The role of different sliding resistances in limit analysis of hemispherical masonry domes

A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development. This paper reports the first two steps of that work. It first introduces a revision to an existing limit analysis approach using the membrane theory with finite hoop stresses to find the minimum thickness of a hemispherical dome under its own weight and composed of conventional blocks with finite isotropic friction. The coordinates of an initial axisymmetric membrane surface are the optimization variables. During the optimization, the membrane satisfies the equilibrium conditions and meets the sliding constraints where intersects the block interfaces. The results of the revised procedure are compared to those obtained by other approaches finding the thinnest dome. A heuristic method using convex contact model is then introduced to find the sliding resistance of the corrugated interlocking interfaces. Sliding of such interfaces is constrained by the Coulomb’s friction law and by the shear resistance of the locks keeping the blocks together along two orthogonal directions. The role of these two different sliding resistances is discussed and the heuristic method is applied to the revised limit analysis method

Interlocking joints with multiple locks: Torsion-Shear failure analysis using discrete element and equilibrium-based SiDMACIB models

SiDMACIB (Structurally informed Design of Masonry Assemblages Composed of Interlocking Blocks) is the first numerical model capable of extending the equilibrium problem of limit analysis to interlocking assemblies. Adopting the concave formulation, this model can compute the stress state at the corrugated faces with orthotropic behaviour, such as their combined torsion-shear capacity. Generally speaking, finding the plastic torsion-shear capacity of planar faces shared between conventional blocks is still a fresh topic, while investigating this capacity for interlocking interfaces is particularly rather unexplored. Upon the authors’ previous works that focused on interlocking blocks with a single lock, in this paper, an extension to blocks composed of several locks (multi-lock interfaces) is presented and the SiDMACIB model is upgraded accordingly. For this purpose, the shear-torsion results obtained from the original SiDMACIB formulation are validated and subsequently compared with those derived from distinct element analysis conducted using the 3DEC 7.0 software. Based on this comparison, revisions to the SiDMACIB model are proposed, involving a reduction in the number of locks affecting torsion-shear capacity

The role of different sliding resistances in limit analysis of hemispherical masonry domes

A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development. This paper reports the first two steps of that work. It first introduces a revision to an existing limit analysis approach using the membrane theory to find the minimum thickness of a hemispherical dome under its own weight and composed of conventional blocks with finite isotropic friction. The coordinates of an initial axisymmetric membrane surface are the optimization variables. During the optimization, the membrane satisfies the equilibrium conditions and meets the sliding constraints where intersects the block interfaces. The results of the revised procedure are compared to those obtained by other approaches finding the thinnest dome. A heuristic method using convex contact model is then introduced to find the sliding resistance of the corrugated interlocking interfaces. Sliding of such interfaces is constrained by the Coulomb’s friction law and by the shear resistance of the locks keeping the blocks together along two orthogonal directions. The role of these two different sliding resistances is discussed and the heuristic method is applied to the revised limit analysis method

Joint layout design:Finding the strongest connections within segmental masonry arched forms

Segmental arched forms composed of discrete units are among the most common construction systems, ranging from historic masonry vaults to contemporary precast concrete shells. Simple fabrication, transport, and assembly have particularly made these structural systems convenient choices to construct infrastructures such as bridges in challenging environmental conditions. The most important drawback of segmental vaults is basically the poor mechanical behaviour at the joints connecting their constituent segments. The influence of the joint shape and location on structural performances has been widely explored in the literature, including studies on different stereotomy, bond patterns, and interlocking joint shapes. To date, however, a few methods have been developed to design optimal joint layouts, but they are limited to extremely limited geometric parameters and material properties. To remedy this, this paper presents a novel method to design the strongest joint layout in 2D arched structures while allowing joints to take on a range of diverse shapes. To do so, a masonry arched form is represented as a layout of potential joints, and the optimization problems developed based on the two plastic methods of classic limit analysis and discontinuity layout optimization find the joint layout that corresponds to the maximum load-bearing capacity.</p

Interlocking joint shape optimization for structurally informed design of block assemblages

This paper presents a computer aided design tool that analyses the structural feasibility of interlocking assemblages with orthotropic sliding resistance and automatically adjusts the assemblage shape to remove the infeasibility. First, the static problem of limit analysis is extended to the corrugated interfaces. To model different bond patterns and openings, an assemblage is abstracted to different types of joints representing the dry joints between the blocks, joints inside the blocks, and the excluded joints where the openings are located. This problem is then reformulated to measure the structural infeasibility due to the sliding constraint violation. The so-called sliding infeasibility measure shows how far an infeasible model is to become feasible. This problem is used as the objective function of a shape optimization algorithm that minimizes the sliding infeasibility measure through automated change of the interlocking joints, by which the model becomes structurally feasible. The optimization is validated using the discrete element analysis.</p

Environmental and economic impact of retrofitting techniques to prevent out‐of‐plane failure modes of unreinforced masonry buildings

This paper presents an innovative methodology to assess the economic and environmental impact of integrated interventions, namely solutions that improve both structural and energy performance of existing masonry buildings, preventing out‐of‐plane modes and increasing their energy efficiency. The procedure allows the assessment of the environmental and the economic normalized costs of each integrated intervention, considering seismic and energy‐saving indicators. In addition, the work introduces in relative or absolute terms two original indicators, associated with seismic displacement and thermal transmittance. The iso‐cost curves so derived are thus a powerful tool to compare alternative solutions, aiming to identify the most advantageous one. In fact, iso‐cost curves can be used with a twofold objective: to determine the optimal integrated intervention associated with a given economic/environmental impact, or, as an alternative, to derive the pairs of seismic and energy performance indicators associated with a given budget. The analysis of a somehow relevant case study reveals that small energy savings could imply excessive environmental impacts, disproportionally increasing the carbon footprint characterizing each intervention. Iso‐cost curves in terms of absolute indicators are more suitable for assessing the effects of varying acceleration demands on a given building, while iso‐cost curves in terms of relative indicators are more readable to consider a plurality of cases, located in different sites. The promising results confirm the effec-tiveness of the proposed method, stimulating further studies

Torsion–shear behaviour at interlocking joints:Calibration of discrete element-deformable models using experimental and numerical analyses

An interlocking block is a concave polyhedron with non-planar joints connecting the blocks together. The possibility of the fracture within a masonry interlocking block is a major challenge that has remained rather unexplored yet. Different fracture scenarios can be taken into account through considering the crack planes at which the block can be set apart. The plastic failure inside the block can also be represented through the continuum plastic deformation of the block composed of continuum finite elements. For an interlocking block with a cuboid projection above (lock), this paper intends to analyse the torsion–shear behaviour of the lock experimentally and numerically based on the discrete element method. Two strategies are developed to model a concave block: the lock and main body of an interlocking block are set to be rigid and connected with a cohesive contact in between; the concave interlocking polyhedron is set to be deformable with elasto-plastic behaviour. Given the same material properties, the torsion–shear capacities of the lock obtained by the two numerical models and the experimental test are compared to each other. A parametric analysis is then provided to calibrate the deformable model.</p

EXPERIMENTAL VALIDATION OF IN-PLANE FRICTIONAL RESISTANCES IN DRY BLOCK MASONRY WALLS

This paper presents the experimental and analytical validation of the lateral strength of dry block masonry walls under in-plane loading. The analytical evaluation of the in-plane frictional resistances activated at the onset of the rocking-sliding mechanisms is revisited in order to account for the different contributions of the self weight of the wall and additional loads. It is assumed that the wall is arranged in a running bond pattern, with rigid blocks and dry contact interfaces governed by cohesionless Coulomb failure criterion. The accuracy and robustness of the analytical results are assessed by experimentally testing both the resultant frictional resistances and their applications points. Both pure sliding and rocking-sliding failure modes are simulated with a testing device designed and realized ad hoc (no standard equipments and procedures were found in the literature). A good agreement between the analytical and experimental results is shown for the selected cases

Pushover analysis of rocking façades in masonry churches:the role of friction and geometry in identifying homogeneous classes of vulnerability

The out-of-plane failure of façades is one of the most typical local mechanisms in masonry churches recognizable in the aftermath of a seismic event. The analysis of such a failure is addressed in this paper with reference to a small sample of existing masonry churches hit by the seismic event of 21st August 2017 in the Ischia Island (Italy). The main aim is to assess the influence of the geometric parameters of the façades and of the interlocked sidewalls on the vulnerability of the façades to out-of-plane mechanisms, using nonlinear static analysis. According to the displacement-based approach, the pushover analysis is carried out considering the geometric nonlinearity, namely by evaluating the static multiplier for varied kinematic configurations, and by means of a macro-block model involving the stabilising contribution of frictional resistances exerted by the sidewalls of the churches. In order to develop seismic assessments, the seismic demand is represented by ADRS (acceleration-displacement response spectra) for different limit states, obtained according to the Italian seismic code. Then, the capacity is compared with the seismic demand in terms of both forces and displacements and the relevant influence of the frictional resistances and of some geometric parameters on the response are highlighted. Finally, the capacity curves are critically discussed in order to identify ‘a posteriori' homogeneous classes of façades within the examined sample in terms of vulnerability and to develop future statistical analyses and fragility curves for the individuated homogeneous classes.</p

Literature Review of the In-Plane Behavior of Masonry Walls: Theoretical vs. Experimental Results

In-plane strength of masonry walls is affected by the resistant mechanisms activated in the walls, i.e., related to flexural or shear behavior. The latter one can occur in the walls according to different failure modes depending on both mortar and unit strengths and on the type of assembling, i.e., ‘regular’ or ‘irregular’ texture. In this paper, a critical review of the existing design formulations for the in-plane strength of masonry walls is firstly presented, with important information on the achievable failure modes depending on the geometrical and mechanical features of the masonry fabric. Then, experimental tests are collected from the literature and a comparison between theoretical and experimental results is carried out. The presented analyses are aimed to highlight the differences between the existing formulations and to identify the most suitable ones