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.

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model, a quasi-3D numerical model is established for coastal regions of shallow water. The characteristics of this model are that the velocity profiles;can be obtained at the same time when the equations of the value of difference between the horizontal current velocity and its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent with the results of the 2D, model. The circulating flow in the rectangular area induced by wind is simulated and applied to the tidal flow field of the radial sandbanks in the South Yellow Sea. The computational results from this quasi-3D model are in good agreement with analytical results and observed data. The solution of the finite difference equations has been found to be stable, and the model is simple, effective and practical.

Image processing based three-dimensional model reconstruction for cross-platform numerical simulation

Numerical simulation is the most powerful computational and analysis tool for a large variety of engineering and physical problems.For a complex problem relating to multi-field,multi-process and multi-scale,different computing tools have to be developed so as to solve particular fields at different scales and for different processes.Therefore,the integration of different types of software is inevitable.However,it is difficult to perform the transfer of the meshes and simulated results among software packages because of the lack of shared data formats or encrypted data formats.An image processing based method for three-dimensional model reconstruction for numerical simulation was proposed,which presents a solution to the integration problem by a series of slice or projection images obtained by the post-processing modules of the numerical simulation software.By means of mapping image pixels to meshes of either finite difference or finite element models,the geometry contour can be extracted to export the stereolithography model.The values of results,represented by color,can be deduced and assigned to the meshes.All the models with data can be directly or indirectly integrated into other software as a continued or new numerical simulation.The three-dimensional reconstruction method has been validated in numerical simulation of castings and case studies were provided in this study.

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hangzhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG)terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.

Numerical Simulation of Injection Molding Cooling Process Based on 3D Surface Model

The design of the cooling system of injection molds directly affects both productivity and the quality of the final part. Using the cooling process CAE system to instruct the mold design, the efficiency and quality of design can be improved greatly. At the same time, it is helpful to confirm the cooling system structure and optimize the process conditions. In this paper, the 3D surface model of mold cavity is used to replace the middle-plane model in the simulation by Boundary Element Method, which break the bottleneck of the application of the injection molding simulation softwares base on the middle-plane model. With the improvements of this paper, a practical and commercial simulation software of injection molding cooling process named as HsCAE3D6.0 is developed.

Meshing effects of the 3-D FEM numerical modeling in seismo-electromagnetics:An application in selectivity of seismic electric signal (SES)

We investigated how density and quality of mesh around interest domain affect electromagnetic （EM） responses of 3D Earth layered media using finite element method （FEM）. Effect of different mesh shapes was also investigated using a method of mixing structured and unstructured mesh. As a case study, we estimated the effects of meshing on selectivity phenomenon of seismic electric signal （SES）. Our results suggest that the relative errors resulting from mesh effects may not be negligible, which may lead to some unconvincing explanation of the SES selectivity based on the numerical modeling results.

2D Coupled 3D:A New Numerical Model for Dual - Structured - Aquifer System

This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -3D ) is presented in the Present paper,which is the most suitable one for the dual - structured - aquifer system. An example of Wenyinghu area is shown.By using the 2D-3D model, a satisfied result of the simulated area is achieved.

Sensitivity of Lagrangian Particle Tracking Based on a 3D Numerical Model

The aim of the paper is to investigate in detail the sensitivity of particles displacement based on method of Lagrangian particle tracking in combination with a 3D Eulerian numerical model that was developed by the first author, namely FSUM. The characteristic parameters used for this research include the possibilities of random movement, settling velocity of solid particle, horizontal and vertical diffusion coefficients and condition of particle fixed with a constant distance under water surface. The first part is on the fluid flow model. It includes 3D Navier-Stokes equations together with the initial and boundary conditions that were numerically solved with the finite difference method and coded with FORTRAN 90/95 using parallel technique with OpenMP. A semi-Lagrangian treatment of the advective terms was used. The second part is related to Lagrangian particle tracking model and was solved with the fourth Runge-Kutta method. Model was applied for Strait of Johor and has been calibrated by using measured data on water level and velocity at one station. Eight cases of simulations with many different options were carried out. Through computed cases it shows that random term and settling velocity are very important factors for the behavior of particle trajectory. Although the random diffusion is minor in comparison with flow velocity, but it can rearrange the initial distribution of particles then the cluster of particles become more dispersive during the process of movement. In addition, introducing settling velocity of particle makes a big change on the trajectory of particle that becomes more suitable to sediment transport. The study gave a comprehensive picture on particle movement. The model also showed its possibilities of multiform applications in simulation and prediction for the different problems in practice.

Temperature Distributions in Single Cell of Polymer Electrolyte Fuel Cell Simulated by an 1D Multi-plate Heat-Transfer Model and a 3D Numerical Simulation Model

The purpose of this study is to verify an 1D multi-plate heat-transfer model estimating the temperature distribution on the interface between polymer electrolyte membrane and catalyst layer at cathode in single cell of polymer electrolyte fuel cell, which is named as reaction surface in this study, with a 3D numerical simulation model solving many governing equations on the coupling phenomena in the cell. The results from both models/simulations agreed well. The effects of initial operation temperature, flow rate, and relative humidity of supply gas on temperature distribution on the reaction surface were also investigated. It was found in both 1D and 3D simulations that, the temperature rise （i.e., Treact-Tini） of the reaction surface from initial operation temperature at 70℃ was higher than that at 80℃ irrespective of flow rate of supply gas. The effect of relative humidity of supply gas on Treact- Tini near the inlet of the cell was small. Compared to the previous studies conducted under the similar operation conditions, the Treact - Tini calculated by 1D multi-plate heat-transfer model in this study as well as numerical simulation using 3D model was reasonable.

A three-dimensional numerical study on the effect of geometric asymmetry on arcjet thruster performance

In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.

Loading characteristics of mechanical rib bolts determined through testing and numerical modeling

Underground coal mines use mechanical bolts in addition to other types of bolts to control the rib deformation and to stabilize the yielded coal ribs.Limited research has been conducted to understand the performance of the mechanical bolts in coal ribs.Researchers from the National Institute for Occupational Safety and Health(NIOSH)conducted this work to understand the loading characteristics of mechanical bolts(stiffness and capacity)installed in coal ribs at five underground coal mines.Standard pull-out tests were performed in this study to define the loading characteristics of mechanical rib bolts.Different installation torques were applied to the tested bolts based on the strength of the coal seam.A typical tri-linear load-deformation response for mechanical bolts was obtained from these tests.It was found that the anchorage capacity depended mainly on the coal strength.Guidelines for modeling mechanical bolts have been developed using the tri-linear load-deformation response.The outcome of this research provides essential data for rib support design.

Optimization of room-and-pillar dimensions using automated numerical models

This paper presents an optimization methodology for the geometric configuration of a room–and–pillar mining project,considering safety and operational restrictions while maximizing ore recovery.An underground manganese mine was chosen as a case study to investigate the capabilities of the presented methodology.A software package(OPTIMINE)was implemented to address the computational demand in an automated manner.Three–dimensional finite difference analyses were performed in FLAC3D and used as implicit functions to consider safety in terms of the factor of safety and room convergence.The obtained results showed that recovery could be increased from 44%to more than 80%in a safe manner.

Numerical investigation of rock dynamic fragmentation during rockslides using a coupled 3D FEM-DEM method

Rockslides are one of the most common geological hazards in mountainous areas and can pose significant threats to the safety of human lives and infrastructures. Studying the dynamic fragmentation process, and fragment characteristics of rock blocks during rockslides is of great significance. In this study,the influences of the slope angle on the dynamic fragmentation process, damage and energy evolution,and the fragments’ flying velocity and flying angle were systematically investigated using a coupled 3D FEM-DEM method. An improved fragment search algorithm was first proposed to more effectively extract the information of the fragments after impacting. The input parameters in the numerical modeling were carefully calibrated based on the quasi-static uniaxial compression tests and the rockimpact tests. The complex fragmentation process of rock block sliding along an inclined slope was simulated. The results indicate that the fragmentation intensity gradually increases with increasing the slope angle, and the fragmentation intensity of the front region of the rock block is always higher than that of the rear region. Additionally, the slope angle can significantly affect the damage ratio, energy dissipation, and the ratio of tensile crack to shear crack during the rockslides. The number of the fragments having higher flying velocities and larger flying angles increases with increasing the slope angle,which contributes to a larger spreading distance and a wider deposition area.

Benchmarking of two three-dimensional numerical models in time/space domain to predict railway-induced ground vibrations

In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

Novel modeling on numerical computing the geo-deformation information in coalmine based on the GIS-Excel

Numerical simulation modeling is a hotspot in the geological engineering computing field. Tak- ing a fast Langrangian analysis of continua in 3 dimensions （FLAC3D） numerical modeling on com- puting the geo-deformation information caused by the mining subsidence in a coalmine for example, a new GIS-Excel modeling method is proposed to build geologic strata within the simulation range combined with the coal-seam dip angle of the underground mining working-planes. First of all, the coal-seam model of the numerical computing is built by using the geographic information system （GIS） according to the stripe-through principle and the calculating formula on the size of the model blocks in the paper defined, then the FLAC3D numerical computing model of all geologic strata with- in the simulation range is also built based on the calculating formula of thickness of each stratum and the Excel fast computing advantages. The GIS-Excel method is good at the higher modeling accuracy, seldom making mistakes and consuming less time. The reliability and validity of the method is veri- fied well by its practical applications in the coalmine area.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OVER DREDGED TRENCHES

A 3- D free surface flow in open channels based on the Reynolds equations with the k-ε turbulence closure model is presented in this paper. Insted of the 'rigid lid' approximation, the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

Three Dimensional Numerical Modeling of Flow and Pollutant Transport in a Flooding Area of 2008 US Midwest Flood

This paper presents the development and application of a three-dimensional numerical model for simulating the flow field and pollutant transport in a flood zone near the confluence of the Mississippi River and Iowa River during the US Midwest Flood in 2008. Due to a prolonged precipitation event, a levee along the Iowa River just upstream of Oakville, Iowa broke, and the small town was completely flooded for a couple of weeks. During this period, the high water level in the flood zone reached about 2.5 metersabove the ground, and wind was the major force for the flow circulation. It was observed that some pollutants were leaked from the residential and farming facilities and transported into the flood zone. Leaking of pollutants from these facilities was reported by different news media during the flood and was identified using high resolution satellite imagery. The developed 3D numerical model was first validated using experimental measurements, and then applied to the flood inundated zone in Oakville for simulating the unsteady hydrodynamics and pollutant transport. The simulated pollutant distributions were generally in good agreement with the observed data obtained from satellite imagery.