Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerical simulation on the seismic performance of retrofitted masonry walls based on the combined finite-discrete element method

Due to the long construction life,improper design methods,brittle material properties and poor construction techniques,most existing masonry structures do not perform well during earthquakes.The retrofitting method using an external steel-meshed mortar layer is widely used to retrofit existing masonry buildings.Assessing the seismic performance of masonry walls reinforced by an external steel-meshed mortar layer reasonably and effectively is a difficult subject in the research field of masonry structures.Based on the combined finite-discrete elements method,the numerical models of retrofitted brick walls with four different masonry mortar strengths by an external mortar layer are established.The shear strength of mortar and the contact between the retrofitted mortar layer and the brick blocks are discussed in detail.The failure patterns and load-displacement curves of the retrofitted brick walls were obtained by applying low cycle reciprocating loads to the numerical model,and the bearing capacity and the failure mechanism of the retrofitted walls were obtained by comparing the failure patterns,ultimate bearing capacity,deformability and other aspects with the tests.This study provides a basis for improving the seismic strengthening design method of masonry structures and helps to better assess the seismic performance of masonry structures after retrofitting.

Three-dimensional combined finite-discrete element approach for simulation of single layer powder compaction process

The application of a combined finite-discrete element modeling approach to simu late the three-dimensional microscopic compaction behavior of single-layer met al powder system was described. The process was treated as a static problem,wit h kinematical component being neglected. Due to ill condition,Cholesky’s metho d failed to solve the system equations,while conjugate gradient method was trie d and yielded good results. Deformation of the particles was examined and compar ed with the results of physical modeling experiments. In both cases,the inner p articles were deformed from sphere to polygonal column,with the edges turning f rom arc to straight line. The edge number of a particle was equal to the number of particles surrounding it. And the experiments show that the ductile metal par ticles can be densified only by their plastic deformation without the occurrence of rearrangement phenomenon.

Reliability Prediction of Wrought Carbon Steel Castings under Fatigue Loading Using Coupled Mold Optimization and Finite Element Simulation

The fatigue life and reliability of wrought carbon steel castings produced with an optimized mold design are predicted using a finite element method integrated with reliability calculations.The optimization of the mold is carried out using MAGMASoft mainly based on porosity reduction as a response.After validating the initial mold design with experimental data,a spring flap,a common component of an automotive suspension system is designed and optimized followed by fatigue life prediction based on simulation using Fe-safe.By taking into consideration the variation in both stress and strength,the stress-strength model is used to predict the reliability of the component under fatigue loading.Under typical loading conditions of 70 kN,the analysis showed that 95%of the steel spring flaps achieve infinite life.However,under maximum loading conditions of 90 kN,reliability declined significantly,with only 65%of the spring flaps expected to withstand the stress without failure.The study also identified a safe load-induced stress of 95 MPa on the spring flap.The findings suggest that transitioning from forged to cast spring flaps is a promising option,particularly if further improvements in casting design reduce porosity to negligible levels,potentially achieving 100%reliability under typical loading conditions.This integrated approach of mold optimization coupled with reliability estimation under realistic service loading conditions offers significant potential for the casting industry to produce robust,cost-effective products.

Research and Application of a Multi-Field Co-Simulation Data Extraction Method Based on Adaptive Infinitesimal Element

Regarding the spatial profile extraction method of a multi-field co-simulation dataset,different extraction directions,locations,and numbers of profileswill greatly affect the representativeness and integrity of data.In this study,a multi-field co-simulation data extractionmethod based on adaptive infinitesimal elements is proposed.Themultifield co-simulation dataset based on related infinitesimal elements is constructed,and the candidate directions of data profile extraction undergo dimension reduction by principal component analysis to determine the direction of data extraction.Based on the fireworks algorithm,the data profile with optimal representativeness is searched adaptively in different data extraction intervals to realize the adaptive calculation of data extraction micro-step length.The multi-field co-simulation data extraction process based on adaptive microelement is established and applied to the data extraction process of the multi-field co-simulation dataset of the sintering furnace.Compared with traditional data extraction methods for multi-field co-simulation,the approximate model constructed by the data extracted from the proposed method has higher construction efficiency.Meanwhile,the relative maximum absolute error,root mean square error,and coefficient of determination of the approximationmodel are better than those of the approximation model constructed by the data extracted from traditional methods,indicating higher accuracy,it is verified that the proposed method demonstrates sound adaptability and extraction efficiency.

Bridging element-free Galerkin and pluri-Gaussian simulation for geological uncertainty estimation in an ensemble smoother data assimilation framework

The facies distribution of a reservoir is one of the biggest concerns for geologists,geophysicists,reservoir modelers,and reservoir engineers due to its high importance in the setting of any reliable decisionmaking/optimization of field development planning.The approach for parameterizing the facies distribution as a random variable comes naturally through using the probability fields.Since the prior probability fields of facies come either from a seismic inversion or from other sources of geologic information,they are not conditioned to the data observed from the cores extracted from the wells.This paper presents a regularized element-free Galerkin(R-EFG)method for conditioning facies probability fields to facies observation.The conditioned probability fields respect all the conditions of the probability theory(i.e.all the values are between 0 and 1,and the sum of all fields is a uniform field of 1).This property achieves by an optimization procedure under equality and inequality constraints with the gradient projection method.The conditioned probability fields are further used as the input in the adaptive pluri-Gaussian simulation(APS)methodology and coupled with the ensemble smoother with multiple data assimilation(ES-MDA)for estimation and uncertainty quantification of the facies distribution.The history-matching of the facies models shows a good estimation and uncertainty quantification of facies distribution,a good data match and prediction capabilities.

Optimizing design of lattice materials based on finite element simulation

The optimized design of simple cross-truss and column lattice structures was carried out by the SolidWorks simulation module.The effective density of the structure was calculated according to the weight reduction requirements proposed by the project.Then,the vari-ation curve between the maximum bearing stress of the unit structure and the structural variables was obtained by simulation.Meanwhile,the mathematical equation between the maximum bearing stress and the structural variables could be obtained through MATLAB fitting.The results indicated that with the decrease in the number of cells,the compressive strength of the prepared column lattice increased(400 to 4 cells,compressive strength 29 MPa to 160 MPa).However,the yield strength increased with the number of cells.The compression strength of the simple cross-truss lattice samples indicated an increase trend with the decrease of the pillar size(an increase of the number of units),reaching 91 MPa(pillar diameter 0.52 mm,number of units 25).While the yield strength increased with the increasing of the number of units.In addition,the additive manufacturing processes of simple cubic lattice and simple cross-pillar lattice were investigated using selective laser melting.The compression performance obtained from the experiment is compared with the simulation results,which are in good agreement.The results of this paper can provide an important reference for optimizing design of lattice materials.

Standard spectrum measurement and simulation of elemental capture spectroscopy log

We have established a set of laboratory measurements which is used for capturing element gammma spectrum. Standard captured gamma ray spectra for ten elements, including Si, Ca, Fe, are obtained using the measurements for the first time in China. We also simulated the capture gamma ray spectra of the ten elements using Monte Carlo methodology with the same parameters of our experimental measurements. Comparing the experiment and simulation results with the data from the International Atomic Energy Agency＇s Nuclear Data Center, we obtained the standard captured gamma ray spectra of the ten elements, which, as calibration spectra, are used to calibrate the raw spectrum in data processing. This method solved the key problem during the conversion from the original measuring spectrum to the yield of each element in the data processing. The method can effectively improve the accuracy of the element yield calculation.

Mathematical modeling and simulations of stress mitigation by coating polycrystalline particles in lithium-ion batteries

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCo_(z)O_(2)(x≥0.8)(NMC)particles with poly(3,4-ethylenedioxythiophene)(PEDOT).The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion,and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport,promoting the lithium distribution across the secondary particles more homogeneously.Besides,the lower stiffness,higher ionic conductivity,and larger thickness of the coating layer improve the stress mitigation.This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels.

GPGPU-parallelised hybrid finite-discrete element modelling of rock chipping and fragmentation process in mechanical cutting

Mechanical cutting provides one of the most flexible and environmentally friendly excavation methods.It has attracted numerous efforts to model the rock chipping and fragmentation process,especially using the explicit finite element method(FEM) and bonded particle model(BPM),in order to improve cutting efficiency.This study investigates the application of a general-purpose graphic-processing-unit parallelised hybrid finite-discrete element method(FDEM) which enjoys the advantages of both explicit FEM and BPM,in modelling the rock chipping and fragmentation process in the rock scratch test of mechanical rock cutting.The input parameters of FDEM are determined through a calibration procedure of modelling conventional Brazilian tensile and uniaxial compressive tests of limestone,A series of scratch tests with various cutting velocities,cutter rake angles and cutting depths is then modelled using FDEM with calibrated input parameters.A few cycles of cutter/rock interactions,including their engagement and detachment process,are modelled for each case,which is conducted for the first time to the best knowledge of the authors,thanks to the general purpose graphic processing units(GPGPU) parallelisation.The failure mechanism,cutting force,chipping morphology and effect of various factors on them are discussed on the basis of the modelled results.Finally,it is concluded that GPGPU-parallelised FDEM provides a powerful tool to further study rock cutting and improve cutting efficiencies since it can explicitly capture different fracture mechanisms contributing to the rock chipping as well as chip formation and the separation process in mechanical cutting.Moreover,it is concluded that chipping is mostly owed to the mix-mode Ⅰ-Ⅱ fracture in all cases although mode Ⅱ cracks and mode Ⅰ cracks are the dominant failures in rock cutting with shallow and deep cutting depths,respectively.The chip morphology is found to be a function of cutter velocdty,cutting depth and cutter rake angle.

COUPLED SIMULATION OF 3D ELECTRO-MAGNETO-FLOW FIELD IN HALL-HEROULT CELLS USING FINITE ELEMENT METHOD

Two full 3D steady mathematical models are developed by finite element method （FEM） to calcalate coupled physics fields. the electro-magnetic model is built and solved first and so is the fluid motion model with the acquired electromagnetic force as source body forces in Navier-Stokes equations. Effects caused by the ferromagnetic shell, busbar system around, and open boundary problem as well as inside induced current were considered in terms of the magnetic field. Furthermore, a new modeling method is found to set up solid models and then mesh them entirely with so-called structuralized grids, namely hex-mesh. Examples of 75kA prebaked cell with two kinds of busbar arrangements are presented. Results agree with those disclosed in the literature and confirm that the coupled simulation is valid. It is also concluded that the usage of these models facilitates the consistent analysis of the electric field to magnetic field and then flow motion to the greater extent, local distributions of current density and magnetic flux density are very much dependent on the cell structure, the steel shell is a shield to reduce the magnetic field and flow pattern is two dimensional in the main body of the metal pad.

Applications of finite element simulation in orthopedic and trauma surgery

Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography(CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element(FE) simulation lets us know the biomechanical changes that take place after hipprostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints applied to the correction of deformities, providing the recovering force-displacement and angle-moment curves that characterize the mechanical behavior of the splint in the overall range of movement.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

Finite element analysis and simulation for cold precision forging of a helical gear

To investigate the effects of billet geometry on the cold precision forging process of a helical gear, six different billet geometries were designed utilizing the relief-hole principle. And the influences of the billet geometry on the forming load and the deformation uniformity were analyzed by three-dimensional （3D） finite element method （FEM） under the commercial software DEFORM 3D. The billet geometry was optimized to meet lower forming load and better deformation uniformity requirement. Deformation mechanism was studied through the distribution of flow velocity field and effective strain field. The forging experiments of the helical gear were successfully performed using lead material as a model material under the same process conditions used in the FE simulations. The results show that the forming load decreases as the diameter of relief-hole do increases, but the effect of do on the deformation uniformity is very complicated. The forming load is lower and the deformation is more uniform when do is 10 mm.

RESEARCH ON THE SELECTION OF FRICTION MODELS IN THE FINITE ELEMENT SIMULATION OF WARM EXTRUSION

During the process of finite element simulation of precision warm forging, the selection of friction models has a direct effect on the precision accuracy of finite element simulation results. Among all the factors which influence the selection of friction models, the distribution rule of normal stress at the tool-workpiece interface is a key one. To find out the distribution rule of normal stress at the tool-workpiece interface, this paper has made a systematic research on three typical plastic deformation processes: forward extrusion, backward extrusion, and lateral extrusion by a method of finite element simulation. Then on the base of synthesizing and correcting traditional friction models, a new general friction model which is fit for warm extrusion is developed at last.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Finite element simulation of inertia friction welding of superalloy bars

A thermo-mechanical coupling.finite element model was built to investigate the inertia friction welding of GH4169 bars. The remeshing and map solution techniques were adopted. Ttle whole welding process was investigated by adopting an innovative heat generation model and the flywheel rotational speed measured via the experiment. The simulated evolution of axial shortening shows a good agreement with the experiment. In addition, extensive .strain concentration presents in the interface and flash, and the largest ,strain exists near the flash root. Moreover, an intere.sting thermal reflux phenomenon during the cooling stage was found.

Discrete element simulation of mechanical characteristic of conditioned sands in earth pressure balance shield tunneling

The discrete element method (DEM) was used to simulate the flow characteristic and strength characteristic of the conditioned sands in the earth pressure balance (EPB) tunneling. In the laboratory the conditioned sands were reproduced and the slump test and the direct shear test of the conditioned sands were implemented. A DEM equivalent model that can simulate the macro mechanical characteristic of the conditioned sands was proposed,and the corresponding numerical models of the slump test and the shear test were established. By selecting proper DEM model parameters,the errors of the slump values between the simulation results and the test results are in the range of 10.3%-14.3%,and the error of the curves between the shear displacement and the shear stress calculated with the DEM simulation is 4.68%-16.5% compared with that of the laboratory direct shear test. This illustrates that the proposed DEM equivalent model can approximately simulate the mechanical characteristics of the conditioned sands,which provides the basis for further simulation of the interaction between the conditioned soil and the chamber pressure system of the EPB machine.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

Finite Element Numerical Simulation of Ground Subsidence in Liangjia Colliery

Being aimed at the ground subsidence due to underground coal mining,a numerical model of rock was established and an appropriate method of numerical simulation was put forward.Using the measured subsidence data on the ground,the equivalent mechanical parameters of the rock stratums can be back-calculated by the properly treatment of coal excavation area,then the ground subsidence of other coal mining area can be predicted by FFM.It provided reference for the treatment of the buildings on the ground of this colliery.