Three-dimensional Finite Difference Research Articles

Mechanical Properties of Sheet Pile Cofferdam during Adjacent Open Cut Tunnel Construction near Lake Bottom

In water-related projects, the application of steel sheet pile cofferdams is becoming more and more widespread, and the influence of tunnel construction on the mechanical properties of adjacent cofferdams is important. In this study, the object of research was the mechanical properties of large-span steel sheet pile cofferdams. The open-cut tunnel project was located in Suzhou Yinshan Lake, China. According to the actual construction steps of the tunnel foundation pit, assuming that the soil was a small strain hardening soil model, combined with on-site monitoring data, a three-dimensional elastoplastic finite difference model was established. The results show that during tunnel construction, the maximum settlement of the cofferdam appeared at 0.27~0.53 m on the side of the foundation pit; the maximum horizontal displacement of the steel sheet pile occurred at the pile bottom of foundation pit side, and the seepage gradually increased during construction, eventually resulting in water gushing at the bottom of the foundation pit. After the completion of tunnel construction, the settlement value of the cofferdam presented a pattern that first increased and then decreased from the side of the foundation pit to the side of the adjacent lakeside; the steel cofferdam tilted toward the side of the foundation pit, with a maximum inclination angle of 3.37°. It should be pointed out that as the construction progressed, the axial force of the tie rods in the steel cofferdam changed from a U-shaped distribution to a V-shaped distribution. This study could provide a reference for the impact of tunnel foundation pit construction on adjacent steel cofferdam and could also provide a reference for the safety research of open-cut tunnel construction.

Face stability of shallowly buried large-section EPB box jacking crossing the Beijing-Hangzhou Grand Canal

The mechanical response of conditioned soil in an earth chamber is crucial for maintaining the face stability of earth pressure balance (EPB) box jacking. This study presents the project of a shallowly buried large-section box jacking crossing the Beijing-Hangzhou Grand Canal in Suzhou, China. The characteristics of tunneling parameters, such as the earth chamber pressure pe, total jacking force Pf and frictional force Ffric, were revealed by field measurements. A refined three-dimensional finite difference model was developed using the fluid–solid coupling analysis mode to evaluate the tunnel face stability, in which the geometric configurations of box jacking machine and the contact interfaces between different components were considered explicitly. In addition, the differences between driving and stoppage of box jacking machine were also considered. Upon the successful calibration of the numerical model, the transfer mechanism and the face support efficacy of conditioned soil are evaluated. In the end, a parametric study was conducted to discuss the influences of conditioned soil permeability, shear strength and thickness. The results indicate that the permeability of conditioned soil has no significant influence on its mechanical response, and a larger shear strength can obviously enhance the stress level at the lower part of the earth chamber. In addition, a larger thickness of conditioned soil can reduce its transfer coefficient and the fluctuation of earth chamber pressure.

3D numerical modeling of a rigid inclusion reinforced railway embankment under cyclic loading

Rigid inclusion reinforcements of embankments are increasingly used in traffic route engineering to ensure the long-term system sustainability and to enhance the soft subsoils load-bearing capacity under static and cyclic loading conditions in an economical and practical way. This paper presents a three-dimensional numerical finite difference model to assess the performance of a rigid inclusion reinforced railway embankment subjected to cyclic loading. A slice model of the railway embankment is considered based on full-scale physical tests. The advanced elasto-plastic SANISAND constitutive model is considered for the granular layer in the rigid inclusion reinforced railway embankment. The responses of the system under cyclic loading are outlined concerning settlements, stress distribution and axial–flexural response of the rigid inclusions.

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.

Forward modeling of P- and S-waves response of fractures intersected with horizontal wells in tight reservoirs

Horizontal wells play an important role in expanding the drilling volume of reservoirs and oil production area, and are widely used in unconventional reservoirs. Fractures have a positive effect on reservoir permeability, but fractures can also cause accidents such as casing deformation and inter-well frac-hit. It is of great significance to identify and evaluate fractures intersected with horizontal wells in tight reservoirs. In this paper, a three-dimensional numerical model of horizontal wells and fractures in tight reservoirs is designed. The responses of monopole P-wave and dipole S-wave to fractures with different width, dip angle and filling medium are systematically studied, by using three-dimensional finite difference algorithm. The results show that when the fracture is filled with calcite, the amplitude attenuation of monopole P-wave and dipole S-wave has a monotonic exponential increase with the increase of fracture width and the decrease of fracture dip angle. In the real data processing, the amplitude attenuation of P- and S-waves can be used to jointly evaluate the fracture filled with calcite. When the fracture is filled with water, both P- and S-waves have prominent amplitude attenuation. P wave amplitude attenuation does not have a monotonic variation with the increase of fracture width but it has a monotonic increase with the decrease of fracture dip angle. S wave amplitude attenuation has a monotonic increase with the increase of fracture width and the decrease of fracture dip angle. The amplitude attenuation of P- and S- waves rises significantly when the fracture is filled with natural gas. This study is crucial for better understanding the response of P- and S-waves to fractures intersected with borehole in tight reservoirs, and it provides useful information for the inversion of fracture parameters by using P- and S-waves.

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.

Deep learning accelerated discovery of photonic power dividers

Abstract This article applies deep learning-accelerated inverse design algorithms and discovers a spectrum of photonic power dividers with exceptional performance metrics despite the simplicity in the design geometry. The deep learning models exhibit high precisions on the order of 10−6 to 10−8 for both TE and TM polarizations of light. These models enable ultrafast search for an empirically describable subspace that simultaneously satisfy compact footprints, ultralow losses, ultrawide bandwidth, and exceptional robustness against fabrication randomness. We demonstrate a spectrum of devices for silicon photonics with programmable power splitting ratios, excess losses as small as 0.14 dB, to the best of our knowledge, the smallest footprints on the scale of sub-λ 2, and low loss bandwidths covering the whole telecommunication spectrum of O, S, E, C, L and U-bands. The robustness of the devices is statistically checked against the fabrication randomness and are numerically verified using the full three-dimensional finite difference time domain calculation.

Research on evolution characteristics of multi-information and stability of goaf under deep tunnel

In order to ensure the safety of construction and operation of the tunnel near the goaf. Based on dynamic numerical analysis, three-dimensional finite difference numerical simulation software was developed by FISH programming. Then, on basis of the construction of practical engineering, the safety distance and energy evolution mechanism in an underlying mining goaf area of deep tunnel are studied. The results show that according to the different safe distance in an underlying mining goaf area of deep tunnel, the tunnel structure is divided into danger zone, influence zone and safe zone. The relationship between the cumulative horizontal energy and stress ratio can be divided into three stages: acceleration, average stability and deceleration. The energy evolution of the three stages can also better reflect the damage and failure mechanism inside the surrounding rock mass. The measured field curve shows that when the safety distance is 12 m, the goaf has limited influence on the stability of the tunnel, and the construction in an underlying mining goaf area of deep tunnel is stable on the whole and meets the safety requirements. The best safe distance between the tunnel and goaf is about one time of the tunnel span.

Numerical Estimation of Shaft Stability and Surface Deformation Induced by Underground Mining Transferred from Open-Pit Mining in Jinfeng Gold Mine

In this study, a three-dimensional finite difference numerical model of the Jinfeng Gold Mine, including surface topography, ore body, shafts, and main faults, was built to estimate the shaft stability and surface deformation induced by underground mining transferred from open-pit mining. Satellite monitoring data of surface displacement at several points was used to calibrate the numerical model. The sequence of excavation and filling in the simulation was determined according to the mining schemes with appropriate simplification. The distribution of large deformations in simulation is consistent with the cracking areas on the slopes and surface. Besides, shaft deformation in the simulation is small, which is consistent with the reality that there are no large deformations of shafts in the underground mining activities above 30 m level. After the completion of simulated underground mining, the deformations of shafts and surface are generally far less than the critical deformation. Hence, we concluded that the shafts and surface of the Jinfeng Gold Mine can remain stable in the underground mining stage. Overall, the method in the study provides references for the estimation of shaft stability and surface deformation in the underground mining stage of mine transfer from open pit.

Heterogeneous sparse matrix–vector multiplication via compressed sparse row format

Sparse matrix–vector multiplication (SpMV) is one of the most important kernels in high-performance computing (HPC), yet SpMV normally suffers from ill performance on many devices. Due to ill performance, SpMV normally requires special care to store and tune for a given device. Moreover, HPC is facing heterogeneous hardware containing multiple different compute units, e.g., many-core CPUs and GPUs. Therefore, an emerging goal has been to produce heterogeneous formats and methods that allow critical kernels, e.g., SpMV, to be executed on different devices with portable performance and minimal changes to format and method. This paper presents a heterogeneous format based on CSR, named CSR-k, that can be tuned quickly and outperforms the average performance of Intel MKL on Intel Xeon Platinum 838 and AMD Epyc 7742 CPUs while still outperforming NVIDIA’s cuSPARSE and Sandia National Laboratories’ KokkosKernels on NVIDIA A100 and V100 for regular sparse matrices, i.e., sparse matrices where the number of nonzeros per row has a variance ≤10, such as those commonly generated from two and three-dimensional finite difference and element problems. In particular, CSR-k achieves this with reordering and by grouping rows into a hierarchical structure of super-rows and super–super-rows that are represented by just a few extra arrays of pointers. Due to its simplicity, a model can be tuned for a device, and this model can be used to select super-row and super–super-rows sizes in constant time.

An optimized three-dimensional time-space domain staggered-grid finite-difference method

Numerical simulation of three-dimensional (3D) seismic wavefields forms the basis of the research on the migration methods of 3D seismic data based on wave equations. Because the simulation precision of wavefield extrapolation determines the imaging accuracy to a certain extent, it is very important to study how to enhance the forward modeling precision of 3D seismic wavefields. Thus, we build on an optimized 3D staggered-grid finite-difference (SFD) method with high simulation precision based on two-dimensional (2D) seismic modeling. Since it generates the corresponding difference coefficients by utilizing the least square (LS) method to minimize the objective function constructed by the time-space domain dispersion relation of the 3D acoustic wave equation, our optimized time-space domain LS-based 3D SFD method can effectively enhance the modeling precision of the 3D seismic wavefields in theory compared with the 3D SFD methods based on the Taylor-series expansion (TE), especially for the large wavenumber range. Examining the numerical dispersion, algorithm stability and computational cost, we compare our optimized time-space domain LS-based 3D SFD method with three conventional TE-based and LS-based 3D SFD methods to illustrate and demonstrate its effectiveness and feasibility. The numerical examples from different 3D models suggest that our optimized time-space domain LS-based 3D SFD method can generate less numerical dispersion and higher simulation accuracy for 3D seismic wavefields than three other conventional 3D SFD methods, but its stability condition is stricter and its computational cost is slightly higher.

Silicon-based compact mode converter using bricked subwavelength grating

Facing the increasing capacity requirements of on-chip optical interconnects, mode division multiplexing technology (MDM), which fully uses the different spatial eigenmodes at the same wavelength as independent channels to transmit optical signals, has attracted tremendous interest. Mode-order converter that can convert the fundamental mode into high-order mode is a key component in MDM system. However, it is still very challenging to achieve compact mode-order converters with high performances. Subwavelength grating (SWG) can be equivalent to homogenous material, which has the prominent advantages such as controlling over birefringence, dispersion and anisotropy, thus making photonic devices possess high performance. Wheras the conventional SWG only needs single-etch step, but the implementation of SWG structure usually requires a fabrication resolution on the order of 100 nm and below, which is difficult for current wafer-scale fabrication technology. The anisotropic response of SWG can be further engineered by introducing bricked topology structure, providing an additional degree of freedom in the design. Meanwhile, the requirement for fabrication resolution can also be reduced (> 100 nm). In this work, we experimentally demonstrate compact TE<sub>0</sub>-TE<sub>1</sub> mode-order converter and TE<sub>0</sub>-TE<sub>2</sub> mode-order converter by using a bricked subwavelength grating (BSWG) based on a silicon-on-insulator (SOI) with the BSWG having a minimum feature size of 145 nm. In the proposed mode-order converter, a quasi-TE<sub>0</sub> mode is generated in the BSWG region, which can be regarded as an effective bridge between the two TE modes to be converted. Flexible mode conversion can be realized by only choosing appropriate structural parameters for specific mode transitions between input/output modes and the quasi-TE<sub>0</sub> mode. By combining three-dimensional (3D) finite difference time domain (FDTD) and particle swarm optimization (PSO) method, TE<sub>0</sub>-TE<sub>1</sub> mode-order converter and TE<sub>0</sub>-TE<sub>2</sub> mode-order converter are optimally designed. They can convert TE<sub>0</sub> mode into TE<sub>1</sub> and TE<sub>2</sub> mode with conversion length of 9.39 µm and 11.27 µm, respectively. The simulation results show that the insertion loss of < 1 dB and crosstalk of < –15 dB are achieved for both TE<sub>0</sub>-TE<sub>1</sub> mode-order converter and TE<sub>0</sub>-TE<sub>2</sub> mode-order converter, their corresponding working bandwidths being 128 nm (1511–1639 nm) and 126 nm (1527–1653 nm), respectively. The measurement results indicate that insertion loss and crosstalk are, respectively, less than 2.5 dB and –10 dB in a bandwidth of 68 nm (1512–1580 nm, limited by the laser tuning range and grating coupler).

Full-wave multiphysics model for simulation and investigation of terahertz photoconductive antenna using LUMERICAL and CST softwares

In this work, the physical mechanism of the full-wave multiphysics model is described underlying the simulation of terahertz photoconductive antenna (PCA) using hybrid softwares incorporating LUMERICAL and CST. The feature of this simulation is that the multiphysical phenomena that occur in the PCA, such as light-matter interaction, photoexcited carriers, and full-wave propagation, are considered and embodied in the simulation. The accuracy of the presented simulation framework is verified by comparing its results with some commercial softwares such as COMSOL, SILVACO, and the numerical of three-dimensional finite difference time domain (3-D FDTD) method.Themethod. The maximum discrepancy of the simulation results between this hybrid software framework and others is less than 2%, which indicates the accuracy of these simulation results. In addition, this hybrid simulation framework can be used to characterize the parameter-dependent performance of a PCA. The obtained results are used as a guideline to present modified PCAs where a nanostructure is added inside the antenna gap to enhance the PCA performance. The two modified PCAs are defined as nano-line and nano-crossline PCAs, where nano-lines are connected to one or both contacts. The conversion efficiencies of the nano-line and nano-crossline PCAs are enhanced by 28.5 and 64 times, respectively, with respect to conventional PCA.

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.

Tunnel-soil-bridge seismic interaction on soft clay

Seismic tunnel-soil-bridge interaction in high plasticity soft clays can lead to significant ground motion variability, affecting on-ground structures located next to or above underground facilities. This technical note presents a numerical study aiming at establishing tunnel-bridge seismic interaction effects on soft clays. Initially, we revised this interaction considering the impact that frequency content, intensity, and strong ground motion duration have on the interplay between incoming seismic waves reflected in the tunnel and the energy feeding back from the bridge swinging back and forth during a large earthquake. Series of three-dimensional finite difference models were developed. Seismic analyses considered both normal and subduction events with a return period of 250 years. From the results gathered in these analyses, the ground motion modification in the surrounding soil occurs in both the transverse and longitudinal components due to tunnel-bridge interaction. The tunnel underneath the bridge establishes detrimental soil-structure interaction effects for normal and subduction events.

Efficiency Evaluation of Bone Conduction Devices Using Three-Dimensional Finite-Difference Time-Domain Head Model

Efficiency Evaluation of Bone Conduction Devices Using Three-Dimensional Finite-Difference Time-Domain Head Model

Instability Monitoring and Numerical Analysis of Typical Coal Mines in Southwest China Based on DS-InSAR.

Most of the coal mines in Southwest China are located in mountainous areas with high vegetation coverage, and most activities are carried out under the mountains. The deformation monitoring and mechanical behavior analysis of the mining area helps reveal the typical mountain deformation and failure mechanism caused by underground mining activities and reduce the risk of mountain collapse in the mining area. In this manuscript, a research method for mountain stability in mining areas is proposed, which combines InSAR deformation monitoring with numerical analysis. Based on the high-precision deformation information obtained by DS-InSAR and the landslide range, a three-dimensional explicit finite difference numerical analysis method was used to reconstruct the landslide model. According to the layout of the coal mining working face, the variation mechanism of overlying stratum stress and the mountain slip in the coal mining process is inverted, and the mechanism of mountain failure and instability in the mining area is analysed. Based on the sentinel data, the experiment performed time series monitoring and inversion analysis of the mountain collapse in Nayong, Guizhou, China. The results show that mining activities a certain distance from the mountain will affect mountain stability, and there are specific mechanisms. From 2015 to 2017, the stress redistribution of overlying strata above the goaf area resulted in dense longitudinal cracks in the landslide body due to coal mining. The mountain is in a continuous damage state, and the supporting force to prevent collapse continues to decrease, resulting in a gradual decrease in landslide stability. Both the time series DS-InSAR monitoring results and numerical simulation results verify the actual occurrence and development of the on-site subsidence.

Measurement resolution of acoustic reflection imaging logging with a cylindrical phased array acoustic receiver station

Azimuthal acoustic reflection imaging logging plays an important role in the exploration and development of fracture-cavity reservoirs, because it can image geological structures within tens of meters around the borehole. However, minimal evaluations have been conducted for the detection of small-scale geological anomalies, particularly the simultaneous measurement of multiple small-scale scatterers. In this study, the scanning-reception implementations of phased array acoustic receiver stations in the Borehole Azimuthal Acoustic Reflection Imaging Tool (BAR) were developed based on the beamforming principle. The measurement responses of BAR were simulated and the scanning-reception performances of arcuate phased array (APA) and cylindrical phased array (CPA) acoustic receiver stations were compared using a three-dimensional (3D) finite difference algorithm for one or two small-scale caves in a formation away from a fluid-filled borehole. The azimuth and elevation measurement resolutions of CPA acoustic receiver stations were determined by analyzing the scattered wavefields under the circumstances of two caves on the same horizontal or vertical plane. Numerical simulation results showed that the echo waves scattered from small-scale caves were similar to those reflected by large-scale formation interfaces outside the borehole. The azimuth angle of a single cave could be obtained by calculating the amplitudes of P–P echoes at different azimuths received by the APA acoustic receiver station. Compared with the APA scanning-reception mode, the 3D scanning-reception mode based on the CPA acoustic receiver station was more applicable when two caves were simultaneously located outside the borehole. Under the calculation conditions of this study, the CPA acoustic receiver station had a limit azimuth resolution of ∼60°–90° and a limit elevation resolution of ∼8.8°–17.4° when two scatterers were located on the same horizontal or vertical plane. This work verified the superiority of the CPA scanning-reception mode for the detection of small-scale geological anomalies and provided a theoretical basis for the wider application of BAR.

Novel 3D coupled convection–diffusion model algorithm

The potential of a partial differential equations model is to anticipate its computational behavior. The simulation of a transient 3D coupled convection–diffusion system using a numerical model is described. The main objective of this article is to offer effective limited contrast compact finite difference techniques for use with nonlinear coupled partial differential systems that mimic overseeing differential frameworks. The three-dimensional compact finite difference formulation serves as the model’s foundation. An analytical model has been used to validate finite difference techniques that are numerically compact. By examining the consistency and union of the arrangement, which may be seen from figures and information tables, we can evaluate the model and the suggested numerical schemes. The schemes are unconditionally stable and accurate up to two orders in time and six orders in space, according to the results of the stability and accuracy tests. The implicit method used in the algorithm’s design was examined for stability criteria. Because mesh-independent solutions for non-linear differential systems are expensive, block tridiagonal matrix structures, measured in terms of L2 and L∞ norms, which are inherent characteristics of schemes and have excellent agreement with the investigation arrangement, are created.

Цифровая модель техногенеза подземных вод как элемент устойчивого развития городской среды

The purpose of this study is to create a digital twin of the sludge reservoir, which allows modeling and predicting the impact of technogenic formation on the sustainability of urban development, in particular, on the state of groundwater. The research methodology is to simulate groundwater based on numerical simulation using the ModTech 2.21 program. This program is designed to solve problems of various equations and partial derivatives that describe the geo-filtration of the environment, using a numerical method on a three-dimensional finite-difference grid. In order to assess the sustainable development of the urban environment in the city of Sterlitomak, a digital twin of the urban area was created in terms of groundwater. Sludge accumulator «White Sea» is a unique man-made object located in the city of Sterlitomak and affecting groundwater due to infiltration losses of distiller fluid through the bed of the sludge reservoir. According to the simulation results, the infiltration losses of the SHBM are 3078 m3/day or 1123470 m3/year. The incoming part of the balance is formed due to the attraction of river runoff, infiltration nutrition, and the outgoing part is due to the discharge of groundwater into surface water. The model assessment was carried out in relation to the conditions of migration of the main pollutant component in the territory of the «White Sea» - chlorides. With the help of the created digital model, it is possible to assess, predict and manage the situation in the urban environment in terms of groundwater. Digitalization through the use of intelligent solutions and innovations in the field of digital technologies makes it possible to understand the processes occurring in social, man-made, and natural systems at a new level. The next step in creating digital twins can be models of electronic maps of soil cover or vegetation, the state of the air basin, and more. The same models can be created on the basis of economic and social indicators. This is necessary for planning the sustainable development of the urban environment.