Rocking behaviour of multi-block columns subjected to pulse-type ground motion accelerations

Ancient columns, made with a variety of materials such as marble, granite, stone or masonry are an important part of the
European cultural heritage. In particular columns of ancient temples in Greece and Sicily which support only the architrave are
characterized by small axial load values. This feature together with the slenderness typical of these structural members clearly
highlights as the evaluation of the rocking behaviour is a key aspect of their safety assessment and maintenance. It has to be noted
that the rocking response of rectangular cross-sectional columns modelled as monolithic rigid elements, has been widely investigated
since the first theoretical study carried out by Housner (1963). However, the assumption of monolithic member, although being
widely used and accepted for practical engineering applications, is not valid for more complex systems such as multi-block columns
made of stacked stone blocks, with or without mortar beds. In these cases, in fact, a correct analysis of the system should consider
rocking and sliding phenomena between the individual blocks of the structure. Due to the high non-linearity of the problem, the
evaluation of the dynamic behaviour of multi-block columns has been mostly studied in the literature using a numerical approach
such as the Discrete Element Method (DEM). This paper presents an introductory study about a proposed analytical-numerical
approach for analysing the rocking behaviour of multi-block columns subjected to a sine-pulse type ground motion. Based on the
approach proposed by Spanos (2001) for a system made of two rigid blocks, the Eulero-Lagrange method to obtain the motion
equations of the system is discussed and numerical applications are performed with case studies reported in the literature and with a
real acceleration record. The rocking response of single block and multi-block columns is compared and considerations are made
about the overturning conditions and on the effect of forcing function’s frequency.
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Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Simulation von Förderprozessen bei Vibrationsförderanlagen

Die erzielbare Fördergeschwindigkeit bei Vibrationsförderern hängt maßgeblich von der Bewegungsfunktion des Förderorganes ab. Für die gezielte Simulation dieser Anlagen mittels der diskreten Elemente Methode (DEM) ist es notwendig die geometrisch vernetzen Förderorgannachbildungen mit praxisrelevanten Bewegungsfunktionen zu beaufschlagen. Der Artikel beschreibt die Einbindung dieser Bewegungsfunktionen in die quellenoffene DEM-Software LIGGGHTS. Während des Simulationsprozesses wird eine Bewegung vernetzter CAD-Modelle durch trigonometrische Reihen ermöglicht.

Simulation der peristaltischen Förderung von Stückgütern als Schüttgut

Im Beitrag wird ein neuartiges Förderprinzip zur federnden Aufnahme und zum Transport von massenhaft anfallenden Paketstrukturen vorgestellt. Das Förderprinzip beruht auf einem flächigen Tragmittel in Form eines veränderbaren, elastischen Verbundes von kleinskaligen Fördermodulen. Das konzipierte Transportprinzip mit peristaltischen Eigenschaften soll entstehende Staus der Pakete schnell auflösen und eine dedizierte Steuerung von Teilmengen zulassen, um den erforderlichen Durchsatz innerhalb eines Materialflusssystems zu erreichen. Diese Lösung ermöglicht eine sinnvolle Verknüpfung von Wirkprinzipien der Schüttgut- und Stückgutförderung zur Aufnahme und Fortbewegung von Pakete als Schüttgut. Die Grundfunktionalität des Förderkonzepts wird durch die numerische Simulation auf Basis der Diskrete Elemente Methode sowie der Mehrkörpersimulation überprüft.

Effect of granule morphology on breakage behaviour during compression

In the area of dry particle breakage, Discrete Element Method (DEM) simulations have been widely used to analyse the sensitivity of various physical parameters to the behaviour of agglomerates during breakage. This paper looks at the effect of agglomerate shape and structure on the mechanisms and extent of breakage of dry agglomerates under compressive load using DEM simulations. In the simulations, a spherical-shaped agglomerate produced within the DEM code is compared with an irregularly shaped agglomerate, whose structure is that of an actual granule that was characterised with X-ray microtomography (muCT). Both agglomerates have identical particle size distribution, coordination number and surface energy values, with only the agglomerate shape and structure differing between the two. The work here details the breakage behaviour with a number of traditional DEM output parameters (i.e., contact/cluster distributions) with showing vastly different behaviour between the two agglomerates. (C) 2004 Elsevier B.V. All rights reserved.

Micromechanics of agglomerate damage processes

This thesis reports a detailed investigation of the micromechanics of agglomerate behaviour under free-fall impact, double (punch) impact and diametrical compression tests using the simulation software TRUBAL. The software is based on the discrete element method (DEM) which incorporates the Newtonian equations of motion and contact mechanics theory to model the interparticle interactions. Four agglomerates have been used: three dense (differing in interface energy and contact density) and one loose. Although the simulated agglomerates are relatively coarse-grained, the results obtained are in good agreement with laboratory test results reported in the literature. The computer simulation results show that, in all three types of test, the loose agglomerate cannot fracture as it is unable to store sufficient elastic energy. Instead, it becomes flattened for low loading-rates and shattered or crushed at higher loading-rates. In impact tests, the dense agglomerates experience only local damage at low impact velocities. Semi-brittle fracture and fragmentation are produced over a range of higher impact velocities and at very high impact velocities shattering occurs. The dense agglomerates fracture in two or three large fragments in the diametrical compression tests. Local damage at the agglomerate-platen interface always occurs prior to fracture and consists of local bond breakage (microcrack formation) and local dislocations (compaction). The fracture process is dynamic and much more complex than that suggested by continuum fracture mechanics theory. Cracks are always initiated from the contact zones and propagate towards the agglomerate centre. Fracture occurs a short time after the start of unloading when a fracture crack "selection" process takes place. The detailed investigation of the agglomerate damage processes includes an examination of the evolution of the fracture surface. Detailed comparisons of the behaviour of the same agglomerate in all three types of test are presented. The particle size distribution curves of the debris are also examined, for both free-fall and double impact tests.

Computer simulation of moist agglomerate collisions

This thesis considers the computer simulation of moist agglomerate collisions using the discrete element method (DEM). The study is confined to pendular state moist agglomerates, at which liquid is presented as either absorbed immobile films or pendular liquid bridges and the interparticle force is modelled as the adhesive contact force and interstitial liquid bridge force. Algorithms used to model the contact force due to surface adhesion, tangential friction and particle deformation have been derived by other researchers and are briefly described in the thesis. A theoretical study of the pendular liquid bridge force between spherical particles has been made and the algorithms for the modelling of the pendular liquid bridge force between spherical particles have been developed and incorporated into the Aston version of the DEM program TRUBAL. It has been found that, for static liquid bridges, the more explicit criterion for specifying the stable solution and critical separation is provided by the total free energy. The critical separation is given by the cube root of liquid bridge volume to a good approximation and the 'gorge method' of evaluation based on the toroidal approximation leads to errors in the calculated force of less than 10%. Three dimensional computer simulations of an agglomerate impacting orthogonally with a wall are reported. The results demonstrate the effectiveness of adding viscous binder to prevent attrition, a common practice in process engineering. Results of simulated agglomerate-agglomerate collisions show that, for colinear agglomerate impacts, there is an optimum velocity which results in a near spherical shape of the coalesced agglomerate and, hence, minimises attrition due to subsequent collisions. The relationship between the optimum impact velocity and the liquid viscosity and surface tension is illustrated. The effect of varying the angle of impact on the coalescence/attrition behaviour is also reported. (DX 187, 340).

Numerical simulation for dynamic positioning in pack ice

This thesis investigates the numerical modelling of Dynamic Position (DP) in pack ice. A two-dimensional numerical model for ship-ice interaction was developed using the Discrete Element Method (DEM). A viscous-elastic ice rheology was adopted to model the dynamic behaviour of the ice floes. Both the ship-ice and the ice-ice contacts were considered in the interaction force. The environment forces and the hydrodynamic forces were calculated by empirical formulas. After the current position and external forces were calculated, a Proportional-Integral-Derivative (PID) control and thrust allocation algorithms were applied on the vessel to control its motion and heading. The numerical model was coded in Fortran 90 and validated by comparing computation results to published data. Validation work was first carried out for the ship-ice interaction calculation, and former researchers’ simulation and model test results were used for the comparison. With confidence in the interaction model, case studies were conducted to predict the DP capability of a sample Arctic DP vessel.

Modeling of burden distribution in the blast furnace

The blast furnace is the main ironmaking production unit in the world which converts iron ore with coke and hot blast into liquid iron, hot metal, which is used for steelmaking. The furnace acts as a counter-current reactor charged with layers of raw material of very different gas permeability. The arrangement of these layers, or burden distribution, is the most important factor influencing the gas flow conditions inside the furnace, which dictate the efficiency of the heat transfer and reduction processes. For proper control the furnace operators should know the overall conditions in the furnace and be able to predict how control actions affect the state of the furnace. However, due to high temperatures and pressure, hostile atmosphere and mechanical wear it is very difficult to measure internal variables. Instead, the operators have to rely extensively on measurements obtained at the boundaries of the furnace and make their decisions on the basis of heuristic rules and results from mathematical models. It is particularly difficult to understand the distribution of the burden materials because of the complex behavior of the particulate materials during charging. The aim of this doctoral thesis is to clarify some aspects of burden distribution and to develop tools that can aid the decision-making process in the control of the burden and gas distribution in the blast furnace. A relatively simple mathematical model was created for simulation of the distribution of the burden material with a bell-less top charging system. The model developed is fast and it can therefore be used by the operators to gain understanding of the formation of layers for different charging programs. The results were verified by findings from charging experiments using a small-scale charging rig at the laboratory. A basic gas flow model was developed which utilized the results of the burden distribution model to estimate the gas permeability of the upper part of the blast furnace. This combined formulation for gas and burden distribution made it possible to implement a search for the best combination of charging parameters to achieve a target gas temperature distribution. As this mathematical task is discontinuous and non-differentiable, a genetic algorithm was applied to solve the optimization problem. It was demonstrated that the method was able to evolve optimal charging programs that fulfilled the target conditions. Even though the burden distribution model provides information about the layer structure, it neglects some effects which influence the results, such as mixed layer formation and coke collapse. A more accurate numerical method for studying particle mechanics, the Discrete Element Method (DEM), was used to study some aspects of the charging process more closely. Model charging programs were simulated using DEM and compared with the results from small-scale experiments. The mixed layer was defined and the voidage of mixed layers was estimated. The mixed layer was found to have about 12% less voidage than layers of the individual burden components. Finally, a model for predicting the extent of coke collapse when heavier pellets are charged over a layer of lighter coke particles was formulated based on slope stability theory, and was used to update the coke layer distribution after charging in the mathematical model. In designing this revision, results from DEM simulations and charging experiments for some charging programs were used. The findings from the coke collapse analysis can be used to design charging programs with more stable coke layers.

Numerical modelling of deformation behaviour of red blood cells in microvessels using the coupled SPH-DEM method

This thesis developed an advanced computational model to investigate the motion and deformation properties of red blood cells in capillaries. The novel model is based on the meshfree particle methods and is capable of modelling the large deformation of red blood cells moving through blood vessels. The developed model was employed to simulate the deformation behaviour of healthy and malaria infected red blood cells as well as the motion of red blood cells in stenosed capillaries.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Study of gas cavity size hysteresis in a packed bed using DEM

When a high velocity gas jet is introduced into a packed bed a cavity is formed. The size of the cavity shows hysteresis on increasing and decreasing gas flow rates. This hysteresis leads to different cavity sizes at same gas flow rate depending on the bed history. The size of cavity affects the gas flow profiles in the packed bed. In this study the cavity size hysteresis phenomenon has been modeled using discrete element method along with turbulent gas flow. A reasonable agreement has been found between computed and experimental results on cavity size ysteresis. The effect of various parameters, such as nozzle height from the bed bottom and packing height, on the cavity size hysteresis has been studied. It is found that inter-particle interaction forces along with gas drag and bed porosity play an important role in describing the cavity size hysteresis. The injection of gas flow allows the particles to go to an unconstrained state than they were previously in, and their ability to remain in that state, even under decreased gas drag force, leads to the phenomenon of cavity size hysteresis. (c) 2007 Elsevier Ltd. All rights reserved.

A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

岩石爆炸增渗模型实验及DEM数值模拟研究

岩体中爆炸提高矿石的渗透性可以极大地提高采矿效率，是碎裂岩型矿床预裂浸出法的关键技术。混凝土与岩体都具有脆性材料的特性，因此用浇筑于铁桶中的混凝土试件进行模型实验研究岩体的爆炸增渗效果。铁桶可以提高实验效率，使边界条件更为简单和易于操作，但是，实验和原型的差异需要论证。用自主开发的基于连续介质力学模型的离散元方法，模拟了有铁桶边界的模型实验，验证了数值模拟方法的可行性及有效性，给出了有弹性侧限边界约束的混凝土和较大尺度无反射边界条件的岩石中的爆炸差别。在此基础上，分析了岩石中爆炸造成的岩石破坏规律。计算结果表明：岩石破坏面总面积和破坏区的最大裂缝宽度受药量和岩石的抗拉强度影响，破坏面总面积和裂缝宽度随药量增加而增大，随抗拉强度增大而减小；在药量相同的条件下，实际岩石环境下的岩块破坏程度比铁桶约束的大。模型实验和数值模拟相结合的办法可以对混凝土和岩石的爆炸破坏给出较为合理的结果。

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.