Seismic fragility curves of as-built single-span masonry arch bridges

Masonry arch bridges are crucial elements in the railway transportation network throughout Europe. Although significant advances in seismic risk assessment of various bridge types have been made by developing fragility curves of generalized classes of structures, there are no comparable tools for masonry arch structures. In this context, this paper presents the construction of seismic fragility curves of single-span masonry bridges according to the limit analysis method. An iterative procedure is implemented to define the capacity curve of the equivalent single degree of freedom system through non-linear kinematic analysis. The process involves determination of the collapse mechanism, calculation of the limit load multiplier, and definition of the thrust line. The intrinsic variability of the seismic action is incorporated with the use of different sets of elastic spectra compatible with EC 8 Type-1 spectrum for various types of soil, with peak ground acceleration varying over the range 0.05–1.5 g. The fragility curves of the generalized classes of single-span masonry bridges are finally obtained from the effective ranges of the main geometric and material parameters affecting arch bridge capacity.     

Seismic behaviour of masonry buildings built of low compressive strength units

Seismic behaviour of masonry buildings, built of low compressive strength units, is discussed. Although such materials have already been tested and approved for use from mechanical and thermal insulation point of view, the knowledge regarding their structural behaviour is still lacking. In order to investigate the resistance and deformation capacity of this particular type of masonry construction in seismic conditions, a series of eight walls and model of a two-storey full scale confined masonry building have been tested by subjecting the specimens to cyclic shear loads. All tests were conducted under a combination of constant vertical load and quasi static, cyclically imposed horizontal load. The behaviour of tested specimens was of typical shear type. Compared with the behaviour of plain masonry walls, the presence of tie-columns resulted into higher resistance and displacement capacity, as well as smaller lateral resistance degradation. The response of the model was determined by storey mechanism with predominant shear behaviour of the walls and failure mechanism of the same type as in the case of individual confined masonry walls. Adequate seismic behaviour of this particular masonry structural type can be expected under the condition that the buildings are built as confined masonry system with limited number of stories.     

Failure of masonry arches under impulse base motion

Recent seismic events have caused damage or collapse of invaluable historical buildings, further proving the vulnerability of unreinforced masonry (URM) structures to earthquakes. This study aims to understand failure of masonry arches—typical components of URM historic structures—subjected to horizontal ground acceleration impulses. An analytical model is developed to describe the dynamic behaviour of the arch and is used to predict the combinations of impulse magnitudes and durations which lead to its collapse. The model considers impact of the rigid blocks through several cycles of motion, illustrating that failure can occur at lower ground accelerations than previously believed. The resulting failure domains are of potential use for design and assessment purposes. Predictions of the analytical model are compared with results of numerical modelling by the distinct element method, and the good agreement between results validates the analytical model and at the same time confirms the potential of the distinct element framework as a method of evaluating complex URM structures under dynamic loading. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of load reduction factors for clay masonry walls

The in‐plane cyclic behaviour of three types of unreinforced clay masonry was characterized by means of laboratory tests on full‐scale specimens. The masonry walls were assembled with various bonding arrangements (head joints made with mortar pockets, dry head joints with mechanical interlocking, thin‐layer mortar bed joints), which are not yet inserted in seismic codes. Experimental behaviour was modelled with an analytical hysteretic model able to predict lateral load–displacement curves in case of shear failure of the unreinforced walls. According to the experimental results and those of the selected analytical model, parametric study to evaluate the reduction in lateral strength demand produced by non‐linear behaviour in masonry walls, i.e. the load reduction factor was carried out by non‐linear dynamic analyses. The calculated values of the load reduction factor were modest. The differences in values found for the three masonry types, although consistent with them, were not great. This may indicate that, in the ultimate limit state, the type of masonry cannot significantly affect the behaviour of an entire building. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic capacity of irregular unreinforced masonry walls with openings

Masonry buildings are often characterized by geometric irregularities. In many cases, such buildings meet global regularity requirements provided by seismic codes, but they are composed by irregular walls with openings. The latter are masonry walls characterized by (i) openings of different sizes, (ii) openings misaligned in the horizontal and/or vertical direction, or (iii) a variable number of openings per story. An irregular layout of openings can induce not only a nonuniform distribution of gravity loads among masonry piers but also unfavorable damage localizations resulting in a premature collapse of the wall and hence a higher seismic vulnerability. This paper is aimed at providing a simplified methodology to assess the effects of irregularities on the in‐plane seismic capacity of unreinforced masonry (URM) walls with openings. To this end, a macroelement method was developed and validated through experimental results available in the literature. The proposed methodology was based on the quantification of wall irregularities by means of geometric indices and their effects on seismic capacity of URM walls with openings through both sensitivity and regression analyses. Sensitivity analysis was based on a high number of static pushover analyses and allowed to assess variations in key seismic capacity parameters. Regression analysis let to describe each capacity parameter under varying irregularity index, providing empirical models for seismic assessment of irregular URM walls with openings. The in‐plane seismic capacity was found to be significantly affected by wall irregularities, especially in the case of openings with different heights. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental and analytical studies on earthquake resisting behaviour of confined concrete block masonry structures

To improve the seismic performance of masonry structures, confined masonry that improves the seismic resistance of masonry structures by the confining effect of surrounding bond beams and tie columns is constructed. This study investigated the earthquake resisting behaviour of confined masonry structures that are being studied and constructed in China. The structural system consists of unreinforced block masonry walls with surrounding reinforced concrete bond beams and tie columns. The characteristics of the structure include: (1) damage to blocks is reduced and brittle failure is avoided by the comparatively lower strength of the joint mortar than that of the blocks, (2) the masonry walls and surrounding reinforced concrete bond beams and tie columns are securely jointed by the shear keys of the tie columns. In this study, wall specimens made of concrete blocks were tested under a cyclic lateral load and simulated by a rigid body spring model that models non‐linear behaviour by rigid bodies and boundary springs. The results of studies outline the resisting mechanism, indicating that a rigid body spring model is considered appropriate for analysing this type of structure. Copyright © 2006 John Wiley & Sons, Ltd.     

Calibration and application of a continuum damage model on the simulation of stone masonry structures: Gondar church as a case study

The conservation and rehabilitation of monuments is a matter of important investigation, and the need for accurate structural analysis, capable of effectively predicting the structural behaviour of this type of constructions, under static and dynamic loads, is increasing. Currently there are numerous computational methods and tools, supported by different theories and strategies with different levels of complexity, computation time and cost which are available to perform such analyses. A complex analysis is not always synonym of a better result and the choice of a method over another depends mostly on the purpose of the analysis. This work aims at evaluating the capacity of a non linear continuum damage model (Faria et al. in Int J Solids Struct 35(14):1533–1558, 1998), originally developed for concrete structures, to simulate the behaviour of stone masonry structures. In particular, the seismic response of an old stone masonry construction, the Gondar church, is analysed considering different levels of geometrical and material complexity. The verification and calibration procedures use the experimental results from tests performed on stone masonry walls at the Laboratory for Earthquake and Structural Engineering of the Faculty of Engineering of Porto University and from other tests found in the bibliography (Vasconcelos in Experimental investigations on the mechanics of stone masonry: Characterization of granites and behaviour of ancient masonry shear walls. PhD Thesis, Universidade do Minho, Guimar?es, Portugal, 2005). The results are compared, assessing the differences and the importance of using complex tools, such as the continuum damage model, to better simulate and understand the global behaviour of such constructions.     

Out‐of‐plane seismic behaviour of rocking masonry walls

The evaluation of the out‐of‐plane behaviour of unreinforced walls is one of the most debated topics in the seismic assessment of existing masonry buildings. The discontinuous nature of masonry and its interaction with the remainder of the building make the dynamic modelling of out‐of‐plane response troublesome. In this paper, the results of a shaking table laboratory campaign on a tuff masonry, natural scale, U‐shaped assemblage (façade adjacent to transverse walls) are presented. The tests, excited by scaled natural accelerograms, replicate the behaviour of external walls in existing masonry buildings, from the beginning of rocking motion to overturning. Two approaches have been developed for modelling the out‐of‐plane seismic behaviour: the discrete element method and an SDOF analytic model. Both approaches are shown to be capable of reproducing the experimental behaviour in terms of maximum rotation and time history dynamic response. Finally, test results and numerical time history simulations have been compared with the Italian seismic code assessment procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental investigation of seismic behaviour of the ancient Protiron monument model

Throughout history, dry-stone masonry structures have been strengthened with different types of metal connectors in order to increase their resistance which enabled their survival, especially in the seismically active area. One such example is the ancient Protiron monument placed in the Peristyle square of the Diocletian's Palace in Split, Croatia. The Protiron was built at the turn of the 3rd century as a stone masonry structure with dowels embedded between its base, columns, capitals and broad gable. The stone blocks in the broad gable were connected by metal clamps during restoration at the beginning of the 20th century. In order to study the seismic performance of the strengthened stone masonry structures, an experimental investigation of seismic behaviour of a physical model of the Protiron was performed on the shaking table. The model was designed as a true replica model in a length scale of 1:4 and exposed to representative earthquake with increasing intensities up to collapse. The tests provided a clear insight into system behaviour, damage mechanism and failure under intensive seismic load, especially into the efficiency of connecting elements, which had a special role in increasing seismic resistance and protection of the structure from collapse. Additionally, this experiment provided valuable data for verification and calibration of numerical models for strengthened stone masonry structures.     

Generation of fragility curves for Turkish masonry buildings considering in‐plane failure modes

This study focuses on the seismic safety evaluation of masonry buildings in Turkey for in‐plane failure modes using fragility curves. Masonry buildings are classified and a set of fragility curves are generated for each class. The major structural parameters in the classification of masonry buildings are considered as the number of stories, load‐bearing wall material, regularity in plan and the arrangement of walls (required length, openings in walls, etc.), in accordance with the observations from previous earthquakes and field databases. The fragility curves are generated by using time history (for demand) and pushover (for capacity) analyses. From the generated sets of fragility curves, it is observed that the damage state probabilities are significantly influenced from the number of stories and wall material strength. In the second stage of the study, the generated fragility curves are employed to estimate the damage of masonry buildings in Dinar after the 1995 earthquake. The estimated damage by fragility information is compared with the inspected visual damage as assessed from the Damage Evaluation Form. For the quantification of fragility‐based damage, a single‐valued index, named as ‘vulnerability score’ (VS), is proposed. There seems to be a fair agreement between the two damage measures. In addition to this, decisions regarding the repair or demolition of masonry buildings in Dinar due to visual damage inspection are on comparable grounds with the relative measure obtained from VS of the same buildings. Hence, the fragility‐based procedure can provide an alternative for the seismic safety evaluation of masonry buildings in Turkey. Copyright © 2007 John Wiley & Sons, Ltd.     

Bidirectional behavior of unreinforced masonry walls

Most of the studies related to the modeling of masonry structures have by far investigated either the in‐plane (IP) or the out‐of‐plane (OP) behavior of walls. However, seismic loads mostly impose simultaneous IP and OP demands on load‐bearing or shear masonry walls. Thus, there is a need to reconsider design equations of unreinforced masonry walls by taking into account bidirectional effects. The intent of this study is to investigate the bidirectional behavior of an unreinforced masonry wall with a typical aspect ratio under different displacement‐controlled loading directions making use of finite element analysis. For this purpose, the numerical procedure is first validated against the results of the tests on walls with different failure modes conducted by the authors. Afterward, the response of the wall systems is evaluated with increasing top displacement having different orientations. A set of 19 monotonic and three cyclic loading analyses are performed, and the results are discussed in terms of the variation of failure modes and load–displacement diagrams. Moreover, the results of wall capacity in each loading condition are compared with those of the ASCE41‐06 formulations. The results indicate that the direction of the resultant force, vectorial summation of IP and OP forces, of the wall is initially proportional to the ratio of stiffness in the IP and the OP directions. However, with the increase of damage, the resultant force direction inclines towards the wall's longitudinal direction regardless of the direction of the imposed displacement. Finally, recommendations are made for applicability of ASCE41‐06 formulations under different bidirectional loading conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic evaluation of concrete dams via continuum damage models

In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) and arch dams (3D representation). The method allows for non-linear material behaviour of the dam, ‘transparent fictitious boundaries’ for dealing properly with in-coming and out-going seismic waves, and an efficient procedure to deal with dam-soil-fluid interaction. The mechanical behaviour of concrete is modelled using an isotropic damage model which allows for tension and compression damage, and exhibits stiffness recovery upon load reversals. Emphasis is placed in the treatment of fluid-structure interaction, regarding both formulation and efficiency aspects. A gravity dam and an arch dam are analysed subjected to artificially generated earthquakes of different intensities, and the results are used to study the degree of (un)safety of the dams.     

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.     

PERFORMANCE EVALUATION OF A THREE-STOREY UNREINFORCED MASONRY BUILDING DURING THE 1992 ERZİNCAN EARTHQUAKE

Seismic performance of a three-storey unreinforced masonry building which survived the 1992 Erzincan earthquake without damage is evaluated. Mechanical properties of the masonry walls have been determined experimentally by using identical brick and mortar used in construction. An accurate material model is developed for masonry and employed in a computer program for the non-linear dynamic analysis of masonry buildings. The analytical results based on measured material properties indicated that masonry buildings which satisfy basic seismic code requirements possess remarkable lateral strength, stiffness and energy dissipation capacity. Accordingly, a simple elastic design approach is rendered suitable for unreinforced masonry under seismic excitations, provided that realistic material properties are employed in design.     

Seismic performance evaluation of steel arch bridges against major earthquakes. Part 2: simplified verification procedure

The performance‐based philosophy has been accepted as a more reasonable design concept for engineering structures. For this purpose, capacity evaluation and demand prediction procedures for civil engineering structures under earthquake excitations are of great significance. This work presents a displacement‐based seismic performance verification procedure including capacity and seismic demand predictions for steel arch bridges and investigates its applicability. Pushover analyses is employed as a basis in this method to investigate the structure's behaviors. A failure criterion for steel members accounting for the effect of local buckling is involved and an equivalent single‐degree‐of‐freedom (ESDOF) system with a simplified bilinear hysteretic model formulated using pushover analyses results is introduced to estimate the displacement capacity and maximum demand of steel arch bridges under major earthquakes. To check the accuracy of the proposed method, seismic capacities and demands from multi‐degree‐of‐freedom (MDOF) time‐history analyses with Level‐II design earthquake record inputs modeling major earthquakes are used as benchmarks for comparison. By a case study, it is clarified that the proposed prediction procedure can give accurate estimations of displacement capacities and demands of the steel arch bridge in the transverse direction, while insufficient for the longitudinal direction, which confirms the conclusion drawn in other structure types about the applicability of pushover analyses. Copyright © 2004 John Wiley & Sons, Ltd.     

单调及低周往复荷载作用下砌体非线性分析

带构造柱和圈梁的约束砌体结构在四川灾区乡镇房屋重建中被广泛采用,其抗震性能是人们所关心的.基于绵竹市土门镇当地重建房屋常用建筑材料的实验数据以及通用有限元软件ANSYS中Solid 65单元的性质和特点,用有限元模型模拟了粘土砖砌体在不同压应力状态(σ-/fm)下沿通缝截面抗剪强度试验,给出了相关单元在模拟砖砌体开裂中闭合及开口剪力传递系数的建议值;利用这些结果,分别建立了带约束(构造柱、圈梁等)和不带约束砌体墙的有限元模型,进而分析了他们在单调荷载以及低周往复荷载作用下的抗震性能.结果表明,与不带约束的墙体相比,带约束墙体在单调水平荷载作用下的初裂性能、极值荷载和延性都有很大的提高,在低周往复荷载作用下其耗能能力得到了改善.所得结果可供相应结构抗震设计的参考.     

On the seismic behaviour of monolithic lunar arches subjected to moonquakes

With a new era emerging in the field of lunar exploration and habitation, there is a need for research on structural forms made of local soil material (regolith), which will be able to endure the extreme conditions in harsh environments (e.g., extreme temperature fluctuations, solar and cosmic radiation, meteor showers, strong ground motions, etc.). The present work focuses on understanding the dynamic and seismic behaviour of certain structural typologies of monolithic arches by means of finite element analysis (FEA). These typologies were extensively investigated previously, using static analyses accounting for the reduced gravitational field on the moon, and proved to be of the optimum shape against certain loading scenarios. Specifically, these optimal monolithic arch forms (named enhanced varying-thickness arches – EVTAs) examined herewith, are described by varying-thickness geometry, properly enhanced at certain weak points for increasing their structural stability. Aiming at a fair comparison, the seismic behaviour of EVTAs is contrasted to that of their corresponding monolithic constant-thickness (CTAs) counterparts (having the same amount of structural material). After defining an appropriate damage state, the authors conduct preliminary pushover analyses to determine the structural capacity of the arches against lateral loading. Subsequently, the modal analysis of the EVTAs shows that the second/vertical mode exhibits a natural period almost equal to that of their first/translational mode and substantially longer than the corresponding second/vertical mode of their CTA counterparts, indicating a potential vulnerability along the vertical excitation. Furthermore, taking into account that shallow moonquakes are comparable to intraplate earthquakes in terms of hazard potential, the authors produce sets of stochastic seismic excitations used as time histories for seismic analyses. The probability of exceedance of the defined damage state as a function of the peak ground acceleration (PGA) is presented through indicative fragility curves, where the structural superiority of EVTAs against their CTA counterparts is demonstrated.     

Modelling the out‐of‐plane seismic behaviour of masonry walls by rigid elements

A computational model for evaluating the dynamical response and the damage of large masonry walls subjected to out‐of‐plane seismic actions is presented. During earthquakes, these actions are often the main cause of damage for the front wall and lateral walls of old masonry‐built churches and monuments. Since the crack patterns often tend to subdivide the plane walls into a number of blocks, the model assumes such walls as a series of quadrilateral plane rigid elements connected to each other in the middle of their adjoining sides. Only the out‐of‐plane displacements are considered, and the connections are regarded as spherical elasto‐plastic joints which allow rotations whose axis is in the plane of the undeformed wall. The hysteretic characteristics of these joints are defined so as to approximate the brittle behaviour of masonry material and the degradation due to cyclic loadings. The numerical results obtained using a limited number of elements show that the global out‐of‐plane response of the masonry walls and the mechanical degradation at each connection are in accord with the observed behaviour of real churches hit by strong earthquakes. Copyright © 2000 John Wiley & Sons, Ltd.     

Cyclic testing of a single bay reinforced concrete frames with various types of masonry infill

In this paper, a contribution of various types of masonry infill to the behaviour of reinforced concrete frames under lateral loads is presented. As a part of the bigger project, ten one‐bay, one‐storey reinforced concrete frames were designed according to the EC8, built in a scale 1:2.5, infilled with masonry and tested under constant vertical and cyclic lateral load. The masonry wall had various strength properties, namely, high strength hollow clay brick blocks, medium strength hollow clay brick blocks and low strength lightweight autoclaved aerated concrete blocks. There were no additional shear connectors between the masonry and frame. The results showed that the composite ‘framed wall’ structure had much higher stiffness, damping and initial strength than the bare frame structure. Masonry infill filled in the load capacity gap from very low (0.05%) to drifts when the frame took over (0.75%). The structures behaved as linear monolithic elements to drifts of 0.1%, reached the maximum lateral capacities at drift of 0.3%, maintained it to drifts of 0.75% and after that their behaviour depended on the frame. Masonry infill had severe damage at drift levels of about 0.75% but contributed to the overall system resistance to drifts of about 1%. At that drift level, the frame had only minor damage and was tested to drifts of about 2% without any loss of capacity. Improvement of the ‘infill provisions’ in the codes could be sought by taking into account the contribution of a common masonry that reduces expected damages by lowering the drift levels. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic performance of masonry walls retrofitted with steel reinforced grout

An innovative solution for the seismic protection of existing masonry structures is proposed and investigated through shake table tests on a natural scale wall assemblage. After a former test series carried out without reinforcement, the specimen was retrofitted using Steel Reinforced Grout. The strengthening system comprises horizontal strips of ultra‐high strength steel cords, externally bonded to the masonry with hydraulic lime mortar, and connectors to transversal walls, applied within the thickness of the plaster layer. In order to assess the seismic performance of the retrofitted wall, natural accelerograms were applied with increasing intensity up to failure. Test results provide a deep understanding of the effectiveness of mortar‐based composites for improving the out‐of‐plane seismic capacity of masonry walls, in comparison with traditional reinforcements with steel tie‐bars. The structural implications of the proposed solution in terms of dynamic properties and damage development under earthquake loads are also discussed.Copyright © 2015 John Wiley & Sons, Ltd.