Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Numerical modeling of destress blasting for strata separation

Destress blasting(DB)implemented along the perimeter of safety pillars is a special application of destressing in coal longwall mining.The goal is to separate relatively more deformed mined areas from safety pillars,such as shaft pillars or cross-cut pillars,to reduce the transfer of high stresses to the protective pillar.This case study aims to numerically simulate selected destress blasts in the Czech part of the Upper Silesian Coal Basin and examine its impact on stress transfer to the safety pillar area.To separate the area between the protective pillar and the longwall(LW),two fans of five 93-mm blast holes(length of 93e100 m)were drilled from the gate roads into the overburden strata.Each set of blast holes was fired separately in two stages without time delay.The explosive charge(gelatin-type of explosive)of each stage is 3450 kg.The two DB stages were fired when the longwall face was approximately 158 m and 152 m away from the blast.A 3D mine-wide model is built and validated with in situ stress measured with hydrofracturing.Mining and destressing in three 5-m thick coal seams are simulated in the region.Numerical modeling of DB is successfully conducted using a rock fragmentation factor a of 0.05 and a stress reduction/dissipation factor β of 0.95.Buffering of transfer of additional stress from the mining area into the safety pillar is evaluated by comparison of yielding volume before and after DB.It is shown that yielding volume drops after DB by nearly 80%in the area of the destressing panel and near the safety shaft pillar.

Flow-Induced Clogging in Microfiltration Membranes: Numerical Modeling and Parametric Study

Microfiltration membrane technology has been widely used in various industries for solid-liquid separation. However, pore clogging remains a persistent challenge. This study employs (CFD) and discrete element method (DEM) models to enhance our understanding of microfiltration membrane clogging. The models were validated by comparing them to experimental data, demonstrating reasonable consistency. Subsequently, a parametric study was conducted on a cross-flow model, exploring the influence of key parameters on clogging. Findings show that clogging is a complex phenomenon affected by various factors. The mean inlet velocity and transmembrane flux were found to directly impact clogging, while the confinement ratio and cosine of the membrane pore entrance angle had an inverse relationship with it. Two clog types were identified: internal (inside the pore) and external (arching at the pore entrance), with the confinement ratio determining the type. This study introduced a dimensionless number as a quantitative clogging indicator based on transmembrane flux, Reynolds number, filtration time, entrance angle cosine, and confinement ratio. While this hypothesis held true in simulations, future studies should explore variations in clogging indicators, and improved modeling of clogging characteristics. Calibration between numerical and physical times and consideration of particle volume fraction will enhance understanding.

Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation(Em)is one of the most important design parameters in designing many structures in and on rock.This parameter can be obtained by in situ tests,empirical relations between deformation modulus and rock mass classifcation,and estimating from laboratory tests results.In this paper,a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming(GP)and numerical modeling.A database of 40,960 datasets,including vertical stress(rz),horizontal to vertical stresses ratio(k),Poisson’s ratio(m),radius of circular tunnel(r)and wall displacement of circular tunnel on the horizontal diameter(d)for input parameters and modulus of deformation for output,was established.The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries.The resulting RMSE of 0.86 and correlation coeffcient of97%of the proposed equation demonstrated the capability of the computer program(CP)generated by GP.

Numerical modeling for rockbursts:A state-of-the-art review

As the depth of excavation increases,rockburst becomes one of the most serious geological hazards damaging equipment and facilities and even causing fatalities in mining and civil engineering.This has forced researchers worldwide to identify different methods to investigate rockburst-related problems.However,some problems,such as the mechanisms and the prediction of rockbursts,continue to be studied because rockburst is a very complicated phenomenon influenced by the uncertainty and complexity in geological conditions,in situ stresses,induced stresses,etc.Numerical modeling is a widely used method for investigating rockbursts.To date,great achievements have been made owing to the rapid development of information technology(IT)and computer equipment.Hence,it is necessary and meaningful to conduct a review of the current state of the studies for rockburst numerical modeling.In this paper,the categories and the origin of different numerical approaches employed in modeling rockbursts are reviewed and the current usage of various numerical modeling approaches is investigated by a literature research.Later,a state-of-the-art review is implemented to investigate the application of numerical modeling in the mechanism study,and prediction and prevention of rockbursts.The main achievements and problems are highlighted.Finally,this paper discusses the limitations and the future research of numerical modeling for rockbursts.An approach is proposed to provide researchers with a systematic and reasonable numerical modeling framework.

Numerical modeling of metamorphic core complex formation:Implications for the destruction of the North China Craton

Widespread magmatism, metamorphic core complexes(MCCs), and significant lithospheric thinning occurred during the Mesozoic in the North China Craton(NCC). It has been suggested that the coeval exhumation of MCCs with uniform northwest-southeast shear senses and magmatism probably resulted from a decratonization event during the retreat of the paleo-Pacific Plate. Here we used two-dimensional finite element thermomechanical numerical models to investigate critical parameters controlling the formation of MCCs under far-field extensional stress. We observed three end-member deformation modes: the MCC mode, the symmetric-dome mode, and the pure-shear mode. The MCC mode requires a Moho temperature of ≥700 ℃ and an extensional strain rate of ≥5 × 10^(-16)s^(-1), implying that the lithosphere had already thinned when the MCC was formed in the Mesozoic. Considering that the widespread MCCs have the same northwest-southeast extension direction in the NCC, we suggest that the MCCs are surface expressions of both large-scale extension and craton destruction and that rollback of the paleo-Pacific slab might be the common driving force.

Experimental Simulation and Numerical Modeling of Deformation and Damage Evolution of Pre-Holed Sandstones After Heat Treatment

The deformation and damage evolution of sandstone after heat treatment greatly influence the efficient and safe development of deep geothermal energy extraction.To investigate this issue,laboratory confined compression tests and numerical simulations were conducted on pre-holed sandstone specimens after heat treatment.The laboratory test results show that the failure modes are closely related to the heat treatment temperature,with increasing treatment temperature,the failure modes change from mixed and shear modes to a splitting mode.The cracks always initiate from the sidewalls of the hole and then propagate.The failure process inside the hole proceeds as follows:calm period,particle ejection period,rock fragment exfoliation period and rock failure period.The specimens have different final failure features for the entire rock after heat treatment,but have the same failure features inside the hole.These phenomena can be explained by numerical simulations.The numerical simulations reveal that the failure modes in the numerical results agree very well with those observed in the experimental results.The damage zone always occurs at sidewalls of the hole and then propagates to the entire rock affected by shear or tensile damage.From 20℃to 200℃,thermal effect may promote shear damage and restrain tensile damage,while from 200℃to 800℃,thermal effect promotes tensile damage and restrains shear damage.Notably,the damage zone near the sidewalls of the hole has the same distribution range and pattern.Finally,the differences in the mechanisms due to increasing heat temperature are evaluated using scanning electron microscope(SEM)observations.

Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials

The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The Perfectly Matched Layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators.

Evaluation of the performance of yielding rockbolts during rockbursts using numerical modeling method

Rockburst;Rockburst damage;Yielding rockbolt;Numerical modeling;UDEC;Underground miningThe assessment of yielding rockbolt performance during rockbursts with actual seismic loading is essential for rock-burst supporting designs.In this paper,two types of yielding rockbolts(D-bolt and Roofex)and the fully resin-grouted rebar bolt are modeled via the"rockbolt"element in universal distinct element code(UDEC)after an exact calibration procedure.A two-dimensional(2D)model of a deep tunnel is built to fully evaluate the performance(e.g.,capacity of energy-absorption and control of rock damage)of yielding and traditional rockbolts based on the simulated rockbursts.The influence of different rockburst magnitudes is also studied.The results suggest that the D-bolt can effectively control and mitigate rockburst damage during a weak rockburst because of its high strength and deformation capacity.The Roofex is too"soft"or"smooth"to limit the movement of ejected rocks and restrain the large deformation,although it has an excellent deformation capacity.The resin-grouted rebar bolt can maintain a high axial force level during rockbursts but is easy to break during dynamic shocks,which fails to control rapid rock bulking or ejection.Three types of rockbolts cannot control the large deformation and mitigate rockburst damage effectively during violent rockbursts.The rockburst damage severity can be significantly reduced by additional support with cable bolts.This study highlights the effectiveness of numerical modeling methods in assessing the complex performance of yielding rockbolts during rockbursts,which can provide some references to improve and optimize the design of rock supporting in burst-prone grounds.

Estimation of mountain block recharge on the northern Tianshan Mountains using numerical modeling

Mountain block recharge(MBR),an important water resource,is a widespread process that recharges lowland aquifers.However,little is known about MBR due to the limited climatic and geologic data in mountainous regions such as the northern central foothills of Tianshan.Here,we present an approach to quantify MBR through the combination of water balance calculations and numerical modeling.MBR calculated from the water balance in the data-limited Tianshan Mountains is employed as a fluid-flux boundary condition in the numerical model of the plain.To verify the performance of the model,mean absolute error and root mean square error were used.Results show that the volume of water that is recharging the aquifer via MBR is 107.29 million m^(3)/yr,accounting for 2.2% of the total precipitation that falls in the mountains.Additionally,53.3% of that precipitation enters the plain aquifer via runoff,totaling 2,652.68 million m^(3)/yr.The lower volume of MBR is attributed to a major range-bounding anticline with apparent low permeability in the Tianshan Mountains.Through numerical modeling of groundwater,MBR coming from bedrock was found to be significant,accounting for 14% of total aquifer recharge in the plain,only after the portion of runoff seepage.This research contributes to a deeper understanding of MBR,and may provide instructions for estimating groundwater recharge in arid and semi-arid areas.

Meshing effects of the 3-D FEM numerical modeling in seismo-electromagnetics:An application in selectivity of seismic electric signal (SES)

We investigated how density and quality of mesh around interest domain affect electromagnetic (EM) responses of 3D Earth layered media using finite element method(FEM).Effect of different mesh shapes was also investigated using a method of mixing structured and unstructured mesh.As a case study,we estimated the effects of meshing on selectivity phenomenon of seismic electric signal(SES).Our results suggest that the relative errors resulting from mesh effects may not be negligible,which may lead to some unconvincing explanation of the SES selectivity based on the numerical modeling results.

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer func-tions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions observation.

Analysis and Numerical Modeling of a 20 W Microwave Electrothermal Thruster

The microwave electrothermal thruster (MET) is an electric propulsion device that uses an electromagnetic resonant cavity within which free-floating plasma is ignited and sustained in a propellant gas.The thrust is generated when the heated propellant gas is exhausted out of a gas-dynamic nozzle.For an empty cavity without any perturbing regions—e.g.,dielectric regions or antenna regions—it is fairly straightforward to accurately calculate the cavity's resonant frequency and describe the electric field intensity distribution within the cavity.However,actual METs do contain perturbing regions,which means that analytical solutions are no longer possible to fully characterize the device.Hence,the numerical methods to simulate the electric field intensity and distribution within the resonant cavity were employed.The simulation results are that with the cap height increasing,the resonant frequency and electric field strength decrease,also increasing the permittivity of dielectric material causes decreasing the resonant frequency and electric field strength.A decrease in resonant frequency and maximum electric field strength,and an increase in resonant bandwidth,were observed with increasing antenna depth.Rounding an antenna of a given depth equals decreasing the depth.

Particles-induced turbulence: A critical review of physical concepts,numerical modelings and experimental investigations

The presence of solid particles or water droplets in continuous fluid flow can either induce turbulence attenuation or amplification. The modification of the state of the turbulence depends on the characteristics of the particles, such as volume fraction, mean diameter, mass density, or carrier phase flow properties. In this brief review, the main physical concepts related to the most important physical aspects of turbulence modulation are summarized. Different criteria used to distinguish the enhancement or the attenuation effects of the particles on the carrier phase flows are recalled. For the interest of large-scale industrial applications, several theoretical,experimental and empirical approaches are discussed, which provides an interesting framework for the study of the effect of particles on turbulence behavior modification.

Numerical modeling of global seismic phases and its application in seismic phase identification

Earthquake data include informative seismic phases that require identification for imaging the Earth's structural interior.In order to identify the phases,we created a numerical method to calculate the traveltimes and raypaths by a shooting technique based upon the IASP91 Earth model,and it can calculate the traveltimes and raypaths for not only the seismic phases in the traditional traveltime tables such as IASP91,AK135,but also some phases such as pPcP,pPKIKP,and PPPPP.It is not necessary for this method to mesh the Earth model,and the results from the numerical modeling and its application show that the absolute differences between the calculated and theoretical traveltimes from the ISAP91 tables are less than 0.1 s.Thus,it is simple in manipulation and fast in computation,and can provide a reliable theoretical prediction for the identification of a seismic phase within the acquired earthquake data.

Numerical Modeling of Dust Propagation in the Atmosphere of a City with Complex Terrain. The Case of Background Eastern Light Air

Micro-scale processes of dust distribution in the city of Tbilisi with very complex topography are modeled using a 3D regional model of atmospheric processes and numerical integration of the transport-diffusion equation of the impurity. The Terrain-following coordinate system is used to take into account the influence of a very complex relief on the process of atmospheric pollution. Modeling is carried out using horizontal grid steps of 300 m and 400 m along latitude and longitude, respectively. Cases of the stationary background eastern light air are considered. In the model, motor transport is considered as a nonstationary source of pollution from which dust is emitted into the atmosphere. Modeling of dust micro-scale diffusion process showed that the city air pollution depends on the spatial distribution of the main sources of city pollution, i.e. on vehicle traffic intensity, as well as on the spatial distribution of highways, and micro-orography of city and relief of the surrounding territories. It is shown that the dust pollution level in the surface layer of the atmosphere is minimal at 6 a.m. Ground-level concentration rapidly grows with the increase of vehicle traffic intensity and at 12 a.m. reaches maximum allowable concentration (MAC = 0.5 mg/m3) in the vicinity of central city mains. From 12 a.m. to 9 p.m. maximum dust concentration values are within the limits of 0.9 - 1.2 MAC. In the mentioned time interval formation of the high pollution zones, the slow growth of their areas and the value of ground-level concentrations take place. These zones are located in both central and peripheral parts of the city. Their disposition and area sizes depend on the spatial distribution of local wind-generated under the action of complex terrain, as well as on the processes of turbulent and advective dust transfer. From 9 p.m. to 24 p.m. reduction of dust pollution and ground-level concentration takes place. After midnight the city dust pollution process continues quasi-periodically.

NUMERICAL MODELING OF RADIATIVE TRANSFER FOR MICROWAVE REMOTE SENSING

An overall vector radiative transfer theory was developed for numerical modeling, in both active and passive microwave remote sensing. The Theory and approaches are briefly summerized.To quantitatively understand scattering and thermal emission from targets in active and passive remote sensing, we have developed an overall vector radiative transfer theory for a set of theoretical models of discrete scatterer and continuous random media for the earth terrain (wet soil, vegetation, snow, sea-ice, etc.) and atmosphere, and numerical approaches for simulation, data analysis, and parameter sensitivity test. Our numerical results favorably agreed with experimental data in microwave re mote sensing of various earth surfaces. Main approaches are briefly summerized herewith.

Kagome Project:Physical and Numerical Modeling Comparison for a Post-formed Elastic Gridshell

An elastic gridshell is an efficient constructive typology for crossing large spans with little material.A flat elastic grid is built before buckling the structure into shape,in active and post-formed bending.The design and structural analysis of such a structure requires a stage of form finding that can mainly be done:(1)With a physical model:either by a suspended net method,or an active bending model;(2)With a numerical model performed by dynamic relaxation.All these solutions have various biases and assumptions that make them reflect more or less the reality.These three methods have been applied by Happold and Liddell[1]during the design of the Frei Otto’s Mannheim Gridshell which has allowed us to compare the results,and to highlight the significant differences between digital and physical models.Based on our own algorithm called ELASTICA[2],our study focuses on:(1)Comparing the results of the ELASTICA’s numerical models to load tests on physical models;(2)The identification of the various factors that can influence the results and explain the observed differences,some of which are then studied;(3)Applying the results to build a full-scale interlaced lattice elastic gridshell based on the Japanese Kagome pattern.

State Key Lab of Numerical Modeling for Atmospheric Science and Geophysical Fluid Dynamics

The State Key Laboratory of Numerical Modeling for Atmospheric Science and Geophysical Fluid Dynamics (LASG) was set up as early as in 1985. It has been appraised as an Excellent State Key Lab in each of the three national assessments organized by State Economic Planning Commission, National Natural Science Foundation (NSFC) and the Ministry of Science and Technology (MOST) in 1991, 1996 and 2000, respectively.