Recent Advances on the Mechanics of Masonry Structures

The special collection on Recent Advances on the Mechanics of Masonry Structures is available in the ASCE Library (https://ascelibrary.org/jenmdt/advances_mechanics_of_masonry_structures).

Masonry, one of the oldest construction materials of mankind, consists of solid blocks such as stones or bricks that are laid in mortar or being held together by dry frictional contacts. The discrete built-up of masonry makes its behavior nonlinear and highly discontinuous. Although, masonry at low static stress levels it may still be modeled as a linearly elastic system, after the formation of first cracks the behavior becomes increasingly nonlinear until finally reaching collapse. The geometry of the individual stones and of the joints between them also significantly affects the behavior of masonry, making it inhomogeneous and noncontinuous.

While masonry is among the most important construction materials today, its importance is strengthened by the fact that historic structures mostly consist of masonry. Over the centuries or even millennia these structures have inevitably suffered different damages due to effects like earthquakes, soil settlements, material degradation, or improper intervention. Consequently, regular assessment of masonry structures is needed in order to check their load-bearing capacity and safety levels. Structural engineers and architects often face the problem that a damaged masonry building and perhaps its different strengthening possibilities have to be analyzed in such a way that the response of the structure to future mechanical effects should be reliably modeled. Hence, suitable methods should be used for such calculations that can properly capture the most relevant features of the mechanical behavior.

Seismic analysis of masonry structures deserves special emphasis due to the challenging contradiction that masonry is vulnerable to earthquakes because of the possibility of the individual blocks to slide or move separately from their neighbors; conversely, masonry has a high energy dissipation capability, and even seriously damaged structures in which the blocks performed significant relative displacements can retain a high level of their load-bearing capacity. No wonder that seismic analysis is the most actively studied field of masonry mechanics.

Calculation methods existing today embrace a wide variety of discrete-element simulations, limit state analysis tools, nonlinear finite-element modeling, and different blocky models. These modern methods brought new insights into the understanding of issues like how the different structural types carry their loads, how the available strengthening techniques influence the behavior by redistributing the internal forces or stiffening some parts of the structure while leaving others unaffected, and how a specific structure will behave under usual effects throughout its expected lifetime or under an extreme effects like an explosion or an earthquake.

This special collection for the Journal of Engineering Mechanics focuses on recent advances in the analysis and modeling of masonry structures. This special collection consists of 10 invited technical contributions from high-profile international researchers in the area of computational modeling of masonry structures, as well as the author presentations initially scheduled for the Minisymposium MS-72 at the 2020 ASCE International Conference, held April 5–8, 2020 in Durham, UK. A synopsis of each contribution is presented subsequently.

Facades of masonry buildings composed of piers and spandrels are vulnerable to in-plane actions resulting from seismicity and soil subsidence. With the view to increase vulnerability and safety of masonry structures, Drougkas et al. (2021) presented the development of analytical models to determine the in-plane damage initiation and force capacity of masonry walls with openings. The model accounted for all potential damage and failure modes for in-plane loaded walls. Model results were compared with numerous experimental cases and good accuracy was achieved. The proposed model presents opportunities for future work related to the simulations of structural reinforcement, such as in the form of embedded bars.

In an attempt to understand the response of masonry structure to explosions, Masi et al. (2021) presented scaling laws for the rigid body response of masonry structures under blast load. The proposed scaling laws have been validated against numerical and experimental tests. Then, the application to blocky masonry structures was investigated. As an example, multidrum stone columns were considered. It was shown that the presence of complex behavior, such as wobbling, and impacts can be simulated. It should be highlighted that this work presents the first step toward the design of reduced-scale experiments of masonry structures, providing appropriate scaling laws that assure the similarity of both blast loading and structural dynamic response. All data, models, and codes supporting this research are available by the authors.

In addition, Ferrante et al. (2021) presented the influence of stereotomy on discrete approaches applied to an ancient church in Muccia, Italy. The structure was modeled considering the actual stereotomy of blocks and other three hypothetical arrangements of blocks of the masonry walls, to adequately investigate the existing crack pattern and vulnerabilities of the church. Indeed, the findings presented in this work allowed a better understanding of the global and local behavior of the structure, which led to adequate restoration works of the Church.

An advanced nonlinear mechanical numerical model based on the micromodeling approach to evaluate the evolution of damage on an already damaged structure strengthened with TRM material was presented by Giordano et al. (2021). The model was first calibrated using modal analysis. The model presented a good compromise between computational efficiency and accuracy to evaluate the global capacity curve and damage patterns. The model was able to estimate the initial elastic phase, peak load, ductility, and failure mechanism scenario.

Aita and Sinopoli (2021) examined the collapse of nonsymmetric masonry arches, modeled as assemblages of rigid voussoirs linked by unilateral constraints, and characterized by infinite compressive strength and finite Coulomb’s friction. The alternative approach developed in this paper allows solution finding that corresponds to both the limit equilibrium condition and the definition of a collapse mechanism with one degree of freedom, as thickness and friction coefficient vary.

Vlachakis et al. (2021) presented numerical block-based simulations of rocking structures using novel universal viscous damping models. In particular, the proposed viscous damping model made use of novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motions. Results were compared with experimental findings and good agreement was observed. Note that, even though the proposed numerical (viscous damping) model was evaluated against the two most observed out-of-plane collapse mechanisms of unreinforced masonry structures, to further enhance its applicability, a more thorough investigation against additional collapse mechanisms (e.g., the vertical spanning strip wall or the corner mechanism) is required. Such analyses, though, should be accompanied by extensive experimental campaigns, which are currently lacking in the literature and thus are topics of future research.

The special collection focused on the behavior of confined masonry and in particular the response of masonry infills. For example, Sirotti et al. (2021) presented the development and validation of new Bouc-Wen data-driven hysteresis model for masonry infilled RC frames. In this case, the infill panel was schematized as a single degree-of-freedom element, whose constitutive law was given by the proposed hysteresis model. The model combined a degrading Bouc-Wen element with a slip-lock element, which is introduced specifically to reproduce the pinching effect due to crack openings in the masonry panel. The model was calibrated using a genetic algorithm–based optimization on single-story, single-bay RC infills subjected to cyclic loading. The potential of the model to simulate dynamic and stochastic phenomena was also addressed.

In a similar topic, Pradhan et al. (2021) showed prediction equations for the out-of-plane capacity of unreinforced masonry infill walls based on a macroelement model using an extensive parametric analysis, such as variation in geometrical and mechanical properties. From the results analysis it was shown that the out-of-plane strength of infills was largely influenced by compressive strength, slenderness ratio, aspect ratio, and additionally by the level of in-plane damage. The reduction of the out-of-plane strength and stiffness due to in-plane damage was largely governed by the strength and the slenderness ratio of the unreinforced masonry infill wall. The reliability of the proposed model was also proved by comparisons with experimental results and some of the analytical models already available in the literature.

Grillanda et al. (2021) presented advanced modeling investigations into historical masonry umbrella vaults subjected to settlement and cracking development using Non-Uniform Rational B-Splines (NURBS) kinematic analysis. The principle of virtual works has been applied and a discontinuous displacement field deriving from an imposed settlement was obtained. Therefore, a metaheuristic mesh adaptation procedure was applied to find the correct disposition of fracture lines. Different settlement typologies were adopted in the analyses to reproduce the crack pattern observed on the umbrella vault. Lastly, an inverse analysis was conducted to estimate the shape of the occurred settlements starting from the observed crack pattern.

Rios et al. (2022) presented statistical assessment of in-plane masonry panels using limit analysis with sliding mechanism. A discrete modeling approach based on a nonstandard limit analysis approach was adopted, which was capable of reproducing sliding mechanisms. The parametric analysis presented was able to objectively identify the effect that the panel ratio, block ration, bond type, and friction ratio have in the collapse load and mechanism. All the analyses show the importance in the collapse behavior of the size and the disposition of the bricks that determine the level of interlocking among bricks, and then the cohesion of the whole.