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In this paper, a novel numerical method for strucural analysis, called the Hybrid Discrete-Finite Element Method (HybriDFEM), is presented. In this method, a structure is modeled as an assembly of rigid blocks in contact. All the deformation is concentrated at the interfaces, which are modeled as series of distributed nonlinear multidirectional springs. The method shares similarities with the Discrete Element Methods (DEM) in its ability to account for contact interfaces and/or block deformability, and with the Applied Element Method (AEM) in the representation of interfaces as a series of normal and shear springs. However, it is close to the FEM in the way it is formulated, which offers the possibility to readily link both methods for potential hybrid applications. This paper focuses on the modeling of continuous and discontinuous frames with the HybriDFEM. It is shown how the model can do so with a nonlinear material model, and considering (or not) nonlinear geometric effects through large nodal displacements. Different nonlinear solution procedures implemented in HybriDFEM are demonstrated, such as load-control and various displacement-controlled methods. This model is able to simulate contacts between rigid or deformable units, an important feature when it comes to the modeling of, e.g., unreinforced masonry structures, with a reasonable computational cost and a formulation that is cast within the framework of the classical FEM.

This work explains the development of a viscous damping model using the condensed tangent stiffness of the structure. It eliminates the spurious damping forces and avoids the high levels of damping presented by the condensed damping model defined with the initial properties. Additionally, this article elucidates some of the problems of the existing condensed models and compares them with Rayleigh or total initial stiffness proportional damping. The proposed damping model and the existing models are compared using a reinforced concrete frame subjected to a ground motion, where the main arguments to justify the newly proposed damping model are highlighted.

The substitution of reinforcing steel with shape memory alloys has been offered as a solution for reducing residual displacements in reinforced concrete (RC) walls. This paper presents some recent experimental and numerical research efforts conducted by the authors and colleagues in the iMMC at UCLouvain focusing on the seismic performance of RC walls detailed with shape memory alloys. A summary of an experimental campaign is provided, which involved testing two large-scale planar RC walls. Some results from numerical simulations using state-of-the-art finite element modelling are also presented. Current and future research will focus, among others, on developing a more robust connection between the shape memory alloy and conventional steel rebars for implementation in concrete structures.

Pushover analyses are often used to evaluate the seismic performance of a structure. They give an estimate of the ultimate displacement a structure can undergo, as well as of the residual resisting forces in the post-peak response. When modelling masonry structures composed of multiple blocks, obtaining the post-peak branch of the pushover curve can be difficult with a classic displacement-control strategy. This paper describes a strategy designed to compute this branch for multi-block systems subjected to a given pattern of forces, without the need to apply a displacement-control algorithm. The strategy is general, therefore straightforwardly implementable in different software tools and applicable to complex block assemblies. In the present work, it is implemented in two different DEM software, namely LMCG90 and UDEC, and tested on a benchmark problem for evaluating the in-plane response of masonry walls.

Although distributed plasticity beam elements include formulations that verify a strict equilibrium of the axial forces along the element length, known as force-based (FB) approaches, the classical conventional displacement-based (DB) elements show advantages in simulating the response of some structural members. However, the latter do not verify strong equilibrium of the axial forces, but only the weak or integral form of equilibrium. To fix this issue, several authors recently proposed enhanced strain formulations that respect a strict equilibrium along the axial direction, obtained through iterations on the cross-sectional average strain in each section. Unfortunately, most research efforts on innovative beam formulations have been directed towards planar (2D) elements, instead of spatial (or 3D) formulations. This work thus presents the implementation of a 3D axially equilibrated DB (DB/ae) beam element in the finite element software OpenSees, as an enhancement of the classical displacement-based (DB/c) formulation. In order to present advantages and drawbacks of the proposed 3D DB/ae beam element, its numerical responses are compared with those obtained from the DB/c and FB elements, first with reference to an application example featuring bidirectional loading, and then taking the experimental data from one series of quasi-static bidirectional cyclic tests, related to two reinforced concrete (RC) thin walls, as benchmark.

When using a plastic hinge analysis, the displacement capacity of a reinforced concrete wall is highly dependent on the assumed value for the plastic hinge length (Lp). Most of the expressions that are available in the literature have been derived specifically for beams, columns, bridge piers, or planar (rectangular) walls with an applicability to a small range of design values. This paper introduces an expression for the Lp derived from recent research using an extensive database of experimental and numerical results of both planar and non-planar walls. The design expression presented for Lp is found to provide more conservative estimates in comparison to that currently used in some building codes of 0.5 times the wall length. The assessment expression for Lp can provide more reasonable estimates, which will in turn provide more accurate estimates of the displacement capacity of the wall.

Reinforced concrete core walls form the backbone of millions of buildings internationally, bracing the structure against wind and earthquake loading. Due largely to plan asymmetry, a torsional response of a building is possible, where the core wall will resist the twisting actions. There is currently no evidence for the torsional capacity of reinforced concrete U-shaped core walls, which are a popular wall geometry used in construction practice. An experimental campaign will be soon conducted in the laboratory LEMSC of the institute iMMC at UCLouvain, Belgium, to test three large-scale reinforced concrete U-shaped walls subjected to different combinations of flexure and torsion. A blind prediction competition was organised by the authors to estimate salient behaviour and performance characteristics of the walls subjected to pure flexure and pure torsion. This paper presents a summary of the experimental campaign and some blind predictions by the authors using finite element modelling. These predictions, as well as others submitted for the competition, will be compared to the experimental results during the conference presentation.

This paper presents a tangent-stiffness-proportional viscous damping model independent of the geometric stiffness for time-history response simulation of frame structures. The nonlinear geometric effects are considered using a corotational formulation that allows to isolate the nonlinear effects of material and geometric sources, as well as the corresponding tangent stiffness contributions. Therefore, non-directly modelled sources of energy dissipation can be made proportional just to the material stiffness matrix term. After presenting the formulation and discussing the physical significance of the proposed model, an illustrative example of a slender reinforced concrete column is presented. Comparisons with the widely used total-tangent-stiffness-proportional approach show the advantages of the current proposal.

This work compares the force-based (FB) design of moment resisting frames, as proposed in the next generation of Eurocode 8, with a complete displacement-based (DB)design approach, also introduced in the future code. After describing some of the evolutions in the FB approach, namely regarding the use of behaviour factor components, the main concepts of the DB approach are addressed, including the associated global and local verifications. The FB design of a set of reinforced concrete frames is described, followed by their nonlinear static analyses and DB-like verifications. These results are used to estimate the components of the behaviour factor, which are then compared with those adopted initially for the FB design. The level of conservativeness of the FB approach is estimated by comparing the ratios between the plastic deformation demand and capacity with the target values.

The seismic performance of buildings depends critically on the stiffness and strength of storey diaphragms. Whilst for modern reinforced concrete or steel structures the connection between floors and lateral resisting members is often assumed as monolithic, timber floors and ceilings in masonry buildings are susceptible to sliding in their supports. In fact, the anchorage of timber beams in masonry walls and intermediate supports relies partly or totally on a frictional type of resisting mechanism. The present work contributes to characterize this behaviour by presenting the results of an extensive experimental programme with cyclic friction triplet tests between mortar and timber units, and between timber and timber units. These were produced to be representative of connection typologies characteristic of pre-modern and contemporary construction periods. Each test was performed under a constant level of contact pressure, which was increased throughout each series to cover a range of normal forces foreseeable in building connections. Other aspects are also discussed, such as the influence of cumulative loading or velocity. The experimental data is made available for public use(https://doi.org/10.5281/zenodo.3348328).

Reinforced concrete buildings typically utilise structural (or shear) walls as their primary lateral load resisting system. The U-shaped wall is a popular cross-sectional shape used in construction as it can enclose a service core, elevators (lifts), stairs and bathroom facilities. Although U-shaped walls are prevalent throughout the reinforced concrete building stock of both regions of high seismicity and low-to-moderate seismicity, there have been very few studies and experimental tests conducted on non-rectangular reinforced concrete walls. Some Latin American countries have recently moved to construction of mid- and high-rise reinforced concrete buildings with structural walls. In order to reduce material costs, which are critical in these areas of South America with respect to labour costs, very thin walls with only one layer of non-ductile steel reinforcing bars are being used. Until recently, building codes allowed this type of construction in Australia, where there is likely to be an abundance of highly stressed, lightly reinforced precast walls embedded within the building stock. To the authors knowledge, there are no experimental results for reinforce concrete U-shaped walls detailed with a single layer of vertical reinforcement. Thus, the seismic performance of such walls is largely unknown. Therefore, large-scale tests of thin U-shaped walls with a single layer of vertical reinforcement were conducted in the Earthquake Engineering and Structural Dynamics Laboratory at École Polytechnique Fèdèrale de Lausanne (EPFL), Switzerland. This research paper presents some of the design considerations as well as the test setup and loading protocol of the Ushaped walls under horizontal quasi-static cyclic loading. The initial results of the test are then briefly discussed, including the force-displacement hysteresis and failure mechanisms.

Reinforced concrete (RC) U-shaped core walls are commonly used in buildings to provide lateral resistance for wind and earthquake actions. While there is an abundance of these structural elements within the building stocks of both low-to-moderate and high seismic regions, there have been few experimental studies focusing on the seismic resistance of RC walls with a U-shaped cross-section. Building codes in some Latin American countries, such as Colombia, currently allow very thin RC walls with a single layer of reinforcement to be constructed. This type of construction is similar to practices in Australia, prior to the revised Concrete Structures building code coming into effect in 2019. Large-scale tests of two thin RC U-shaped walls with a single layer of vertical reinforcement were conducted in the Earthquake Engineering Structural Dynamics Laboratory at École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. This paper presents some of the test setups and loading protocols used to test the walls, as well as the initial results, including local and global failure modes.

Lap splices are essential to avoid premature failure of reinforced concrete structural members. Before modern earthquake guidelines, lap splices were often placed in plastic hinge regions that undergo inelastic deformations under seismic loading. The seismic performance assessment of such members requires not only the evaluation of the lap splice strength but also its deformation capacity. While the former was assessed in several previous studies, the latter is still rather unknown. This paper addresses the results of a recently concluded experimental programme on spliced RC walls boundary elements tested under uniaxial tension-compression cyclic loading. The study investigated the influence of lap splice length, confining reinforcement and loading history on the deformation capacity of lap splices. The test results showed that the deformation capacity of lap splices: (i) increases with lap splice length; (ii) increases with confining reinforcement, although its effectiveness is dependent on the lap splice length; (iii) decreases with larger imposed compression levels; (iv) is larger for bottom-casted with respect to top-casted lap splices. Finally, an empirical model is proposed to estimate the strain capacity of lap splices, which provides a good fit with the experimental results.

The seismic behaviour of reinforced concrete framed structures involves a number of nonlinear material and geometrical phenomena that are impossible to model exhaustively in a single model. Furthermore, past studies showed that the most correct modelling options from the scientific viewpoint are sometimes challenged by experimental results. Over the years, attempts have been made to identify and measure the importance of different modelling options. This work intends to consolidate some of these findings and further extend them in order to progressively bridge the gap between solidly established theoretical principles and shaking table test results. The response of three different structures used in international blind prediction test challenges serves as benchmark to assess the goodness-of-fit of alternative numerical solutions. The interpretation of the results highlights the sensitivity of the response with respect to the modelling choices and provides indications towards the development of optimized numerical analyses. N/A

The seismic assessment of existing masonry buildings is based on the prediction of their nonlinear response under lateral loading. This requires a reliable estimation of the force and displacement demand. For this purpose, modelling strategies using structural component elements are widely applied both in research and in engineering practice, since they can provide a satisfactory description of the cyclic behaviour of a masonry building with a limited computational cost. One of such modelling strategies are equivalent frame models, in which beam elements describe the response of piers and spandrels. This paper proposes the use of two-node, force-based beam elements with distributed inelasticity to model the in-plane response of modern unreinforced brick masonry panels. The nonlinearity of the response is described through the use of numerically integrated fibre sections and a suitable material model, implemented for this scope in the open-source platform “OpenSees”, describing a coupling at the local level between axial and shear response. Experimental results from a shear and compression test are used to validate the approach and justify some details of the proposed modelling strategy. Since the experimental data included also local displacement measures, the comparison of the numerical and experimental results is extended to curvatures and shear strains. The good agreement between numerical and experimental response confirms the applicability of the proposed approach for modelling the cyclic response of unreinforced brick masonry walls.

Reinforced concrete (RC) structures with tri-dimensional asymmetries tend to exhibit torsional effects that are of great concern in the field of earthquake engineering, in particular at large ductility levels where they become more relevant [MAN09]. In nuclear facilities, this issue assumes particular relevance considering that these structures are designed to respond essentially in the elastic range with a controlled level of deformations and accelerations when subjected to strong ground motions. Within the previous framework, the research project SMART 2013 (‘Seismic design and best-estimate Methods Assessment for Reinforced concrete buildings subjected to Torsion and non-linear effects’) was conducted in order to improve the knowledge on the seismic response of irregular RC structures (experimental test) and to provide reference data for modelling developments and validation (benchmark). Past blind prediction contests showed that, by making use of appropriate modelling options, the seismic response of structures can be predicted with satisfactory accuracy [SOU14]. Nonetheless, they have also evidenced a significant dispersion of predictions between the different participating teams, as demonstrated by the results obtained in the past blind prediction contest [NEE10]. After a short description of the SMART 2013 mock-up and corresponding loading, the present paper describes the properties of the numerical model used by one the participating teams and the comparison of its results with those obtained from the experiments.

The use of thin reinforced concrete walls (thickness of 8 to 12 cm) in Latin America has become a popular building construction practice in the last two decades. Several existing studies indicate that the inelastic deformation capacity could be limited and the level of damage could be severe even at low levels of plastic rotation. There is a lack of experimental data and practically no field post-earthquake observations related to the behavior of this construction system; therefore, a research effort was recently launched to gather further information about the geometry, materials, reinforcement detailing and response of these thin RC walls. The main variables of interest indentified during the early stage of the study were the slenderness ratio, axial load ratio, reinforcement detailing, and cross section geometry. Based on such study, several prototypes have been defined for experimental testing. This paper presents the preliminary results of a T-shaped single layer reinforced concrete wall with a shear span ratio of 2. The reinforcement comprises ductile conventional steel bars, with not additional steel at the web boundary. A reversed cyclic load pattern was applied to the specimen, keeping an axial load ratio of 5% based on the specified concrete compressive strength. The results obtained indicated a limited capacity of inelastic deformation, reaching an average plastic rotation of 0.75% before flexural traction failure, followed by concrete crushing during a posterior cycle.

Reinforced concrete (RC) framed structures subjected to seismic loading often show localized deformations at the extremities of the members associated with the slippage of reinforcing bars along their anchorage length. Despite this phenomenon being responsible for up to 40% of the total lateral deformation of RC members, the numerical simulation of this behaviour still presents several limitations. This paper introduces a modelling strategy wherein, for the first time, an explicit bond-slip model is developed to be used in connection with a fibre-based beam-column element through a zero-length link element. The proposed element adopts an advanced bond stress-slip constitutive relation capable of representing the effects of cyclic degradation or rebar yielding, among others. The numerical model is validated through a comparison with experimental results, evidencing a remarkable efficiency, accuracy and numerical stability.

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits since they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force-based formulations. Classical displacement-based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement-based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi-static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement-based or force-based elements are used to model the structural members.