A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

Failure characteristics and fracture mechanism of overburden rock induced by mining:A case study in China

This study employs similar simulation testing and discrete element simulation coupling to analyze the failure and deformation processes of a model coal seam's roof.The caving area of the overburden rock is divided into three zones:the delamination fracture zone,broken fracture zone,and compaction zone.The caving and fracture zones'heights are approximately 110 m above the coal seam,with a maximum subsidence of 11 m.The delamination fracture zone's porosity range is between 0.2 and 0.3,while the remainder of the roof predominantly exhibits a porosity of less than 0.1.In addition,the numerical model's stress analysis revealed that the overburden rock's displacement zone forms an'arch-beam'structure starting from 160 m,with the maximum and minimum stress values decreasing as the distance of advancement increases.In the stress beam interval of the overburden rock,the maximum value changes periodically as the advancement distance increases.Based on a comparative analysis between observable data from on-site work and numerical simulation results,the stress data from the numerical simulation are essentially consistent with the actual results detected on-site,indicating the validity of the numerical simulation results.

Steady-State Modeling of Heat Transfer on the Recovery System of Condensing Boiler

The increase of energy production is very important nowadays. It is necessary to improve the performance and efficiency of heat production facilities. The objective is to reduce pollutant emissions and regulate investment costs. One of the solutions is to control fuel and electricity consumption. This article develops a new model of simulation heat diffusion on the recovery system of condensing boiler. The method is based on the first and second thermodynamic systems. The Numerical discrete Model (NDM) was applied using MATLAB to simulate different characteristics of heat transfer in the recovery system. The result shows that the recovery unit can absorb the following temperatures;the range from 88°C to 90.7°C when the length of the tube is between respectively 110 and 111 m. the energy efficiency was between 0.55 and 0.57 which allowed confirming the model. This new model has some advantages such as;the use of an instantaneous calculation time. The heat recovered by the water tank can also serve as preheating different systems. One part of the heat recovered will be accumulated to be used as domestic hot water.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Orbital-Free Density Functional Theory for Molecular Structure Calculations

We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Cumulative damage effect on debris slopes under frequent microseisms

Debris slopes are widely distributed across the Three Gorges Reservoir area in China,and seasonal fluctuations of the water level in the area tend to cause high-frequency microseisms that subsequently induce landslides on such debris slopes.In this study,a cumulative damage model of debris slope with varying slope characteristics under the effects of frequent microseisms was established,based on the accurate definition of slope damage variables.The cumulative damage behaviour and the mechanisms of slope instability and sliding under frequent microseisms were thus systematically investigated through a series of shaking table tests and discrete element numerical simulations,and the influences of related parameters such as bedrock,dry density and stone content were discussed.The results showed that the instability mode of a debris slope can be divided into a vibration-compaction stage,a crack generation stage,a crack development stage,and an instability stage.Under the action of frequent microseisms,debris slope undergoes the last three stages cyclically,which causes the accumulation to slide out in layers under the synergistic action of tension and shear,causing the slope to become destabilised.There are two sliding surfaces as well as the parallel tensile surfaces in the final instability of the debris slope.In the process of instability,the development trend of the damage accumulation curve remains similar for debris slopes with different parameters.However,the initial vibration compaction effect in the bedrock-free model is stronger than that in the bedrock model,with the overall cumulative damage degree in the former being lower than that of the latter.The damage degree of the debris slope with high dry density also develops more slowly than that of the debris slope with low dry density.The damage development rate of the debris slope does not always decrease with the increase of stone content.The damage degree growth rate of the debris slope with the optimal stone content is the lowest,and the increase or decrease of the stone content makes the debris slope instability happen earlier.The numerical simulation study also further reveals that the damage in the debris slope mainly develops in the form of crack formation and penetration,in which,shear failure occurs more frequently in the debris slope.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su^zestions for future study are also oresented.

Study of electronic structures and absorption bands of BaMgF_4 crystal with F colour centre

The electronic structures of BaMgF4 crystals containing an F colour centre are studied within the framework of the fully relativistic self-consistent Direc-Slater theory, using a numerically discrete variational （DV-Xa） method. It is concluded from the calculated results that the energy levels of the F colour centre are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F colour centre is about 5.12 eV, which corresponds to the 242-nm absorption band. These calculated results can explain the origin of the absorption bands.

Discrete element method for high-temperature spread in compacted powder systems

The discrete element method is applied to investigate high-temperature spread in compacted metallic particle systems formed by high-velocity compaction. Assuming that heat transfer only occurs at contact zone between particles, a discrete equation based on continuum mechanics is proposed to investigate the heat flux. Heat generated internally by friction between moving particles is determined by kinetic equations. For the proposed model, numerical results are obtained by a particle-flow-code-based program. Temperature profiles are determined at different locations and times. At a fixed location, the increase in temperature shows a logarithmic relationship with time. Investigation of three different systems indicates that the geometric distribution of the particulate material is one of the main influencing factors for the heat conduction process. Higher temperature is generated for denser packing, and vice versa. For smaller uniform particles, heat transfers more rapidly.

A Numerical Study of Quantum Decoherence

The present paper provides a numerical investigation of the decoherence effect induced on a quantum heavy particle by the scattering with a light one.The time dependent two-particle Schr¨odinger equation is solved by means of a time-splitting method.The damping undergone by the non-diagonal terms of the heavy particle density matrix is estimated numerically,as well as the error in the Joos-Zeh approximation formula.

A Model of a Quantum Particle in a Quantum Environment: A Numerical Study

We define and investigate,via numerical analysis,a one dimensional toymodel of a cloud chamber.An energetic quantum particle,whose initial state is a superposition of two identical wave packets with opposite average momentum,interacts during its evolution and exchanges(small amounts of)energy with an array of localized spins.Triggered by the interaction with the environment,the initial superposition state turns into an incoherent sum of two states describing the following situation:or the particle is going to the left and a large number of spins on the left side changed their states,or the same is happening on the right side.This evolution is reminiscent of what happens in a cloud chamber where a quantum particle,emitted as a spherical wave by a radioactive source,marks its passage inside a supersaturated vapour-chamber in the form of a sequence of small liquid bubbles arranging themselves around a pssible classical trajectory of the particle.

Comparative Study on Two Methods for Calculating the Gravitational Potential of a Prism

The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitational potential of a prism. Discrete element method can be used to determine the gravitational potential of a prism, and can approximate the true gravitational potential values with sufficient accuracy (the smaller each element is, the more accurate the result is). Although Nagy's approach provided a closed expression, one does not know whether it is valid, due to the fact that this approach has not been confirmed in literatures. In this paper, a study on the comparison of Nagy's approach with discrete element method is presented. The results show that Nagy's formulas for determining the gravitational potential of a prism are valid in the domain both inside and outside the prism.