The response of masonry structures to impacts is a topic of significant importance due to its implications in structural integrity and safety. In this paper, the impulsive response of unreinforced brick masonry walls to impacts was investigated through a series of laboratory pendulum tests. Four double-wythe clay brick masonry wall strips were constructed between reinforced concrete slabs and subjected to moderate-velocity impacts. The tests included both point-load and line-load impacts, with a non-rigid support condition for the upper wall support to simulate realistic axial load applications. Measurements included: load cells monitoring the axial load applied to the top of the walls, capturing the arching generated upon impact; high-speed cameras used in conjunction with 3D DIC, to monitor strain rates and crack evolution on the wall surface; and 3D LiDAR scans, to support the documentation of post-test observed damage. The findings offered a comprehensive and detailed analysis of the structural response of brick masonry walls subjected to impacts. By focusing on specific response metrics, the study elucidated the various failure mechanisms generated by the impacts. Additionally, the energy transferred during the impacts was quantified, providing a direct measure of the energy absorption capacity of the walls and its correlation with the observed failures.

Outer walls are a crucial component of the building envelope, providing insulation and structural support. While they are originally designed to support axial loads, these walls can be subjected to extreme loads, like the ones generated by impacts and blasts. Unreinforced brick masonry walls are particularly vulnerable to these actions and pose significant risks when damaged, including flying debris and progressive collapse. Careful engineering judgment is required to evaluate their resistance and design their strengthening in order to address this problem. A 3D FEM-based meso-scale modelling strategy is developed to simulate the response of masonry walls to blasts and impacts. The models were created in a general-purpose proprietary FEA software package, by making use of material models available in it. Bricks were modelled as nonlinear solid elements, while mortar joints were modelled by contact interfaces with cohesive-damage frictional behaviour. The models were built and verified upon the findings of impact pendulum and quasi-static four-point bending tests, both conducted at RISE Research Institutes of Sweden under various wall configurations. Once validated, the ability of this modelling strategy to conduct blast simulations was demonstrated for one of the tested wall configurations. This numerical work complements the experimental work previously conducted at RISE to characterize the response of brick masonry walls under impulsive loads. The modelling strategy presented here can assist the analyst evaluate the resistance of brick facades to these loads, allowing for a more precise assessment of urban areas at risk of damage.

The HybriDFEM method, short for Hybrid Discrete-Finite Element Method, combines both discrete and finite element approaches in a single numerical model: the method adopts a discrete representation of the structure, but the formulation is designed to integrate continuous parts that can be simulated by the Finite Element Method, allowing hybrid numerical mock-ups to be built. The scope of application of the method is expanded from its original development for uniaxially-discretized (1D) structures to modeling biaxially-discretized (2D) structures and systems of beams connected through rigid-node connections. The possibility to integrate finite elements within HybriDFEM in 2D is initially formalized. A two-step contact detection algorithm, in which the interface detection is preceded by a preliminary rough detection, is then presented. Finally, different approaches to modeling contact are introduced, depending on whether it is meant to reflect the behavior of a continuous material, flexible interfaces, or point-wise contact. These new capabilities of the 2D HybriDFEM method are validated on a series of selected examples including solutions from analytical models, classical finite elements, and limit analysis; among others, the HybriDFEM method is used to evaluate the axial and shear stress distribution in a linear elastic beam with negligible error relative to analytical solutions, and to predict the collapse load of in-plane loaded masonry frames with an error below 0.05% compared to solutions from limit analysis. The adequacy of the method to enhance discrete simulations by integrating finite elements is illustrated in a conclusive example via the pushover analysis of a flexible masonry frame.

The dynamic characterization of structures using discrete models, as well as the application of modal superposition to compute their dynamic response, has been rarely explored in the literature. This is at odds with the international relevance of discrete models in structural assessment, and the multiple fields of application of modal analysis and superposition, from structural health monitoring to seismic engineering. This paper introduces a 2D discrete formulation, developed within a finite element framework, to address this gap. Initially conceived for nonlinear static analyses as HybriDFEM (Hybrid Discrete-Finite Element Method), it is now augmented with a procedure to compute the mass matrix, natural frequencies, mode shapes, and response-related quantities such as modal and dynamic contribution factors or effective modal mass. Moreover, using the structural tangent stiffness matrix in the eigenvalue problem allows tracking the evolution of natural frequencies and modes in structures loaded into their nonlinear material and geometric range. The formulation is validated through several examples, where it compares well with results from engineering beam theories, refined finite element models, and numerical time-integration methods. In an application example studying the evolution of modal properties of a progressively damaged frame, HybriDFEM is coupled with finite elements, highlighting its novel approach to integrating discrete and finite elements for enhanced structural modal analysis and superposition.

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modeling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modeled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element.

The most widespread numerical simulation method for structural response is undoubtedly the Finite Element Method (FEM). However, despite being powerful for modelling continuous structures, it is not fit for handling strong discontinuities. The Discrete Element Method (DEM) simulates interactions between rigid or deformable elements in contact, hence explicitly capturing the discontinuous nature of the structural response, particularly when subjected to extreme loadings. Nevertheless, it requires a time-stepping algorithm even for solving static or buckling problems. The Hybrid Discrete-Finite Element Method, shortly HybriDFEM, was recently introduced in the context of modelling one-dimensional beam-like members. Those members are divided along their longitudinal axis in a series of rectangular rigid blocks, and the deformation is concentrated at the interfaces between adjacent blocks, modelled as distributed nonlinear multidirectional springs. The method, developed within a FEM-like setting, allows for hybridisation with other finite elements (e.g., beam elements). Next to its ability to explicitly model pre-existing discontinuities along the member (e.g. masonry stereotomy), the method can be used for modelling continuous members with satisfactory accuracy by appropriately scaling the interface springs. As such, the HybriDFEM’s formulation can accommodate hybrid discrete-continuous systems. In this paper, the HybriDFEM formulation is extended to 2D, with rectangular blocks in contact on all four faces. First, the algorithm to detect blocks in contact will be explained. Second, specific characteristics of the HybriDFEM applied to masonry modelling are presented. Then, the method is benchmarked against a two-dimensional problem from the literature where the in-plane capacity of walls made masonry blocks is investigated.

This report describes the laboratory work undertaken to characterize the hydromechanical behaviour of a natural rock fracture under varying normal loading. The hydraulic transmissivity of a granite specimen with a sealed (unopened) quasi-planar natural fracture of length 200 mm and width 200 mm was measured. The transmissivity measurements were conducted in the two perpendicular directions of the fracture, repeating them at five different normal compression stress levels, namely, ~0, 1, 2, 4, and 8 MPa, and flow gradients. The fracture was mechanically opened, and the measurements were repeated to investigate the effect of opening the fracture on its hydraulic transmissivity and hydromechanical behaviour. For one direction, the change in transmissivity was explored for high normal compression stress levels, up to ~40 MPa. Laminar flow conditions were ensured at every stage of the experimental campaign by working at very low Reynolds numbers (<1). The equivalent hydraulic aperture of the fracture was derived by resorting to the parallel-plate model theory. The hydraulic aperture was compared to the mechanical aperture, which was obtained by measuring the deformation of the specimen. In addition to the transmissivity tests, the geometry of the lateral walls and surfaces of the fracture was documented and measured by a series of tools, namely, digital scans, high-resolution pictures, optical readings by a stand microscope, and contact pressure-sheet measurements. The results achieved in this campaign shed light on the hydraulic transmissivity of sealed (unopened) and consequently opened natural fractures, and its dependency to the applied normal compression stress at low to very-low flow rates.

Groups of contiguous unreinforced stone masonry buildings are a common type of housing seen in old European downtowns. However, assessing their response to earthquakes poses several challenges to the analysts, especially when the housing units are laid out in compact configurations. In fact, in those circumstances a modeling technique that allows for the dynamic interaction of the units is required. The numerical study carried out in this paper makes use of a rigid block modeling approach implemented into in-house software tools to simulate the static behavior and dynamic response of an aggregate stone masonry building. Said approach is used to reproduce the results of bi-axial shake-table tests that were performed on a building prototype as part of the activities organized within the Adjacent Interacting Masonry Structures project, sponsored by the Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe. The experimental mock-up consisted of two adjacent interacting units with matching layout but different height. Two rigid block models are used to investigate the seismic response of the mock-up: a 3D model allowing for the limit analysis of the building on one hand, and a 2D model allowing for the non-linear static pushover and time-history analysis on the other. The 3D model was built for the blind prediction of the test results, as part of a competition organized to test different modeling approaches that are nowadays available to the analysts. The 2D model was implemented once the experimental data were made available, to deepen the investigation by non-linear static pushover and time-history analysis. In both models, the stonework is idealized into an assemblage of rigid blocks interacting via no-tension frictional interfaces, and mathematical programming is utilized to solve the optimization problems associated to the different types of analysis. Differences between numerical and experimental failure mechanisms, base shears, peak ground accelerations, and displacement histories are discussed. Potentialities and limitations of the adopted rigid block models for limit, pushover and time-history analyses are pointed out on the basis of their comparisons with the experimental results.

City centres of Europe are often composed of unreinforced masonry structural aggregates, whose seismic response is challenging to predict. To advance the state of the art on the seismic response of these aggregates, the Adjacent Interacting Masonry Structures (AIMS) subproject from Horizon 2020 project Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA) provides shake-table test data of a two-unit, double-leaf stone masonry aggregate subjected to two horizontal components of dynamic excitation. A blind prediction was organized with participants from academia and industry to test modelling approaches and assumptions and to learn about the extent of uncertainty in modelling for such masonry aggregates. The participants were provided with the full set of material and geometrical data, construction details and original seismic input and asked to predict prior to the test the expected seismic response in terms of damage mechanisms, base-shear forces, and roof displacements. The modelling approaches used differ significantly in the level of detail and the modelling assumptions. This paper provides an overview of the adopted modelling approaches and their subsequent predictions. It further discusses the range of assumptions made when modelling masonry walls, floors and connections, and aims at discovering how the common solutions regarding modelling masonry in general, and masonry aggregates in particular, affect the results. The results are evaluated both in terms of damage mechanisms, base shear forces, displacements and interface openings in both directions, and then compared with the experimental results. The modelling approaches featuring Discrete Element Method (DEM) led to the best predictions in terms of displacements, while a submission using rigid block limit analysis led to the best prediction in terms of damage mechanisms. Large coefficients of variation of predicted displacements and general underestimation of displacements in comparison with experimental results, except for DEM models, highlight the need for further consensus building on suitable modelling assumptions for such masonry aggregates.

Masonry bridges are among the most sustainable structures ever to have been built. The long service time, the resilience to carry larger loads than originally intended, and significantly lower life cycle cost compared to other bridge types suggest that we should consider the design and construction of new masonry bridges, even if their initial cost is greater than that of steel or concrete bridges The aim of this work is to understand the structural behaviour and study the collapse of a single-span masonry hydrostatic shell, that is a shell designed specifically to carry a hydrostatic load. Due to the complexity of the masonry shell interacting with fill, it is necessary to use a combination of computational methods and load tests on physical models in their structural assessment. We perform a load test to failure on a physical model spanning 770 mm made from 3D printed blocks and analyse the model using the Discrete Element Method (DEM) in Dassault Systemes Abaqus. ` The physical model behaved well and predicts that the bridge could be used at full scale. The preliminary results from a computational DEM model are found to be qualitatively good, but greatly overestimate the collapse load of the bridge.