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 simulation of microwave-induced cracking and melting of granite based on mineral microscopic models

This study introduces a coupled electromagnetic–thermal–mechanical model to reveal the mechanisms of microcracking and mineral melting of polymineralic rocks under microwave radiation.Experimental tests validate the rationality of the proposed model.Embedding microscopic mineral sections into the granite model for simulation shows that uneven temperature gradients create distinct molten,porous,and nonmolten zones on the fracture surface.Moreover,the varying thermal expansion coefficients and Young's moduli among the minerals induce significant thermal stress at the mineral boundaries.Quartz and biotite with higher thermal expansion coefficients are subjected to compression,whereas plagioclase with smaller coefficients experiences tensile stress.In the molten zone,quartz undergoes transgranular cracking due to theα–βphase transition.The local high temperatures also induce melting phase transitions in biotite and feldspar.This numerical study provides new insights into the distribution of thermal stress and mineral phase changes in rocks under microwave irradiation.

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.

Resistance of full-scale beams against close-in explosions.Numerical modeling and field tests

This paper explores the performances of a finite element simulation including four concrete models applied to a full-scale reinforced concrete beam subjected to blast loading. Field test data has been used to compare model results for each case. The numerical modelling has been, carried out using the suitable code LS-DYNA. This code integrates blast load routine(CONWEP) for the explosive description and four different material models for the concrete including: Karagozian & Case Concrete, Winfrith, Continuous Surface Cap Model and Riedel-Hiermaier-Thoma models, with concrete meshing based on 10, 15, and 20 mm. Six full-scale beams were tested: four of them used for the initial calibration of the numerical model and two more tests at lower scaled distances. For calibration, field data obtained employing pressure and accelerometers transducers were compared with the results derived from the numerical simulation. Damage surfaces and the shape of rupture in the beams have been used as references for comparison. Influence of the meshing on accelerations has been put in evidence and for some models the shape and size of the damage in the beams produced maximum differences around 15%. In all cases, the variations between material and mesh models are shown and discussed.

Unified numerical predictor-corrector guidance based on characteristic model

Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of trying.A unified numerical predictor-corrector guidance method based on characteristic models for aerocapture is proposed.The numerical predictor-corrector guidance method is used to achieve autonomy and high accuracy,and the characteristic model control method is introduced to achieve robustness.At the same time,by transforming path constraints,characteristic model equations including apogee deviation and altitude differentiation are established.Based on the characteristic model equations,a unified guidance law which can satisfy path constraints and guidance objectives simultaneously is designed.In guidance problems,guidance deviation is not directly obtained from the output of the dynamics at present,but is calculated through integral and algebraic equations.Therefore,the method of directly discretizing differential equations cannot be used to establish characteristic models,which brings great difficulty to characteristic modeling.A method for characteristic modeling of guidance problems is proposed,and convergence analysis of the proposed guidance law is also provided.Finally,a joint numerical simulation of guidance and control considering navigation deviation and various uncertainties is conducted to verify the effectiveness of the proposed method.The proposed unified method can be extended to general aerodynamic entry guidance designs,providing theoretical and methodological support for them.

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike.

Numerical analysis of high‑speed railway slab tracks using calibrated and validated 3D time‑domain modelling

Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.

Explosion resistance performance of reinforced concrete box girder coated with polyurea:Model test and numerical simulation

To study the anti-explosion protection effect of polyurea coating on reinforced concrete box girder,two segmental girder specimens were made at a scale of 1:3,numbered as G(without polyurea coating)and PCG(with polyurea coating).The failure characteristics and dynamic responses of the specimens were compared through conducting explosion tests.The reliability of the numerical simulation using LS-DYNA software was verified by the test results.The effects of different scaled distances,reinforcement ratios,concrete strengths,coating thicknesses and ranges of polyurea were studied.The results show that the polyurea coating can effectively enhance the anti-explosion performance of the girder.The top plate of middle chamber in specimen G forms an elliptical penetrating hole,while that in specimen PCG only shows a very slight local dent.The peak vertical displacement and residual displacement of PCG decrease by 74.8% and 73.7%,respectively,compared with those of specimen G.For the TNT explosion with small equivalent,the polyurea coating has a more significant protective effect on reducing the size of fracture.With the increase of TNT equivalent,the protective effect of polyurea on reducing girder displacement becomes more significant.The optimal reinforcement ratio,concrete strength,thickness and range of polyurea coating were also drawn.

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. .

A Third-Order Scheme for Numerical Fluxes to Guarantee Non-Negative Coefficients for Advection-Diffusion Equations

According to Godunov theorem for numerical calculations of advection equations, there exist no high-er-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. In case of advection-diffusion equations, so far there have been not found stable schemes with positive difference coefficients in a family of numerical schemes exceeding the second-order accuracy. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter by using the same stencil number as convemtional third-order shemes such as KAWAMURA and UTOPIA schemes. We extend the present method into multi-dimensional equations. Numerical experiments for linear and nonlinear advection-diffusion equations were performed and the present scheme’s applicability to nonlinear Burger’s equation was confirmed.

Numerical study of fatigue damage of asphalt concrete using cohesive zone model

In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is established to indicate the gradual degradation of cohesive properties of asphalt concrete under cyclic loading. Then the model is implemented in the finite element software ABAQUS through a user-defined subroutine. Based on the proposed model, an indirect tensile fatigue test is finally simulated. The fatigue lives obtained through numerical analysis show good agreement with laboratory results. Fatigue damage accumulates in a nonlinear manner during the cyclic loading process and damage initiation phase is the major part of fatigue failure. As the stress ratio increases, the time of the steady damage growth stage decreases significantly. It is found that the proposed fatigue damage evolution model can serve as an accurate and efficient tool for the prediction of fatigue damage of asphalt concrete.

The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model

Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wave-field simulation in the porous medium is limited to two-dimensions and two-components （2D2C） or two-dimensions and three-components （2D3C）. There is no previous report on wave simulation in three- dimensions and three-components. Only through three dimensional numerical simulations can we have an overall understanding of wave field coupling relations and the spatial distribution characteristics between the solid and fluid phases in the dual-phase anisotropic medium. In this paper, based on the BISQ equation, we present elastic wave propagation in a three dimensional dual-phase anisotropic medium simulated by the staggered-grid high-order finite-difference method. We analyze the resulting wave fields and show that the results are an improvement.

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.

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.

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 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.