Three-dimensional limit analysis of ancient masonry buildings with rigid block models

Abstract

Limit analysis with rigid block models is a tool successfully used in recent years for the assessment of ancient masonry structural elements and small buildings. In this paper, the interface yield functions for three-dimensional models are defined at interpolation points, instead of using the generalised stresses approach. This approach leads to very simple expressions for the yield functions and flow rules and therefore, renders the mathematical programming problem easier to solve than the generalised stresses formulation. The solution for the limit analysis problem is obtained using the load-path following approach. The validation of the present proposal shows good agreement compared with non-linear finite element results.

Masonry arches simulations using cohesion parameter as code enrichment for limit analysis approach

“…Collapse loads are given in Table 1 for both unreinforced and reinforced scenarios as reported by Orduña [52], Baraldi et al [51] and as obtained with ALMA 2.0 in this work. Orduña reported an ultimate load value of 18.0 kN derived by the LA approach, whereas Baraldi et al found comparable values for the FEM approach 18.0 kN and somewhat lower values for the DEM and analytical approaches, 17.8 kN and 17.77 kN, respectively.…”

“…A semi-circular arch with a backfill is studied as the first case study that is initially assessed for the unreinforced scenario using LA by [52] and then using FEM, DEM and an analytical approach by [51]. The outcomes of the two studies are in good accordance with ALMA 2.0 where slight discrepancies are observed due to some differences in the original geometry assumptions.…”

“…In this first case, a semi-circular arch first studied by Orduña [52] and then by Baraldi et al [51] is considered. The arch has for geometry an internal radius of 235 cm, a ring thickness of 30 cm and an out-of-plane depth of 100 cm.…”

“…The specific weight of the masonry is 20 kN/m 3 , whereas the backfill has a weight of 15 kN/m 3 . The friction coefficient between the dry joints is taken as tan φ = 0.75, as reported on [52]. Finally, null cohesion was considered for all joints.…”

“…In order to validate the ability of ALMA 2.0 to reproduce the strengthening effect of such reinforcements in masonry arches, two examples have been chosen from literature, namely first and second case study. The first case study was originally published by Orduña [52] and then numerically reproduced using different modeling approaches (FEM, DEM and analytical) by Baraldi et al [51] in order to apply and assess the effect of partial reinforcement. The second case study is based on the extensive experimental campaign performed by Oliveira et al [50] whose main objective, among others, was to provide results that may be used as calibration/validation benchmarks for numerical models of composite reinforced masonry arches.…”