Internal blast loading in a buried lined tunnel

The paper presents a comprehensive approach to simulate an explosion occurring inside a buried axisymmetric lined cavity. The approach considers all the stages of the process: detonation of the internal charge; the shock wave propagation in the internal gas and its following interaction with the cavity's shell lining including multiple reflections; soil–structure dynamic interaction, including multiple gap opening/closure and wave propagation in the surrounding medium. The cavity's lining is modeled as a Timoshenko elastic plastic shell. The soil is modeled by the Grigoryan model that takes into account both bulk and shear elastic plastic behavior, including the effect of soil pressure on the yield strength for the stress tensor deviator. The gas-dynamics problem is solved by the modified Godunov method, based on a fixed Eulerian mesh with the so-called mixed cell. The variational difference method is applied to solve the problem in the soil and in the shell domains. The contact pressures acting on the lining due to both the detonation products on the internal side and the soil on its outer side are computed by solving the coupled system of finite differences equations of gas, shell and soil dynamics using a simple iteration method. The problems of a blast-hole charge and of a periodical system of spherical blast charges that are placed at equal distances from each other were solved. The explosion occurs within a cylindrical steel pipeline, surrounded by an elastic plastic loess soil. The effect of the soil elastic plastic pressure-density behavior and its shear properties on the soil–structure interaction (including the gap opening/closure process) was studied.     

Underground explosion of a cylindrical charge near a buried wall

The paper investigates the explosion characteristics of a cylindrical explosive that is buried in soil close to a rigid obstacle. The soil is modeled as a bulk compressible elastic plastic medium, including full bulk locking and dependence of the current deviatoric yield stress on the pressure. The Lagrange approach and the modified variational-difference method are used to simulate the process. The pressure distribution along the rigid obstacle has been studied for various stand of distances of the explosive from the obstacle. It was shown that when the explosion is relatively close to the obstacle, the envelope of the pressure distributions (connecting the maximum stress values of all distributions along the wall) shows a maximum value that is located at some distance away from the axis of symmetry and not along the axis as is the case for a distant explosion. It was found that this phenomenon appears when the interaction of the reflected wave with the explosive cavity yields significant deformation of the cavity frontal part that it is sharply deformed and becomes planar. When the explosive stand of distance from the obstacle is moderate or large, the explosion cavity remains cylindrical during all times and the peak pressure is developed along the axis of symmetry.     

Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity

The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated. The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity–vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtained in terms of a modified Rayleigh number Ra^*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.     

分数导数黏弹性准饱和土中球空腔振动特性

在频率域内用解析方法研究分析了简谐轴对称荷载和流体压力作用下分数导数黏弹性准饱和中球空腔的稳态响应问题。将土骨架等效为具有分数阶导数本构关系的黏弹性体,基于Biot两相饱和介质模型,通过势函数推导求得了边界部分透水时分数导数粘弹性准饱和土中球空腔的位移、应力和孔压等的解析解。根据界面连续性条件,确定了待定系数的表达式。在此基础上,考察了准饱和土各参数对动力响应的影响,结果表明：轴对称荷载和流体压力两种情况时,相对渗透系数对动力响应的影响有较大的差异。分数导数本构模型更合理地描述了准饱和土中球空腔的振动特性。     

Dynamic response analysis of a building structure subjected to ground shock from a tunnel explosion

Dynamic responses of a multi-storey building without or with a sliding base-isolation device to ground shock induced by an in-tunnel explosion are numerically analyzed in this paper. The effect of an adjacent tunnel in between the building and the explosion tunnel, which affects ground shock propagation, is also considered in the analysis. Different modeling methods, such as the eight-node iso-parametric finite element and mass-lumped system, are used to establish the coupling model consisting of the two adjacent tunnels, the surrounding soil medium with the Lysmer viscous boundary condition and the multi-storey building with or without the sliding base-isolation device. In numerical calculations, a continuous friction model, which is different from the traditional Coulomb friction model, is adopted to improve the computational efficiency and reduce the accumulated errors. Some example analyses are subsequently performed to study the response characteristics of the building and the sliding base-isolation device to ground shock. The effect of the adjacent tunnel in between the building and the explosion tunnel on the ground shock wave propagation is also investigated in the study. The final conclusions based on the numerical results will provide some guidance in engineering practice.     

饱和地基中二维空沟远场被动隔振研究

针对饱和地基中二维空沟远场被动隔振问题,首先,基于饱和多孔介质频域边界单元法,建立了以薄层法(TLM)基本解作为动力Green函数的饱和土半解析边界元法,该方法可有效的分析饱和半空间的动力问题,是解决土-结构动力相互作用问题的一种有效工具。在此基础上,推导得到了空沟对Rayleigh波散射的二维边界元方程,对空沟的远场隔振问题进行了详细的参数分析。结果表明：设置空沟能够对地面振动起到较好的隔振作用;当空沟深度小于1个Rayleigh波波长时,提高空沟深度能够有效的提高其隔振效果;而空沟宽度对隔振效果的影响相对较小;饱和地基参数改变对空沟隔振效果影响不大。     

Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

饱和土中大直径嵌岩桩纵向振动特性研究

根据B iot饱和土理论和R ay le igh-Love杆理论,计及土层及桩的径向运动影响,导出了考虑横向惯性效应的端承桩与饱和土的纵向耦合振动频域的解析解和时域半解析解,对比了考虑与不考虑横向惯性效应时,大直径嵌岩桩纵向振动引起的土层复阻抗的异同以及桩顶导纳和时域反射的特征。研究表明:长径比越小,横向惯性效应越明显,而泊松比和激振频率对饱和土层阻抗及桩顶响应也有重要影响。通过工程实例对比表明,当桩的长径比较小时,用考虑横向惯性效应的计算方法可以得到更好的拟合效果。     

Two-phase lattice Boltzmann simulation of natural convection in a Cu-water nanofluid-filled porous cavity: Effects of thermal boundary conditions on heat transfer and entropy generation

The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (10³?≤?Ra?≤?10⁵) and Darcy number (10^?1?≤?Da?≤?10^?6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.     

A study of the interaction between a guardrail post and soil during quasi-static and dynamic loading

A roadside guardrail system is anchored in gravel beside a roadway to eliminate the risk of fatal accidents during off-road crashes and collisions with hazardous roadside objects. The desired safety behaviour is ensured not only by the guardrail structure itself, but also by the interaction between the gravel and the guardrail post. The interaction of gravel with a Sigma-post of a standard Swedish guardrail was studied in experiments and numerical analysis. The aim was to measure the strength of the single post embedded in gravel and use the data to validate a computer model for the investigation of the soil–post interaction. A quasi-static and dynamic test series were designed and carried out. Two corridors were formed by the test data for the quasi-static and dynamic loading conditions, respectively. A parametric study was subsequently conducted to investigate the influence of the gravel stiffness on the soil–post interaction through computer simulations using LS-DYNA. The numerical results showed that the LS-DYNA soil and concrete model and the Cowper–Symonds steel model effectively captured the soil–post interaction since the calculated strength of the post agreed with the corridors of the test data. The input parameters for the soil and concrete material model were recommended for roadside gravel in crash analyses.     

Effects of local thermal non-equilibrium on the pore pressure and thermal stresses around a spherical cavity in a porous medium

In this paper, we use a local thermal non-equilibrium (LTNE) thermo-poroelasticity theory to investigate temperatures, pore pressure and thermal stresses around a spherical cavity in an infinite fluid saturated porous medium. In the LTNE theory, the solid and fluid phases undergo different temperature variations which induce additional pore pressure and thermal stresses. The asymptotic short time solutions of temperature, pore pressure and thermal stresses are obtained using the Laplace transform technique. Numerical results for two porous materials (clay and sandstone) are presented to examine the effects of LTNE on the temperature, pore pressure and thermal stresses around the spherical cavity. The results show that for the clay, the LTNE radial stress has a significantly larger peak value (magnitude) than that of the classical radial stress. The influence of LTNE on the pore pressure and tangential stress, however, are marginal. For the sandstone, both the radial stress (magnitude) and pore pressure are significantly increased by the LTNE effect.     

饱和土中桩-桩竖向动力相互作用因子研究

桩桩动力相互作用的研究是研究群桩动力阻抗的基础,而桩桩动力相互作用通常利用动力相互作用因子来反映。将饱和土视为液同两相介质,利用薄层法得到了饱和土的竖向动力阻抗,进而得到饱和土中桩桩竖向动力相互作用因子。通过分析桩土力学参数对竖向动力相互作用因子的影响发现：桩间距、耦合系数、桩土模量比等参数对竖向动力相互作用因子有较大的影响,液固耦合系数较大时也有一定的影响。     

下卧饱和半空间粘弹性土层上基础阻抗函数的分析

由于地下水的影响,实际土层一般由含水土层和不含水土层组成。由于求解的复杂性,目前基础阻抗函数的求解中很少考虑这种地基情形。根据干土是饱和土的特殊情形这一事实,通过将液相压缩模量、孔隙比以及惯性耦合质量密度取为零,可以使干土的动力反应统一到饱和土动力反应求解方案中,从而可通过饱和地基上基础阻抗函数的一种求解方法,解决饱和土和干土并存时基础阻抗函数的求解问题。地基无限域的影响通过局部透射人工边界考虑。通过算例验证了该方法的可行性,并考察了干土层厚度以及基础埋深对动力阻抗的影响。     

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

A time‐discontinuous Galerkin finite element method (DGFEM) for dynamics and wave propagation in non‐linear solids and saturated porous media is presented. The main distinct characteristic of the proposed DGFEM is that the specific P3–P1 interpolation approximation, which uses piecewise cubic (Hermite's polynomial) and linear interpolations for both displacements and velocities, in the time domain is particularly proposed. Consequently, continuity of the displacement vector at each discrete time instant is exactly ensured, whereas discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously saved, particularly in the materially non‐linear problems, as compared with that required for the existing DGFEM. Both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non‐linear problems. Numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain. Copyright © 2003 John Wiley & Sons, Ltd.     

饱和土中管桩对倾斜入射弹性波的隔离

在Biot饱和土波动方程的基础上,分析了全空间均质饱和土体中单排空心管桩对倾斜入射弹性波的隔离效果。将倾斜入射波和散射波的势函数展开成Fourier-Bessel函数的无穷级数的形式,利用一组圆柱坐标系统和Graff加法转换定理,通过施加桩土界面处的应力和位移连续的边界条件,求解出散射波势函数的待定系数,进而得到饱和土体中任意点的位移和应力。数值算例分析了饱和土体的渗透性和管桩的壁厚等参数对管桩隔离效果的影响。结果表明：空心管桩的隔离效果要好于实心排桩;随着饱和土体渗透性的降低,管桩的隔离效果越好,但当渗透性降低到一定程度后,再减小土体渗透性对管桩的隔离效果影响不大。     

Convective instability in a gravity modulated anisotropic thermally stable porous medium

The effect of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer in which the applied temperature gradient is opposite to that of gravity is investigated. The flow through the porous layer is governed by an extended form of Darcy’s law incorporating Brinkman’s boundary layer correction. The permeability and thermal conductivity of the medium are assumed to be transversely anisotropic. A stability analysis based on the method of small perturbations is performed using normal mode assumption. The study is focussed on low amplitude gravity modulation and the thresholds are found using Mathieu’s functions. The emergence of instability via the synchronous and subharmonic modes and the transition between them are discussed as a function of the physical parameters of interest.     

Dynamic response and damage evolution in composite materials subjected to underwater explosive loading: An experimental and computational study

The effect of underwater shock loading on an E-Glass/Epoxy composite material has been studied. The work consists of experimental testing, utilizing a water filled conical shock tube and computational simulations, utilizing the commercially available LS-DYNA finite element code. Two test series have been performed and simulated: (1) a reduced energy series which allowed for the use of strain gages and (2) a series with increased energy which imparted material damage. The strain gage data and the computational results show a high level of correlation using the Russell error measure. The finite element models are also shown to be able to simulate the onset of material damage by both in-plane and delamination mechanisms.     

Green函数对饱和土隧道内集中荷载作用振动位移反应的计算

由于快速列车与城市地铁的发展,饱和土隧道内集中荷载作用的反应问题日显重要。Green函数对辐射条件的满足,积分方程的精确解答,Dirichlet条件下的通用性,使它对隧道内动荷载作用的土动力反应问题计算有着特有的优越性,作者根据已求得两相饱和介质Green函数,利用Lamb积分公式,结合隧道断面特征,以解析积分法推导了集中冲击荷载与简谐荷载圆形断面隧道内振动位移反应表达式闭合解、反应时程曲线、瞬态和稳态的振动形态;并根据它们的单位脉冲响应函数结合Duhamel积分求得隧道在地震荷载作用下的动力反应。另外窗形隧道受集中冲击荷载作用相关弹性波时程曲线也在文中给出。     

Simulation of quench for the cable-in-conduit-conductor in HT-7U superconducting Tokamak magnets using porous medium model

A cable-in-conduit-conductor (CICC) consists of superconducting cable, copper, supercritical helium and conduit. To keep the operating temperature of superconducting cable lower than its current sharing temperature, the supercritical helium is forced flow through the CICC. The supercritical helium through the cable bundle has the complex directional changes due to the interaction between the supercritical helium and strands. The structure of CICC is characterized with the porous medium. The quench characteristics of CICC are analyzed by the model which the temperature difference between the strands and helium is assumed to be very small due to the heating induced flow to generate high heat transfer coefficient of supercritical helium. A moving mesh method is developed for the numerical solution of the problem with the steep drop for temperature and density of supercritical helium in the short front region of the normal zone. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the arguments for density, temperature and velocity of supercritical helium. Existence and uniqueness of the discretised equations using a moving mesh are also established. The coupled equation for porous medium is solved using the finite element method with the artificial viscosity term. The validation of the code is tested by comparing it with the other codes with good accuracy. The converged properties of numerical solution due to quench in CICC are studied. We present preliminary estimates of the maximum conductor temperature rise and helium pressure during a quench in the inner layer of toroidal field (TF) magnet for HT-7U. The quench scenarios with different dump time constants of 6.25, 12, and 21.1 s are considered. The goal of such work is to guide the protection scheme and a detailed prediction of the quench evolution of magnet.