Finite-discrete Element Method Research Articles

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.

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.

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.

Analysis and countermeasures of asymmetric failure in layered surrounding rock tunnels based on FDEM: A case study

In recent years, deep tunnel projects in many regions of China have frequently encountered severe asymmetric failure issues in layered rock structures when crossing through such strata. The unpredictability of the direction and extent of these failures has posed significant challenges for subsequent support design. This paper investigates the asymmetric failure mechanisms of layered rock masses in the Hutou Beishan Mega Tunnel using the Finite-Discrete Element Method (FDEM). First, the smeared method within the FDEM framework is employed to analyze crack evolution, stress states, and asymmetric failure characteristics during tunnel excavation, with the simulation results being compared against field observations for validation. Subsequently, the effects of layer thickness, bedding angle, lateral pressure coefficient, and rock mechanical properties on the asymmetric failure of layered rock masses are systematically explored. The simulation results indicate that the bedding angle and lateral pressure coefficient are the primary factors contributing to the unpredictability of the direction and extent of asymmetric failure in layered rock masses. Based on the analysis of the failure characteristics of these rock masses, the study classifies asymmetric failure into three typical types, providing valuable reference points for predicting the zones and depths of concentrated damage after excavation and for optimizing tunnel support design.

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.

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.

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

In underground hydraulic tunnel engineering, particularlydeep-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.

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.

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.

Mechanical properties and failure behavior of heterogeneous granite: Insights from a new Weibull-based FDEM numerical model

Granite is often encountered in underground engineering, and its mechanical properties and failure behavior directly determine its stability and seepage characteristics. Unlike other rocks, granite is usually considered heterogeneous. Based on the Weibull distribution, this paper proposes a novel modeling method for heterogeneous granite via the combined finite-discrete element method (FDEM), and the mechanical properties and failure behavior of granite under uniaxial and triaxial compression, Brazilian splitting, and direct tension, as well as the influence of the loading rate, were investigated. The research results indicate that (1) the new modeling method can be used to construct a heterogeneous granite numerical model that includes three types of randomness (mineral spatial distribution randomness, mineral size randomness, and mineral shape randomness) and can quantitatively change the mineral composition; (2) uniaxial and triaxial compression simulation tests reveal that as the content of weak minerals (biotite) increases, the uniaxial compressive strength and equivalent cohesion decrease as a power function, and Young's modulus decreases as a linear function, while the equivalent internal friction angle decreases as an exponential function; (3) heterogeneous granite exhibits different mechanical properties and failure behaviors under Brazilian splitting and direct tension due to their different failure modes; typically, the tensile strength obtained from direct tension testing is lower than the value obtained from Brazilian splitting testing; and (4) as the loading rate increases, the strength, stiffness, and number of cracks of the specimen first stabilize and then increase as a power function, with a critical rate of v=1 m/s.

Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue

This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.

Erosive wear and particle attrition in multi-stage solar particle receivers and screw conveyors: A CFD-DEM approach with machine learning and artificial neural networks

A coupled finite volume and discrete element method (CFD-DEM) numerical model is developed to unravel the fundamental mechanisms of granular transport, surface erosive wear and particle attrition in multistage solar particle receivers (MSPR) and screw conveyors (SC). Additionally, various regression-based supervised machine learning (ML) and artificial neural networks (ANN) are trained and optimized with the goal of quickly quantifying erosion and attrition thereby overcoming (a) the inherent challenges of high computational expense of CFD-DEM simulations and (b) exorbitant time required to post-process and extract DEM results. This study is the first of its kind to harness a synergistic numerical framework (CFD-DEM, ML, ANN) to unravel the fundamental mechanisms of erosion and attrition in MSPRs, non-vibrationally induced SCs, and vibrationally-induced SCs. It is found that the packing distribution, particle curtain width, and severity of particle scattering in a MSPR exhibits a subtle variation with particle diameter. In the context of SCs, the magnitudes of erosion and attrition are contingent on the particle diameter and flow operating conditions such as screw blade velocity, vibrational frequency and vibrational amplitude. Interestingly, a vibrationally-induced SC (VI-SC) exhibits superior performance in terms of low erosion and attrition unlike non-vibrationally induced SC (NVI-SC). It is found that MSPRs with 750–1000 µm particles and SCs with 750–1000 µm coupled with vibrational frequencies and vibrational amplitudes of 5 Hz and 0.007 m, respectively, are the preferred configurations due to minimum particle scattering, low erosive wear and low particle attrition. The trained and optimized ML models such as XGBoost, CatBoost, and Multilayer Perceptron (MLP) exhibit superior performance in predicting erosive wear and particle attrition on unseen DEM data, whereas the Multiple Linear Regression (MLR) and Gaussian Process Regression (GPR) ML exhibit poor performance prediction. For the first time, new information on fundamental granular flow dynamics, erosive wear and particle attrition in MSPRs and SCs is discerned. The methodology allows scientists to quickly examine material degradation for a myriad of industrial applications such as concentrated solar thermal (CST), among others.

Effects of Thermoforming Parameters on Woven Carbon Fiber Thermoplastic Composites.

The quality of woven carbon fiber fabric/polycarbonate thermoplastic composites after thermoforming and demolding was investigated using finite element simulation and the Taguchi orthogonal array. The simulation utilized a discrete approach with a micro-mechanical model to describe the deformation of woven carbon fabric, combined with a resin model. This simulation was validated with bias extension tests at five temperatures. The thermoforming process parameters considered were blank temperature, mold temperature, and blank holding pressure, with three levels for each factor. Optimal values for the fiber-enclosed angle, spring-back angle, mold shape fitness, and the strain of the U-shaped workpiece were desired. The results indicated that the comparison of the stress-displacement curve of bias extension tests verified the application of the discrete finite element method. Results from the Taguchi array indicated that blank holding pressure was the dominant parameter, with the optimal value being 1.18 kPa. Blank temperature was the second most significant factor, effective in the range of 160 °C to 230 °C, while mold temperature had a minor effect. Furthermore, the four quality values are dependent and have a similar trend. The best combination was identified as a blank holding press of 1.18 kPa, a blank temperature of 230 °C, and a mold temperature of 190 °C.

Finite-discrete element modelling of fracture development in bimrocks

Block-in-matrix rocks (bimrocks) are a complex geological feature composed of hard blocks in a weak matrix bonded together via a weak interface. The failure mechanism and deformation behavior of the bimrocks is quite complex due to the simultaneous existence of blocks with different shapes, strengths and proportions in a matrix. Therefore, it is of great importance to characterize the bimrocks under different situations. This study employs the combined finite-discrete element method (FDEM) to characterize the failure pattern and load carrying capacity of the bimrocks considering changes in various parameters, including block size, volumetric block proportion (VBP), the strength ratio of block-matrix interface to matrix, and the shape of the blocks (angular, circular, and elliptical shapes). First, the robustness and feasibility of the FDEM in modeling fracture development is verified against an analytical solution as well as a series of experimental tests accompanied with the digital image correlation (DIC) method. Then, the verified model is used to model disc specimens with various block shapes and properties. The results indicate the remarkable influence of VBP, block size and block-matrix interface characteristics on the bimrock mechanical behavior under the same VBP. The results are assessed based on macroscopic observations to investigate the influence of determinative physical properties of bimrocks. The results are also evaluated based on the mode of failure, mode I, II, or mixed mode, to qualitatively elucidate the influence of key factors on the formation of different cracks in different places, including the interface of matrix-blocks or intergrain or intragrain. The results show that since the loading is a quasi-static scheme, all the cracks are intergrain and no intragrain crack is observed for any VBP. The simulations outcomes shows that the block sizes determine the failure pattern, failure mode, and load–displacement behavior, where the larger blocks exhibiting the lowest load carrying capacity due to experiencing more interface breakage in shear. It is found that the VBP is a crucial parameter in the deformation of the bimrocks, showing that the strength of the bimrocks significantly increases with a decrease in the VBPs and the ones with greater VBPs experience more breakage and thus less resistance to loading. The block-interface strength is found to be the most critical factor in the deformation of the bimrocks (regardless of the value of the VBP). Finally, the effect of block shape is shown to have a considerable impact on bimrocks with the higher VBPs (more than 70%).