Kinematic Stability of Masonry Arches

Abstract

To quantify the safety of masonry arches and vaults using limit-analysis, various types of safety factors have been devised. The most well-known were introduced by Heyman: a “static factor of safety” (or load factor) assessing how vulnerable the structure is to increases in the living loads and a “geometrical factor of safety” assessing how critical the thickness of the structure is for its stability. In non seismic areas, one of the main risks of total or partial collapse of arches and vaults is excessive displacement of the supports (following walls or soil deformation). Limit analysis technique can be used to analyse this risk, quantifying movements permitted before collapse and evolution of the thrust on the supports. This analysis can be combined with pathological investigations and displacement monitoring to study the evolution of the risk and define a “kinematic factor of safety”. A software program was developed (a) to compute domains of stability for particular mechanisms of deformation, (b) to study possibility of transitions between mechanisms during deformation and (c) to interactively study the influence of movements of the supports on thrust and stability. Scaled physical models are used to validate the limit analysis approach, using an experimental rig where horizontal and vertical displacements are controlled by computer. A high-speed camera is used to study transition between mechanisms. Finally it is referred to techniques integrating this kinematic approach into a more general probabilistic approach, taking into account various uncertainties in the structure (shape, thickness, loads, movements).

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

“…A Complementarity Problem/Mathematical Programming (CM/MP) numerical formulation and self-made implementation, recently developed by the authors [12,13] within a MATLAB environment, with the target to specifically enquire finite-friction effects on masonry arches [22,[53][54][55][56][57][58][59][60][61][62], is here adapted to the numerical analysis of symmetric circular masonry arches relying on infinite (say high) friction and employed for a further independent validation and interpretation of the arch characteristics in the least-thickness condition, as by the solution of a numerical optimization problem. The general formulation is first briefly introduced, in its main traits, and described in the needs of adaptation of the computational implementation, towards the present numerical optimization analysis.…”

Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis

“…For the analysis of arched structures, subject to vertical loads, lateral inertial loads and support movements, targeted investigational tools have been developed [24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Furthermore, effective strengthening strategies, such as those based on composite materials [38][39][40][41][42][43][44][45][46][47], are currently the subject of an extensive research.…”

Large displacement analysis of dry-joint masonry arches subject to inclined support movements

“…Several research works recently addressed the abovementioned problems using (i) analytical and computational methods based on the application of the theorems of limit analysis developed by Heyman [2,7] (e.g., [1,6,[8][9][10][11][12][13][14][15]), (ii) modern computational methods, such as FE, discrete element (DE) and rigid block modelling (e.g., [4,5,11,[16][17][18][19][20][21]) and/or (iii) experimental investigations (e.g., [1, 4-6, 11-13, 15, 18, 19). Most of these studies adopted the three simplified assumptions of i) infinite compressive strength, (ii) no tensile strength and (iii) no sliding failure, introduced by Heyman [2,7] to describe the behaviour of masonry structures.…”