, and the damage rate of drilling fluid to wellbore stability gradually decreases with the seepage time.

Crack Propagation in Heterogeneous Gravity Dams Due to Overflow Using Polygonal Grain-Based Distinct Element Method

Crack Propagation in Heterogeneous Gravity Dams Due to Overflow Using Polygonal Grain-Based Distinct Element Method