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.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Numerical modeling of destress blasting for strata separation

Destress blasting(DB)implemented along the perimeter of safety pillars is a special application of destressing in coal longwall mining.The goal is to separate relatively more deformed mined areas from safety pillars,such as shaft pillars or cross-cut pillars,to reduce the transfer of high stresses to the protective pillar.This case study aims to numerically simulate selected destress blasts in the Czech part of the Upper Silesian Coal Basin and examine its impact on stress transfer to the safety pillar area.To separate the area between the protective pillar and the longwall(LW),two fans of five 93-mm blast holes(length of 93e100 m)were drilled from the gate roads into the overburden strata.Each set of blast holes was fired separately in two stages without time delay.The explosive charge(gelatin-type of explosive)of each stage is 3450 kg.The two DB stages were fired when the longwall face was approximately 158 m and 152 m away from the blast.A 3D mine-wide model is built and validated with in situ stress measured with hydrofracturing.Mining and destressing in three 5-m thick coal seams are simulated in the region.Numerical modeling of DB is successfully conducted using a rock fragmentation factor a of 0.05 and a stress reduction/dissipation factor β of 0.95.Buffering of transfer of additional stress from the mining area into the safety pillar is evaluated by comparison of yielding volume before and after DB.It is shown that yielding volume drops after DB by nearly 80%in the area of the destressing panel and near the safety shaft pillar.

Flow-Induced Clogging in Microfiltration Membranes: Numerical Modeling and Parametric Study

Microfiltration membrane technology has been widely used in various industries for solid-liquid separation. However, pore clogging remains a persistent challenge. This study employs (CFD) and discrete element method (DEM) models to enhance our understanding of microfiltration membrane clogging. The models were validated by comparing them to experimental data, demonstrating reasonable consistency. Subsequently, a parametric study was conducted on a cross-flow model, exploring the influence of key parameters on clogging. Findings show that clogging is a complex phenomenon affected by various factors. The mean inlet velocity and transmembrane flux were found to directly impact clogging, while the confinement ratio and cosine of the membrane pore entrance angle had an inverse relationship with it. Two clog types were identified: internal (inside the pore) and external (arching at the pore entrance), with the confinement ratio determining the type. This study introduced a dimensionless number as a quantitative clogging indicator based on transmembrane flux, Reynolds number, filtration time, entrance angle cosine, and confinement ratio. While this hypothesis held true in simulations, future studies should explore variations in clogging indicators, and improved modeling of clogging characteristics. Calibration between numerical and physical times and consideration of particle volume fraction will enhance understanding.

A Heavy Sea Fog Event over the Yellow Sea in March 2005: Analysis and Numerical Modeling

In this paper, a heavy sea fog episode that occurred over the Yellow Sea on 9 March 2005 is investigated. The sea fog patch, with a spatial scale of several hundred kilometers at its mature stage, reduced visibility along the Shandong Peninsula coast to 100 m or much less at some sites. Satellite images, surface observations and soundings at islands and coasts, and analyses from the Japan Meteorology Agency （JMA） axe used to describe and analyze this event. The analysis indicates that this sea fog can be categorized as advection cooling fog. The main features of this sea fog including fog area and its movement axe reasonably reproduced by the Fifth-generation Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model （MM5）. Model results suggest that the formation and evolution of this event can be outlined as： （1） southerly warm/moist advection of low-level air resulted in a strong sea-surface-based inversion with a thickness of about 600 m; （2） when the inversion moved from the warmer East Sea to the colder Yellow Sea, a thermal internal boundary layer （TIBL） gradually formed at the base of the inversion while the sea fog grew in response to cooling and moistening by turbulence mixing; （3） the sea fog developed as the TIBL moved northward and （4） strong northerly cold and dry wind destroyed the TIBL and dissipated the sea fog. The principal findings of this study axe that sea fog forms in response to relatively persistent southerly waxm/moist wind and a cold sea surface, and that turbulence mixing by wind shear is the primary mechanism for the cooling and moistening the marine layer. In addition, the study of sensitivity experiments indicates that deterministic numerical modeling offers a promising approach to the prediction of sea fog over the Yellow Sea but it may be more efficient to consider ensemble numerical modeling because of the extreme sensitivity to model input.

Examining the effect of adverse geological conditions on jamming of a single shielded TBM in Uluabat tunnel using numerical modeling

Severe shield jamming events have been reported during excavation of Uluabat tunnel through adverse geological conditions, which resulted in several stoppages at advancing a single shielded tunnel boring machine(TBM). To study the jamming mechanism, three-dimensional(3D) simulation of the machine and surrounding ground was implemented using the finite difference code FLAC3D. Numerical analyses were performed for three sections along the tunnel with a higher risk for entrapment due to the combination of overburden and geological conditions. The computational results including longitudinal displacement contours and ground pressure profiles around the shield allow a better understanding of ground behavior within the excavation. Furthermore, they allow realistically assessing the impact of adverse geological conditions on shield jamming. The calculated thrust forces, which are required to move the machine forward, are in good agreement with field observations and measurements. It also proves that the numerical analysis can effectively be used for evaluating the effect of adverse geological environment on TBM entrapments and can be applied to prediction of loads on the shield and preestimating of the required thrust force during excavation through adverse ground conditions.

Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation(Em)is one of the most important design parameters in designing many structures in and on rock.This parameter can be obtained by in situ tests,empirical relations between deformation modulus and rock mass classifcation,and estimating from laboratory tests results.In this paper,a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming(GP)and numerical modeling.A database of 40,960 datasets,including vertical stress(rz),horizontal to vertical stresses ratio(k),Poisson’s ratio(m),radius of circular tunnel(r)and wall displacement of circular tunnel on the horizontal diameter(d)for input parameters and modulus of deformation for output,was established.The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries.The resulting RMSE of 0.86 and correlation coeffcient of97%of the proposed equation demonstrated the capability of the computer program(CP)generated by GP.

Numerical modeling of wave equation by a truncated high-order finite-difference method

Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.

Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates

The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear co- ordinates show good agreemenl with the data obtained in three typical physical expedments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.

Numerical modeling for rockbursts:A state-of-the-art review

As the depth of excavation increases,rockburst becomes one of the most serious geological hazards damaging equipment and facilities and even causing fatalities in mining and civil engineering.This has forced researchers worldwide to identify different methods to investigate rockburst-related problems.However,some problems,such as the mechanisms and the prediction of rockbursts,continue to be studied because rockburst is a very complicated phenomenon influenced by the uncertainty and complexity in geological conditions,in situ stresses,induced stresses,etc.Numerical modeling is a widely used method for investigating rockbursts.To date,great achievements have been made owing to the rapid development of information technology(IT)and computer equipment.Hence,it is necessary and meaningful to conduct a review of the current state of the studies for rockburst numerical modeling.In this paper,the categories and the origin of different numerical approaches employed in modeling rockbursts are reviewed and the current usage of various numerical modeling approaches is investigated by a literature research.Later,a state-of-the-art review is implemented to investigate the application of numerical modeling in the mechanism study,and prediction and prevention of rockbursts.The main achievements and problems are highlighted.Finally,this paper discusses the limitations and the future research of numerical modeling for rockbursts.An approach is proposed to provide researchers with a systematic and reasonable numerical modeling framework.

Numerical modeling of deep-seated landslides interacting with man-made structures

This paper describes the interaction between deep-seated landslides and man-made structures such as dams, penstocks, viaducts, and tunnels. Selected case studies are reported first with the intent to gain insights into the complexities associated with the interaction of these structures with deep-seated landslides(generally referred to as deep-seated gravity slope deformations, DSGSDs). The main features, which characterize these landslides, are mentioned together with the interaction problems encountered in each case. Given the main objective of this paper, the numerical modeling methods adopted are outlined as means for increase in the understanding of the interaction problems being investigated. With the above in mind, the attention moves to an important and unique case history dealing with the interaction of a large-size twin-tunnel excavated with an earth pressure balance(EPB)tunnel boring machine(TBM) and a deep-seated landslide, which was reactivated due to the stress changes induced by tunnel excavation in landslide shear zone. The geological and geotechnical conditions are described together with the available monitoring data on the landslide movements, based on the advanced and conventional monitoring tools used. Numerical modeling is illustrated as an aid to back-analyze the monitored surface and subsurface deformations and to assist in finding the appropriate engineering solution for putting the tunnel into service and as a follow-up means for future understanding and control of the interaction problems. The simulation is based on a novel time-dependent model representing the landslide behavior.

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

Numerical Modeling of Basin-Range Tectonics Related to Continent-Continent Collision

Continent-continent collision is the most important driving mechanism for the occurrence of various geological processes in the continental lithosphere. How to recognize and determine continent-continent collision, especially its four-dimensional temporal-spatial evolution, is a subject that geological communities have long been concerned about and studied. Continent-continent collision is mainly manifested by strong underthrusting (subduction) of the underlying block along an intracontinental subduction zone and continuous obduction (thrusting propagation) of the overlying block along the intracontinental subduction zone, the occurrence of a basin-range tectonic framework in a direction perpendicular to the subduction zone and the flexure and disruption of the Moho. On the basis of numerical modeling, the authors discuss in detail the couplings between various amounts and rates of displacement caused by basin subsidence, mountain uplift and Moho updoming and downflexure during obduction (thrusting propagation) and subduction and the migration pattern of basin centers. They are probably indications or criteria for judgment or determination of continent-continent collision.

Evaluation of behaviors of earth and rockfill dams during construction and initial impounding using instrumentation data and numerical modeling

In this study,the behavior of Gavoshan dam was evaluated during construction and the first impounding.A two-dimensional（2D） numerical analysis was conducted based on a finite difference method on the largest cross-section of the dam using the results of instrument measurements and back analysis.These evaluations will be completed in the case that back analysis is carried out in order to control the degree of the accuracy and the level of confidence of the measured behavior since each of the measurements could be controlled by comparing it to the result obtained from the numerical model.Following that,by comparing the results of the numerical analysis with the measured values,it is indicated that there is a proper consistency between these two values.Moreover,it was observed that the dam performance was suitable regarding the induced pore water pressure,the pore water pressure ratio r;,settlement,induced stresses,arching degree,and hydraulic fracturing probability during the construction and initial impounding periods.The results demonstrated that the maximum settlement of the core was 238 cm at the end of construction.In the following 6 years after construction（initial impounding and exploitation period）,the accumulative settlement of the dam was 270 cm.It is clear that 88% of the total settlement of the dam took place during dam construction.The reason is that the clay core was smashed in the wet side,i.e.the optimum moisture content.Whereas the average curving ratio was 0.64 during dam construction; at the end of the initial impounding,the maximum amount of curving ratio in the upstream was 0.81,and the minimum（critical） amount in the downstream was 0.52.It was also concluded that this dam is safe in comparison with the behaviors of other similar dams in the world.

An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases： 1） tidal forcing, 2） seiche oscillation, 3） wind setup in a closed bay, and 4） onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters.

Numerical modeling of tectonic stress field and fault activity in North China

On the basis of a 3-dimension visco-elastic finite element model of lithosphere in North China, we numerically simulate the recent mutative figures of tectonic stress field. Annual change characteristics of stress field are： 1 ） Maximum principal tensile stress is about 3 -9 kPaa-1 and its azimuth lie in NNW-SSE. 2） Maximum principal compressive stress is about 1 - 6 kPaa-1 and its azimuth lie in NEE-SWW. 3 ） Maximum principal tensile stress is higher both in the west region and Liaoning Province. 4） Variation of tectonic stress field benefits fault movement in the west part and northeast part of North China. 5 ）Annual accumulative rates of Coulomb fracture stress in Tanlu fault belt have segmentation patterns： Jiashan-Guangji segment is the high- est （6 kPaa - 1 ） , Anshan-Liaodongwan segment is the second （5 kPaa - l ） , and others are relatively lower （ 3 - 4 kPaa-1 ）.

Three-Dimensional Numerical Modeling of an Ar-N_2 Plasma Arc Inside a Non-Transferred Torch

A three-dimensional numerical model is developed to study the behaviour of an argon-nitrogen plasma arc inside a non-transferred torch. In this model, both the entire cathode and anode nozzle are considered to simulate the plasma arc. The argon-nitrogen plasma arc is simulated for different arc currents and gas flow rates of argon. Various combinations of arc core radius and arc length, which correspond to a given torch power, are predicted. A most feasible combination of the same, which corresponds to an actual physical situation of the arc inside the torch, is identified using the thermodynamic principle of minimum entropy production for a particular torch power. The effect of the arc current and gas flow rate on the plasma arc characteristics and torch efficiency is explained. The effect of the nitrogen content in the plasma gas on the torch power and efficiency is clearly detected. Predicted torch efficiencies are comparable to the measured ones and the effect of the arc current and gas flow rate on predicted and measured efficiencies is almost similar. The efficiency of the torch, cathode and anode losses and core temperature and velocity at the nozzle exit are reported for five different cases.

Numerical modeling of metamorphic core complex formation:Implications for the destruction of the North China Craton

Widespread magmatism, metamorphic core complexes(MCCs), and significant lithospheric thinning occurred during the Mesozoic in the North China Craton(NCC). It has been suggested that the coeval exhumation of MCCs with uniform northwest-southeast shear senses and magmatism probably resulted from a decratonization event during the retreat of the paleo-Pacific Plate. Here we used two-dimensional finite element thermomechanical numerical models to investigate critical parameters controlling the formation of MCCs under far-field extensional stress. We observed three end-member deformation modes: the MCC mode, the symmetric-dome mode, and the pure-shear mode. The MCC mode requires a Moho temperature of ≥700 ℃ and an extensional strain rate of ≥5 × 10^(-16)s^(-1), implying that the lithosphere had already thinned when the MCC was formed in the Mesozoic. Considering that the widespread MCCs have the same northwest-southeast extension direction in the NCC, we suggest that the MCCs are surface expressions of both large-scale extension and craton destruction and that rollback of the paleo-Pacific slab might be the common driving force.

Numerical modeling and simulation of PEM fuel cells: Progress and perspective

This paper provides a comprehensive review on the research and development in multi-scale numerical modeling and simulation of PEM fuel cells. An overview of recent progress in PEM fuel cell modeling has been provided. Fundamental transport phenomena in PEM fuel cells and the corresponding mathematical formulation of macroscale models are analyzed. Various important issues in PEM fuel cell modeling and simulation are examined in detail, including fluid flow and species transport, electron and proton transport, heat transfer and thermal management, liquid water transport and water management, transient response behaviors, and cold-start processes. Key areas for further improvements have also been discussed.