A novel index to evaluate discretization methods: A case study of flood susceptibility assessment based on random forest

The selection of a suitable discretization method(DM) to discretize spatially continuous variables(SCVs)is critical in ML-based natural hazard susceptibility assessment. However, few studies start to consider the influence due to the selected DMs and how to efficiently select a suitable DM for each SCV. These issues were well addressed in this study. The information loss rate(ILR), an index based on the information entropy, seems can be used to select optimal DM for each SCV. However, the ILR fails to show the actual influence of discretization because such index only considers the total amount of information of the discretized variables departing from the original SCV. Facing this issue, we propose an index, information change rate(ICR), that focuses on the changed amount of information due to the discretization based on each cell, enabling the identification of the optimal DM. We develop a case study with Random Forest(training/testing ratio of 7 : 3) to assess flood susceptibility in Wanan County, China.The area under the curve-based and susceptibility maps-based approaches were presented to compare the ILR and ICR. The results show the ICR-based optimal DMs are more rational than the ILR-based ones in both cases. Moreover, we observed the ILR values are unnaturally small(<1%), whereas the ICR values are obviously more in line with general recognition(usually 10%–30%). The above results all demonstrate the superiority of the ICR. We consider this study fills up the existing research gaps, improving the MLbased natural hazard susceptibility assessments.

Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions

Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.

A Conservative Gradient Discretization Method for Parabolic Equations

In this paper,we propose a new conservative gradient discretization method(GDM)for one-dimensional parabolic partial differential equations(PDEs).We use the implicit Euler method for the temporal discretization and conservative gradient discretization method for spatial discretization.The method is based on a new cellcentered meshes,and it is locally conservative.It has smaller truncation error than the classical finite volume method on uniform meshes.We use the framework of the gradient discretization method to analyze the stability and convergence.The numerical experiments show that the new method has second-order convergence.Moreover,it is more accurate than the classical finite volume method in flux error,L2 error and L¥error.

Damage Mechanism of Ultra-thin Asphalt Overlay(UTAO) based on Discrete Element Method

Aiming to analyze the damage mechanism of UTAO from the perspective of meso-mechanical mechanism using discrete element method(DEM),we conducted study of diseases problems of UTAO in several provinces in China,and found that aggregate spalling was one of the main disease types of UTAO.A discrete element model of UTAO pavement structure was constructed to explore the meso-mechanical mechanism of UTAO damage under the influence of layer thickness,gradation,and bonding modulus.The experimental results show that,as the thickness of UTAO decreasing,the maximum value and the mean value of the contact force between all aggregate particles gradually increase,which leads to aggregates more prone to spalling.Compared with OGFC-5 UTAO,AC-5 UTAO presents smaller maximum and average values of all contact forces,and the loading pressure in AC-5 UTAO is fully diffused in the lateral direction.In addition,the increment of pavement modulus strengthens the overall force of aggregate particles inside UTAO,resulting in aggregate particles peeling off more easily.The increase of bonding modulus changes the position where the maximum value of the tangential force appears,whereas has no effect on the normal force.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

Dynamic failure process of expanded polystyrene particle lightweight soil under cyclic loading using discrete element method

Expanded polystyrene(EPS)particle-based lightweight soil,which is a type of lightweight filler,is mainly used in road engineering.The stability of subgrades under dynamic loading is attracting increased research attention.The traditional method for studying the dynamic strength characteristics of soils is dynamic triaxial testing,and the discrete element simulation of lightweight soils under cyclic load has rarely been considered.To study the meso-mechanisms of the dynamic failure processes of EPS particle lightweight soils,a discrete element numerical model is established using the particle flow code(PFC)software.The contact force,displacement field,and velocity field of lightweight soil under different cumulative compressive strains are studied.The results show that the hysteresis curves of lightweight soil present characteristics of strain accumulation,which reflect the cyclic effects of the dynamic load.When the confining pressure increases,the contact force of the particles also increases.The confining pressure can restrain the motion of the particle system and increase the dynamic strength of the sample.When the confining pressure is held constant,an increase in compressive strain causes minimal change in the contact force between soil particles.However,the contact force between the EPS particles decreases,and their displacement direction points vertically toward the center of the sample.Under an increase in compressive strain,the velocity direction of the particle system changes from a random distribution and points vertically toward the center of the sample.When the compressive strain is 5%,the number of particles deflected in the particle velocity direction increases significantly,and the cumulative rate of deformation in the lightweight soil accelerates.Therefore,it is feasible to use 5%compressive strain as the dynamic strength standard for lightweight soil.Discrete element methods provide a new approach toward the dynamic performance evaluation of lightweight soil subgrades.

Optimizing Bucket Elevator Performance through a Blend of Discrete Element Method, Response Surface Methodology, and Firefly Algorithm Approaches

This research introduces a novel approach to enhancing bucket elevator design and operation through the integration of discrete element method(DEM)simulation,design of experiments(DOE),and metaheuristic optimization algorithms.Specifically,the study employs the firefly algorithm(FA),a metaheuristic optimization technique,to optimize bucket elevator parameters for maximizing transport mass and mass flow rate discharge of granular materials under specified working conditions.The experimental methodology involves several key steps:screening experiments to identify significant factors affecting bucket elevator operation,central composite design(CCD)experiments to further explore these factors,and response surface methodology(RSM)to create predictive models for transport mass and mass flow rate discharge.The FA algorithm is then applied to optimize these models,and the results are validated through simulation and empirical experiments.The study validates the optimized parameters through simulation and empirical experiments,comparing results with DEM simulation.The outcomes demonstrate the effectiveness of the FA algorithm in identifying optimal bucket parameters,showcasing less than 10%and 15%deviation for transport mass and mass flow rate discharge,respectively,between predicted and actual values.Overall,this research provides insights into the critical factors influencing bucket elevator operation and offers a systematic methodology for optimizing bucket parameters,contributing to more efficient material handling in various industrial applications.

Virtual rutting test of asphalt mixture using discrete element method

In order to investigate the permanent deformation behavior of asphalt mixtures from discontinuity, the virtual rutting test of asphalt mixtures is developed by the discrete element method （DEM）. A digital specimen generation procedure considering aggregate gradation and irregular shape is developed based on the probability theory and the Monte Carlo method. The virtual rutting test is then conducted based on the generated digital specimen. In addition, on the basis of the time-temperature superposition （TTS） principle, a calculation method is used to reduce the computation time of the virtual rutting test. The simulation results are compared with the laboratory measurements. The results show that the calculation method based on the TFS principle in the discrete element （DE） viscoelastic model can significantly reduce the computation time. The deformation law of asphalt mixtures in the virtual rutting test is similar to the laboratory measurements, and the deformation and the dynamic stability of the virtual rutting test are slightly greater than the laboratory measurements. The two-dimensional virtual rutting test can predict the permanent deformation performance of asphalt mixtures.

Numerical analysis of multicomponent responses of surface-hole transient electromagnetic method

We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.

Virtual fracture test of asphalt mixture based on discrete element method

In order to study fracture behaviors of asphalt mixtures, virtual tests of the two-dimensional（2D） microstructure based on the discrete element method（ DEM） are designed. The virtual structure of the 2D digital specimen of asphalt mixture is generated based on a particle generation program, in which the gradation and the irregular shapes of aggregates are considered. With the 2D digital specimens, a DEM-based mixture model is established and center-point beam fracture simulation tests are conducted by the DEM. Meanwhile, a series of calibration tests are carried out in laboratory to evaluate the DEM model and validate the methods of virtual fracture tests. The test results indicate that the fracture intensity of asphalt mixtures predicted by the DEM matches very well with the intensity obtained in laboratory. It is concluded that the microstructural virtual tests can be used as a supplemental tool to evaluate fracture properties of asphalt mixtures.

A Flexible-Segment-Model-Based Dynamics Calculation Method for Free Hanging Marine Risers in Re-Entry

In re-entry, the drilling riser hanging to the holding vessel takes on a free hanging state, waiting to be moved from the initial random position to the wellhead. For the re-entry, dynamics calculation is often done to predict the riser motion or evaluate the structural safety. A dynamics calculation method based on Flexible Segment Model （FSM） is proposed for free hanging marine risers. In FSM, a riser is discretized into a series of flexible segments. For each flexible segment, its deflection feature and external forces are analyzed independently. For the whole riser, the nonlinear governing equations are listed according to the moment equilibrium at nodes. For the solution of the nonlinear equations, a linearization iteration scheme is provided in the paper. Owing to its flexibility, each segment can match a long part of the riser body, which enables that good results can be obtained even with a small number of segments. Moreover, the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points. The FSM-based dynamics calculation is timesaving and stable, so suitable for the shape prediction or real-time control of free hanging marine risers.

A study on the discrete image method for calculation of transient electromagnetic fields in geological media

We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized： the real number of the electromagnetic field solution based on the Gaver-Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the ＂ground excitation-stratum measurement method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drill- hole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research.

An Improved Preisach Distribution Function Identification Method Considering the Reversible Magnetization

This paper presents an identification method of the scalar Preisach model to consider the effect of reversible magnetization in the process of distribution function identification.By reconsidering the identification process by stripping the influence of reversible components from the measurement data,the Preisach distribution function is identified by the pure irreversible components.In this way,the simulation accuracy of both limiting hysteresis loops and the inner internal symmetrical small hysteresis loop is ensured.Furthermore,through a discrete Preisach plane with a hybrid discretization method,the irreversible magnetic flux density components are computed more efficiently through the improved Preisach model.Finally,the proposed method results are compared with the traditional method and the traditional method considering reversible magnetization and validated by the laboratory test for the B30P105 electrical steel by Epstein frame.

Geo-engineered buffer capacity of two-layered absorbing system under the impact of rock avalanches based on Discrete Element Method

Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer protection galleries do not have sufficient buffer capacity, a two-layered absorbing system has been designed. This study aims to find whether an expanded poly-styrol （EPS） cushion, which is used in the soil-covered protection galleries for shock absorption, could be positioned under dynamic loadings. The dynamic impacts of the two-layered absorbing system under the conditions of rock avalanches are numerically simulated through a 2D discrete dement method. By selecting reasonable parameters, a series of numerical experiments were conducted to find the best combination for the two- layered absorbing system. The values of the EPS layer area as a percentage of the total area were set as 0% （Sl）, 22~ （S2）, and 70% （$3）. 22~ of the area of the EPS layer was found to be a reasonable value, and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system. The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system. The soil layer can absorb the shock energy effectively and S2 （0.4-m thick EPS cushion covered with soil layer） is the most efficient combination, which can reduce the impact force, compared with the other combinations.

Discrete element method of improved performance of railway ballast bed using elastic sleeper

With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method(DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.

A review of methods,applications and limitations for incorporating fluid flow in the discrete element method

The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to non-continuum.The wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this code.By comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is proved.Furthermore,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to non-continuum.The results of calculation can be displayed by animation.The damage modes are similar to the experimental results.The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum.It also shows that the discrete element method(DEM)will have broad prospects for development and application.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.

Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method

A user-defined three-dimensional （3D） discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete （AC）. The 3D discrete element method （DEM） model of AC was constructed employing a user-defined computer program developed using the ＂Fish＂ language in PFC3D. Important microstructural features of AC were modeled, including aggregate gradation, air voids and mastic. The irregular shape of aggregate particle was modeled using a clump of spheres. The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test, based on which the dynamic modulus and phase angle were calculated from the output stress- strain relationship. The effects of air void content, aggregate stiffness and volumetric fraction on AC modulus were further investigated. The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies. The user- defined 3D model also demonstrated significant improvement over the general existing two-dimensional models.