Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD

The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes. The dumped quarry materials in the core are protected by progressively coarser particulates. The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core. Design guidance on the mass and shape of these units is based on empirical equations derived from scaled physical model tests. The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking, displacement and collisions sufficient to cause breakage of units. Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave-structure interaction remains poor. We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique. The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization. We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.     

Boundary element method for wave trapping by a multi-layered trapezoidal breakwater near a sloping rigid wall

This study examines the multiple layers in a rubble mound breakwater and their effect on reflection and dissipation of incoming ocean waves. The numerical model is developed using multi-domain boundary element method for oblique water wave trapping near a sloping wall by a multi-layered trapezoidal porous structure, which is utilized to model armour, filter and core layers while examining the hydrodynamics in different configurations. Both, the constant element and linear element approaches to boundary element method are discussed. The cases of bottom-standing porous structures as being submerged and fully extended are considered. The wave hydrodynamics over the structure is described by the reflection and dissipation coefficients along with the forces acting on the sloping wall, and is influenced by wave and structural parametrics of the system. The influence of armour layer in different configurations is highlighted for various structural and wave parameters.

     

Numerical modeling of fluid-particle interaction in granular media

Fluid-particle interaction underpins important behavior of granular media. Particle-scale simulation may help to provide key microscopic information governing the interaction and offer better understanding of granular media as a whole. This paper presents a coupled computational fluid dynamics and discrete element method (CFD-DEM) approach for this purpose. The granular particle system is modeled by DEM, while the fluid flow is simulated by solving the locally averaged Navier–Stokes equation with CFD. The coupling is considered by exchanging such interaction forces as drag force and buoyancy force between the DEM and CFD. The approach is benchmarked by two classic geomechanics problems for which analytical solutions are available, and is further applied to the prediction of sand heap formation in water through hopper flow. It is demonstrated that the key characteristic of granular materials interacting with pore water can be successfully captured by the proposed method.     

作用在岩体裂隙网络中的渗透力分析

从岩体裂隙网络渗流的特点出发, 以单裂隙渗透力分析为基础, 分析了二维及三维情况下岩体裂隙网络渗流对岩体裂隙壁施加的两种作用力: 垂直于裂隙壁使裂隙产生扩容的法向渗透静水压力以及平行于裂隙壁和裂隙水流方向一致的切向动水压力, 推导出二维及三维情况下裂隙单元因这两种作用力而产生的等效结点力, 并应用算例定量分析了岩体裂隙网络渗透静水压力和动水压力共同作用对岩体应力的影响, 结果显示: (a)渗透力作用下裂隙上部岩体压应力减小, 而裂隙下部岩体压应力增大, 最大压应力增大 10 .5 3%; (b)渗透力作用下裂隙岩体拉应力增大, 最大拉应力增大 9.0 9%; (c)裂隙渗透力使岩体剪应力增大, 最大值达 2 3.75 %。     

An effective limiting algorithm for particle-based numerical simulations of compressible flows

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.     

冲击荷载作用下滤波混凝土的动态响应与层裂损伤数值研究

借鉴局域共振材料的工作机制,通过在混凝土基体中嵌入滤波单元,设计出具有应力波衰减特性的滤波混凝土。通过将滤波混凝土结构简化为质量弹簧力学系统来分析滤波混凝土对应力波的衰减机制。采用数值模拟方法,对比研究了冲击荷载作用下普通混凝土模型和滤波混凝土模型中应力波的传播特性和层裂破坏模式。通过参数分析,研究了滤波单元的材料和几何属性对其储能效果的影响。研究结果表明：滤波单元有效降低了混凝土基体中应力波的传播速度和应力峰值;滤波单元的储能机制有效降低了混凝土基体中的能量;金属球的质量越大,滤波单元的储能效果越好,但弹性层的弹性模量和厚度需要通过适当分析进行设计以实现滤波单元的储能最大化;滤波混凝土基体的局部损伤耗散了荷载中的大量能量,有效降低了结构自由面附近的破坏程度。     

A two-phase, two-component model for vertical upward gas-liquid annular flow

In this paper, a new two-fluid two-component computational fluid dynamics (CFD) model is developed to simulate vertical upward two-phase annular flow. The two-phase VOF scheme is utilized to model the roll wave flow, and the gas core is described by a two-component phase consisting of liquid droplets and gas phase. The entrainment and deposition processes are taken into account by source terms of the governing equations. Unlike the previous models, the newly developed model includes the effect of liquid roll waves directly determined from the CFD code, which is able to provide more detailed and, the most important, more self-standing information for both the gas core flow and the film flow as well as their interactions. Predicted results are compared with experimental data, and a good agreement is achieved.     

Numerical prediction of rock mass damage due to accidental explosions in an underground ammunition storage chamber

Accidental detonations in an underground ammunition storage chamber inside a rock mass may cause severe damage to the rock mass around the chamber, adjacent tunnels and chambers, ground surface, and in the worst case cause sympathetic detonation of explosives in adjacent storage chambers. To prevent such damage, underground ammunition storage chambers are often situated at minimum depth below the ground surface, and spaced at minimum distance from each other, so that damage, should it occur, is limited to the accidental chamber. Different codes and regulations for ammunition storage chambers specify minimum embedment depth and separation distance for underground ammunition storage chambers. They are usually given in terms of the rock mass properties and the weight of explosive stored in chambers. Some empirical formulae, usually based on the peak particle velocity of the stress wave or the maximum strain of the rock mass, are also available to estimate the damage zones in the rock mass from an explosion. All these empirical methods do not include the effects of explosion details, such as the loading density, chamber geometry and explosive distribution. In this paper, a previously calibrated numerical model is used to estimate the damage zones in a granite mass resulting from an accidental explosion in an underground ammunition storage chamber. Effects of various explosion conditions on rock mass damage are investigated. On the basis of the numerical results, some empirical formulae are derived to predict damage zones around the explosion chamber, as well as safe embedment depth of the storage chamber and safe separation distance between adjacent chambers. The numerical results are also compared with available empirical formulae and code specifications. It should be noted that the characteristics of stress wave propagation around an ammunition storage chamber has been published in a preceding paper (Int. J. Blast. Fragm. 5:57–90, 2001.     

Landslides riding on basal pressure waves

An instability of the Kelvin-Helmholtz type is shown to exist at the interface between an elastic mass moving at a uniform sliding velocity U and an underlying thin basal layer of high-shear granular flow. The generated basal wave will force out-of-phase perturbations in overburden pressure and sliding velocity and hence, a net reduction in the total power loss to friction. This, along with the net working of the basal pressure forces, will result in a net retrieval of energy from the basal zone to the mean motion of the sliding mass, thus effectively reducing the drag at the base. The mechanism is shown to be just as effective for the case of dry slides (no pore fluid), as for the case of wet slides. This confirms that the existence of low-viscosity pore fluid is not necessary for the development of lowdrag, long-runout landslide events.     

某抽水蓄能电站地下洞室围岩岩体质量特征分析

考虑材料的黏性效应建立了II型动态扩展裂纹尖端的力学模型,假设黏性 系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并 给出边界条件作为扩展裂纹定解的补充条件,对理想塑性材料中平面应变扩展裂纹尖端场进 行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了II型裂纹数值解的性质随各参 数的变化规律. 分析表明应力和应变均具有幂奇异性,对于II型裂纹,裂尖场不含弹性卸载 区. 引入Airy应力函数,求得了II型准静态裂纹尖端场的控制方程,并进行了数值分析, 给出了裂纹尖端的应力应变场. 当裂纹扩展速度($M\to 0$)趋于零时,动态解趋 于准静态解,表明准静态解是动态解的特殊形式.     

A massively parallel GPU‐accelerated model for analysis of fully nonlinear free surface waves

We implement and evaluate a massively parallel and scalable algorithm based on a multigrid preconditioned Defect Correction method for the simulation of fully nonlinear free surface flows. The simulations are based on a potential model that describes wave propagation over uneven bottoms in three space dimensions and is useful for fast analysis and prediction purposes in coastal and offshore engineering. A dedicated numerical model based on the proposed algorithm is executed in parallel by utilizing affordable modern special purpose graphics processing unit (GPU). The model is based on a low‐storage flexible‐order accurate finite difference method that is known to be efficient and scalable on a CPU core (single thread). To achieve parallel performance of the relatively complex numerical model, we investigate a new trend in high‐performance computing where many‐core GPUs are utilized as high‐throughput co‐processors to the CPU. We describe and demonstrate how this approach makes it possible to do fast desktop computations for large nonlinear wave problems in numerical wave tanks (NWTs) with close to 50/100 million total grid points in double/single precision with 4 GB global device memory available. A new code base has been developed in C++ and compute unified device architecture C and is found to improve the runtime more than an order in magnitude in double precision arithmetic for the same accuracy over an existing CPU (single thread) Fortran 90 code when executed on a single modern GPU. These significant improvements are achieved by carefully implementing the algorithm to minimize data‐transfer and take advantage of the massive multi‐threading capability of the GPU device. Copyright © 2011 John Wiley & Sons, Ltd.     

金华山软岩铁路隧道施工过程围岩屈服接近度分析

隧道施工过程中围岩处于复杂应力状态下,隧道围岩屈服区演化特征的确定对于围岩稳定性分析和开挖支护方案优化具有重要的意义。采用屈服接近度指标衡量围岩破坏接近程度可以合理地描述复杂应力状态下围岩的应力危险性,对Mohr-Coulomb类岩体材料的屈服接近度函数进行了相应的推导,并在非线性有限元用户子程序上编程予以实现。介绍了赣州-龙岩铁路DKl33+095～DKl38+237段软弱围岩单线隧道正台阶步施工方案以及湿喷纤维混凝土支护方案。为了对该隧道施工过程中隧道围岩屈服区的演化特征进行合理评价,采用非线性有限元法对软弱围岩条件下的铁路隧道施工过程进行了数值模拟,分析了施工过程中隧道围岩屈服接近度分布特征,判定了隧道台阶步施工过程中隧道围岩的稳定性。分析结果表明:该隧道施工过程中围岩破坏区主要发生在下台阶步施工过程中;屈服接近度指标比传统的塑性区分布提供的信息更加丰富,有利于工程技术人员定量地评价隧道开挖支护方案。     

钢筋混凝土开孔深梁有限元分析与设计研究Finite element analysis of RC deep beams with openings and researching of the design method

钢筋混凝土深梁受力不同于浅梁,梁腹开孔后受力更趋复杂。现有的设计方法对深梁行为的解释不够完备,设计结果的适用性难以判断,设计规范也没有给出开孔深梁的设计条文。为研究深梁设计方法的有效性,本文采用了非线性有限元分析方法,引入适合混凝土结构非线性分析的断裂塑性模型,并考虑钢筋粘结滑移效应,对一系列开双孔或偏孔钢筋混凝土深梁试验进行仿真分析,所得结果与试验结果吻合良好,能够准确预测深梁在裂缝、破坏形态及承载力等方面的受力特征。研究表明现有的深梁设计方法中,压拉杆模型方法相较内力法和应力图形法更加经济有效。在仿真分析的基础上,提出了一种对开孔深梁具有普遍适用性的非线性设计方法,其设计结果具有高承载力、较好延性、经济的配筋量和充分的材料利用率的优点。     

脆性材料中应力波衰减规律与层裂实验设计的数值模拟

对混凝土、岩石类脆性材料的层裂实验进行了有限元模拟,研究了应力波在此类材料中传播的衰减规律,包括两类机制:弹性波因大尺寸试样的几何弥散产生的小幅度线性衰减、与应变率相关的黏塑性波因本构关系导致的指数衰减。在此基础上,提出了包含常数项的指数型应力波峰值拟合公式。建议采用可以忽略应力波衰减影响的细长形试样进行层裂实验。混凝土类脆性材料层裂破坏模拟结果显示,有限元模拟得到的层裂片厚度与一维应力波理论得到的结果非常吻合,验证了按一维应力波理论确定层裂强度的实验方法的有效性。通过对比3种不同入射波形下层裂片的形状和净拉应力波形,发现不对称的入射波形状更有利于实验获得平直的层裂断面和较准确的层裂强度。     

离散元法在求解三维冲击动力学问题中的应用

提出了三维连结型离散模型,建立了可实现连结型模型(用于连续介质)-接触型模型(用于非连续介质)转化的三维离散元计算程序,用来模拟连续介质转变为非连续介质的力学过程．利用该计算程序对冲击载荷下混凝土块体内(连续体情况下)的应力波传播过程进行了数值模拟．将计算结果的数值与LS-DYNA程序计算的结果进行比较,验证了该计算程序的计算精度．在此基础上,模拟了混凝土块体的动态破坏(连续介质向非连续介质转化)过程．其计算结果可用动画显示,得到的破坏形式与由实验得到的破坏形式相近．两个算例说明该离散元模型及其计算程序是模拟计算伴随有连续介质向非连续介质转变的动态破坏问题的有力工具．     

爆炸荷载作用下围岩与地下结构的动力相互作用

利用ANSYS/LS-DYNA非线性显式动力有限元程序和流固耦合计算方法,对炸药在地下拱形结构上方岩石中垂直爆炸过程进行数值模拟,借助波动理论p-u Hugoniot线对爆炸冲击波在围岩与结构之间的传播和加卸载过程进行理论分析;得到了不同跨度拱形结构与围岩之间的最大相互作用力及相互作用力分布图。研究结果表明:冲击波由高阻抗围岩向低阻抗混凝土传播时,围岩卸载,应力减小;反向传播时,岩石加载,应力增大;爆距为5 m时爆炸冲击波对40 m跨度拱形结构整体产生拉压震荡,引起的震动效应显著。     

公伯峡电站开挖边坡古风化岩松弛与工程特性变化研究

利用公伯峡电站泄水洞左岸边坡开挖过程中获得的各种资料,分析、研究边坡在开挖后岩体松弛程度和工程特性的变化。分析表明,边坡开挖后,一定深度范围内边坡岩体将松弛,松弛带的厚度可以通过现场调查、地震波速、声波速度来划分。岩体发生松弛后,松弛带岩体力学参数明显降低。开挖后尽快支护是防止边坡岩体松弛有效方法之一。     

岩石破裂滑动过程及其声发射数值模拟

运用岩石破裂与失稳过程分析RFPA2D系统, 对滑动形成过程进行了数值模拟研究。滑动岩体似为非均匀弹 -脆岩石材料, 模拟结果再现了滑动形成从变形到破坏直至失稳的全过程及其声发射规律。     

Study of linear response identification techniques and reduced‐order model generation for a 2D CFD scheme

Reduced‐Order Models (ROMs) have been the focus of research in various engineering situations, but it is only relatively recently that such techniques have begun to be introduced into the CFD field. The purpose of generating such models is to capture the dominant dynamics of the full set of CFD equations, but at much lower cost. One method that has been successfully implemented in the field of fluid flows is based on the calculation of the linear pulse responses of the CFD scheme coupled with an Eigensystem Realization algorithm (ERA), resulting in a compact aerodynamic model. The key to the models is the identification of the linear responses of the non‐linear CFD code. Two different methods have been developed and reported in literature for linear response identification; the first method linearizes the CFD code and the second method uses Volterra theory and the non‐linear code. As these methods were developed independently they have not previously been brought together and compared. This paper first explains the subtle, but fundamental differences between the two methods. In addition, a series of test cases are shown to demonstrate the performance and drawbacks of the ROMs derived from the different linear responses. The conclusions of this study provide useful guidance for the implementation of either of the two approaches to obtain the linear responses of an existing CFD code. Copyright © 2006 John Wiley & Sons, Ltd.     

Influences of the wall thickness on the granular dispersion in a dense gas–solid coaxial jet

The granular dispersion for different wall thicknesses of the inner channel in a dense gas–solid coaxial jet is investigated by morphology. In the wave dispersion, the Kelvin–Helmholtz instability has a strong influence on the granular stream. However, increasing the wall thickness damps the K–H instability, namely weakens the wave dispersion. Consequently, the non-dimensional wavelength increases and the non-dimensional amplitude decreases as the wall thickness increases for the same annular gas velocity. The instability analysis combining with the modification of the vorticity thickness of the annular gas stream indicates that the non-dimensional wavelength increases linearly with the non-dimensional modified vorticity thickness. The relation between the amplitude of the granular dispersion and the non-dimensional modified vorticity thickness is reliable for the wave dispersion as well. In addition, the granular dispersion angle is proportional to the annular gas velocity, which slightly depends on the wall thickness.