Limit analysis approach for the in-plane collapse of masonry arches

Abstract

The present paper deals with the numerical evaluation of the in-plane collapse behaviour of unreinforced masonry arches and portals characterized by different geometries subjected to several loading conditions and modelled as assemblages of rigid blocks in contact through no-tensional and frictional interfaces. This study has been conducted using a new in-house code, which represents the updated version of the numerical procedure presented in the pioneering work of Baggio and Trovalusci (2000). The minimization problem corresponding to the Upper Bound (or kinematic) approach of Limit Analysis is written as a Linear Programming Problem solved taking advantages of the algorithms nowadays available. An important feature of the code is the capability to provide information about the sliding collapse of masonry structures, adopting the assumption of dilatancy in the analytic description of the yielding surface, permitting to overcome the classical Heyman's hypothesis which limited the investigation of collapse to only hinging modes. A key contribution of the work is the comparison of results in terms of collapse multipliers and collapse mechanisms considering different literature contributes as benchmark references. The presented study reveals the suitability of approaches based on mathematical programming and the crucial role played by sliding.

Rotation and sliding collapse mechanisms for in plane masonry pointed arches: statistical parametric assessment

“…Sharpness is equal to the division of the arch excentricity by the distance from O to the center of the arch at its base, S h = e/R c . The numerical values for Slenderness and Sharpness adopted in this work correspond with those experimentally reported by [7] and numerically validated by [26]. Therefore, the combination of three sharpness values and four slenderness values resulted in the twelve arches shown in Figure 3.…”

“…The new version of ALMA by the adoption of the recent coding language Python T M and the advantages of the novel optimization subroutine, such as MOSEK library (www.mosek.com), overcomes the limit in terms of number of blocks with respect to the original version [13] and it has been improved in order to take into account foundation settlement [21], cohesion between the joints and retrofitting tie [23]. The capabilities of ALMA 2.0 to reproduce the structural response of in-plane masonry pointed arches has already been validated [26] using as benchmark the experimental results and numerical simulations performed by Misseri et al [7].…”

Real-time Structural Stability of Domes through Limit Analysis: Application to St. Peter’s Dome

“…Analytical or semi-analytical approaches based on limit analysis theorems can be found (Como 2019;Pepe, Pingaro, and Trovalusci 2021;Pepe, et al 2020;Portioli, et al 2014;Chiozzi, et al 2017;G. Milani, Lourenço, and Tralli 2006), but more attention has been given to numerical strategies based on the Finite Element (FE) (Fortunato, Funari, and Lonetti 2017) and Discrete Element (DE) (Mehrotra, Arede, and DeJong 2015;Savalle, Vincens, and Hans 2020;Simon, and Bagi 2014) methods.…”

Micromechanical Analysis of Unreinforced and Reinforced Masonry Arches

“…In this framework, limit analysis approach is a consolidated tool for the assessment of the arch safety. Starting from the first applications of Heyman [6], many other enriched models have been proposed, where Heyman's hypotheses are partially or all removed [7,8,9] . The success of these models is mainly due to their simplicity and the reduced number of material parameters required in the analysis.…”