Finite-discrete Element Method Research Articles

Rate-dependent FDEM numerical simulation of dynamic tensile fracture and failure behavior in frozen soil

Considering that the dynamic fracture and failure behaviors of frozen soil play a crucial role in the safety and stability of engineering foundations in cold regions, this study aimed to reveal the dynamic tensile mechanical properties and damage failure mechanisms of frozen soil under impact loading. Dynamic Brazilian disk (BD) tests were conducted on frozen soil at different temperatures and loading velocities using a split Hopkinson pressure bar (SHPB) apparatus, followed by numerical simulations using the finite discrete element method (FDEM), focusing on the dynamic tensile deformation characteristics, failure patterns, tensile strength, and energy dissipation mechanisms of the frozen soil. The experimental results indicated that the dynamic tensile mechanical properties of frozen soil were influenced by both temperature and loading velocity. As the temperature decreased and loading velocity increased, the tensile strength of frozen soil significantly increased and showed a linear correlation with the loading velocity. At lower loading velocities, the cracks tended to propagate along the paths of least resistance, forming fewer but longer macrocracks. With increasing loading velocities, the number of cracks markedly increased, and their distribution became more diffuse, leading to a greater extent of failure in the frozen soil. An exponential damage cohesive interface model that considers rate effects was proposed to describe the dynamic tensile fracture mechanical behavior of frozen soil accurately. This model addresses the rate sensitivity of frozen soil and effectively accounts for the temperature effect by considering the volume of ice content and cryogenic suction. A comparison of the FDEM numerical simulation results with the experimental data indicated a good consistency in the overall trends, thus validating the effectiveness and applicability of the FDEM in simulating the dynamic tensile mechanical behavior of frozen soil.

Optimal error estimate of unconditionally positivity-preserving, mass-conserving and energy stable method for the Keller-Segel chemotaxis model

In this paper, we prove the optimal error estimate of an unconditionally positivity-preserving, mass-conserving and energy stable method for the Keller-Segel chemotaxis equations. Applying a log-transformation to preserve the positivity and utilizing a recovery to ensure the mass-conversing, we consider a decoupled and linear fully discrete finite element method for the Keller-Segel chemotaxis equations. Then, supposing that the initial mass is less than certain critical threshold which guarantees that the system does not blow up at a finite time, and deriving the errors of the temporal and spatial discretizations in a proper sequence to avoid extra regularity requirements of the weak solutions, we prove that the method is unconditionally energy stable and can achieve the optimal convergence order in L 2 L^2 norm under weaker assumptions on the solutions than the existent ones. The shown numerical examples confirm the correctness of the theoretical prediction.

Study on secondary collapse of the bottom frame masonry structure in semi-ruined state based on FEM–FDEM

The bottom frame masonry structure (BFMS) in a semi-ruined state is vulnerable to secondary collapse under strong aftershocks, posing a significant risk to rescuers during post-earthquake operations. Therefore, investigating the mechanisms and characteristics of secondary collapse of BFMS in a semi-ruined state (BFMS-SR) under aftershocks is critical. This paper proposes a numerical modeling framework for BFMS under mainshock-aftershock conditions, utilizing a combination of the finite element method (FEM) and the finite discrete element method (FDEM). The validation demonstrates that FEM–FDEM can effectively reproduce the transition of BFMS from an intact state to a semi-ruined state, ultimately leading to a secondary collapse state. Subsequently, the mechanisms and structural response characteristics of BFMS-SR under aftershocks are analyzed. The secondary collapse of the BFMS-SR under aftershocks is primarily governed by column hinge development. Furthermore, according to the time-history curve of absolute vertical velocity, the secondary collapse of BFMS-SR exhibits four distinct stages: stabilization, structural response development, secondary collapse, and post-collapse. The end of the stabilization phase is proposed as the early-warning threshold for secondary collapse of BFMS-SR under aftershocks, aiding in post-earthquake rescue operations.

Finite element modeling of the influence of FRP techniques on the seismic behavior of an arch stone bridge of historical interest

In this paper, a masonry bridge is simulated in order to assess both its structural and seismic vulnerability. Therefore, the present study aimed to approximately analyze the real behavior of Mikron Bridge structure. The modeling was conducted by combining the finite element method (FEM) and discrete element method (DEM) using the ABAQUS® software. By comparing the results of numerical and experimental modal analyses, the accuracy of simulation was verified. To simulate the seismic behavior of the Mikron Bridge, the component of Erzincan earthquake occurred in 1992 was used. The results extracted from the seismic analysis show that some parts of the bridge structure are damaged but not destroyed.

Finite element modeling of the influence of FRP techniques on the seismic behavior of an arch stone bridge of historical interest

In this paper, a masonry bridge is simulated in order to assess both its structural and seismic vulnerability. Therefore, the present study aimed to approximately analyze the real behavior of Mikron Bridge structure. The modeling was conducted by combining the finite element method (FEM) and discrete element method (DEM) using the ABAQUS® software. By comparing the results of numerical and experimental modal analyses, the accuracy of simulation was verified. To simulate the seismic behavior of the Mikron Bridge, the component of Erzincan earthquake occurred in 1992 was used. The results extracted from the seismic analysis show that some parts of the bridge structure are damaged but not destroyed.

FINITE ELEMENT ANALYSIS OF LINEARLY EXTRAPOLATED BLENDED BACKWARD DIFFERENCE FORMULA (BLEBDF) FOR THE NATURAL CONVECTION FLOWS

In this paper, we study the stability and convergence of fully discrete finite element method with grad-div stabilization for the incompressible non-isothermal fluid flows. The proposed scheme uses finite element discretization in space and linearly extrapolated blended Backward Differentiation Formula (BLEBDF) in time. We prove the unconditional stability over finite time interval and optimally convergence of the scheme. We also present numerical experiments to verify our theoretical convergence rates and show the reliability of the scheme.

FEM, DEM and FDEM applications on impact fracture of glass and laminated glass – a review

Structural glass components are prevalently used in engineering. Due to the brittle nature, glass or laminated glass may fracture during an impact action, and the subsequent flying fragments may spread over a wide range, resulting in human injuries and asset losses. In this article, the authors aimed at providing a comprehensive review concerning the numerical applications on the impact fracture of glass and laminated glass, giving emphasis to the literatures published in the last two decades. Relevant numerical applications employing the finite element method (including element deletion method, extended finite element method and some other continuum-based approaches), discrete element method and combined finite-discrete element method were reviewed in-depth, and features of the simulations were summarised. Discussions on the impact fracture characteristics from different computational approaches were performed. Insights into the accuracy, efficiency, ease of implementation and range of applicability were also provided. This review is meant for the rapid and beneficial understanding towards the impact fracture mechanism of glass and laminated glass.

Diffusion law and diffusion model for backfill grouting in loess shield tunnel at different soil moisture

Loess is a special type of soil whose properties are significantly affected by water. However, the grout diffusion law for backfill grouting in loess shield tunnels remains unknown. Based on a visual model experimental device, three experiments were conducted with 10%, 20%, and 30% loess moisture. A finite discrete element method was used to verify the grout diffusion mode, and parameters such as the tunnel buried depth, grout viscosity, and elastic modulus were considered to analyse the grout diffusion law. Experiments and numerical simulations show that the screening diffusion of grout occurs at low loess moisture, whereas splitting diffusion occurs at high loess moisture. The farthest splitting diffusion distance decreases as the tunnel buried depth, grout viscosity, and elastic modulus increase. In addition, based on capillary theory and geotechnical strength criteria, screening diffusion and splitting diffusion models were established. This study investigated the grout diffusion law and grout diffusion model, providing a reference for the design and construction of loess shield tunnels.

A finite discrete element approach for modeling of desiccation fracturing around underground openings in Opalinus clay

Understanding and predicting potential failure mechanisms during the excavation and open drift stages of geological repository construction are among the crucial aspects of performance evaluation and safety assessment of nuclear waste storage facilities. The development of the Excavation Damage Zone (EDZ) and the generation of shrinkage-induced cracks during operational phases are prominent examples of failure mechanisms that can compromise the integrity of the repository systems. This study presents an integrated framework for investigating shrinkage-induced cracking of Opalinus Clay in niches and tunnels. To achieve this, the hybrid Finite Discrete Element Method (FDEM) is employed. The methodology incorporates a two-way staggered hydro-mechanical coupling scheme, where solid phase analysis relies on 2D FDEM and fluid flow is modeled using the nonlinear Richards’ equation and solved via Finite Volume discretization. To account for the effects of EDZ, characterized by a pronounced increase in hydraulic conductivity, a numerical simulation of tunnel excavation is first carried out. The resulting failure pattern around underground openings is then abstracted through the definition of an altered hydraulic conductivity field. Comparison of the numerical results with field observations demonstrates the framework’s ability to capture a wide range of failure mechanisms inherent in various stages of underground repository construction in Opalinus Clay.

Research on the Stability of Lining Structures Under Different Fault Moments Based on FDM-DEM

Currently, research on employing finite difference method and discrete element method (FDM-DEM) coupling to assess the stability of tunnel lining structures is limited. This study utilized the FDM-DEM coupling approach, with the F2 fault of the East Tianshan Tunnel as a case study, to develop a numerical model in conjunction with PFC3D 6.0 and FLAC3D 6.0 software. We conducted a comprehensive analysis of the displacement deformation and crack progression of the tunnel lining structure under varying dislocation momentum conditions, unveiling the underlying mechanisms. The findings indicated that as the dislocation increased, the extent of damage to the vault intensified, and the particle contact force within the tunnel lining shifted from compression to tension, significantly contributing to the crack formation. Fault dislocation influenced the gradual expansion of cracks from the vault to the spandrel and arch waist, with the crack width increasing alongside the rising dislocation momentum. In particular, under substantial dislocation momentum, the overall stability of the tunnel lining was markedly diminished. The safety factor at the tunnel section declined progressively as the dislocation momentum escalated, with values of 2.53, 2.49, 2.43, 2.39, and 2.32 corresponding to dislocation momenta of 0.01 m, 0.05 m, 0.1 m, 0.15 m, and 0.2 m, respectively. This research offers valuable insights and a reference framework for investigating the stability of tunnel lining structures in proximity to fault dislocations, pinpointing potential failure points, and bolstering the structural integrity of tunnels.

Study on multi-cluster fracture interlaced competition propagation model of hydraulic fracturing in heterogeneous reservoir

The heterogeneity of the reservoir plays a crucial role in influencing the propagation of multi-cluster hydraulic fractures in horizontal wells. To explore this impact, a seepage-stress-damage coupled model was developed in this study for analyzing the competitive propagation of multi-cluster fractures utilizing the finite-discrete element method. Utilizing the model, a random assignment program has been developed to establish the coupling distribution of mechanical parameters between matrix elements and discrete elements for characterizing the reservoir heterogeneity. Simultaneously, a wellbore flow model describing the pressure drop of fracturing fluid flow is developed by introducing pipe flow element and fluid connection element, enabling the realization of dynamic flow distribution. Based on the developed model, an investigation is conducted into the impact of pumping rates, fracturing fluid viscosity, and perforation parameters on the fracture propagation of multi-cluster fracturing. The study findings suggest that as reservoir heterogeneity increases, the distribution of rock strength becomes more uneven, resulting in a more complex morphology of fracture propagation. Higher pumping rates lead to elevated pressure within fractures, thereby facilitating the uniform propagation of multi-cluster fractures, particularly in reservoir characterized by medium to high heterogeneity. Increasing the viscosity of fracturing fluid can diminish the tortuosity of multi-cluster fracture propagation, albeit with a somewhat limited enhancement in uniformity. As reservoir heterogeneity intensifies, the interference between fractures escalates, necessitating a reduced number of perforations to heighten perforation friction and enhance the balanced propagation of multi-cluster fractures. This research offers theoretical guidance and a scientific foundation for the design of schemes and optimization of parameters in staged multi-cluster fracturing technology for horizontal wells in heterogeneous reservoirs.

Optimization of drawing sequence in longwall top coal caving mining through an FDM‐DEM model

AbstractThe Longwall top coal caving (LTCC) technology is regarded as one of the most crucial approaches for exploiting thick coal seams. A crucial and effective approach for improving the recovery rate of top coal and reducing coal resource losses in LTCC faces is to reasonably select process parameters based on actual mining and geological conditions of different mines. The main focus of this paper is the engineering background of the 12,309 LTCC face in Wangjialing Coal Mine. A numerical model is developed using FALC3D and PFC3D software, employing a finite difference method and discrete element method. This model takes into account predetermined cutting and caving ratios, as well as drawing intervals. To examine the caving process and roof particles, three different drawing sequences were examined: sequential drawing, segmented sequential drawing, and intermittent drawing. The findings suggest that, in terms of the reset shape of the drawing body before individual and entire caving, the segmented sequential drawing method exhibits noticeable drawbacks compared to the other two methods. From the perspective of the drawing weight, following “closing drawing opening when seeing gangue”, the sequential drawing, segmented sequential drawing, and intermittent drawing methods can yield 32.42 t, 26.87 t, and 35.78 t of top coal, with corresponding recovery rates of 73.39%, 60.81%, and 82.97%. Therefore, it can be concluded that intermittent drawing is suitable for implementation on LTCC working face 12,309.

Size-Dependent Mechanical Properties and Excavation Responses of Basalt with Hidden Cracks at Baihetan Hydropower Station through DFN–FDEM Modeling

Basalt is an important geotechnical material for engineering construction in Southwest China. However, it has complicated structural features due to its special origin, particularly the widespread occurrence of hidden cracks. Such discontinuities significantly affect the mechanical properties and engineering stability of basalt, and related research is lacking and unsystematic. In this work, taking the underground caverns in the Baihetan Hydropower Station as the engineering background, the size-dependent mechanical behaviors and excavation responses of basalt with hidden cracks were systematically explored based on a synthetic rock mass (SRM) model combining the finite-discrete element method (FDEM) and discrete fracture network (DFN) method. The results showed that: (1) The DFN–FDEM model generated based on the statistical characteristics of the geometric parameters of hidden cracks can consider the real structural characteristics of basalt, whereby the mechanical behaviors found in laboratory tests and at the engineering site could be exactly reproduced. (2) The representative elementary volume (REV) size of basalt blocks containing hidden cracks was 0.5 m, and the mechanical properties obtained at this size were considered equivalent continuum properties. With an increase in the sample dimensions, the mechanical properties reflected in the stress–strain curves changed from elastic–brittle to elastic–plastic or ductile, the strength failure criterion changed from linear to nonlinear, and the failure modes changed from fragmentation failure to local structure-controlled failure and then to splitting failure. (3) The surrounding rock mass near the excavation face of underground caverns typically showed a spalling failure mode, mainly affected by the complex structural characteristics and high in situ stresses, i.e., a tensile fracture mechanism characterized by stress–structure coupling. The research findings not only shed new light on the failure mechanisms and size-dependent mechanical behaviors of hard brittle rocks represented by basalt but also further enrich the basic theory and technical methods for multi-scale analyses in geotechnical engineering, which could provide a reference for the design optimization, construction scheme formulation, and disaster prevention of deep engineering projects.

Study on the characteristics of blast-induced damage zone by using the wave velocity field inversion technique

The rock excavation by drilling and blasting method would lead to damage around the blasting hole, which could significantly affect the long-term stability of surrounding rock mass in tunnel, slope, or bedrock. To qualify the characteristics of blast-induced damage zone, we proposed a wave velocity field inversion imaging method, which combines multistencils fast marching methods and simultaneous iterative reconstructive technique to quickly inverse and quantify the blast-induced cracked zone surrounding the borehole. The finite-discrete element method, which has advantages in simulating the fracture and fragmentation of rocks, was used to simulate the blasting process and acoustic wave testing. The ground vibrations induced by the blasting were monitored simultaneously and the acoustic waveforms are used to invert the wave velocity field before and after blasts. The inverted wave velocity field is compared with the blast-induced cracked zone, and the relationship between the radius of the crushed zone and the cracked zone under different charges was studied. It is found that the ratio of the crushed zone radius and the cracked zone radius decreases with the increasing charge. Moreover, the relationship between the peak particle velocity at 30 m away from the borehole (PPV30) and the distribution of the cracked zone was determined.

A novel FDEM-GSA method with applications in deformation and damage analysis of surrounding rock in deep-buried tunnels

In underground hydraulic tunnel engineering, particularly deep-buried projects, the deformations and stability of the surrounding rock are critical to the construction process. Due to the complex depositional environment of such tunnels, multiple factors influence the stability of the surrounding rock during construction. This paper proposes a novel hybrid method combining Finite-Discrete Element Method (FDEM) with Global Sensitivity Analysis (GSA) and machine learning. The FDEM model is used to establish an approximate relationship between input and output parameters, and its accuracy is validated through comparison with monitoring data. On the basis of data simulated by the FDEM model, a meta-model is developed by Particle Swarm Optimization-Extreme Gradient Boosting (PSO-XGBoost). 10,000 data sets are generated using the meta-model for Sobol sensitivity analysis. The proposed analysis framework is applied to study the deep-buried water diversion tunnel in the Central Yunnan Water Diversion Project (CYWDP). The results indicate that in deep-buried tunnel environments, as the tunnel depth increases, the dominant factor influencing the deformation of the surrounding rock transitions from tunnel depth to the mechanical properties of the rock itself. These findings provide valuable insights for optimizing construction plans in similar tunnel projects and offer a new perspective on sensitivity analysis frameworks based on numerical computations.

Hybrid finite element and laplace transform method for efficient numerical solutions of fractional PDEs on graphics processing units

Fractional Partial Differential equations (FPDEs) are essential for modeling complex systems across various scientific and engineering areas. However, efficiently solving FPDEs presents significant computational challenges due to their inherent memory effects, often leading to increased execution times for numerical solutions. This study proposes a highly parallelizable hybrid computational approach that combines the Finite Element Method (FEM) for spatial discretization with Numerical Inversion of the Laplace Transform (NILT) for time-domain solutions, optimized for execution on Graphics Processing Units (GPUs). The NILT method’s high parallelizability, stemming from the independence of its series terms, combined with the robust spatial discretization provided by FEM, enables the efficient and accurate solution of FPDEs on GPUs, demonstrating substantial performance improvements over traditional CPU-based implementations. We observe a generalized pattern in execution time behavior that accounts for both the number of nodes and the number of NILT terms. Specifically, execution time scales quadratically with the number of nodes, while showing only a logarithmic marginal increase with the number of NILT terms These behaviors not only enables consistent performance assessment but also highlights potential areas for algorithm optimization. Validation against exact solutions of fractional diffusion and wave equations, employing Caputo, modified Caputo-Fabrizio, and modified Atangana-Baleanu derivatives, demonstrates the accuracy and convergence of the hybrid FEM-NILT method. Notably, the exact solutions of wave equation are novel in literature. The results highlight the method’s potential for enabling high-precision, large-scale simulations in fractional calculus applications, thereby advancing computational capabilities and efficiency in the field.

Multi-Scale Integrated Corrosion-Adjusted Seismic Fragility Framework for Critical Infrastructure Resilience

This study presents a novel framework for integrating corrosion effects into critical infrastructure seismic risk assessment, focusing on reinforced concrete (RC) structures. Unlike traditional seismic fragility curves, which often overlook time-dependent degradation such as corrosion, this methodology introduces an approach incorporating corrosion-induced degradation into seismic fragility curves. This framework combines time-dependent corrosion simulation with numerical modeling, using the finite–discrete element method (FDEM) to assess the reduction in structural capacity. These results are used to adjust the seismic fragility curves, capturing the increased vulnerability due to corrosion. A key novelty of this work is the development of a comprehensive risk assessment that merges the corrosion-adjusted fragility curves with seismic hazard data to estimate long-term seismic risk, introducing a cumulative risk ratio to quantify the total risk over the structure’s lifecycle. This framework is demonstrated through a case study of a one-story RC moment frame building, evaluating its seismic risk under various corrosion scenarios and locations. The simulation results showed a good fit, with a 3% to 14% difference between the case study and simulations up to 75 years. This fitness highlights the model’s accuracy in predicting structural degradation due to corrosion. Furthermore, the findings reveal a significant increase in seismic risk, particularly in moderate and intensive corrosion environments, by 59% and 100%, respectively. These insights emphasize the critical importance of incorporating corrosion effects into seismic risk assessments, offering a more accurate and effective strategy to enhance infrastructure resilience throughout its lifecycle.

A new combined finite-discrete element method for stability analysis of soil-rock mixture slopes

PurposeThe purpose of this paper is to propose a new combined finite-discrete element method (FDEM) to analyze the mechanical properties, failure behavior and slope stability of soil rock mixtures (SRM), in which the rocks within the SRM model have shape randomness, size randomness and spatial distribution randomness.Design/methodology/approachBased on the modeling method of heterogeneous rocks, the SRM numerical model can be built and by adjusting the boundary between soil and rock, an SRM numerical model with any rock content can be obtained. The reliability and robustness of the new modeling method can be verified by uniaxial compression simulation. In addition, this paper investigates the effects of rock topology, rock content, slope height and slope inclination on the stability of SRM slopes.FindingsInvestigations of the influences of rock content, slope height and slope inclination of SRM slopes showed that the slope height had little effect on the failure mode. The influences of rock content and slope inclination on the slope failure mode were significant. With increasing rock content and slope dip angle, SRM slopes gradually transitioned from a single shear failure mode to a multi-shear fracture failure mode, and shear fractures showed irregular and bifurcated characteristics in which the cut-off values of rock content and slope inclination were 20% and 80°, respectively.Originality/valueThis paper proposed a new modeling method for SRMs based on FDEM, with rocks having random shapes, sizes and spatial distributions.

Failure mechanism of a tunnel in a soil–rock mixture based on a new combined finite–discrete element method

The mechanical properties and failure characteristics of soil–rock mixtures (SRMs) directly affect the stability of tunnels constructed in SRMs. A new SRM modelling method based on the combined finite–discrete element method (FDEM) was proposed. Using this new SRM modelling method based on the FDEM, the mechanical characteristics and failure behaviour of SRM samples under uniaxial compression, as well as the failure mechanism of SRMs around a tunnel, were further investigated. The study results support the following findings: (1) The modelling of SRM samples can be achieved using a heterogeneous rock modelling method based on the Weibull distribution. By adjusting the relevant parameters, such as the soil–rock boundaries, element sizes and modelling control points, SRM models with different rock contents and morphologies can be obtained. (2) The simulation results of uniaxial compression tests of SRM samples with different element sizes and morphologies validate the reliability and robustness of the new modelling method. In addition, with increasing rock content, VBP (volumetric block proportion), the uniaxial compressive strength and Young’s modulus increase exponentially, but the samples all undergo single shear failure within the soil or along the soil–rock interfaces, and the shear failure angles are all close to the theoretical values. (3) Tunnels in SRMs with different rock contents all exhibit X-shaped conjugate shear failure, but the fracture network propagation depth, the maximum displacement around the tunnel, and the failure degree of the tunnel in the SRM roughly decreases via a power function as the rock content increases. In addition, as the rock content increases, such as when VBP = 40%, large rocks have a significant blocking effect on fracture propagation, resulting in an asymmetric fracture network around the tunnel. (4) The comparisons of uniaxial compression and tunnel excavation simulation results with previous theoretical results, laboratory test results, and numerical simulation results verify the correctness of the new modelling method proposed in this paper.

Research on simulating coal crack development under high voltage electric pulse stress waves using zero thickness cohesive elements

High voltage electric pulse (HVEP) technology has demonstrated significant potential in enhancing coal seam permeability. However, there is a notable gap in numerical simulation studies that investigate the cracks development patterns in coal under the influence of this technology. In this study, a HVEP coal rock fracturing system was utilized to conduct a physical simulation experiment of coal sample electrical fragmentation. A finite-discrete element method (FDEM) model, incorporating zero-thickness cohesive elements, was developed to simulate the process of stress wave-induced crack propagation in coal, triggered by the plasma channel. The results indicate that over time, the stress wave typically exhibits an initial rapid rise followed by an oscillatory decline. The peak value of the stress wave decreases significantly with distance, stabilizing beyond a propagation distance of 10 mm. Furthermore, the fracturing efficacy of coal by HVEP stress waves is closely linked to specific characteristic parameters: within the range of 75–125 MPa, a positive correlation exists between the stress wave peak and the complexity of the coal crack network. Reducing the stress wave loading rate can increase the crack area to some extent, although excessively slow loading rates may lead to excessive energy dissipation during propagation, which is detrimental to crack expansion. Conversely, when the ratio of β to α ranges from 1 to 100, decelerating the attenuation rate of the stress wave aids in generating stress concentration within the crack zone, thereby facilitating crack propagation. The established numerical model aims to advance understanding of HVEP’s fracturing mechanisms and enhance its application in coalbed methane extraction.