Comprehensive analysis of slope stability and determination of stable slopes in the Chador-Malu iron ore mine using numerical and limit equilibrium methods

One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part II:Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.

Analysis profile of the fully grouted rock bolt in jointed rock using analytical and numerical methods

The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

NUMERICAL RESOLVENT METHODS FOR CONSTRAINED PROBLEMS IN MECHANICS

Resolvent methods are presented for generating systematically iterative numerical algorithms for constrained problems in mechanics.The abstract framework corresponds to a general mixed finite element subdif-ferential model,with dual and primal evolution versions,which is shown to apply to problems of fluid dynamics,transport phenomena and solid mechanics,among others.In this manner,Uzawa's type methods and penalization-duality schemes,as well as macro-hybrid formulations,are generalized to non necessarily potential nanlinear mechanical problems.

Comparative Analysis for Evaluating Wind Energy Resources Using Intelligent Optimization Algorithms and Numerical Methods

Statistical distributions are used to model wind speed,and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed.Accurate estimation of Weibull parameters,the scale(c)and shape(k),is crucial in describing the actual wind speed data and evaluating the wind energy potential.Therefore,this study compares the most common conventional numerical(CN)estimation methods and the recent intelligent optimization algorithms(IOA)to show how precise estimation of c and k affects the wind energy resource assessments.In addition,this study conducts technical and economic feasibility studies for five sites in the northern part of Saudi Arabia,namely Aljouf,Rafha,Tabuk,Turaif,and Yanbo.Results exhibit that IOAs have better performance in attaining optimal Weibull parameters and provided an adequate description of the observed wind speed data.Also,with six wind turbine technologies rating between 1 and 3MW,the technical and economic assessment results reveal that the CN methods tend to overestimate the energy output and underestimate the cost of energy($/kWh)compared to the assessments by IOAs.The energy cost analyses show that Turaif is the windiest site,with an electricity cost of$0.016906/kWh.The highest wind energy output is obtained with the wind turbine having a rated power of 2.5 MW at all considered sites with electricity costs not exceeding$0.02739/kWh.Finally,the outcomes of this study exhibit the potential of wind energy in Saudi Arabia,and its environmental goals can be acquired by harvesting wind energy.

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications(NM-TMA) publishes high-quality original

Effects of Numerical Methods on the Calculation of Developing Plane Channel Flow

In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.

Multiparameter Numerical Investigation of Two Types of Moving Interactions Between the Deep-Sea Mining Vehicle Track Plate and Seabed Soil:Digging and Rotating Motions

To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions of the track plate are important links in the contact between the driving mechanism of the DSMV and seabed soil.In this study,a numerical simulation is conducted using the coupled Eulerian–Lagrangian(CEL)large deformation numerical method to investigate the interaction between the track plate of the DSMV and the seabed soil under two working conditions:rotating condition and digging condition.First,a soil numerical model is established based on the elastoplastic mechanical characterization using the basic physical and mechanical properties of the seabed soil obtained by in situ sampling.Subsequently,the soil disturbance mechanism and the dynamic mechanical response of the track plate under rotating and digging conditions are obtained through the analysis of the sensitivity of the motion parameters,the grouser structure,the layered soil features and the soil heterogeneity.The results indicate that the above parameters remarkably influence the interaction between the DSMV and the seabed soil.Therefore,it is important to consider the rotating and digging motion of the DSMV in practical engineering to develop a detailed optimization design of the track plate.

Numerical investigation of geostress influence on the grouting reinforcement effectiveness of tunnel surrounding rock mass in fault fracture zones

Grouting is a widely used approach to reinforce broken surrounding rock mass during the construction of underground tunnels in fault fracture zones,and its reinforcement effectiveness is highly affected by geostress.In this study,a numerical manifold method(NMM)based simulator has been developed to examine the impact of geostress conditions on grouting reinforcement during tunnel excavation.To develop this simulator,a detection technique for identifying slurry migration channels and an improved fluid-solid coupling(FeS)framework,which considers the influence of fracture properties and geostress states,is developed and incorporated into a zero-thickness cohesive element(ZE)based NMM(Co-NMM)for simulating tunnel excavation.Additionally,to simulate coagulation of injected slurry,a bonding repair algorithm is further proposed based on the ZE model.To verify the accuracy of the proposed simulator,a series of simulations about slurry migration in single fractures and fracture networks are numerically reproduced,and the results align well with analytical and laboratory test results.Furthermore,these numerical results show that neglecting the influence of geostress condition can lead to a serious over-estimation of slurry migration range and reinforcement effectiveness.After validations,a series of simulations about tunnel grouting reinforcement and tunnel excavation in fault fracture zones with varying fracture densities under different geostress conditions are conducted.Based on these simula-tions,the influence of geostress conditions and the optimization of grouting schemes are discussed.

SOME DEVELOPMENTS IN VISCOUS FLUID DYNAMICS AND ITS NUMERICAL METHODS

Viscous fluid flows contain abundant "physical phenomena and the viscous fluid dynamics is of wide applications in the fields of natural and engineering sciences. After the basic equations of viscousfluiddynamics (i.e., the Navier-Stokes equations) came out, one of the most important contributions to the discipline was the boundary layer (BL) theory and the BL equations presented by Prandtl

Numerical Predictions of Laminar Forced Convection Heat Transfer with and without Buoyancy Effects from an Isothermal Horizontal Flat Plate to Supercritical Nitrogen

Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing downwards.Computations are performed by varying the value ofΔT from5 to 30 K and P_(∞)/P_(cr)ratio from1.1 to 1.5.Variation of all the thermophysical properties of supercritical Nitrogen is considered.The wall temperatures are chosen in such a way that two values of Tw are less than T∗(T*is the temperature at which the fluid has a maximum value of Cp for the given pressure),one value equal to T∗and two values greater than T∗.Three different values of U∞are used to obtain Re∞range of 3.6×10_(4)to 4.74×10^(5)for forced convection without buoyancy effects and Gr_(∞)/Re^(2)_(∞)range of 0.011 to 3.107 for the case where buoyancy effects are predominant.Six different forms of correlations are proposed based on numerical predictions and are compared with actual numerical predictions.It has been found that in all six forms of correlations,the maximum deviations are found to occur in those cases where the pseudocritical temperature TT∗lies between the wall temperature and bulk fluid temperature.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

NUMERICAL MODEL OF WAVE FORCES ON CONTINUOUS CYLINDER STRUCTURES

A numerical model of wave force upon continuous cylinder structures with a large diameter using the boundary element method (BEM) is presented. A numerical model of reflecting wave upon continuous cylinders was established on the basis of linear wave theory.The fundamental solution to the Helmholtz equation within an infinite strip area that explicitly satisfies two infinite parallel boundaries is used together with Radiation condition rather than the solution of an infinite area.According to the proposed theory and method,the computer programs have been composed in Visual C ++ Development Studio.Several examples show that the technique and its program are feasible and efficient.And the wave forces upon continuous cylinders can be decreased by as much as 14%～24% under a ratio of D/L= 0.09～0.19 compared with the square caissons.

Numerical simulation of the direct reduction of pellets in a rotary hearth furnace for zinc-containing metallurgical dust treatment

A mathematical model was established to describe the direct reduction of pellets in a rotary hearth furnace （RHF）. In the model, heat transfer, mass transfer, and gas-solid chemical reactions were taken into account. The behaviors of iron metallization and dezincification were analyzed by the numerical method, which was validated by experimental data of the direct reduction of pellets in a Si-Mo furnace. The simulation results show that if the production targets of iron metallization and dezincification are up to 80% and 90%, respectively, the furnace temperature for high-temperature sections must be set higher than 1300~ C. Moreover, an undersupply of secondary air by 20% will lead to a decline in iron metallization rate of discharged pellets by 10% and a decrease in dezincing rate by 13%. In addition, if the residence time of pellets in the furnace is over 20 min, its further extension will hardly lead to an obvious increase in production indexes under the same furnace temperature curve.

Numerical and test study on vertical vibration characteristics of pile group in slope soil topography

Topography effects on the vertical vibration responses of pile group are revealed though numerical analysis and model tests.First,a series of model tests with different topography of ground and bedrock are conducted.The results indicate that displacement amplitude of the pile head in sloping ground topography is larger than in horizontal ground.Differential displacement at various positions of the pile cap is observed in non-horizontal topography.Afterwards,a numerical algorithm is employed to further explore the essential response characteristics in group piles of different topography configurations,which has been verified by the test results.The lengths of the exposed and frictional segment,together with the thickness of the subsoil layer,are the dominant factors which cause non-axisymmetric vibration at the pile cap.

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

Numerical manifold method modeling of coupled processes in fractured geological media at multiple scales

The greatest challenges of rigorously modeling coupled hydro-mechanical(HM)processes in fractured geological media at different scales are associated with computational geometry.These challenges include dynamic shearing and opening of intersecting fractures at discrete fracture scales as a result of coupled processes,and contact alteration along rough fracture surfaces that triggers structural and physical changes of fractures at micro-asperity scale.In this paper,these challenges are tackled by developing a comprehensive modeling approach for coupled processes in fractured geological media based on numerical manifold method(NMM)at multiple scales.Based on their distinct geometric features,fractures are categorized into three different scales:dominant fracture,discrete fracture,and discontinuum asperity scales.Here the scale is relative,that of the fracture relative to that of the research interest or domain.Different geometric representations of fractures at different scales are used,and different governing equations and constitutive relationships are applied.For dominant fractures,a finite thickness zone model is developed to treat a fracture as a porous nonlinear domain.Nonlinear fracture mechanical behavior is accurately modeled with an implicit approach based on strain energy.For discrete fractures,a zero-dimensional model was developed for analyzing fluid flow and mechanics in fractures that are geometrically treated as boundaries of the rock matrix.With the zero-dimensional model,these fractures can be modeled with arbitrary orientations and intersections.They can be fluid conduits or seals,and can be open,bonded or sliding.For the discontinuum asperity scale,the geometry of rough fracture surfaces is explicitly represented and contacts involving dynamic alteration of contacts among asperities are rigorously calculated.Using this approach,fracture alteration caused by deformation,re-arrangement and sliding of rough surfaces can be captured.Our comprehensive model is able to handle the computational challenges with accurate representation of intersections and shearing of fractures at the discrete fracture scale and rigorously treats contacts along rough fracture surfaces at the discontinuum asperity scale.With future development of three-dimensional(3D)geometric representation of discrete fracture networks in porous rock and contacts among multi-body systems,this model is promising as a basis of 3D fully coupled analysis of fractures at multiple scales,for advancing understanding and optimizing energy recovery and storage in fractured geological media.