In plane loaded masonry walls: DEM and FEM/DEM models. A critical review

This work is dedicated to the assessment of the nonlinear behaviour of masonry panels with regular texture and subject to in-plane loads, by means of numerical pushover analysis and an analytical homogenized model. Two numerical models are considered and adopted for performing a set of numerical tests: a discrete model developed by authors and a discrete/finite element model frequently adopted in rock mechanics field and effectively extended to masonry structures. In both models the hypotheses of rigid blocks and elastic–plastic joints following a Mohr–Coulomb yield criterion are adopted. The aim of this work is twofold: (1) a comparison and a calibration of the numerical models, evaluating their effectiveness in determining ultimate loads and collapse mechanisms of masonry panels, by assuming a nonlinear homogenized model for regular masonry as reference solution; (2) the evaluation of sensitivity of masonry behaviour and numerical models to panel dimension ratio and to varying masonry texture. In a first case study, sliding collapse mechanisms changing to overturning collapse mechanisms for increasing panel and block height-to-width ratio are obtained and the results given by the numerical models turn out to be in good agreement. Furthermore, a second case study, dedicated to square panels supported at base ends and vertically loaded, shows different ‘arch mechanisms’ depending on block height-to-width ratio.     

Mathematical modelling of the container cranes under seismic loading and proving by shake table

This paper is concerned with modelling of the behaviour of container cranes under seismic loadings. For this purpose, physical and mathematical models are prepared. A six degrees-of-freedom non-linear mathematical model is developed in order to understand the dynamic behaviour of cranes under the seismic loadings. In order to determine the seismic behaviour of the container cranes against earthquakes, a 1/20 scaled crane model was designed and constructed. For the comparison of the models, the real earthquake records were used. The results are used to observe the destructive effects and compared with the period values of the most critical sections on the crane structure. When time and frequency domains are compared, it is seen that mathematical modelling of the container crane structure shows reasonable results under dynamic loadings. It will be available to take precautions and to increase seismic performance of cranes with the help of the developed dynamic model. Also, the developed mathematical model will be able to be used as a crane model in active vibration control studies in order to decrease the structural vibrations on container cranes.     

Stress analysis of masonry vaults and static efficacy of FRP repairs

In the paper, the basic principles for the analysis of structures made by Not-Resisting-Tension (NRT) material are introduced; the theory is then applied for investigating the static behaviour of a NRT masonry arch model and to test the effect of reinforcements made by FRP strips of variable length. A wide experimental campaign is developed and numerical/experimental comparison is provided in order to evaluate the skill of the adopted model in capturing the real behaviour of the structure with or without reinforcement.     

砖石古塔模型振动台试验的离散元模拟分析

砖石古塔块体间黏结强度较低,受地震作用易产生裂缝后发生破坏,为研究砖石古塔在地震作用下开裂及裂缝发展机制,以玄奘塔1/8缩尺模型结构为对象,建立离散元模型,计算了地震波激励下结构的加速度及位移反应,与振动台试验结果进行对比,分析了塔体开裂破坏全过程。结果表明,数值计算所得结构的加速度及位移反应与振动台试验结果一致,当地震烈度较低时,两者顶层位移变化曲线基本一致;烈度提高后,塔体开裂导致结构动力响应的计算值与试验结果出现差异,但两者的变化规律相同。在地震波激励下,塔体首层先开裂,随地震烈度的提高延伸至中部塔层,块体第2层出现阶梯状错动,模型损伤过程与试验裂缝发展状况基本吻合。研究结果为砖石古塔地震损伤及破坏过程分析提供了参考。     

砌体结构破坏倒塌过程的离散单元模拟

基于传统颗粒离散单元模型（DEM）,开发了一种绑定式离散单元模型（BTDEM）用于砌体结构崩塌机制的研究,并对一个典型砌体结构的破坏倒塌过程进行数值模拟。结果证实BTDEM方法能够详细地模拟出砌体建筑结构的崩塌过程,同时还可以模拟出砌块的破碎,是一种普适性较强的模拟砌体结构建筑的高效数值方法。BTDEM方法具有计算速度...     

Assessment of nonlinear seismic performance of a restored historical arch bridge using ambient vibrations

Historic masonry arch bridges are vital components of transportation systems in many countries worldwide, ensuring the ready access of goods and services to millions of people. The structural failure of these historic structures would severely and adversely impact the economies of these nations due to the massive disruptions of transportation systems accompanying such failures. To successfully maintain these aging masonry structures, performance assessment must incorporate the unique mechanical characteristics of masonry. Therefore, the preferred analysis technique must go beyond a linear approach. This study assesses the earthquake performance of a restored historical masonry arch bridge through nonlinear finite element analysis incorporating the Drucker–Prager damage criterion. The case study structure is the Mikron Arch Bridge, a nineteenth century Ottoman Era structure built over the Firtina River near Rize, Turkey, and restored in 1998. The Mikron Arch Bridge was first subjected to ambient vibration testing, during which accelerometers were placed at several points on the bridge span to record the bridge vibratory response. The investigators then used Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification techniques to extract the experimental natural frequencies, mode shapes, and damping ratios from these measurements. Experimental results were compared with those obtained by the linear finite element analysis of the bridge. Good agreement between mode shapes was observed during this comparison, though natural frequencies disagree by 8–10%. The boundary conditions of the linear finite element model of Mikron Arch Bridge are adjusted such that the analytical predictions agree with the ambient vibration test results. By introducing the Drucker–Prager damage criterion, the calibrated linear FE model was next extended into a nonlinear model. Nonlinear analysis of seismic behavior of Mikron arch bridge was performed considering the acceleration record of Erzincan earthquake in 1992 that occurred near the Mikron Bridge region. The displacement and stress results were observed to be allowable level of the stone material. Moreover, linear FE model calibrations elicited a significant influence on the nonlinear FE model simulations.     

Effects of material and geometric non-linearities on the collapse load of masonry arches

This paper addresses the influence of both the constitutive and geometric non-linearities on the collapse load of masonry arches. The non-linear mechanical behavior of masonry is embedded into the constitutive equation, which assigns the generalized stresses to each pair of generalized strains, thereby accounting for the material's lack of resistance to tension as well as its limited compressive strength. We first apply the methods of limit analysis to explicitly evaluate the collapse load for various circular arches subjected to their own weight and either to a load uniformly distributed per unit span, or to a point load acting at the crown. Subsequently, in order to highlight the influence of P-δ effects, the collapse load is determined via an expressly developed numerical method that also accounts for the geometric non-linearity.     

A micro-mechanical homogenisation model for masonry: Application to shear walls

An improved micro-mechanical model for masonry homogenisation in the non-linear domain, is proposed and validated by comparison with experimental and numerical results available in the literature. Suitably chosen deformation mechanisms, coupled with damage and plasticity models, can simulate the behaviour of a basic periodic cell up to complete degradation and failure. The micro-mechanical model can be implemented in any standard finite element program as a user supplied subroutine defining the mechanical behaviour of an equivalent homogenised material. This work shows that, with the proposed model, it is possible to capture and reproduce the fundamental features of a masonry shear wall up to collapse with a coarse finite element mesh. The main advantage of such homogenisation approach is obviously the possibility to simulate real complex structures while taking into consideration the arrangement of units and mortar, which would otherwise require impractical amount of finite elements and computer resources.     

Checking in elastic range of the thrusting monumental structures

Meccanica - The subject is the research of the collapse multiplier of a masonry arch operating even in elastic range. The approach permits the knowledge of the stresses and the failures under the...     

A preliminary approach of dynamic identification of slender buildings by neuronal networks

The study of the dynamic behavior of slender masonry structures is usually related to the preservation of the historic heritage. This study, for bell towers and industrial masonry chimneys, is particularly relevant in areas with an important seismic hazard. The analysis of the dynamic behavior of masonry structures is particularly complex due to the multiple effects that can affect the variation of its main frequencies along the seasons of the year: temperature and humidity. Moreover, these dynamic properties also vary considerably in structures built in areas where land subsidence due to the variation of the phreatic level along the year is particularly evident: the stiffness of the soil–structure interaction also varies. This paper presents a study to evaluate the possibility of detecting the variation of groundwater level based on the readings obtained using accelerometers in different positions on the structure. To do this a general case study was considered: a 3D numerical model of a bellower. The variation of the phreatic level was evaluated between 0 and −20 m, and 81 cases studies were developed modifying the rigidity of the soil–structure interaction associated to a position of the phreatic level. To simulate the dispositions of accelerometers on a real construction, 16 points of the numerical model were selected along the structure to obtain modal displacements in two orthogonal directions. Through an adjustment by using neural networks, a good correlation has been observed between the predicted position of the water table and acceleration readings obtained from the numerical model. It is possible to conclude that with a discrete register of accelerations on the tower it is possible to predict the water table depth.     

考虑混凝土应变率变化的高拱坝非线性动力响应研究

提出一种新的应变率相关的混凝土非线性弹塑性损伤模型。采用此模型对混凝土拱坝的非线性地震响应作了分析。在综合考虑坝-地基-库水动力相互作用和坝缝非线性接触的基础上，着重研究了混凝土应交率相关效应及加载历史对混凝土极限强度等重要参数及拱坝响应的影响，并与采用不考虑应交率影响的混凝土损伤模型计算结果进行了对比分析。结果表明，拱坝考虑横缝作用后的坝面应变率分布不同于整体拱坝。应交率分布形态不仅可以很好地表征拱坝的振动形态，而且对于高拱坝的动力响应的影响也不可忽略。     

Effect of ventricle motion on the dynamic behaviour of chorded mitral valves

An Immersed Boundary (IB) model is employed to investigate the dynamic behaviour of a novel chorded mitral prosthesis, which is in the early stages of its development, under physiological flow conditions. In vivo magnetic resonance images (MRIs) of the left ventricle are analysed to determine the relative motion of the mitral annulus and the papillary muscle regions of the ventricle. The dynamic boundary conditions are incorporated into IB simulations to test the valve in a more realistic dynamic geometric environment. The IB model has successfully identified the effect of the dynamic boundary conditions on the mechanical behaviour of the valve and revealed the strengths and weaknesses of the current mitral design. The mechanical performance of the prosthesis is compared with recent studies of native porcine valves; differences in mechanical behaviour are observed. Potential improvements for the design of the prosthesis are proposed.     

An Investigation of the Seismic Behaviour of an Ancient Masonry Bastion Using Non-Destructive and Numerical Methods

Determining the structural behavior of masonry structures is a challenge due to their lack of homogeneity. The seismic behavior of masonry structures is especially complex. The aim of this study was to examine the structural behavior of Za?anos Bastion using both experimental and numerical methods. The Operational Modal Analysis technique, including the Enhanced Frequency Domain Decomposition Method, and the Stochastic Subspace Identification Method were used to illustrate experimentally the dynamic characteristic of the bastion. A finite element model was developed using ANSYS software in order that the dynamic characteristics of the bastion, including natural frequencies and mode shapes, could be calculated numerically. Seismic analysis was carried out using the 1999 Kocaeli earthquake ground motion record to determine the linear and nonlinear seismic behavior of the bastion. The Turkish Earthquake Code and its general technical specifications were used to evaluate the seismic results. The results show that the maximum and minimum principal stresses exerted on the masonry components exceeded the code requirements at some points, but in general the requirements for the stresses were satisfied.     

A computational model for the limit analysis of three-dimensional masonry structures

This paper extends previous work on the limit analysis of ductile frames and plane masonry arches to the limit analysis of three-dimensional masonry structures. A lower-bound approach is developed which can handle three-dimensional collapse mechanisms involving any combination of sliding, twisting and hingeing at the block interfaces. A computer program for determining the collapse load of such structures is used to study (a) the equilibrium limits of a block with four contact points resting on an inclined plane and (b) the collapse of a semicircular arch of four blocks. The paper also describes experimental and computational work on a radially symmetric model dome of 380 blocks subject to foundation settlement.

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Sommario Il presentre contributo estende al campo delle structture tridimensionali in muratura un precedente lavoro sull'analisi limite di telai duttili ed archi in muratura piani. Si e' sviluppato un approccio statico che analizza meccanismi di collasso tridimensionale ottenuti per combinazione dei meccanismi semplici di scorrimento e rotazione nel piano e fuori dal piano delle superfici di interfaccia tra i blocchi. Si descrivono (a) i limiti di equilibrio di un blocco con 4 punti di contatto su base inclinata, (b) le condizioni di collasso di un arco semicircolare costituito da quattro blocchi, applicando un programma di calcolo redatto per l'analisi e la definizione del carico di collasso di tali strutture. La terza parte dell'articolo presenta il lavoro sperimentale e di calcolo sviluppato su un modello di cupola a simmetria radiale costituita da 380 blocchi soggetta a cedimenti fondali.

     

Research of air-cushion isolation effects on high arch dam reservoir

A three-dimensional (3D) finite element model of air-cushion isolated arch dam is presented with the nonlinear gas-liquid-solid multi-field dynamic coupling effect taken into account.In this model,the displacement formulation in Lagrange method,pressure formulation in Euler method,nonlinear contact model based on Coulomb friction law are applied to the air-cushion,reservoir and contraction joint domain,respectively.The dynamic response of Jinping I arch dam with a height of 305 m is analyzed using the seismic records of the Wenchuan Earthquake in 2008.Numerical results show that the air-cushion isolation reduces significantly the hydrodynamic pressure as well as the opening width for the contraction joints of high arch dam.     

Predictive model for the collapse load of masonry assemblage with two piers joined by a spandrel

The masonry assemblage composed of two piers connected by a spandrel can be considered a repetitive unit in large masonry walls with openings, occurring in masonry buildings. In this work, the collapse load of the above-mentioned masonry assemblage is predicted by solving a system of nonlinear equations, where the normal force in the spandrel is a root of an equilibrium equation of fourth degree. Piers and spandrel are assumed rigid and nonlinearity (crushing and no tensile strength) is concentrated at the pier-foundation and pier–spandrel interfaces. The model also takes into account the effect of a timber lintel supporting the spandrel and anchored into the two adjacent piers. This approach valid for assemblages with one spandrel can be extended for the evaluation of the collapse load of structures composed of N piers connected by N ? 1 spandrels. The system of nonlinear equations is easily solved with an iterative method and the collapse load provided by the solution agrees well with the experimental result.     

Dynamic response of rocking cracked masonry walls

The behaviour of masonry constructions results to be very far from the one characterizing ductile structures. In masonry constructions, the seismic action activates a rocking motion rather than a dissipating mechanism. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behaviour, until a failure condition is attained. Aim of the paper is to investigate the dynamic behaviour of masonry single storey walls, according to Housner’s studies and innovatively introducing the effect of diagonal cracks developing from the toes of the piers and shown by typical post-earthquake cracking patterns. The proposed procedure can be easily applied to the case of multi-storey regular masonry walls with openings representing the main resistant structural components of a masonry building. Starting from the evaluation of the incipient rocking acceleration of the system, the free and forced motions of the wall are examined. In the paper, according to the classical Housner’s approach, the energy dissipation occurring during the impact is modelled. Finally, a numerical application, considering a simple constant horizontal acceleration impulse of given duration has been carried out.

     

Un modèle discret du couplage entre les fils dans une structure tisséeA discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yarns is introduced, the potential energy of which is calculated. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yarn. The contact force is then expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yarn are analysed. The consideration of the coupling enhances the rigidity of the response of the yarn; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yarn. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 331 (2003).     

A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint

Impact affects the dynamic characteristics of mechanical multi-body systems and damages those rotating parts, such as the joint rolling element bearings, which are high-precision, defect intolerant components. Based on multi-body dynamic theory, Hertzian contact theory, and a continuous contact model, this study proposed a modelling method that can describe the dynamic behaviour of planar mechanical multi-body systems containing a rolling ball bearing joint under impact. In this method, the rigid bodies and bearing joint were connected according to their joint force constraints; the impact constraint between the multi-body system and the target rigid body was constructed using a continuous contact force model. Based on this method, the reflection relationship between the external impacts of the mechanical multi-body system and the variation law governing the dynamic load on the rolling bearing joint were revealed. Subsequently, an impact multi-body system, which was composed of a sliding–crank mechanism containing a rolling ball bearing joint and the target rigid body with an elastic support, was analysed to explore the dynamic response of such a complex discontinuous dynamic system andthe relevant relationship governing the dynamic load on the rolling bearing joint. In addition, a multi-body dynamic simulation software was used to build a virtual prototype of the impact slider–crank system. Compared with the theoretical model, the prototype had an additional deep groove ball bearing. That is to say, the prototype model took account of the specific geometric structural characteristics and the complex contact relationship of the inner and outer races, rolling balls, and bearing cage. Finally, the effectiveness of the theoretical method proposed in this study was verified by comparative analysis of the results. The results suggested that the external impact of a mechanical multi-body system was prone to induce sudden changes in the equivalent reaction force on its bearing joint and the dynamic load carried on its rolling balls. This study provided an effective method for exploring the distribution characteristics of dynamic loads on rolling ball bearing joints under working impact load conditions. Moreover, it offered support for the parameter optimisation of geometric structure, performance evaluation, and dynamic design of the rolling ball bearings.     

A kinematic FE limit analysis model for thick English bond masonry walls

Two-wythes masonry walls arranged in English bond texture were often used in the past as bearing panels in seismic area. On the other hand, earthquake surveys have demonstrated that masonry strength under horizontal actions is usually insufficient, causing premature collapses of masonry buildings, often ascribed to out-of-plane actions. Furthermore, many codes of practice impose for new brickwork walls a minimal slenderness, which for instance is fixed by the Italian O.P.C.M. 3431 equal to 12 for artificial bricks and 10 for natural blocks masonry.For the above reasons, the analysis at failure of English bond brickwork walls under out-of-plane actions is a topic that deserves consideration, despite the fact that almost the totality of the studies of masonry at failure is devoted to running bond arrangements. Furthermore, it must be noted that an approach based on the analysis of running bond texture – in comparison with English bond pattern – is not suitable for the investigation of the behavior of bearing panels.In this framework, in the present paper, a Reissner–Mindlin kinematic limit analysis approach is presented for the derivation of the macroscopic failure surfaces of two-wythes masonry arranged in English bond texture. In particular, the behavior of a 3D system constituted by infinitely resistant bricks connected by joints reduced to interfaces with frictional behavior and limited tensile/compressive strength is identified with a 2D Reissner–Mindlin plate. In this way, assuming both an associated flow rule for the constituent materials and a finite subclass of possible deformation modes, an upper bound approximation of macroscopic English bond masonry failure surfaces is obtained as a function of macroscopic bending moments, torsion and shear forces.Several examples of technical relevance are treated both at a cell level and at a structural level, addressing the differences in terms of collapse loads and failure surfaces due to different textures and constituent laws for joints. Finally, two meaningful structural examples consisting of a panel in cylindrical flexion and a masonry slab constrained at three edges and out-of-plane loaded are discussed. A detailed comparison in terms of deformed shapes at collapse and failure loads between a 2D FE Reissner–Mindlin limit analysis approach and a full 3D heterogeneous FE model shows the reliability of the results obtained using the kinematic identification approach proposed.