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.

A NUMERICAL MODEL OF LEFT VENTRICLE AND AORTIC VALVE FUNCTION OF ITS AFTERLOAD(Ⅰ)

Due to the study of the function of heart and aoritic valve, we set up a physicalmodel of left ventricle, aortic valve and afterload and derive theoretical equation of each part from the model. Then we calculate the hasic equations within phystology and impair parameters. Bwsed on this, we will discus fully in the next paper the effectofleyt ventricular afterloadon valve opining, ejection and valve Jumction .etc

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

An Improved Coupling of Numerical and Physical Models for Simulating Wave Propagation

An improved coupling of numerical and physical models for simulating 2D wave propagation is developed in this paper. In the proposed model, an unstructured finite element model （FEM） based Boussinesq equations is applied for the numerical wave simulation, and a 2D piston-type wavemaker is used for the physical wave generation. An innovative scheme combining fourth-order Lagrange interpolation and Runge-Kutta scheme is described for solving the coupling equation. A Transfer function modulation method is presented to minimize the errors induced from the hydrodynamic invalidity of the coupling model and/or the mechanical capability of the wavemaker in area where nonlinearities or dispersion predominate. The overall performance and applicability of the coupling model has been experimentally validated by accounting for both regular and irregular waves and varying bathymetry. Experimental results show that the proposed numerical scheme and transfer function modulation method are efficient for the data transfer from the numerical model to the physical model up to a deterministic level.

Functionalized Data Operator Model for System Analysis and Forecasting

A deconvolution data processing is developed for obtaining a Functionalized Data Operator (FDO) model that is trained to approximate past and present, input-output data relations. The FDO model is designed to predict future output features for deviated input vectors from any expected, feared of conceivable, future input for optimum control, forecast, or early-warning hazard evaluation. The linearized FDO provides fast analytical, input-output solution in matrix equation form. If the FDO is invertible, the necessary input for a desired output may be explicitly evaluated. A numerical example is presented for FDO model identification and hazard evaluation for methane inflow into the working face in an underground mine: First, a Physics-Based Operator (PBO) model to match monitored data. Second, FDO models are identified for matching the observed, short-term variations with time in the measured data of methane inflow, varying model parameters and simplifications following the parsimony concept of Occam’s Razor. The numerical coefficients of the PBO and FDO models are found to differ by two to three orders of magnitude for methane release as a function of short-time barometric pressure variations. As being data-driven, the significantly different results from an FDO versus PBO model is either an indication of methane release processes poorly understood and modeled in PBO, missing some physics for the pressure spikes;or of problems in the monitored data fluctuations, erroneously sampled with time;or of false correlation. Either way, the FDO model is originated from the functionalized form of the monitored data, and its result is considered experimentally significant within the specified RMS error of model matching.

Physical and numerical modelling of biomimetic approaches of natural hydrophobic surfaces

Physical and numerical models of the hydrophobic and self-cleaning characteristics of an object surface are developed, and a micro/meso scope numerical approach and simulation based on the lattice Boltzmann method (LBM) is achieved. The modelling focuses on surface tension dominated behaviour of water droplets in air spreading on hydrophilic surface with hydrophobic strips of different sizes and contact angles under different physical and interfacial conditions. Applying the LBM model, the drop-lets behaviours on heterogeneous partial wetting surfaces are studied and simulated. In the simulations, the interactions between the fluid-fluid interface and the partial wetting wall are typically considered; the phenomena of droplets spreading and breaking up, as well as the effect of hydrophobic strips on the surface wettability or self-cleaning characteristics are simulated and studied.

Comparison between a numerical model and an investigating model on the uplift of the Qinghai-Xizang (Tibetan) Plateau

A comparison between a numerical model (NM) and an investigating model (IM) on the uplift of the Qinghai_Xizang Plateau was conducted. Results show that the NM is capable of describing the uplifting processes of the plateau. They are in good agreement with each other concerning the major uplifting processes.

FDS中非矩形边界隧道的自动建模

FDS(Fire Dynamics Simulator)作为一种高效的火灾模拟软件,在对非长方体隧道进行火灾模拟时有很大局限性。文章提出了一种用矩形方块来拟合圆弧墙或斜线墙的算法;通过编制可视化软件来自动生成FDS输入数据,解决了在FDS中对非矩形边界隧道的建模问题;最后给出了一个在FDS中对非矩形边界隧道火灾的数值模拟实例,验证了算法的可行性。

基于FDS的壁面烟熏图痕试验及重构研究

根据烟气颗粒在壁面上黏附的机理和影响因素,先建立烟熏图痕形成的半物理模型,再将其与火灾流体模拟软件FDS相耦合,后编译出可以重现烟熏图痕的FDS可执行程序;同时进行了壁面烟熏图痕的实体试验,分析了燃烧时间、火源位置、燃料种类对烟熏图痕形成的影响;而且利用重新编译的FDS程序对实体试验进行了数值重构,对比讨论了实体试验结果与模拟结果。结果表明,嵌入了烟熏半物理模型的程序能较好地重构出试验得到的烟熏图痕,证明了该模型是有效的,可以用于烟熏痕迹的预测。该技术弥补了现有软件的不足,进一步完善了数值重构技术,可以辅助火灾调查工作。

常用火灾数值模拟软件FDS的应用探讨

通过对FDS模型构建、网格划分等方面进行分析,指出了其应用中存在的局限性,并就如何初步判断FDS软件使用的正确性进行了分析,以推广火灾数值模拟软件FDS的应用。

基于FDS的地下单室火灾模拟验证实验

为了验证火灾模拟软件FDS(Fire Dynamics Simulator)的准确性,针对地下建筑单室特点,选取某工程内一个值班室作为研究对象,并根据相似准则建立了小尺度火灾房间模型。通过小尺度单室火灾实验,对烟气的扩散特性进行研究,同时利用FDS模拟软件进行单室火灾模拟,并将实验结果与模拟结果进行对比分析。结果表明,实验烟气温度随时间的变化趋势与FDS模拟结果一致,验证了火灾模拟软件FDS的准确性,证实了FDS用于模拟预测单室火灾的发展与迁移的适用性和合理性,对火灾的控制研究具有一定的参考价值。

基于FDS的半潜式生活平台火灾风险研究

以某海洋平台生活区为例构建火灾风险数学模型,利用FDS火灾数值模拟软件分析烟气的蔓延规律、结合不同类型舱室可燃物种类以及人员应急撤离运动情况的量化分析,确定危险舱室具体位置。基于贝叶斯网络将危险舱室的火灾风险模型细化成包含舱室各种特性的函数。

FDS模型在大型会展中心火灾疏散中的应用

以大型会展中心发生火灾时进行合理人员疏散、降低人员伤亡为目的,选定特定的国际会展中心进行火灾风险评估。对FDS火灾数值模拟理论进行分析,采用场模拟层次的大涡模拟技术,建立FDS火灾三维模型,通过模型演示了火灾现场人员疏散时间、人员逃生条件等因素的边界条件,为人群疏散避险提供指导依据。

A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials

Classical continuum mechanics which leads to a local continuum model,encounters challenges when the discontinuity appears,while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost.A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages.This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials.Then this hybrid local/nonlocal continuum model is applied to fracture simulation.Some numerical examples like a plate with a hole,Brazilian disk,notched plate and beam,are performed for verification and validation.In addition,a peridynamic software is introduced,which was recently developed for the simulation of the hybrid local/nonlocal continuum model.

Numeral eddy current sensor modelling based on genetic neural network

This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network （GNN） according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method.

基于FDS的办公楼火灾数值模拟分析

针对烟气在多层建筑中的蔓延情况进行研究。利用FDS软件,对某三层办公楼进行火灾数值模拟。依据最不利原则,针对自然排烟时单室开窗和不开窗两种情况,各设置三个火源位置在不同楼层的工况进行模拟与分析,对着火房间和走廊的温度以及二氧化碳、一氧化碳和氧气浓度等多个方面进行观测,与人能承受的“忍耐值”进行比较,提出最佳逃生的安全时间和保证人员安全的疏散路径。

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C（ω） of the spin operator σz for the biased sub-Ohmic spin-boson model. The small-ω behavior C（ω） ∝ ω～s is found to be universal and independent of the bias ε and the coupling strength α（except at the quantum critical point α = αc and ε = 0）. Our NRG data also show C（ω） ∝ χ～2ω～s for a wide range of parameters, including the biased strong coupling regime（ε = 0 and α 〉 αc）, supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C（ω） on α and ε is understood in terms of the competition between ε and the crossover energy scale ω0^＊of the unbiased case. C（ω） is stable with respect to ε for ε《ε^＊. For ε 》ε^＊, it is suppressed by ε in the low frequency regime. We establish that ε^＊∝（ω0^＊）^1/θ holds for all sub-Ohmic regime 0≤s 〈 1, with θ = 2/（3s） for 0 〈 s≤1/2 and θ = 2/（1 ＋ s） for 1/2 〈 s 〈 1. The variation of C（ω） with α and ε is summarized into a crossover phase diagram on the α–ε plane.

Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Novel extended C-m models of flow stress for accurate mechanical and metallurgical calculations and comparison with traditional flow models

Here,we developed novel extended piecewise bilinear power law(C-m)models to describe flow stresses under broad ranges of strain,strain rate,and temperature for mechanical and metallurgical calculations during metal forming at elevated temperatures.The traditional C-m model is improved upon by formulating the material parameters C and m,defined at sample strains and temperatures as functions of the strain rate.The coefficients are described as a linear combination of the basis functions defined in piecewise patches of the sample strain and temperature domain.A comparison with traditional closed-form function flow models revealed that our approach using the extended piecewise bilinear C-m model is superior in terms of accuracy,ease of use,and adaptability;additionally,the extended C-m model was applicable to numerical analysis of mechanical,metallurgical,and microstructural problems.Moreover,metallurgy-related values can be calculated directly from the flow stress information.Although the proposed model was developed for materials at elevated temperatures,it can be applied over a broad temperature range.