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The nonstandard finite-difference time-domain (NS-FDTD) method is implemented in the differential form on orthogonal grids, hence the benefit of opting for very fine resolutions in order to accurately treat curved surfaces in real-world applications, which indisputably increases the overall computational burden. In particular, these issues can hinder the electromagnetic design of structures with electrically-large size, such as aircrafts. To alleviate this shortcoming, a nonstandard path integral (PI) model for the NS-FDTD method is proposed in this paper, based on the fact that the PI form of Maxwell’s equations is fairly more suitable to treat objects with smooth surfaces than the differential form. The proposed concept uses a pair of basic and complementary path integrals for H-node calculations. Moreover, to attain the desired accuracy level, compared to the NS-FDTD method on square grids, the two path integrals are combined via a set of optimization parameters, determined from the dispersion equation of the PI formula. Through the latter, numerical simulations verify that the new PI model has almost the same modeling precision as the NS-FDTD technique. The featured methodology is applied to several realistic curved structures, which promptly substantiates that the combined use of the featured PI scheme greatly improves the NS-FDTD competences in the case of arbitrarily-shaped objects, modeled by means of coarse orthogonal grids.

This paper reports a typical case history of deep braced excavation for constructing the main bridge cushion cap of the Yangwan River Bridge to explore the excavation performance under embankment surcharge load. Three-dimensional finite difference analysis, simulating the whole construction process of this case history, was performed to capture the effects of the embankment–excavation distance, revel level, and excavation bottom sealing on the responses of the earth retaining structure and the ground. It was found that both the ground surface settlement and the retaining structure deformation are larger on the near-embankment side than the far-embankment side. The responses on the near-embankment side are more sensitive to the embankment–excavation distance and the river level. However, the effects of these parameters diminish greatly when the embankment–excavation distance exceeds 1.5 times the excavation depth. The excavation bottom sealing measures can reduce the retaining structure deformation, and effectively restrain basal heave. This restraint weakens as the excavation bottom sealing thickness exceeds 1 m.

High temperatures are generated due to the sliding contacts between the rubbing surfaces of the friction clutch system. In this work, by considering the effective thermal contact conductance under sliding conditions, a simulation model of a two-dimensional transient temperature field of the clutch disc was developed. A numerical solution to obtain the surface temperature at different radii was presented based on the finite difference method. Compared with the experimental data, the proposed model for estimating the surface temperature is more accurate than the conventional prediction method. The results showed that the errors of the calculated temperatures at radii of 114 and 106 mm have obviously reduced by 12.98% and 12.60%, respectively. In addition, the influences of pressure and relative speed on the surface temperature were investigated. The temperature increases with the increase of the relative speed and pressure during the sliding period, and there is an interaction effect between pressure and speed on the surface temperature rise.

Appropriate simulation set parameters are the precondition to obtain accurate results; while the simulation results are affected by multiple factors, it is thus crucial to investigate the sensibility of different factors. This paper first analyses the application situation of numerical simulation software in the field of geotechnical engineering and finds that Fast Lagrangian analysis of continua in three dimensions (FLAC3D) has been widely used on roadways or tunnels. Then, taking the roadway excavation process as the engineering background, FLAC3D was used to create 171 schemes of different simulation parameters and analyze the influence of different factors on the simulation results. The findings show that there is a considerable difference in the degree of effect of different parameters on the simulation results. Most of the factors have a remarkable effect on the numerical simulation results (displacement and stress), and only some factors (parameter uniformity and density) have almost no effect on the results. Meanwhile, the trend of displacement and stress is opposite in most cases. In addition, some neglected factors can also have a considerable effect on the simulation results, such as the zone amount; therefore, it is necessary to avoid the variation of nonstudy factors as possible when carrying out the numerical simulation. This study may significantly assist concerned engineers and technicians in developing a more organized and thorough grasp of the impacts of various parameters on simulation outcomes.

The rock mass around an excavation is generally traversed by different geological discontinuities such as faults, folds, slips, joints, etc. Fault is one of the major geological discontinuities which creates lot of difficulties during underground winning of coal. Entire stress regime and ground conditions in the formation are altered in and around the faults. Faults also impose detrimental effects by introducing impurities, including clay and various forms of mineral matter into the coal seams; opening of pathways for the influx of water and gas into the underground workings; displacing the coal seams upward/downwards making the coal seams difficult or sometimes impractical to mine. Appropriate evaluation of the effect of the fault on the stability of the underground workings is a requisite for safe design of the underground mining structures. In this paper, a study has been carried out to assess the effect of the fault on the stability of underground coal mines by numerical simulation with distinct element method (DEM). On the calibrated DEM model, parametric study has been performed by varying the selected parameters, the dip and the friction angles of the fault. The analysis of variance (ANOVA) shows that both the factors have statistically significant effect on the strength of the coal pillar. Similarly, the displacement of the immediate roof and the height of the disturbed strata are evaluated by the DEM modelling and statistical analysis when the fault passes through the middle of the gallery. The results of ANOVA for both cases indicate that the both factors have significant effect on the displacement of the immediate roof and the height of the disturbed strata. It is obtained from the study that the low angle fault causes high instability in the immediate roof. The paper has been supplemented with the field observations where instability in underground roadways of a coal mine in India is caused by the fault. It was observed in VK-7 incline mine of Singareni Collieries Company Limited, India that there was sudden failure of immediate roof of a roadway where a low angle fault crosses the middle of the roadway. The findings of the paper help to understand the behaviour of the coal pillar and the surrounding rock mass in the presence of the fault. The study would also help to take appropriate decisions about the unstable regions of the working safeguarding safety in underground coal mines.

Chimney subsidence can cause surface subsidence (ground settlement) in the form of a pit or sag when there is a mine roof collapse in a mine entry. Surface subsidence occurs when the roof collapse propagates upward and does not choke itself off due to the associated volume expansion of the rubblized fallen materials and where no sufficiently competent rock is present to bridge the cavity. This paper contains a review and evaluation of reported case history data associated with occurrences of surface subsidence related to chimney subsidence. This analysis included investigating the chimney subsidence height potential including relative to the overburden rock conditions, extraction height, mine depth, the width of entry and the roof rock fall distance. Also, this paper provides a summary of the results of an assessment of the bridging capacity of various more common competent coal measures in the roof. This numerical analysis was performed considering linear arch conditions. Parameters which were investigated in this analysis included the competent roof rock strength, thickness, depth, and spanning distance.

This paper presents the development of a 2D finite difference modelling approach and a 3D finite element numerical model for simulating vertical geothermal heat exchangers (GHEs), explaining the theory governing the thermal processes, element discretization and the selection of the appropriate boundary conditions. Both of these models provide fully coupled solutions for the fluid flow in the circulation pipes and the thermal processes between the fluid and solid domains (pipes, grout and soil). The numerical models are verified with a field test and subsequently they are utilized to simulate the thermal performance of a borehole heat exchanger integrated with a single U-tube. Two different thermal operation cases are analyzed; a constant rate heat injection and a fluid injection at a constant temperature. A model validation study is also carried out for the constant rate heat injection case by comparing the numerical results with the available analytical solution for a finite line source. Furthermore, effective thermal conductivity of the ground back-calculated from the results of the numerical analyses is compared with the value used in the numerical models. Comparison of the results obtained from both numerical models and validating model predictions with the analytical solution confirms that both FE and FD models can accurately simulate the heat transfer mechanisms governing the thermal performance of GHE systems.

Under high dynamic load, roadway deformation and failure may occur, posing great challenges. As for now, few studies have been carried out on the impacts of various factors on the deformation of roadway surrounding rocks under high dynamic load, not to mention those on intelligent prediction of the deformation and failure laws. This paper fills these research gaps by studying the deformation and failure characteristics of roadway surrounding rocks and the intelligent prediction method under high dynamic load. The finite difference software Flac3D was used to analyze the influences of roadway buried depth, lithology, and side pressure coefficient on the stability of surrounding rocks and a model was constructed for deformation prediction under high dynamic load. Finally, the influence of various factors on the deformation and their weight was obtained and the deformation can be predicted in line with the BP neural network prediction theory. The results show that the prediction effect is good, with high accuracy.

This paper presents a set of new required programmes written in format data using the built-in programming FISH language available in three-dimensional Fast Lagrangian Analysis of Continua software (FLAC 3D ). These script data files were developed, to overcome difficulties noted during the nailed slope stability prediction. They established to analyse stability of general embankment slope cases under various soil nailing parameters design. To deal with 3D finite difference analysis results in terms of the factor of safety (FOS) and critical slip surface, both 2D finite difference and limit equilibrium (LEM) methods are also conducted. A comparison of the 3D and 2D results indicates that 2D analyses underestimate seriously stability predictions, notably in terms of the FOS. Therefore, it was concluded that, 3D analysis should be used as an alternative to the 2D analyses, even though it requires more time. Some useful conclusions are obtained from this work, which provides a good practice guidance for real life scenarios.

The drained and undrained response of soft clays reinforced with granular columns has been the subject of numerous geotechnical research efforts to date. Although these studies have been essential for the development of design methodologies, the actual/true response of reinforced clay systems under realistic loading rates is likely governed by partially drained conditions that have yet to be investigated. Partial drainage occurs as a result of inevitable radial flow from the clay to the columns throughout the loading phase. Ignoring the positive effect of partial drainage on the short-term stability of foundations and/or embankments on a clay substratum reinforced with free draining columns may lead to over conservative designs. The objective of this study is to investigate the impact of partial drainage on the response of soft clays reinforced with sand column groups. To address this issue, four partially drained triaxial tests were conducted at different strain rates on normally consolidated soft clays reinforced with dense sand columns in a square configuration. Results included the effect of partial drainage on the total deviatoric stress, excess pore water pressure dissipation, volumetric strain, and stress concentration ratio. The results were bracketed between the fully drained and fully undrained responses/graphs that served as upper and lower bounds, respectively. A plot of the normalized improvement index vs tfailure/t50 showed full mobilization of strength at a time ratio of 15. Numerical modeling using finite difference of the pore water pressure dissipation during shearing was conducted. The consolidation results obtained from the numerical analyses were compared to measurements from the experimental program. The calculated degree of consolidation from the finite difference analysis correlated very well with the measured levels of consolidation during the tests. The results from the test program and the associated analyses presented in this paper contribute to enhancing our current understanding of the response of reinforced clay systems and may be a step on the road towards improving existing design methodologies.