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Silos generally work as storage structures between supply and demand for various goods, and their structural safety has long been of interest to the civil engineering profession. This is especially true for dynamically loaded silos, e.g., in case of seismic excitation. Particularly thin-walled cylindrical silos are highly vulnerable to seismic induced pressures, which can cause critical buckling phenomena of the silo shell. The analysis of silos can be carried out in two different ways. In the first, the seismic loading is modeled through statically equivalent loads acting on the shell. Alternatively, a time history analysis might be carried out, in which nonlinear phenomena due to the filling as well as the interaction between the shell and the granular material are taken into account. The paper presents a comparison of these approaches. The model used for the nonlinear time history analysis considers the granular material by means of the intergranular strain approach for hypoplasticity theory. The interaction effects between the granular material and the shell is represented by contact elements. Additionally, soil–structure interaction effects are taken into account.
Multi-dimensional fragility analysis of a RC building with components using response surface method
(2017)
Conventional fragility curves describe the vulnerability of the main structure under external hazards. However, in complex structures such as nuclear power plants, the safety or the risk depends also on the components associated with a system. The classical fault tree analysis gives an overall view of the failure and contains several subsystems to the main event, however, the interactions in the subsystems are not well represented. In order to represent the interaction of the components, a method suggested by Cimellaro et al. (2006) using multidimensional performance limit state functions to obtain the system fragility curves is adopted. This approach gives the possibility of deriving the cumulative fragility taking into account the interaction of the response of different components. In this paper, this approach is used to evaluate seismic risk of a representative electrical building infrastructure, including the component, of a nuclear power plant. A simplified model of the structure, with nonlinear material behavior is employed for the analysis in Abaqus©. The input variables considered are the material parameters, boundary conditions and the seismic input. The variability of the seismic input is obtained from selected ground motion time histories of spectrum compatible synthetic ccelerograms. Unlike the usual Monte Carlo methods used for the probabilistic analysis of the structure, a computationally effective response surface method is used. This method reduces the computational effort of the calculations by reducing the required
number of samples.
This paper proposes a quick and simplified method to describe masonry vaults in global seismic analyses of buildings. An equivalent macro-element constituted by a set of six trusses, two for each transverse, longitudinal and diagonal direction, is introduced. The equivalent trusses, whose stiffness is calculated by fully modeled vaults of different geometry, mechanical properties and boundary conditions, simulate the vault in both global analysis and local analysis, such as kinematic or rocking approaches. A parametric study was carried out to investigate the influence of geometrical characteristics and mechanical features on the equivalent stiffness values. The method was numerically validated by performing modal and transient analysis on a three naves-church in the elastic range. Vibration modes and displacement time-histories were compared showing satisfying agreement between the complete and the simplified models. This procedure is particularly useful in engineering practice because it allows to assess, in a simplified way, the effectiveness of strengthening interventions for reducing horizontal relative displacements between vault supports.
In this paper, a coupled multiphase model considering both non-linearities of water retention curves and solid state modeling is proposed. The solid displacements and the pressures of both water and air phases are unknowns of the proposed model. The finite element method is used to solve the governing differential equations. The proposed method is demonstrated through simulation of seepage test and partially consolidation problem. Then, implementation of the model is done by using hypoplasticity for the solid phase and analyzing the fully saturated triaxial experiments. In integration of the constitutive law error controlling is improved and comparisons done accordingly. In this work, the advantages and limitations of the numerical model are discussed.
In recent years, many onshore wind turbines are erected in seismic active regions and on soils with poor load bearing capacity, where pile grids are inevitable to transfer the loads into the ground. In this contribution, a realistic multi pile grid is designed to analyze the dynamics of a wind turbine tower including frequency dependent soil-structure-interaction. It turns out that different foundations on varying soil configurations heavily influence the vibration response. While the vibration amplitude is mostly attenuated, certain unfavorable combinations of structure and soil parameters lead to amplification in the range of the system's natural frequencies. This testifies the need for overall dynamic analysis in the assessment of the dynamic stability and the holistic frequency tuning of the turbines.
The Effect of Openings on Out-of-Plane Capacity of Masonry Infilled Reinforced Concrete Frames
(2018)
Seismic design of buried pipeline systems for energy and water supply is not only important for plant and operational safety but also for the maintenance of the supply infrastructure after an earthquake. The present paper shows special issues of the seismic wave impacts on buried pipelines, describes calculation methods, proposes approaches and gives calculation examples. This paper regards the effects of transient displacement differences and resulting tensions within the pipeline due to the wave propagation of the earthquake. However, the presented model can also be used to calculate fault rupture induced displacements. Based on a three-dimensional Finite Element Model parameter studies are performed to show the influence of several parameters such as incoming wave angle, wave velocity, backfill height and synthetic displacement time histories. The interaction between the pipeline and the surrounding soil is modeled with non-linear soil springs and the propagating wave is simulated affecting the pipeline punctually, independently in time and space. Special attention is given to long-distance heat pipeline systems. Here, in regular distances expansion bends are arranged to ensure movements of the pipeline due to high temperature. Such expansion bends are usually designed with small bending radii, which during the earthquake lead to high bending stresses in the cross-section of the pipeline. Finally, an interpretation of the results and recommendations are given for the most critical parameters.
Frequency Dependent Impedance Analysis of the Foundation-Soil-Systems of Onshore Wind Turbines
(2018)
Stahlbetonrahmentragwerke mit Mauerwerksausfachungen weisen nach Erdbebenereignissen häufig schwere Schäden auf, da die Ausfachungen ohne weitere konstruktive Maßnahmen mit vollem Kontakt zum Stahlbetonrahmen eingemauert werden. Durch die unplanmäßige Beteiligung am horizontalen Lastabtrag erfahren die Ausfachungen Belastungen in Wandebene und beeinflussen das globale Schwingungsverhalten der Rahmentragwerke. In Kombination mit den gleichzeitig auftretenden seismischen Trägheitskräften senkrecht zur Wand führt dies in vielen Fällen zu einem Versagen der mit niedrigen Festigkeiten ausgeführten Ausfachungen. Dies war der Anlass in dem europäischen Forschungsprojekt INSYSME ein Entkopplungssystem zu entwickeln, mit dem Rahmen und Ausfachung durch ein spezielles Profil aus Elastomeren entkoppelt werden.
Das Profil ermöglicht Relativverschiebungen zwischen Rahmen und Ausfachung und stellt gleichzeitig die Aufnahme von Belastungen senkrecht zur Wand sicher. Der Beitrag erläutert zunächst den Aufbau des Systems und gibt einen Überblick über die in Kleinbauteilversuchen ermittelten Tragfähigkeiten. Zudem werden experimentelle Untersuchungen an mit hochwärmedämmenden Mauerziegeln ausgefachten Stahlbetonrahmen mit und ohne Entkopplungssystem für getrennte und kombinierte Belastungen in und senkrecht zur Wandebene vorgestellt. Auf Grundlage einer Versuchsauswertung und eines Ergebnisvergleichs werden Wirkungsweise und Effektivität des entwickelten Entkopplungssystems demonstriert.
The article presents the investigation of the seismic behaviour of a modern URM building located in the municipality of Finale Emilia in province of Modena, Northern Italy. The building is situated in the centre of the series of the 2012 Northern Italy earthquakes and has not suffered any damage during the earthquake series in 2012. The observed earthquake resistance of the building is compared with predicted resistances based on linear and nonlinear design approaches according to Eurocode. Furthermore, probabilistic analyses based on nonlinear calculation models taking into account scattering of the most relevant input parameters are carried out to identify their influence to the results and to derive fragility curves.
Reinforced concrete (RC) frames with masonry infills are frequently used in seismic regions all over the world. Generally masonry infills are considered as nonstructural elements and thus are typically neglected in the design process. However, the observations made after strong earthquakes have shown that masonry infills can modify the dynamic behavior of the structure significantly. The consequences were total collapses of buildings and loss of human lives. This paper presents the new system INODIS (Innovative Decoupled Infill System) developed within the European research project INSYSME (Innovative Systems for Earthquake Resistant Masonry Enclosures in RC Buildings). INODIS decouples the frame and the masonry infill by means of special U-shaped rubbers placed in between frame and infill. The effectiveness of the system was investigated by means of full scale tests on RC frames with masonry infills subjected to in-plane and out-of-plane loading. Furthermore small specimen tests were conducted to determine material characteristics of the components and the resistances of the connections. Finally, a micromodel was developed to simulate the in-plane behavior of RC frames infilled with AAC blocks with and without installation of the INODIS system.
Im Rahmen des europäischen Verbundprojekts INSYSME wurden von den deutschen Partnern die Systeme IMES und INODIS zur Verbesserung des seismischen Verhaltens von ausgefachten Stahlbetonrahmen entwickelt. Ziel beider Systeme ist es, Stahlbetonrahmen und Ausfachung zu entkoppeln, anstatt die Tragfähigkeit durch aufwendige und kostspielige zusätzliche Bewehrungseinlagen zu erhöhen. Erste Ergebnisse des Systems IMES für Belastungen in und senkrecht zu der Wandebene werden vorgestellt.
Im Rahmen des europäischen Verbundprojekts INSYSME wurden von den deutschen Partnern die Systeme IMES und INODIS zur Verbesserung des seismischen Verhaltens von ausgefachten Stahlbetonrahmen entwickelt. Ziel beider Systeme ist es, Stahlbetonrahmen und Ausfachung zu entkoppeln, anstatt die Tragfähigkeit durch aufwendige und kostspielige zusätzliche Bewehrungseinlagen zu erhöhen. Erste Ergebnisse des Systems IMES für Belastungen in und senkrecht zu der Wandebene werden vorgestellt.
Wind loads have great impact on many engineering structures. Wind storms often cause irreparable damage to the buildings which are exposed to it. Along with the earthquakes, wind represents one of the most common environmental load on structures and is relevant for limit state design. Modern wind codes indicate calculation procedures allowing engineers to deal with structural systems, which are susceptible to conduct wind-excited oscillations. In the codes approximate formulas for wind buffeting are specified which relate the dynamic problem to rather abstract parameter functions. The complete theory behind is not visible in order to simplify the applicability of the procedures. This chapter derives the underlying basic relations of the spectral method for wind buffeting and explains the main important applications of it in order to elucidate part of the theoretical background of computations after the new codes. The stochasticity of the wind processes is addressed, and the analysis of analytical as well as measurement based power spectra is outlined. Short MATLAB codes are added to the Appendix 3 which carry out the computation of a single sided auto-spectrum from a statistically stationary, discrete stochastic process. Two examples are presented.
Industrial units consist of the primary load-carrying structure and various process engineering components, the latter being by far the most important in financial terms. In addition, supply structures such as free-standing tanks and silos are usually required for each plant to ensure the supply of material and product storage. Thus, for the earthquake-proof design of industrial plants, design and construction rules are required for the primary structures, the secondary structures and the supply structures. Within the framework of these rules, possible interactions of primary and secondary structures must also be taken into account. Importance factors are used in seismic design in order to take into account the usually higher risk potential of an industrial unit compared to conventional building structures. Industrial facilities must be able to withstand seismic actions because of possibly wide-ranging damage consequences in addition to losses due to production standstill and the destruction of valuable equipment. The chapter presents an integrated concept for the seismic design of industrial units based on current seismic standards and the latest research results. Special attention is devoted to the seismic design of steel thin-walled silos and tank structures.
The chapter initially provides a summary of the contents of Eurocode 8, its aim being to offer both to the students and to practising engineers an easy introduction into the calculation and dimensioning procedures of this earthquake code. Specifically, the general rules for earthquake-resistant structures, the definition of design response spectra taking behaviour and importance factors into account, the application of linear and non-linear calculation methods and the structural safety verifications at the serviceability and ultimate limit state are presented. The application of linear and non-linear calculation methods and corresponding seismic design rules is demonstrated on practical examples for reinforced concrete, steel and masonry buildings. Furthermore, the seismic assessment of existing buildings is discussed and illustrated on the example of a typical historical masonry building in Italy. The examples are worked out in detail and each step of the design process, from the preliminary analysis to the final design, is explained in detail.
The 2012 Emilia-Romagna earthquake, that mainly struck the homonymous Italian region provoking 28 casualties and damage to thousands of structures and infrastructures, is an exceptional source of information to question, investigate, and challenge the validity of seismic fragility functions and loss curves from an empirical standpoint. Among the most recent seismic events taking place in Europe, that of Emilia-Romagna is quite likely one of the best documented, not only in terms of experienced damages, but also for what concerns occurred losses and necessary reconstruction costs. In fact, in order to manage the compensations in a fair way both to citizens and business owners, soon after the seismic sequence, the regional administrative authority started (1) collecting damage and consequence-related data, (2) evaluating information sources and (3) taking care of the cross-checking of various reports. A specific database—so-called Sistema Informativo Gestione Europa (SFINGE)—was devoted to damaged business activities. As a result, 7 years after the seismic events, scientists can rely on a one-of-a-kind, vast and consistent database, containing information about (among other things): (1) buildings’ location and dimensions, (2) occurred structural damages, (3) experienced direct economic losses and (4) related reconstruction costs. The present work is focused on a specific data subset of SFINGE, whose elements are Long-Span-Beam buildings (mostly precast) deployed for business activities in industry, trade or agriculture. With the available set of data, empirical fragility functions, cost and loss ratio curves are elaborated, that may be included within existing Performance Based Earthquake Engineering assessment toolkits.
Masonry infill walls are commonly used in reinforced concrete (RC) frame structures, also in seismically active areas, although they often experience serious damage during earthquakes. One of the main reasons for their poor behaviour is the connection to the frame, which is usually constructed using mortar. This paper describes the novel solution for infill/frame connection based on application of elastomeric material between them. The system called INODIS (Innovative Decoupled Infill System) has the aim to postpone the activation of infill in in-plane direction and at the same time to provide sufficient out-of-plane support. First, experimental tests on infilled frame specimens are presented and the comparison of the results between traditionally infilled frames and infilled frames with the INODIS system are given. The results are then used for calibration and validation of numerical model, which can be further employed for investigating the influence of some material parameters on the behaviour of infilled frames with the INODIS system.
Erdbebennachweis von Mauerwerksbauten mit realistischen Modellen und erhöhten Verhaltensbeiwerten
(2020)
Die Anwendung des linearen Nachweiskonzepts auf Mauerwerksbauten führt dazu, dass bereits heute Standsicherheitsnachweise für Gebäude mit üblichen Grundrissen in Gebieten mit moderaten Erdbebeneinwirkungen nicht mehr geführt werden können. Diese Problematik wird sich in Deutschland mit der Einführung kontinuierlicher probabilistischer Erdbebenkarten weiter verschärfen. Aufgrund der Erhöhung der seismischen Einwirkungen, die sich vielerorts ergibt, ist es erforderlich, die vorhandenen, bislang nicht berücksichtigten Tragfähigkeitsreserven in nachvollziehbaren Nachweiskonzepten in der Baupraxis verfügbar zu machen. Der vorliegende Beitrag stellt ein Konzept für die gebäudespezifische Ermittlung von erhöhten Verhaltensbeiwerten vor. Die Verhaltensbeiwerte setzen sich aus drei Anteilen zusammen, mit denen die Lastumverteilung im Grundriss, die Verformungsfähigkeit und Energiedissipation sowie die Überfestigkeiten berücksichtigt werden. Für die rechnerische Ermittlung dieser drei Anteile wird ein nichtlineares Nachweiskonzept auf Grundlage von Pushover-Analysen vorgeschlagen, in denen die Interaktionen von Wänden und Geschossdecken durch einen Einspanngrad beschrieben werden. Für die Bestimmung der Einspanngrade wird ein nichtlinearer Modellierungsansatz eingeführt, mit dem die Interaktion von Wänden und Decken abgebildet werden kann. Die Anwendung des Konzepts mit erhöhten gebäudespezifischen Verhaltensbeiwerten wird am Beispiel eines Mehrfamilienhauses aus Kalksandsteinen demonstriert. Die Ergebnisse der linearen Nachweise mit erhöhten Verhaltensbeiwerten für dieses Gebäude liegen deutlich näher an den Ergebnissen nichtlinearer Nachweise und somit bleiben übliche Grundrisse in Erdbebengebieten mit den traditionellen linearen Rechenansätzen nachweisbar.
Mit finanzieller Unterstützung der Deutschen Gesellschaft für Mauerwerks- und Wohnungsbau e.V. (DGfM) und des Deutschen Instituts für Bautechnik in Berlin (DIBt) wurden zwei aufeinander aufbauende Forschungsvorhaben zur Verbesserung der seismischen Nachweise von Mauerwerksbauten in deutschen Erdbebengebieten durchgeführt. Zunächst wurde das seismische Verhalten von drei modernen unbewehrten Mauerwerksgebäuden in der Region Emilia Romagna in Italien während der Erdbebenserie im Jahr 2012 in Kooperation mit der Universität Pavia eingehend untersucht. Aufbauend auf den Erkenntnissen dieser Untersuchungen wurde ein verbessertes seismisches Bemessungskonzept für unbewehrte Mauerwerksbauten erarbeitet. Der Beitrag stellt die wesentlichen Ergebnisse dieser Forschungsarbeiten und deren Eingang in die Normung vor.
Stahlbetonrahmentragwerke mit Ausfachungen aus Mauerwerk weisen nach Erdbeben häufig schwere Schäden auf. Gründe hierfür sind die Beanspruchungen der Ausfachungswände durch die aufgezwungenen Rahmenverformungen in Wandebene und die gleichzeitig auftretenden Trägheitskräfte senkrecht zur Wandebene in Kombination mit der konstruktiven Ausführung des Ausfachungsmauerwerks. Die Ausfachung wird in der Regel knirsch gegen die Rahmenstützen gemauert, wobei der Verschluss der oberen Fuge mit Mörtel oder Montageschaum erfolgt. Dadurch kommt es im Erdbebenfall zu lokalen Interaktionen zwischen Ausfachung und Rahmen, die in der Folge zu einem Versagen einzelner Ausfachungswände oder zu einem sukzessiven Versagen des Gesamtgebäudes führen können. Die beobachteten Schäden waren die Motivation dafür, in dem europäischen Forschungsprojekt INSYSME für Stahlbetonrahmentragwerke mit Ausfachungen aus hochwärmedämmenden Ziegelmauerwerk innovative Lösungen zur Verbesserung des seismischen Verhaltens zu entwickeln. Der vorliegende Beitrag stellt die im Rahmen des Projekts von den deutschen Projektpartnern (Universität Kassel, SDA-engineering GmbH) entwickelten Lösungen vor und vergleicht deren seismisches Verhalten mit der traditionellen Ausführung der Ausfachungswände. Grundlage für den Vergleich sind statisch-zyklische Wandversuche und Simulationen auf Wandebene. Aus den Ergebnissen werden Empfehlungen für die erdbebensichere Auslegung von Stahlbetonrahmentragwerken mit Ausfachungen aus Ziegelmauerwerk abgeleitet.
Armiranobetonske (AB) zgrade sa zidanom ispunom
se izvode u mnogim zemljama širom sveta. Iako se
zidana ispuna posmatra kao nekonstruktivni element, ona
značajno utiče na promenu dinamičkih karakteristika AB
ramovskih konstrukcija u toku zemljotresnog dejstva.
Odskora, značajan napor je utrošen na istraživanje
izolovanih ispuna, koje su odvojene od okolnog rama
obično ostavljanjem prostora između rama i ispune. U
ovom slučaju deformacija rama ne aktivira ispunu i na taj
način ispuna ne utiče na ponašanje rama. Ovaj rad
predstavlja rezultate istraživanja ponašanja AB
ramovskih zgrada sa INODIS sistemom koji izoluje ispunu
u odnosu na okolni ram. Uticaj izolovane ispune je prvo
ispitan na jednospratnim i jednobrodnim ramovima. Ovo
je iskorišćeno kao osnova za parametarsku analizu na
višespratnim i višebrodnim ramovima, kao i na primeru
zgrade. Promena krutosti i dinamičkih karakteristika je
analizirano kao i odgovor pri zemljotresnom dejstvu.
Izvršeno je poređenje sa praznom ramovskom
konstrukcijom kao i ramovima ispunjenim ispunom na
tradicionalni način. Rezultati pokazuju da je ponašanje
ramova sa izolovanom ispunom slično ponašanju praznih
ramova, dok je ponašanje ramova sa tradicionalnom
ispunom daleko drugačije i zahteva kompleksne
numeričke modele. Ovo znači da ukoliko se primeni
adekvatna konstruktivna mera izolacije ispune, proračun
ramovskim zgrada sa zidanom ispunom se može
značajno pojednostaviti.
Masonry is used in many buildings not only for load-bearing walls, but also for non-load-bearing enclosure elements in the form of infill walls. Many studies confirmed that infill walls interact with the surrounding reinforced concrete frame, thus changing dynamic characteristics of the structure. Consequently, masonry infills cannot be neglected in the design process. However, although the relevant standards contain requirements for infill walls, they do not describe how these requirements are to be met concretely. This leads in practice to the fact that the infill walls are neither dimensioned nor constructed correctly. The evidence of this fact is confirmed by the recent earthquakes, which have led to enormous damages, sometimes followed by the total collapse of buildings and loss of human lives. Recently, the increasing effort has been dedicated to the approach of decoupling of masonry infills from the frame elements by introducing the gap in between. This helps in removing the interaction between infills and frame, but raises the question of out-of-plane stability of the panel. This paper presents the results of the experimental campaign showing the out-of-plane behavior of masonry infills decoupled with the system called INODIS (Innovative decoupled infill system), developed within the European project INSYSME (Innovative Systems for Earthquake Resistant Masonry Enclosures in Reinforced Concrete Buildings). Full scale specimens were subjected to the different loading conditions and combinations of in-plane and out-of-plane loading. Out-of-plane capacity of the masonry infills with the INODIS system is compared with traditionally constructed infills, showing that INODIS system provides reliable out-of-plane connection under various loading conditions. In contrast, traditional infills performed very poor in the case of combined and simultaneously applied in-plane and out-of-plane loading, experiencing brittle behavior under small in-plane drifts followed by high out-of-plane displacements. Decoupled infills with the INODIS system have remained stable under out-of-plane loads, even after reaching high in-plane drifts and being damaged.
Seismic behavior of an existing unreinforced masonry building built pre-modern code, located in the City of Ohrid, Republic of North Macedonia has been investigated in this paper. The analyzed school building is selected as an archetype in an ongoing project named “Seismic vulnerability assessment of existing masonry structures in Republic of North Macedonia (SeismoWall)”. Two independent segments were included in this research: Seismic hazard assessment by creating a cite specific response spectra and Seismic vulnerability definition by creating a region - specific series of vulnerability curves for the chosen building topology. A reliable Seismic Hazard Assessment for a selected region is a crucial point for performing a seismic risk analysis of a characteristic building class. In that manner, a scenario – based method that incorporates together the knowledge of tectonic style of the considered region, the active fault characterization, the earth crust model and the historical seismicity named Neo Deterministic approach is used for calculation of the response spectra for the location of the building. Variations of the rupturing process are taken into account in the nucleation point of the rupture, in the rupture velocity pattern and in the istribution of the slip on the fault. The results obtained from the multiple scenarios are obtained as an envelope of the response spectra computed for the cite using the procedure Maximum Credible Seismic Input (MCSI). Capacity of the selected building has been determined by using nonlinear static analysis. MINEA software (SDA Engineering) was used for verification of the structural safety of the chosen unreinforced masonry structure. In the process of optimization of the number of samples, computational cost required in a Monte Carlo simulation is significantly reduced since the simulation is performed on a polynomial response surface function for prediction of the structural response. Performance point, found as the intersection of the capacity of the building and the spectra used, is chosen as a response parameter. Five levels of damage limit states based on the capacity curve of the building are defined in dependency on the yield displacement and the maximum displacement. Maximum likelihood estimation procedure is utilized in the process of vulnerability curves determination. As a result, region specific series of vulnerability curves for the chosen type of masonry structures are defined. The obtained probabilities of exceedance a specific damage states as a result from vulnerability curves are compared with the observed damages happened after the earthquake in July 2017 in the City of Ohrid, North Macedonia.
In many historical centers in Europe, stone masonry is part of building aggregates, which developed when the layout of the city or village was densified. The analysis of such building aggregates is very challenging and modelling guidelines missing. Advances in the development of analysis methods have been impeded by the lack of experimental data on the seismic response of such aggregates. The SERA project AIMS (Seismic Testing of Adjacent Interacting Masonry Structures) provides such experimental data by testing an aggregate of two buildings under two horizontal components of dynamic excitation. With the aim to advance the modelling of unreinforced masonry aggregates, a blind prediction competition is organized before the experimental campaign. Each group has been provided a complete set of construction drawings, material properties, testing sequence and the list of measurements to be reported. The applied modelling approaches span from equivalent frame models to Finite Element models using shell elements and discrete element models with solid elements. This paper compares the first entries, regarding the modelling approaches, results in terms of base shear, roof displacements, interface openings, and the failure modes.