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.

A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.

Numerical Modelling of Coupled Heat and Mass Transfer in Porous Materials: Application to Cinder Block Bricks

In this work, we present numerical modelling of coupled heat and mass transfer within porous materials. Our study focuses on cinder block bricks generally used in building construction. The material is assumed to be placed in air. Moisture content and temperature have been chosen as the main transfer drivers and the equations governing these transfer drivers are based on the Luikov model. These equations are solved by an implicit finite difference scheme. A Fortran code associated with the Thomas algorithm was used to solve the equations. The results show that heat and mass transfer depend on the temperature of the air in contact with the material. As this air temperature rises, the temperature within the material increases, and more rapidly at the material surface. Also, thermal conductivity plays a very important role in the thermal conduction of building materials and influences heat and mass transfer in these materials. Materials with higher thermal conductivity diffuse more heat.

Numerical Models and Methods of Atmospheric Parameters Originating in the Formation of the Earth’s Climatic Cycle

Atmospheric models are physical equations based on the ideal gas law. Applied to the atmosphere, this law yields equations for water, vapor (gas), ice, air, humidity, dryness, fire, and heat, thus defining the model of key atmospheric parameters. The distribution of these parameters across the entire planet Earth is the origin of the formation of the climatic cycle, which is a normal climatic variation. To do this, the Earth is divided into eight (8) parts according to the number of key parameters to be defined in a physical representation of the model. Following this distribution, numerical models calculate the constants for the formation of water, vapor, ice, dryness, thermal energy (fire), heat, air, and humidity. These models vary in complexity depending on the indirect trigonometric direction and simplicity in the sum of neighboring models. Note that the constants obtained from the equations yield 275.156˚K (2.006˚C) for water, 273.1596˚K (0.00963˚C) for vapor, 273.1633˚K (0.0133˚C) for ice, 0.00365 in/s for atmospheric dryness, 1.996 in2/s for humidity, 2.993 in2/s for air, 1 J for thermal energy of fire, and 0.9963 J for heat. In summary, this study aims to define the main parameters and natural phenomena contributing to the modification of planetary climate. .

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.

Fracture of films caused by uniaxial tensions:a numerical model

Surface cracks are commonly observed in coatings and films.When structures with coatings are subject to stretching,opening mode cracks are likely to form on the surface,which may further lead to other forms of damage,such as interfacial delamination and substrate damage.Possible crack forms include cracks extending towards the interface and channeling across the film.In this paper,a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension.The energy release rate and structural stress intensity factors can be obtained accordingly,and the effects of geometry and material features on fracture characteristics are investigated,with most crack patterns being confirmed as unstable.The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films.The results from the numerical model are compared with those obtained by the finite element method(FEM),and the accuracy of the theoretical results is demonstrated.

Stiffness and Shear Stress Distribution of Glulam Beams in Elastic-Plastic Stage:Theory,Experiments and Numerical Modelling

Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to predict the stiffness and shear distribution of glulam beams in elastic-plastic stage,and consequently,the failure of such glulam beams cannot be predicted effectively.To address these issues,an analytical method considering material nonlinearity was proposed for glulam beams,and the calculating equations of deflection and shear stress distribution for different failure modes were established.The proposed method was verified by experiments and numerical models under the corresponding conditions.Results showed that the theoretical calculations were in good agreement with experimental and numerical results,indicating that the equations proposed in this paper were reliable and accurate for such glulam beams with wood material in the elastic-plastic stage ignoring the influence of mechanic properties in radial and tangential directions of wood.Furthermore,the experimental results reported by the previous studies indicated that the method was applicable and could be used as a theoretical reference for predicting the failure of glulam beams.

Zoning Evaluation of Hourly Precipitation in High-resolution Regional Numerical Models over Hainan Island

This study assesses the performance of three high-resolution regional numerical models in predicting hourly rainfall over Hainan Island from April to October for the years from 2020 to 2022.The rainfall amount,frequency,intensity,duration,and diurnal cycle are examined through zoning evaluation.The results show that the China Meteor-ological Administration Guangdong Rapid Update Assimilation Numerical Forecast System(CMA-GD)tends to forecast a higher occurrence of light precipitation.It underestimates the late afternoon precipitation and the occurrence of short-duration events.The China Meteorological Administration Shanghai Numerical Forecast Model System(CMA-SH9)reproduces excessive precipitation at a higher frequency and intensity throughout the island.It overestimates rainfall during the late afternoon and midnight periods.The simulated most frequent peak times of rainfall in CMA-SH9 are 0-1 hour deviations from the observed data.The China Meteorological Administration Mesoscale Weather Numerical Forecasting System(CMA-MESO)displays a similar pattern to rainfall observations but fails to replicate reasonable structure and diurnal variation of frequency-intensity.It underestimates the occurrence of long-duration events and overestimates related rainfall amounts from midnight to early morning.Notably,significant discrepancies are observed in the predictions of the three models for areas with complex terrain,such as the central,southeastern,and southwestern regions of Hainan Island.

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.

Field and numerical modelling on the stability of underground strata in longwall workings

The longwall method is one of the feasible and efficient underground mining methods for greater depth of workings.Recently,Singareni Collieries Company Limited(SCCL),the largest coal-producing government company in the Southern part of India,has deployed a high capacity(2×1152T capacity)power support system in its Adriyala Longwall Project(ALP)at a depth of 375 m.There was a concern about the stability of the longwall workings and the protective pillars.Thus,research work was carried out with the geotechnical instruments and numerical modelling tools to analyze the stability while retreating the longwall panels.The outcomes revealed that the convergence in the gate roads increased with the longwall face advancement and the area of exposure.The pressure of the powered support legs on the dip side was less than the rise side legs,which implies a stable roof condition over the longwall face.An abutment zone was identified ahead of the line of extraction up to 10e25 m and presumed from the Factor of Safety(FoS)criterion that within this zone,the longwall pillar possibly will be of better stability at every stage of extraction.The results obtained from this study would be helpful for the mining engineers to understand the behaviour of underground strata in longwall workings.

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.

Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media

To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.

Numerical modeling of tidal current of LNG terminal in Caofeidian,Bohai Sea

In order to reasonably simulate tidal currents around small structures such as piles in a large-scale model domain, a 2-D hydrodynamic integrated model for Bohai Sea is established with the finite element method. The grid can be discretionarily refined as a non-structure triangle or quadrilateral so that piers can be treated as one or several impermeable elements with an area of 20 to 30 km^2 in a model domain over 85 700 km^2. The computational results of tidal levels and horizontal velocities are in good agreement with the field data. Based on the computed results by the model, the layout of an open 105 DWT liquefied natural gas （LNG）terminal in Caofeidian, Bohal Sea is effectively and reasonably optimized. It can be concluded that the model is suitable and reasonable for direct simulation of tidal currents around small structures in projects.

Numerical modeling of PP- and PS-wave azimuthal anisotropy in HTI media

This study focuses on the factors that may affect the feasibility of performing elliptical anisotropy analysis on azimuthal PP and PS-wave data in HTI media, with the aim of using the modeling results as guidance in real seismic data application. Our results reveal that there is an offset limitation for both PP- and PS-waves in elliptical anisotropy fitting, and that PS-waves show a wider applicable offset range and larger observable azimuthal anisotropy than PP-waves. The major axis of the elliptical fit to the amplitudes of the R-component is perpendicular to the fracture strike, which is opposite to that in PP-wave analysis. The azimuthal interval travel time of PS-waves shows a nearly elliptical distribution and the major axis of the fit ellipse is perpendicular to the fracture strike, which is same as that in PP-wave analysis. For data within the applicable offset range, the anisotropic magnitude obtained from amplitude and travel time attributes of PP- and PS-waves exhibits a dependence on fracture density, and the major to minor axis ratio of the fit ellipse may be used to infer the relative distribution of fracture densities.

Numerical modeling of seabed morphological effects from the construction of artificial islands in Danzhou, Hainan

Haihua Islands is a large artificial island in Danzhou, Hainan. The construction of Haihua Islands changes the hYdrodynamic environment of Yangpu waters, and further affects its morphological change. Delft3D is used to set up a two dimensional nested hydrodynamic and sediment model for Yangpu waters in this paper, and this paper focuses on simulating the velocity and morphological change due to the construction of Haihua Islands after the verification of the model. The seabed deposition is small because of low suspended sediment concentration and less sand source near Yangpu waters. The bed level erodes in the south area of Xiaochan Reef and the Yangpu channel due to the velocity increase in the area.

Assessment of Numerical Models for Live Load Distribution in a Road Slab Bridge

This paper presents comparison of numerical models used in an analysis of a road bridge deck. The models were adapted for computing the live load distribution coefficients in composite concrete bridge deck. The load distribution method was chosen for assessment of the usability of different numerical model in slab bridge deck analysis. The goal of the study is to determine a simplest but still accurate numerical model to estimate live load effects on composite slab bridge. In the analysis, the well-established grillage approach was adapted for representation of the bridge deck as a basic model as well as more sophisticated three-dimensional models which was supposed to better represent the real behavior of the deck under concentrated wheel loads. The bridge deck was effectively modeled using beam and shell elements. The grillage method compares well with the finite-element method. This finding is allowed to establish simplification in numerical modeling of slab bridge decks for live load effect computations.

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.

Numerical modelling of structural controls on fluid flow and mineralization

This paper presents the results of a set of numerical models focussing on structural controls on hydrothermal mineralization. We first give an overview of natural phenomena of structurally-controlled ore formation and the background theory and mechanisms for such controls. We then provide the results of a group of simple 2D numerical models validated through comparison with Cu-vein structure observed near the Shilu Copper deposit （Yangchun, Guangdong Province, China） and finally a case study of 3D numerical modelling applied to the Hodgkinson Province in North Queensland （Australia）. Two modelling approaches, discrete deformation modelling and continuum coupled deformation and fluid flow modelling, are involved. The 2D model-derived patterns are remarkably consistent with the Cu-vein structure from the Shilu Copper deposit, and show that both modelling approaches can realistically simulate the mechanical behaviours of shear and dilatant fractures. The continuum coupled deformation and fluid flow model indicates that pattern of the Cu- veins near the Shilu deposit is the result of shear strain localization, development of dilation and fluid focussing into the dilatant fracture segments. The 3D case-study models （with deformation and fluid flow coupling） on the Hodgkinson Province generated a number of potential gold mineralization