Combined Finite-discrete Element Method Research Articles

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.

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%).

Numerical simulation of multiple hydraulic fracture propagation in heterogeneous coal reservoirs based on combined finite-discrete element method

Multi-stage fracturing in Horizontal well increases the permeability of coalbed methane by generating multiple fractures. However, the heterogeneity of coal reservoirs is a crucial factor that cannot be ignored in the study of multiple hydraulic fracture propagation. Therefore, we established a two-dimensional model for multiple hydraulic fracture propagation based on the combined finite-discrete element method (FDEM) and assigned a Weibull distribution function to the heterogeneity of the physical parameters of the cohesive elements in the model. The objective was to simulate and study the fracture propagation law of multi-cluster fracturing in horizontal wells in heterogeneous coal reservoirs. The research results indicated that: 1) as the heterogeneity of the coal reservoir weakened, the deflection angle of the main fracture increased. More secondary fractures were generated in the coal reservoir, leading to significant discontinuity. 2) The fracturing disturbance area was always concentrated at the tip of the main fracture, with a double wing shape. However, the fracturing disturbance areas at the tips of multiple main fractures could easily converge, with a square shape; 3) It is recommended to use a moderate injection rate and increase the perforation spacing appropriately when hydraulic fracturing is carried out in coal reservoirs with a heterogeneity coefficient m=5.

Blind prediction of fracture in an additively manufactured geomaterial using the finite discrete element method

Modeling fracture and damage processes is a challenging, yet critical capability for promoting safe and sustainable design in geotechnical, energy, and hydrological applications. Numerical methods capable of modeling fracture processes are rarely asked to make blind predictions against experimental observations. Here, we report results from a numerical study of blind fracture prediction in an additively manufactured, three-point bend specimen. We record a number of physical mechanisms associated with the fracture of the specimen and make a blind prediction against experimental results that were unknown when the numerical study was performed. We then compare results from our model to the blind data set. We find that the combined finite discrete element method performs exceptionally well in the simulation and prediction of fracture processes.

A 2D continuous-discontinuous unified pore-fracture seepage model for hydro-mechanical coupling in the combined finite-discrete element method (FDEM) using node binding scheme

The combined finite-discrete element method (FDEM) has been widely used to simulate the dynamic propagation of hydraulic fractures. In the conventional FDEM, a fictitious fluid exchange coefficient between adjacent finite element pairs needs to be specified to alleviate the discontinuous pore seepage in the continuous rock matrix domain. This commonly employed approach inevitably increases computational cost and introduces additional numerical parameters (e.g., fluid exchange coefficient). To circumvent these limitations, we propose a node binding scheme that not only ensures continuous pore seepage simulations in the intact/continuous rock matrix domain, but also allows discontinuous pore pressures on the two sides of a fracture. The computational efficiency of pore seepage simulation using the proposed approach is increased by ∼120 times for a model with ∼6000 triangle elements, and fictitious numerical parameters are not required. A suite of numerical benchmarks is conducted to verify the effectiveness and robustness of the proposed pore-fracture seepage model, and its capability of capturing the dynamic propagation process of fluid-driven fractures is also demonstrated. As an application, a typical example is employed to explore the mechanism of multiple hydraulic fracturing. The proposed hydro-mechanical coupling model may help enhance the applicability and accuracy of FDEM for unconventional energy exploitation.

Modelling dynamic fracture and fragmentation of rocks under multiaxial coupled static and dynamic loads with a parallelised 3D FDEM

In this study, a three-dimensional (3D) combined finite-discrete element method (FDEM) based simulator, which enables the robust simulation of full-scale triaxial Hopkinson bar (Tri-HB) testing system, including the capture of fracture and fragmentation processes of rock specimens as well as the detection and analysis of generated rock fragments, is developed for investigating the dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads. An innovative two-step approach is proposed to first efficiently achieve the static stress state in the entire Tri-HB system and then apply dynamic loading to the system. The proposed approach with the schemes of mass scaling and local damping can significantly reduce the run time for static computation involving cohesive elements and complex contact mechanics in the framework of explicit time-integration. The developed program is well validated by achieving dynamic stress equilibrium in the Tri-HB system and comparing the simulated stress wave profiles with those from laboratory experiments. Then, the progressive dynamic fracture and fragmentation processes of rocks under different static stress conditions in a full-scale Tri-HB system are investigated, which vividly exhibit the confinement dependence of the dynamic behaviours of rocks in the testing system. It is found that, even with the same loading rate, separate input parameter sets for rock need to be established in FDEM for different confinement conditions to capture the actual rate dependent behaviour of rock. Further studies are also conducted to investigate the effect of interfacial friction on the fracture behaviour, and the results indicate that higher interfacial frictions significantly disturb the dynamic stress variations and the true rock behaviour in the system. Through high performance computing of 3D FDEM, this study is expected to contribute to the understanding of dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads in deep underground engineering.

Numerical investigation of the path-dependent frost heave process in frozen rock under different freezing conditions

Frost heave in water-bearing rock masses poses significant threats to geotechnical engineering. This paper developed a novel three-dimensional (3D) frost model, based on the combined finite-discrete element method (FDEM), to investigate the frost heave process in rock masses where thermal transfer, water migration, water-ice phase transition (ice growth) and ice-rock interaction are explicitly simulated. The proposed model is first validated against existing experimental and analytical solutions, and further applied to investigate path-dependent frost heave behavior under various freezing conditions. Results show that freezing direction plays a vital role in the dynamic ice growth and ice-rock interaction, thus affecting the frost heave behavior. In the top-down freezing regime, ice plugs form first at the crack's top surface, sealing the crack and preventing water migration, which can amplify ice pressure. Parametric studies, including rock Young's modulus, ice-rock friction, and rock hydraulic conductivity, further reveal that the temporal aspects of ice development and rock mechanical response strongly affect ice-rock interaction and hence the frost heave mechanism. Furthermore, some typical phenomena (e.g. water/ice extrusion and frost cracking) can also be well captured in this model. This novel numerical framework sheds new light on frost heave behavior and enriches our understanding of frost heave mechanisms and ice-rock interaction processes within cold environment engineering projects.

An enhanced polar-based GPGPU-parallelized contact detection algorithm for 3D FDEM and its application to cracking analysis of shield tunnel segmental linings

This study introduces the three-dimensional combined finite-discrete element method (3D FDEM) to perform cracking analysis of segmental linings under extreme conditions. Considering the complex contact interactions of segments, this study first proposes a polar-based GPGPU-parallelized contact detection algorithm to handle memory issues confronted by existing FDEM algorithms. Initially, a spatial decomposition approach based on the polar coordinate system is implemented during the broad search phase. Each tetrahedral element is positioned within suitable search cells according to the axis-aligned bounding box. Subsequently, element pairs within each search cell are iteratively traversed, and potential contact pairs are identified using the judge cell criteria. After the broad search, a narrow search phase is executed to determine all real contacts. Following the above implementation, a load-structure model encompassing soil spring and external pressure calculations is then proposed. Based on the shape functions and coordinate transformation, the formulations of soil springs and external loads are derived and parallelized in the 3D FDEM framework. Three numerical tests are presented to validate the effectiveness of the proposed approach. Simulation results confirm the suitability of the proposed method for cracking analysis of segmental linings. Compared to the existing methods, it reduces GPU memory usage by 56 ∼ 76 % without extending time, which enhances the computational scale of 3D FDEM simulations. Furthermore, the proposed method is applied to two engineering scenarios, i.e., straight and curved segmental linings, both considering the absence and presence of contact defects between segments. The results show that contact defects can significantly reduce the resistance of the structural system comprising bolts and concrete segments for straight and curved scenarios.

Numerical investigation of mechanical responses and failure features of coal measure strata using combined finite-discrete element method

Investigating the mechanical responses and failure features of the deep coal measure strata (CMS) is essential for designing hydraulic fracturing treatments and preventing geological dynamic hazards in underground engineering. In this paper, a three-dimensional CMS model is established by the combined finite-discrete element method (FDEM). The mechanical properties, stress evolutions and failure features of the CMS with different lithological combinations (sandstone-coal-sandstone (SCS), sandstone-coal-mudstone (SCM) and mudstone-coal-mudstone (MCM)) and thickness ratios are investigated under the uniaxial compressive condition. Results indicate that the SCS combination exhibits the highest uniaxial compressive strength (UCS) and elastic modulus, followed by the SCM and MCM combinations. The mechanical properties of the CMS are predominantly determined by the softer coal layer. The mechanical contrasts in elastic modulus and Poisson’s ratio between adjacent layers cause the generation of additional compressive stress in the softer layer and additional tensile stress in the stiffer layer. Therefore, the softer coal layer exhibits the shear-dominated failure pattern while the stiffer sandstone/mudstone layer displays the tensile-dominated failure pattern in the CMS. Furthermore, as the thickness ratio of the coal layer increases, the UCS, elastic modulus, and interfacial constraint stress decrease in the CMS. Additionally, the UCS and stress–strain relationship in the post-peak stage exhibit the noticeable size effect, whereas the mechanical behaviors in the pre-peak stage and the ultimate fracture patterns show the opposite. The elastic modulus and interfacial constraint stress obtained by the FDEM simulation match well with those calculated by theoretical models. The key findings of this paper can provide fundamental understanding and reliable parameters for multi-scale geomechanical modeling in petroleum and mining engineering.

Effects of Geo-Stress and Natural Fracture Strength on Hydraulic Fracture Propagation in a Deep Fractured Tight Sandstone Reservoir.

Hydraulic fracturing technology has been widely used in the tight reservoir reconstruction. Unfortunately, with the deepening of mining depth and the increase of geo-stress, the propagation mechanism of medium-pressure fractures in the reservoir is significantly different from that of conventional shallow reservoirs. Based on the combined finite discrete element method, this paper conducts numerical simulation research on deep tight sandstone reservoirs in the west. The discrete fracture network modeling method is used to establish a tight sandstone reservoir model with natural bedding, and the influence of geo-stress difference and natural fracture strength on hydraulic fracture propagation law in a high geo-stress environment is discussed in detail. The results show that the difference between geo-stress and the strength of natural fractures has a significant effect on the shape and expansion of hydraulic fractures under the high geo-stress conditions. The greater the difference in ground stress, the more obvious the tendency of the main fractures of the reservoir, and the shorter the branch fractures. With the increase of natural fracture strength, the changes in propagation pressure, fracture length, area, and width, which can be fitted with a linear function with a goodness of fit as high as 0.99. In addition, the morphological results of hydraulic fractures in the simulation are not only affected by the constitutive parameters of the model but also may be affected by the randomness of the natural fracture network, thus, showing a certain degree of dispersion. Therefore, it is extremely necessary to build a reservoir fracturing model in a specific area based on more detailed geological monitoring data to guide actual construction. The above achievements have certain reference significance for the field operation of deep tight sandstone reservoirs.

Propagation and complex morphology of hydraulic fractures in lamellar shales based on finite-discrete element modeling

We explore the controls of stress magnitude and orientation relative to bedding on the resulting morphology/topology of hydraulic fractures using a combined finite-discrete element method (FDEM). Behavior is shown conditioned by the ratio of principal stresses λ=σ3/σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ={\\sigma }_{3}/{\\sigma }_{1}$$\\end{document} and relative inclination of the bedding. When the lateral pressure coefficient (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) is less than 0.67, hydraulic fractures predominantly initiate as tensile fractures along the wellbore, aligning with the maximum principal stress direction. Conversely, for λ≥0.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\ge 0.67$$\\end{document}, shear cracks are favored to initiate for the minor stress difference, leading to a less predictable initiation and extension direction. Simultaneously, diminished stress differences correspond to elevated reservoir breakdown pressures, displaying a linear correlation with lateral pressure coefficients and little influenced by equivalent bedding orientation. Bedding plane orientation significantly impacts the mode and morphology of hydraulic fracture propagation. Bedding parallel to the direction of the minimum principal stress (σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{3}$$\\end{document}) favors layer-penetrating and bifurcated fractures, whereas inclined bedding facilitates the emergence of numerous steering-type and capture-type fractures. Especially at steeper inclinations (β=60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =60^\\circ$$\\end{document}), hydraulic fractures readily extend along the bedding surface, inducing macroscopic shear slip failure. Under high-stress disparities, the breakdown pressure exhibits greater sensitivity to bedding inclination, and its influence pattern aligns with the variations in tensile strength, typically reaching maximum and minimum values at bedding inclination angles of 0° and 60°, respectively.

Numerical Investigation of Tree-Type Hydraulic Fracturing for Balanced Permeability Enhancement of Heterogenous Coal Seams Based on the Finite-Discrete Element Method Model.

Tree-type hydraulic fracturing (TTHF) is a new technology that can enhance the permeability of coal seams in a balanced manner and increase the coalbed methane production rate. However, the heterogeneity of coal seams is a major challenge in achieving balanced permeability enhancement by TTHF. Traditional methods based on digital image processing are difficult to apply in practice. To address these challenges, we proposed a 2D numerical model of coal seams based on the combined finite-discrete element method (FDEM). The elastic modulus of the coal seams obeys a Weibull distribution, and the coal heterogeneity was quantified by an index m. The effects on the fracture initiation pressure, the fracturing influence range, and displacements of TTHF were analyzed from four aspects, including the homogeneity index of coal, the arrangement angle of branch boreholes, the horizontal stress difference, and the injection rate of the fracturing fluid. The results show that TTHF has a significant effect on the balanced permeability enhancement in coal reservoirs, particularly with strong heterogeneity, and the best permeability enhancement for TTHF is achieved when the branch boreholes are arranged at 45°. The branch boreholes are prefabricated in advance to create a pressure relief area around the injection point, and the hydraulic fracture propagation is affected by the horizontal stress difference only when the fracturing influence range exceeds this area. When the horizontal stress difference increases from 0 to 4 MPa, its fracture initiation pressure increases from 8.93 to 10.86 MPa, with an increase of 21.61%. In addition, the initial stage of fluid injection was found to be crucial for achieving balanced permeability enhancement in TTHF, and a higher injection rate can expand the fracturing influence range. The numerical model has profound implications for the field application of TTHF technology.

FDEM analysis of deep rock mass failure and its impact on horizontal bearing capacity in offshore wind turbine piles

Rock-socketed single piles are integral components of offshore wind turbine foundations in rock-based sea areas. Traditional numerical models have been employed to analyze the failure modes and lateral interactions between piles and the rock medium. However, these do not simulate the decline in the horizontal bearing capacity due to rock breakage, posing potential safety risks. In this study, the combined finite-discrete element method (FDEM) was used to simulate the deformation process of submarine rock masses transitioning from an intact to a fractured state. A notable innovation in the proposed approach is the consideration of the effects of the rock mass fracture and pile-rock cohesion on the load-bearing behavior of single-pile foundations. The FDEM model was validated through full-scale lateral load tests. The results showed a distinctive sequence in failure mechanisms, with the tensile failure of the rock mass around the pile at significant depths preceding the compression failure. Local failure at the contact interface significantly reduced the horizontal bearing capacity—a phenomenon that is inadequately represented by conventional finite element models. Furthermore, the cohesion element embedding method was introduced and used to simulate the influence of the tensile properties inherent in grouting materials on the failure strength and mode of the pile-rock interface. This study highlighted the importance of considering the nuanced effects of rock failure in the design of horizontally loaded piles. Failure to do so could lead to nonconservative designs and compromise the safety and efficacy of offshore wind turbine foundations. By pushing the boundaries of numerical modeling with the FDEM, the study aims to provide a more accurate and reliable framework for the design and assessment of rock-socketed single piles for offshore wind energy applications.

A novel mesoscale modelling method for steel fibre-reinforced concrete with the combined finite-discrete element method

This paper proposes a novel mesoscale modelling method to study the effect of steel fibres on the fracture properties of steel fibre reinforced concrete (SFRC) based on an integrated finite-discrete element method (FDEM) framework. The present method models the steel fibre of SFRC as multiple bar elements, while simulating the cement matrix using triangle elements. A comprehensive bond-slip model is also introduced between the triangle element and bar element, enabling accurate reproduction of the interaction behaviour between the concrete matrix and steel fibre. Additionally, the progressive failure process of cohesive elements in FDEM is considered as crack propagation, confirming the superiority of FDEM from continuum to discontinuum. The results of the Brazilian split test and uniaxial compression test validate the capability of the FDEM framework for mode Ι and mode II fractures, while single fibre pull-out tests and 3-point-bending beam tests provide validation of the effectiveness of the integrated FDEM framework for the mesoscale modelling of SFRC. The discussion also covers employing the mesoscale modelling method to investigate the effect of steel fibre on the fracture properties of SFRC. Owing to its merits in quantitative analysis, the present method can serve as a feasible potential tool for mesoscale modelling analysis and SFRC design.

Numerical Investigation on the Grouting Penetration Process of Quick-Setting Grout in Discrete Fractured Rock Mass Based on the Combined Finite–Discrete-Element Method

Numerical Investigation on the Grouting Penetration Process of Quick-Setting Grout in Discrete Fractured Rock Mass Based on the Combined Finite–Discrete-Element Method

Effect of fully-grouted bolts on the failure behaviors of mine pillars: Insights from block-based FDEM modeling

In this study, the Voronoi-based breakable block model (VBBM) based on the combined finite-discrete element method (FDEM) is used to investigate the failure mechanism of mine pillars and the rock-rockbolt interactions. The mechanical parameters of grout-rock and grout-bolt interfaces of a fully-grouted bolt are calibrated via numerical pull-out tests. Then, uniaxial compression tests are carried out on the reinforced pillars. The kinetic energy release rate (KERR) and crack aperture (CA) are used to evaluate the reinforcement effect. The results revealed that the VBBM can effectively characterize the damage failure mechanisms of spalling on the pillar surface and conjugate shear failure in the core zone of the pillar and reproduce the pre-peak nonlinear deformation and post-peak pseudo-ductile behaviors. The passive confining pressure generated by rockbolts is activated only when the rock mass produces sufficient deformation, and the constraints generated by different numbers of rockbolts can only affect the post-peak behavior of the pillar. There is a gradient feature in the internal deformation of the pillar from the shallow surface to the core. If the rockbolt density meets the strain demand, then rockbolts can delay the inward expansion of cracks by generating local constraints and can effectively fix the spalling rock blocks. With increasing support pressure, the CA and KERR exhibit a decreasing trend and strong power-exponential relationships with support pressure, indicating that there is a transition interval of support pressure and an optimal value for setting the rockbolt density.

Predicting Stick-Slips in Sheared Granular Fault Using Machine Learning Optimized Dense Fault Dynamics Data

Predicting earthquakes through reasonable methods can significantly reduce the damage caused by secondary disasters such as tsunamis. Recently, machine learning (ML) approaches have been employed to predict laboratory earthquakes using stick-slip dynamics data obtained from sheared granular fault experiments. Here, we adopt the combined finite-discrete element method (FDEM) to simulate a two-dimensional sheared granular fault system, from which abundant fault dynamics data (i.e., displacement and velocity) during stick-slip cycles are collected at 2203 “sensor” points densely placed along and inside the gouge. We use the simulated data to train LightGBM (Light Gradient Boosting Machine) models and predict the gouge-plate friction coefficient (an indicator of stick-slips and the friction state of the fault). To optimize the data, we build the importance ranking of input features and select those with top feature importance for prediction. We then use the optimized data and their statistics for training and finally reach a LightGBM model with an acceptable prediction accuracy (R2 = 0.94). The SHAP (SHapley Additive exPlanations) values of input features are also calculated to quantify their contributions to the prediction. We show that when sufficient fault dynamics data are available, LightGBM, together with the SHAP value approach, is capable of accurately predicting the friction state of laboratory faults and can also help pinpoint the most critical input features for laboratory earthquake prediction. This work may shed light on natural earthquake prediction and open new possibilities to explore useful earthquake precursors using artificial intelligence.

Fracture characteristic and support effect around deep lined tunnels using CGP-FDEM simulation and field investigation analysis

The lining is one of the main methods of support and is chosen as the primary support for composite and reinforced roadways during mining excavation. Systematic investigations into the supportive effect of lined roadways in deep weak rock masses are highly desirable to improve support design and enhance roadway stability. The fracture characteristics and deformation are more prominent in the lining failure and damage to the surrounding rock. For investigations into the fracture mode and failure characteristics of the lining support, this study proposed a lining element support model in the graphics processing units (GPU) parallel combined finite-discrete element method (FDEM) program using compute unified device architecture (CUDA), referred to as CGP-FDEM. The lining element model and excavation simulation method are implemented in the CGP-FDEM aim of simulation large-scale rock fractures in underground excavations. On this basis, the simulation of deep roadway excavation is performed under various support conditions, including low-strength and high-strength shotcrete, steel arch, and U-profile yieldable steel. Further, a comparative analysis is conducted between the field investigation and simulation results, focusing on fracture-fragmentation and large deformation of the surrounding rock, as well as the failure and fracture mode of the lining elements. Results of individual support effects indicate that the reinforcement conditions mainly affect the excavation damaged zone (EDZ) and the deformation of the surrounding rock. Rock fragmentation and buckling intensify the large deformation and instability of the roadway. Fracture evolution and instability of the surrounding rock can easily occur in weak areas due to severe stress concentration and the accumulation and release of energy. Based on the analysis, the principle of "uniform reinforcement of reactive force throughout the entire section" is proposed to alleviate stress concentrations and maintain the overall stability of the excavation space.

Evaluating the impact of calcite and heterogeneity on the mechanical behavior of coal: A numerical study with grain-based finite-discrete element method

Understanding the mechanical properties and fracture behaviors of coal is essential for the safety of underground mining engineering. This research aims to evaluate the impact of calcite and heterogeneity on the mechanical properties of coal. Neper, a software package for polycrystal generation and meshing, is used to create numerical models with a non-uniform grain size distribution. A random parameter assignment method is proposed to simulate the mechanical properties and failure behavior of coal using the combined finite-discrete element method (FDEM). A comprehensive parametric investigation of the properties of triangular and joint elements is conducted, and calibration procedures are suggested for numerical modeling. The model was calibrated to experimental results and then used to understand the impact of calcite grains on the mechanical behavior of coal. After calibration, a triaxial compression was performed on coal sampleswith and withoutcalcite grains at differentconfining pressures. It is found that the presence of calcite in a coal sample increases Young's modulus and decreases the peak strength of coal. This research uses Voronoi tessellation technology to present a Weibull statistical grain-based model (GBM) to investigate the microstructural heterogeneity induced by grain morphologies. The deformation response, strength characteristics and cracking behavior are investigated by varying the heterogeneity of numerical models under compressive tests with different confining pressures. The simulation results of triaxial compression indicate that the compressive strength increases linearly as the heterogeneity m value increases. The consistency of the numerical results with the experimental observationssuggests that the GBM approachcan be used to better understand the mechanics of brittle rock failure at the micro-structure scale.

An efficient Kriging-based calibration framework for FDEM

The combined finite-discrete element method (FDEM) is a powerful numerical tool to simulate the transition of materials from continuous deformation to discontinuous fracturing and fragmentation. Calibrating parameters using laboratory data is crucial for applying FDEM to engineering-scale analysis. Considering the high computational costs in existing calibration schemes, this study proposes an effective FDEM calibration framework employing the Kriging surrogate model rooted in Uniaxial Compressive Strength (UCS) and Brazilian Tensile Strength (BTS) tests. The sensitivity analysis is first conducted on mesh size, loading rate, and numerical parameters to find a suitable set that balances computational efficiency and accuracy. Subsequently, an efficient mapping relationship between input fracture parameters and simulated strengths is established based on the Kriging surrogate model, replacing the expensive FDEM program for forward calculations. With the fracture parameters treated as unknown variables and experimental strengths available, the objective function is formulated and then solved to estimate fracture parameters. The effectiveness of the proposed method is validated through a numerical example. Compared to the conventional methods, the proposed approach requires fewer simulations of UCS and BTS, which highlights a significant computational efficiency advantage.