A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

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 simulation of microwave-induced cracking and melting of granite based on mineral microscopic models

This study introduces a coupled electromagnetic–thermal–mechanical model to reveal the mechanisms of microcracking and mineral melting of polymineralic rocks under microwave radiation.Experimental tests validate the rationality of the proposed model.Embedding microscopic mineral sections into the granite model for simulation shows that uneven temperature gradients create distinct molten,porous,and nonmolten zones on the fracture surface.Moreover,the varying thermal expansion coefficients and Young's moduli among the minerals induce significant thermal stress at the mineral boundaries.Quartz and biotite with higher thermal expansion coefficients are subjected to compression,whereas plagioclase with smaller coefficients experiences tensile stress.In the molten zone,quartz undergoes transgranular cracking due to theα–βphase transition.The local high temperatures also induce melting phase transitions in biotite and feldspar.This numerical study provides new insights into the distribution of thermal stress and mineral phase changes in rocks under microwave irradiation.

Numerical simulations for radon migration and exhalation behavior during measuring radon exhalation rate with closed-loop method

Accurate measurements of the radon exhalation rate help identify and evaluate radon risk regions in the environment.Among these measurement methods,the closed-loop method is frequently used.However,traditional experiments are insufficient or cannot analyze the radon migration and exhalation patterns at the gas–solid interface in the accumulation chamber.The CFD-based technique was applied to predict the radon concentration distribution in a limited space,allowing radon accumulation and exhalation inside the chamber intuitively and visually.In this study,three radon exhalation rates were defined,and two structural ventilation tubes were designed for the chamber.The consistency of the simulated results with the variation in the radon exhalation rate in a previous experiment or analytical solution was verified.The effects of the vent tube structure and flow rate on the radon uniformity in the chamber;permeability,insertion depth,and flow rate on the radon exhalation rate and the effective diffusion coefficient on back-diffusion were investigated.Based on the results,increasing the inser-tion depth from 1 to 5 cm decreased the effective decay constant by 19.55%,whereas the curve-fitted radon exhalation rate decreased(lower than the initial value)as the deviation from the initial value increased by approximately 7%.Increasing the effective diffusion coefficient from 2.77×10^(-7) to 7.77×10^(-6) m^(2) s^(-1) made the deviation expand from 2.14 to 15.96%.The conclusion is that an increased insertion depth helps reduce leakage in the chamber,subject to notable back-diffusion,and that the closed-loop method is reasonably used for porous media with a low effective diffusion coefficient in view of the back-diffusion effect.The CFD-based simulation is expected to provide guidance for the optimization of the radon exhalation rate measurement method and,thus,the accurate measurement of the radon exhalation rate.

Numerical study on the cavity dynamics for vertical water entries of twin spheres

In this study, a three dimensional(3D) numerical model of six-degrees-of-freedom(6DOF) is applied to simulate the water entries of twin spheres side-by-side at different lateral distances and time intervals.The turbulence structure is described using the shear-stress transport k-ω(SST k-ω) model, and the volume of fluid(VOF) method is used to track the complex air-liquid interface. The motion of spheres during water entry is simulated using an independent overset grid. The numerical model is verified by comparing the cavity evolution results from simulations and experiments. Numerical results reveal that the time interval between the twin water entries evidently affects cavity expansion and contraction behaviors in the radial direction. However, this influence is significantly weakened by increasing the lateral distance between the two spheres. In synchronous water entries, pressure is reduced on the midline of two cavities during surface closure, which is directly related to the cavity volume. The evolution of vortexes inside the two cavities is analyzed using a velocity vector field, which is affected by the lateral distance and time interval of water entries.

Numerical simulation on the multiphase flow and reoxidation of the molten steel in a two-strand tundish during ladle change

A 3D mathematical model was proposed to investigate the molten steel–slag–air multiphase flow in a two-strand slab continuous casting(CC)tundish during ladle change.The study focused on the exposure of the molten steel and the subsequent reoxidation occurrence.The exposure of the molten steel was calculated using the coupled realizable k–εmodel and volume of fluid(VOF)model.The diffusion of dissolved oxygen was determined by solving the user-defined scalar(UDS)equation.Moreover,the user-defined function(UDF)was used to describe the source term in the UDS equation and determine the oxidation rate and oxidation position.The effect of the refilling speed on the molten steel exposure and dissolved oxygen content was also discussed.Increasing the refilling speed during ladle change reduced the refilling time and the exposure duration of the molten steel.However,the elevated refilling speed enlarged the slag eyes and increased the average dissolved oxygen content within the tundish,thereby exacerbating the reoxidation phenomenon.In addition,the time required for the molten steel with a high dissolved oxygen content to exit the tundish varied with the refilling speed.When the inlet speed was 3.0 m·s^(-1)during ladle change,the molten steel with a high dissolved oxygen content exited the outlet in a short period,reaching a maximum dissolved oxygen content of 0.000525wt%.Conversely,when the inlet speed was 1.8 m·s^(-1),the maximum dissolved oxygen content was 0.000382wt%.The refilling speed during the ladle change process must be appropriately decreased to minimize reoxidation effects and enhance the steel product quality.

Numerical analysis of geosynthetic-reinforced embankment performance under moving loads

The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.

Multi-physical fields distribution in billet during helical electromagnetic stirring:A numerical simulation research

Electromagnetic stirring is one of the widely applied techniques to modify the quality of casting billets.Different from conventional rotate stirring,the helical stirring is more professional in assisting multi-dimensional flow of molten metal and eliminating solidification defects.In this study,the single-winding helical stirring(SWHS)was introduced,offering advantages such as smaller volume and lower electromagnetic shielding compared to traditional helical stirring methods.Following a comprehensive numerical simulation,the stirring parameters of SWHS were adjusted to yoke inclination angle of 43°and frequency of 12 Hz.The higher electromagnetic force and flow velocity in drawing direction,as well as the lower temperature gradient induced by the SWHS,are positive factors for homogeneous solidification of billet.The experimental results on Al-8%Si alloy and 0.4%C-1.1%Mn steel demonstrate that compared to rotate stirring,the SWHS process can induce better billet quality and is more effective in accelerating the equiaxed expansion and reducing element segregation.The SWHS process can enhance the equiaxed ratio of the billet by 58.3%and reduce segregation degree of carbon element by 10.97%.Consequently,SWHS holds great promise as a potential approach for improving the quality of continuous casting billets.

Numerical Study on the Effect of Vortex Generators on the Aerodynamic Drag of a High-Speed Train

A relatively high aerodynamic drag is an important factor that hinders the further acceleration of high-speed trains.Using the shear stress transport(SST)k-ωturbulence model,the effect of various vortex generator types on the aerodynamic characteristics of an ICE2(Inter-city Electricity)train has been investigated.The results indi-cate that the vortex generators with wider triangle,trapezoid,and micro-ramp arranged on the surface of the tail car can significantly change the distribution of surface pressure and affect the vorticity intensity in the wake.This alteration effectively reduces the resistance of the tail car.Meanwhile,the micro-ramp vortex generator with its convergent structure at the rear exhibits enhancedflow-guiding capabilities,resulting in a 15.4%reduction in the drag of the tail car.

In-situ measurement via the flow-through method and numerical simulations for radon exhalation during measurements of the radon exhalation rate

Small-scale measurements of the radon exhalation rate using the flow-through and closed-loop methods were conducted on the surface of a uranium tailing pond to better understand the differences between the two methods.An abnormal radon exhalation behavior was observed,leading to computational fluid dynamics(CFD)-based simulations in which dynamic radon migration in a porous medium and accumulation chamber was considered.Based on the in-situ experimental and numerical simulation results,variations in the radon exhalation rate subject to permeability,flow rate,and insertion depth were quantified and analyzed.The in-situ radon exhalation rates measured using the flow-through method were higher than those measured using the closed-loop method,which could be explained by the negative pressure difference between the inside and outside of the chamber during the measurements.The consistency of the variations in the radon exhalation rate between the experiments and simulations suggests the reliability of CFD-based techniques in obtaining the dynamic evolution of transient radon exhalation rates for diffusion and convection at the porous medium-air interface.The synergistic effects of the three factors(insertion depth,flow rate,and permeability)on the negative pressure difference and measured exhalation rate were quantified,and multivariate regression models were established,with positive correlations in most cases;the exhalation rate decreased with increasing insertion depth at a permeability of 1×10^(−11) m^(2).CFD-based simulations can provide theoretical guidance for improving the flow-through method and thus achieve accurate measurements.

Numerical simulation of melt flow and temperature field during DC casting 2024 aluminium alloy under different casting conditions

Casting speed,casting temperature and secondary cooling water flow rate are the main process parameters affecting the DC casting process.These parameters significantly influence the flow and temperature fields during casting,which are crucial for the quality of the ingot and can determine the success or failure of the casting operation.Numerical simulation,with the advantages of low cost,rapid execution,and visualized results,is an important method to study and optimize the DC casting process.In the present work,a simulation model of DC casting 2024 aluminum alloy was established,and the reliability of the model was verified.Then,the influence of casting parameters on flow field and temperature field was studied in detail by numerical simulation method.Results show that with the increase of casting speed,the melt flow becomes faster,the depths of slurry zone and mushy zone increase,and the variation of slurry zone depth is greater than that of mushy zone.With an increase in casting temperature,the melt flow rate increases,the depth of the slurry zone becomes shallower,and the depth of the mushy zone experiences only minor changes.The simulation results further indicate that the increase of the flow rate of the secondary cooling water slightly reduces the depths of both slurry and mushy zone.

Numerical simulation of flow field deposition and erosion characteristics around bridge-road transition section

Wind-sand flow generates erosion and deposition around obstacles such as bridges and roadbeds, resulting in sand damage and endangering railway systems in sandy regions. Previous studies have mainly focused on the flow field around roadbeds, overlooking detailed examinations of sand particle erosion and deposition patterns near bridges and roadbeds. This study employs numerical simulations to analyze the influence of varying heights and wind speeds on sand deposition and erosion characteristics at different locations: the bridge-road transition section(side piers), middle piers, and roadbeds. The results show that the side piers, experience greater accumulation than the middle piers. Similarly, the leeward side of the roadbed witnesses more deposition compared to the windward side. Another finding reveals a reduced sand deposition length as the vertical profile, in alignment with the wind direction, moves further from the bridge abutments at the same clearance height. As wind speeds rise, there’s a decline in sand deposition and a marked increase in erosion around the side piers, middle piers and roadbeds. In conclusion, a bridge clearance that’s too low can cause intense sand damage near the side piers, while an extremely high roadbed may lead to extensive surface sand deposition. Hence, railway bridges in areas prone to sandy winds should strike a balance in clearance height. This research provides valuable guidelines for determining the most suitable bridge and roadbed heights in regions affected by wind and sand.

Recent progresses in the development of tubular segmented-in-series solid oxide fuel cells:Experimental and numerical study

Solid oxide fuel cells(SOFCs)have attracted a great deal of interest because they have the highest efficiency without using any noble metal as catalysts among all the fuel cell technologies.However,traditional SOFCs suffer from having a higher volume,current leakage,complex connections,and difficulty in gas sealing.To solve these problems,Rolls-Royce has fabricated a simple design by stacking cells in series on an insulating porous support,resulting in the tubular segmented-in-series solid oxide fuel cells(SIS-SOFCs),which achieved higher output voltage.This work systematically reviews recent advances in the structures,preparation methods,perform-ances,and stability of tubular SIS-SOFCs in experimental and numerical studies.Finally,the challenges and future development of tubular SIS-SOFCs are also discussed.The findings of this work can help guide the direction and inspire innovation of future development in this field.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

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.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

A Numerical Study on the Effect of the Backflow Hole Position on the Performances of a Self-Priming Pump

A self-priming pump is a centrifugal pump that has the ability to prime itself. Typically, its performance dependson the configuration of its reflux hole. In this study, the ANSYS FLUENT software is used to investigate the effectsof three different radial positions of the reflux hole on gas-liquid two-phase distribution, pressure pulsation, andimp during self-priming. The research results indicate that: (1) The effective channel size for the reflux liquid toenter the volute varies depending on the location of the reflux hole. The effect of the impeller rotation on thereflux liquid becomes more obvious as the setting distance of the reflux aperture decreases. (2) The position ofthe reflux hole significantly affects the gas phase mass fraction inside the impeller, resulting in a significant reductionin the time it takes for the mass fraction to exceed 80%. (3) The position of the reflux hole significantly affectsthe average pressure on each monitoring surface. (4) Placing the reflux hole at a excessively distant radial distancecan result in an excessive vertical component. (5) The self-priming performance of the pump can be improved tosome extent by placing the return hole at a small radial distance.

A Transient-Pressure-Based Numerical Approach for Interlayer Identification in Sand Reservoirs

Almost all sandstone reservoirs contain interlayers. The identification and characterization of these interlayers iscritical for minimizing the uncertainty associated with oilfield development and improving oil and gas recovery.Identifying interlayers outside wells using identification methods based on logging data and machine learning isdifficult and seismic-based identification techniques are expensive. Herein, a numerical model based on seepageand well-testing theories is introduced to identify interlayers using transient pressure data. The proposed modelrelies on the open-source MATLAB Reservoir Simulation Toolbox. The effects of the interlayer thickness, position,and width on the pressure response are thoroughly investigated. A procedure for inverting interlayer parametersin the reservoir using the bottom-hole pressure is also proposed. This method uses only transient pressuredata during well testing and can effectively identify the interlayer distribution near the wellbore at an extremelylow cost. The reliability of the model is verified using effective oilfield examples.

A Numerical Investigation of the Effect of Boundary Conditions on Acoustic Pressure Distribution in a Sonochemical Reactor Chamber

The intensification of physicochemical processes in the sonochemical reactor chamber is widely used in problems of synthesis,extraction and separation.One of the most important mechanisms at play in such processes is the acoustic cavitation due to the non-uniform distribution of acoustic pressure in the chamber.Cavitation has a strong impact on the surface degradation mechanisms.In this work,a numerical calculation of the acoustic pressure distribution inside the reactor chamber was performed using COMSOL Multiphysics.The numerical results have revealed the dependence of the structure of the acoustic pressure field on the boundary conditions for various thicknesses of the piezoelectric transducer.In particular,the amplitude of the acoustic pressure is minimal in the case of absorbing boundaries,and the attenuation becomes more significant as the thickness of the piezoelectric transducer increases.In addition,reflective boundaries play a significant role in the formation and distribution of zones of maximum cavitation activity.

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike.