Three-dimensional Finite-difference Method Research Articles

Impact of combined electric and magnetic fields on the physical properties of GaAs variant quantum ring quarter cross-section in presence of an off-center shallow donor impurity

Impact of combined electric and magnetic fields on the physical properties of GaAs variant quantum ring quarter cross-section in presence of an off-center shallow donor impurity

Excavation method optimization and mechanical responses investigating of a shallow buried super large section tunnels: a case study in Zhejiang

The construction of super large section (SLS) shallow buried tunnels involves challenges related to their large span, high flat rate, and complex construction process. Selecting an appropriate excavation method is crucial for ensuring stability, controlling costs, and managing the construction timeline. This study focuses on the selection of excavation methods and the mechanical responses of SLS tunnels in different types of surrounding rock. The research is based on the Yangjiashan tunnel project in Zhejiang Province, China, which is a four-line highway tunnel with a span of 21.3 m. Three sequential excavation methods were proposed and simulated using the three-dimensional finite difference method: the “upper first and lower later” side drift (SD) method, the central diaphragm method, and the top heading and bench (HB) method. The mechanical response characteristics of tunnel construction under these methods were investigated, including rock deformation, rock pressure, and the internal forces acting on the primary support. By comparing the performance of the three construction methods in rock masses of Grades III to V, the study aimed to determine the optimal construction method for SLS tunnels considering factors such as safety, cost, and schedule. Field tests were conducted to evaluate the effectiveness of the optimized construction scheme. The results of the field monitoring indicated that the “upper first and lower later” SD method in Grade V rock mass and the HB method in Grade III to IV rock mass are feasible and cost-effective under certain conditions. The research findings provide valuable insights for the design and construction of SLS tunnels in complex conditions, serving as a reference for engineers and project managers.

Numerical study on stability of geosynthetic-encased stone column-supported embankments based on equivalent method

The application of geosynthetic-encased stone column-supported embankments (GESC-supported embankments) has garnered significant attention in geotechnical engineering, with limited investigations into their slope stability. In this paper, an equivalent method was proposed to establish GESC-supported embankment models through three-dimensional finite difference method (3D-FDM). Responses of factor of safety (FS) to arrangement tightness of GESCs (e.g., various column diameters, spacings, and quantities under constant area replacement ratio) and hoop effect of geosynthetic encasements (e.g., various geogrid strengths under different shear strengths of soft soil) were studied. For a given area replacement ratio, FS increased non-linearly with the increasing column quantity or the decreasing ratio of column spacing to diameter at high area replacement ratios. GESCs with smaller diameter and spacing proved to be more effective in improving slope stability, and an optimum ratio of column spacing to diameter was observed for practical use. Besides, FS increased linearly with geogrid strength at low geogrid strength levels, but an extremely lack of the shear strength of soft soils or the column quantity was unfavorable for the application of GESCs. Bending failure was the primary failure feature of GESCs under embankment loading, and the geogrid strength influenced slope stability through the bending capacity of GESCs.

P-y Curve for Estimation Lateral Bearing Capacity of Single Bored Pile in Overconsolidated Soils Using The Three-Dimensional Finite Element Method.

The p-y curve method is widely used to predict piles’ lateral bearing capacity. It assumes independent springs with a non-linear modulus of subgrade reaction for analyzing soil resistance (p) and deflection (y). This study determined the lateral bearing capacity using the three-dimensional finite element method (FEM-3D) and finite difference method (FDM), which was later compared with the loading test results. Therefore, the pile head condition is assumed to be the free-head. To determine the lateral bearing capacity, input the lateral deflection at the pile head. In FEM-3D, the pile and lateral deflection in the pile head is modeled using cluster elements and surface-prescribed horizontal displacements, respectively. On the other hand, in FDM, pile heads and boundary conditions are modeled using displacement and moment. The results of the lateral bearing capacity using FEM-3D provide predictions that are close to the loading test, with a difference of about 4.2%. In contrast, the FDM method produced conservative results due to its reliance on semi-empirical formulas. The ultimate soil resistance (Pult) formula in FDM is more suitable for rigid-pile behavior. The prediction of lateral bearing capacity using FEM-3D provides more accurate results due to its ability to model complex soil-pile interaction. The stress history, soil-pile interaction, and more reliable constitutive models can be modeled in FEM-3D.

Three-dimensional lattice Boltzmann and finite difference methods for the simulation of ultrasound and thermal convection in a microcavity

This article presents a three-dimensional numerical analysis of the phenomena of ultrasound propagation in air, thermal convection, and their interaction. The simulations are carried out using a hybrid numerical approach based on the lattice Boltzmann and the finite difference techniques. For validation purposes, our numerical model is verified in the case of the study of ultrasound propagation in the air without the presence of thermal convection. This is performed by comparing the numerically calculated acoustic pressure with the analytical results. After this verification, the focus is on the examination of the heat transfer improvement by the ultrasound emitted by the vibration of a circular piston. This acoustic source is mounted in the center of the left cold surface of a microcavity, which is differentially heated and filled with air. The obtained numerical results indicate that the heat transfer is significantly improved by using 10 MHz ultrasound.

Modeling of heating and cooling behaviors of laminated glass facades exposed to fire with three-dimensional flexibilities

To develop a precise and efficient computer model for predicting the heating and cooling behaviors of laminated glass facades exposed to fire, there is an urgent need to reduce the huge computational requirements associated with simulating heat transfer in layered structures that feature a down-flowing water film. We overcome this challenge by proposing an efficient three-dimensional finite difference method (3DFDM) which has high numerical stability when solving heat transfer equations with water film and air convection. To capture the moving particles of the water film, we developed a unique computational algorithm for particle labeling, which has two significant advantages: (1) it eliminates the time-consuming process of searching for neighboring particles in conventional meshfree methods, and (2) it ensures that every main particle interacts only with limited neighboring particles without utilizing any weights, thus significantly reducing the computational effort. We validated our 3DFDM through experiments in heating and cooling scenarios and compared its thermal results with those obtained from commercial packages to demonstrate its high efficiency and accuracy. Furthermore, we examined the feasibility of our model in evaluating the effects of thickness of the interlayer and water film release time on the cooling behavior of laminated glass during a fire.

Displacement Analyses of Main Structure of Parallel Pit Excavation and Analysis of Countermeasures

To solve the impact on the pre-existing main structure due to the need for early traffic restoration of urban roads within the cross-hub and the difficulty of co-ordinating a construction plan among groups of pits, a construction method combining TD and BU was proposed. By establishing a three-dimensional finite difference method (FDM) of parallel pit excavation considering the small strain constitutive model of the strata, the influence of four different excavation schemes on the pre-existing main structs is studied. The results of the study show that: (1) the asynchronous excavation of the pit on both sides of the cover excavation area causes additional deformation of the steel pipe structs; sequential excavation produces the greatest additional deformation of the steel tube columns, followed by staggered excavation and the least simultaneous excavation; (2) the middle 1 slab enhances the overall stiffness of the main structure in the cover excavation area, reducing the additional deformation caused by the unsynchronized excavation of the pit, with the maximum horizontal deformation of 5.8 mm, a reduction of 61%; (3) the greater the depth of excavation and the closer the distance from the pit, the more obvious the deformation of the steel pipe column; and (4) the function relationship between δhm/H and the relative stiffness coefficient Rd was obtained by fitting, and the maximum controlled mis-step spacing of the foundation excavation on both sides was 4.3 m when the middle 1 floor slab was cast.

Numerical Analysis of Passive Piles under Surcharge Load in Extensively Deep Soft Soil

The three-dimensional finite difference method was used in this study to analyze the deformation and stresses of a passive pile under surcharge load in extensively deep soft soil. A three-dimensional numerical model was proposed and verified by a field test. The horizontal displacements of the pile agreed well with the field results. This study investigated the pile-foundation soil interaction, the load transfer mechanism, the excess pore water pressure (EPWP), and the horizontal resistance of the foundation soil. The results show that the soil in the corner of the loading area developed a large uplift deformation, while the center of the loading area developed a large settlement. The lateral displacement of the pile decreased sharply with the increase of the depth and increased with the surcharge load. The lateral displacement of the soil was negligible when the depth exceeded 30 m. The EPWP increased in a nonlinear way with the increase of the surcharge load and accumulated with the placement of the new lift. The distribution of the lateral earth pressure in the shallow soil layer was complex, and the negative value was observed under a high surcharge load due to the suction effect. The proportion coefficient of the horizontal resistance coefficient showed much smaller value in the situation of large lateral deformation and high surcharge load. The design code overestimated the horizontal resistance of the shallow foundation soil, which should be given attention for the design and analysis of the laterally loaded structures in extensively soft soil.

Oil-gas two-phase seepage model in fractured carbonate reservoirs

Fractures are developed in fractured carbonate reservoirs. Traditional fracture characterization methods and seepage mathematical models cannot accurately describe the complex spatial distribution of large-scale fractures and their stress sensitivity, and do not consider the two-phase seepage of oil and gas, resulting in the dynamic analysis results have large errors. Aiming at this problem, a two-phase seepage model of oil and gas in fractured carbonate reservoirs considering stress sensitivity is established in this paper, and the semi-analytical solution of the model is obtained by using three-dimensional source function theory and finite difference method. The accuracy of the model is verified by comparison with commercial numerical simulation software, the production performance curve of oil and gas two-phase is drawn, and the influence of key seepage parameters of reservoirs and fractures on production performance is analyzed. The results show that the hybrid solution method of 3D source function and finite difference can realize the accurate and efficient solution of 3D discrete fracture oil and gas two-phase seepage model. The stress sensitivity effect leads to serious loss of fracture permeability and increase of fluid seepage resistance, which seriously affects the production of oil wells. The greater the fracture permeability, the higher the initial value of production, and the higher the position of the production curve. The longer fracture length, the higher the production curve in the early and middle production stages, and the slower the production decline.

Numerical Simulation of Long-Term Deterioration of Rock Mass Supported by Shotcrete Lining

The deterioration of rock mass and shotcrete lining has major consequences on the long-term performance of tunnels in the weak rock mass. In this study, the long-term behavior of rock mass and shotcrete in tunnels was simulated by using the three-dimensional finite difference method, considering the nonlinear deterioration mechanism. The degradation of rock mass was simulated by weakening the mechanical parameters, while the deterioration of shotcrete was modeled by decreasing the thickness. The support pressure, internal force, and displacement of the secondary lining were monitored with the gradual degradation of rock mass and shotcrete. As a consequence, the factor of safety (FoS) evolution with time was discussed. The results indicated that 1) the deterioration of both rock mass and shotcrete would significantly increase the rock pressure on the secondary lining, leading to an increase in the displacement (0–14 mm). The FoS of the secondary lining was reduced by 85%. 2) The influence of shotcrete’s deterioration on the secondary lining was relatively less, and the rock pressure on the secondary lining increased from 0 kPa to 13.8 kPa. The long-term safety of the tunnel is remarkably affected by the deterioration of rock mass, depending on the deterioration characteristics of the rock mass. Therefore, the deterioration characteristics of rock mass should be fully considered in tunnel maintenance.

Structures and Settlement Control of Yujingshan High-Speed Railway Tunnel Crossing Massive Rockfill in a Giant Karst Cave

The Yujingshan high-speed railway tunnel crosses a giant cavern system with a 108 × 104 m3 volume chamber and an 18 km long underground river. The massive project, which lasted three years, was eventually awarded the “Overcoming the Challenges” award by the International Tunneling and Underground Space Association (ITA) in 2020. However, since the cave chamber was filled with large-scale rockfill, structural settlement is a non-negligible problem. This paper presents the unique structures of a bridge supporting railway tracks wrapped by tunnel lining and the settlement control of the Yujingshan tunnel crossing massive rockfill in the giant cave. The geological characteristics and design considerations are systematically introduced. A three-dimensional coupling discrete element method (DEM) and finite difference method (FDM) numerical model and 13 months of long-term settlement monitoring were conducted to evaluate the settlement behavior. The results indicate that the morphology of cavern and internal deposits caused the whole rockfill to migrate to the lower left. The tunnel structure consequently developed a significant inclined settlement. The continuous construction load would increase the settlement value by 31.4%. The bottom reinforcement of steel-pipe pile with grouting could effectively inhibit settlement and differential settlement. Considering the simulation results, the tunnel bottom had greater settlement than the limit standard for high-speed railway embankment, which means this special structure form is reasonable for operation. Meanwhile, the monitoring results show that the tunnel bottom settlement in D3K279+891~D3K279+947 had not performed an apparent convergence trend after 13 months. Further structural monitoring and compensation grouting should be actively considered for operation maintenance.

Thermal evolution of non-spherical asteroids in the early solar system

An attempt has been made, probably for the first time, to understand the thermal evolution of non-spherical asteroids in the early solar system, with the short-lived nuclide, 26Al and 60Fe, as the internal radiogenic heat sources. Two numerical techniques, an explicit 3D-FDM (three-dimensional finite difference method) and a semi-implicit 3D-CNM (three-dimensional Crank-Nicholson method), have been developed on the basis of the central difference approximation to solve the heat conduction partial differential equation in cartesian coordinates for an assumed ellipsoid shaped asteroid. The second approach is based on fraction-step semi-implicit method (FSM) that turns out to be much faster in terms of computational time. The numerical techniques can be applied for any irregular shaped asteroids, TNOs (trans-Neptunian objects) or small satellites of outer planets. A comparison of the techniques has been made, for a spherical asteroid of radius 50 km, with the conventional explicit finite difference (FDM) and implicit Crank-Nicholson (CNM) methods based on spherical polar coordinates with temperature dependence on the radial coordinate alone. The newly developed techniques exhibit identical results, thereby, indicating a consistency in the distinct numerical approaches. Further, the results obtained from the techniques are also consistent at a level of up to ~96% when compared with the conventional numerical techniques during the several tens of million years of thermal evolution. The slight differences can be attributed to the nature of discretization (pixelization) of the ellipsoids into an assemblage of unit cubes that can result in a comparatively large surface area for more heat losses, and hence, results in comparatively rapid cooling. The thermal evolution of a wide-size range of asteroids having dimensions identical to (243) Ida, (951) Gaspra, (253) Mathilde, (5) Astraea, (6) Hebe and (3) Juno, was numerically simulated using the newly developed techniques to understand the heating and the cooling of non-spherical asteroids to understand thermal metamorphism. The cartesian coordinate corresponding to the shortest semimajor axis provides the fastest cooling to the ellipsoidal body. The accretion of the asteroids during the initial 2–3 Myr. could have provided diverse scenarios for thermal metamorphism.

Wavelength-selective 2 × 2 optical switch based on a Ge2Sb2Te5-assisted microring

A novel wavelength-selective 2 × 2 optical switch based on a Ge 2 Sb 2 Te 5 (GST)-assisted microring-resonator (MRR) is proposed. The present GST-assisted MRR consists of two access optical waveguides and an MRR coupled with a bent GST-loaded silicon photonic waveguide. The 2 × 2 optical switch is switched ON or OFF by modifying the GST state to be crystalline or amorphous. In particular, the microring waveguide and the bent GST-loaded waveguide are designed to satisfy the phase-matching condition when the GST is crystalline. As a result, the MRR becomes highly lossy and the resonance peak is depressed significantly. On the other hand, when it is off, there is little coupling due to the significant phase mismatching. Consequently, one has a low-loss transmission at the drop port for the resonance wavelength. In this paper, the simulation using the three-dimensional finite-difference method shows that the extinction ratio of the designed photonic switch is ∼ 20 dB at the resonance wavelength, while the excess losses at the through port and drop port are 0.9 dB and 2 dB. In particular, the resonance wavelength changes little between the ON and OFF states, which makes it suitable for multichannel wavelength-division-multiplexing systems.

Evaluation of dynamic stability and analysis of reinforcement measures of a landslide under seismic action: a case study on the Yanyangcun landslide

Earthquakes are a major landslide trigger, and evaluation of the dynamic stability of landslides under seismic action is very important. The Yanyangcun landslide, which is located at route marker K92 of the Xianggelila to Lijiang expressway in Yunnan Province, China, was chosen as a case study. Using the three-dimensional finite difference method and the unbalanced thrust method, three mechanical indices of the sliding zone, including the volume ratio of the elastic or plastic elements, the permanent displacement, and the residual thrusts of the slices, were calculated to evaluate the progressive failure and dynamic stability of the landslide when exposed to different intensities of seismicity. The safety factor of the landslide with reinforcement measures was also assessed. The critical peak seismic acceleration was about 2.29 m/s2, between earthquake intensity of VIII degree and IX degree. The landslide experienced progressive failure by means of shear at the leading edge, tension at the trailing edge, and immobilization of the middle part. The middle part of the sliding zone underwent a “locking effect,” which could effectively resist the immobilization of the plastic zones of the leading edge and the trailing edge. With reinforcement measures, the dynamic stability of the landslide under VIII degree and IX degree events satisfied the allowable safety factor of the local specifications. The results provide guidance for disaster prevention and aseismic design for the Yanyangcun landslide, and can also be used as reference information for dynamic stability evaluation of other landslides threatened by earthquakes.

An iterative Debye dispersion model for a horizontal multi-layered material

An iterative Debye model for a horizontal multi-layered material is found using a circuit model. A three-dimensional Finite Difference Method (3D-FDM) is developed to extract the effective permittivity and conductivity. The results obtained from the FDM and the present method agree very well, which shows the validity of the layered Debye formulas in terms of original circuit parameters. The derived iterative Debye formulas can be used to analyze the relationship between the effective electrical spectra and the electrical parameters of each layer. In addition, it can be applied for multi-layered models with extra-thin thickness geometry, which are probable models in electronic materials. Numerical results show that when the number of layers is more than two, the relaxation factor will not be a constant and more than one transition areas will appear. A thin insulation membrane in a layered model leads to the presence of a low frequency dielectric enhancement and largely decreases the effective conductivity at low frequencies. It was concluded from the numerical simulations that the dielectric enhancement is dependent on the membrane thickness, membrane conductivity, volumetric ratio, and the presence of conductivity contrast between materials.

A procedure for interaction between rock mass and liner for deep circular tunnel based on new solution of longitudinal displacement profile

A new solution for the longitudinal displacement profile (LDP) is proposed based on three-dimensional finite-difference method. The improved convergence-confinement method (CCM) is divided into two stages. In the first stage, the fictitious support pressure can be derived, representing the support pressure acting on the periphery of the tunnel by the rock mass itself. In the second stage, the fictitious support pressure transforms to the pressure on liner, and this progress reflects the interaction between rock mass and liner. According to two-stage analysis, a computing procedure is proposed for calculating pressure and deformation of rock and liner. By comparing with the results of other approaches, the procedure is proved to be correct. The influences of elasticity modulus, thickness of liner, and supporting time are discussed individually. The results indicate that the final pressure on liner can be reduced by reducing stiffness of liner and postponing supporting time. To prevent the liner from yielding, the prior measure is to postpone supporting time, and meanwhile, the liner with lower elasticity modulus and smaller thickness can be selected. In final, a practical example is performed by utilising this procedure, confirming it can provide reference to tunnel engineering design.

Preliminary study on wave field and dispersion characteristics of channel waves in VTI coal seam media

Coal seam is a sedimentary rock with bedding, which can be regarded as VTI medium. VTI medium model is more suitable for real coal seam. However, existing channel wave theories generally assume that coal seams are isotropic for mathematical simplicity, and there is no study on the properties of channel waves in VTI media. In this paper, we deduce the theoretical dispersion equation of Love channel waves in the three-layer VTI model and analyze the parameter effects on the dispersion curve for the first time. The channel wave field in VTI media is simulated by three-dimensional staggered-grid finite difference method. The results indicate that polarization of both qP- and qSV-waves is not parallel or perpendicular to the orientation of the wave traveling in VTI media, while the polarization of SH wave is normal to wave propagation direction at horizontal plane. Therefore, it is wise to use Love channel waves to conduct field exploration because of the uniqueness of dispersion curves in the VTI media for the Love channel waves comparing with that in isotropic media. The velocities of the Love channel wave in VTI media are higher than that in isotropic media. The coal seam thickness primarily influences the Airy frequency phase, while the Airy phase velocity remains stable. Both the S-wave velocity and γ parameter of coal seam significantly affect Airy phase velocity. Severe errors may occur during in the coal thickness inversion when using the dispersion curve of Love channel wave in isotropic media, and dispersion curve in VTI media should be adopted. In terms of the amplitude distribution, Love channel waves appear to have similar patterns in both the VTI media and the isotropic media.

The Freezing of Rice Products in Box Containers: Temperature Profile Prediction, Model Validation and Physical Characteristics

Abstract In this study, a three-dimensional finite difference method is applied to develop a mathematical model for the simulation of heat transfer phenomena in cooked white rice and fried rice in polypropylene boxes during the freezing process. The main objective was to develop a tool for predicting time/temperature profiles that can be applied under various freezing conditions. The results indicate fair agreement between experimental data and model predictions. The model precision can be improved if incorporating the heat transfer mechanism occurring at the head space and the equations for accurately estimating changes of freezing point temperatures and thermophysical properties of rice along freezing process. Textural properties of frozen rice samples after microwave warming were apparently different from the freshly cooked samples. Rapid freezing provided soft and nonsticky texture of cooked white rice after warming while slow freezing resulted in the fried rice with the most similar texture to freshly cooked fried rice.

Coupled characterization and experimental verification of heat transfer and air leakage in a quad-sectional rotary air preheater

Air leakage has a substantial impact on the efficiency of rotary air preheater, and is closely related to their temperature distribution. In this paper, for a quad-sectional rotary air preheater, the coupled model of thermodynamics and air leakage is proposed and verified by the experimental results of a double reheat 1000 MW power generator unit. The air leakage of each chamber, the temperature distribution of the fluid and the matrix can be obtained by using the three-dimensional finite-difference method. On the basis of previous research, the indirect air leakage is considered in the coupled model, as well as the interaction between the heat transfer and the air leakage. The simulation results show that the total air leakage of the quad-sectional air preheater is 33.1% less than that under the tri-sectional preheater condition. Additionally, compared with the experimental results, the difference values of the air leakage rates and the maximum duct outlet temperature are 0.21% and 2.1 °C, respectively, which manifest the model accuracy. The results indicate that, in comparison to previous research methods, this model can accurately obtain the temperature distribution of air preheater.

Numerical simulations of solidification structures and macrosegregation by a cellular automaton model coupled with flow calculations

In this study, a numerical model was developed, and direct simulations were performed to predict solidification grain structures and macrosegregation based on a three-dimensional cellular automaton finite difference (CAFD) method coupled with flow calculation of natural convection and shrinkage flow. First, to evaluate the model coupled with natural convention, simulations of unidirectional solidification for Al-10wt% Mg alloy were performed. Mg-rich plumes rising in the melt were seen due to subsequent upward flow, and Mg-rich channels forming in the mushy zone were observed. Columnar grains were then formed, and they became coarse afterwards. Next, to evaluate the model coupled with shrinkage flow, simulations of casting Al-10wt% Cu alloy in a unique mold, which can form macrosegregation in the central region of the small ingot, were performed. The bridging of columnar grains formed during solidification, and the positive segregation was generated in the region below the bridging. Thus, the main factor for this macrosegregation is the shrinkage flow with bridging. From the comparison of simulation results with and without the chill for the unique mold, it was established that the shrinkage flow and the bridging of solidification structures play an important role in macrosegregation.