Modelling the seismic response of a 2-storey URM benchmark case study: comparison among different equivalent frame models

The paper presents the comparison of the results of non-linear static analyses performed with different software based on the equivalent frame (EF) modelling approach on a simple two-story unreinforced masonry building with rigid diaphragms. This study is part of a wider research activity carried out in the framework of the Italian Network of Seismic Laboratories (ReLUIS) projects, funded by the Italian Department of Civil Protection. Different configurations have been considered varying the layout of the openings on the bearing walls and the structural details. The EF models have been defined adopting as much as possible common assumptions, in order to reduce the epistemic modelling uncertainties and to facilitate the interpretation of the differences in the results obtained by the software. The comparison involved different aspects: the global scale response, in terms of capacity curves, the predicted damage pattern as well as checks at the local scale, in terms of distribution of the generalized forces. Moreover, in order to assess the reliability of the obtained results, the numerical predictions have been compared to an analytical upper bound reference solution. Finally, the sensitivity of the numerical response to the criterion adopted for the EF idealization of masonry walls has been investigated.

Integration of Modelling Approaches for the Seismic Assessment of Complex URM Buildings: The Podestà Palace in Mantua, Italy

This study investigated seismic assessments of the Podestà Palace in Mantua (Italy). This masonry palace has a complex geometrical configuration that resulted from the addition of various units stratified over centuries. This feature makes seismic assessment challenging from a modelling perspective due to the interaction among units. Here, an integrated use of three modelling strategies characterised by a different computational effort and degree of accuracy was employed: (i) the Structural Element Model, according to the Equivalent Frame Approach, to study the global response of the whole structure and to estimate the mutual dynamic interactions among units; (ii) the Macro-Block Model, to assess the out-of-plane response of facades prone to the activation of local mechanisms; and (iii) the Finite Element Model, to deepen the seismic response of some critical parts, highlighted by a global analysis but also roughly described by the Equivalent Frame Model. This integrated approach consists in the use of results achieved from one modelling approach as input for another. For example, the floor spectra estimated by (i) were used to define the seismic input in (ii); for assessing the most critical portions, more accurate models were addressed (as in case (iii)). The comprehensive interpretation of the seismic behaviour obtained by these models also allowed us to address more rationally possible strengthening solutions, such as the in-plane stiffening of vaults (particularly spread in the building), aimed to guarantee a better redistribution of seismic actions in such a complex building.

On the reliability of the equivalent frame models: the case study of the permanently monitored Pizzoli’s town hall

This paper presents the comparison of the results of modal and nonlinear analyses carried out on a 2-story masonry building with rigid diaphragms, inspired by the Pizzoli’s town hall (AQ, Italy). The case study is one of the Benchmark Structures (labeled BS6) in the “URM nonlinear modelling–Benchmark project” funded by the Italian Department of Civil Protection (DPC) within the framework of the ReLUIS projects. The building has been instrumented since 2009 with a permanent monitoring system by the Osservatorio Sismico delle Strutture (OSS) of the DPC and was hit by the 2016/2017 Central Italy earthquake sequence. In the research first phase, modal and nonlinear static analyses were carried out in a blind prediction, without any preliminary calibration of the models, but referring only to commonly made assumptions on materials and modelling. Five computer programs based on the Equivalent Frame Model (EFM) approach were used. Four different structural configurations were considered: with weak spandrels (A), with tie rods coupled to spandrels (B), with RC ring beams coupled to spandrels (C) and with “shear type” idealization (D). In the research second phase, two of the developed EFMs were calibrated in the elastic range using the results of available Ambient Vibration Tests (AVTs). The models were then validated in the nonlinear range by simulating the dynamic response of the structure recorded during the mainshocks of the 2016/2017 Central Italy earthquake. Recorded and numerical results were compared at both the global and local scale.

A comparative study on a complex URM building: part I—sensitivity of the seismic response to different modelling options in the equivalent frame models

The paper presents the comparison of the results of nonlinear static analyses carried out using six software packages (SWs) available at professional level and operating in the field of the equivalent frame (EF) approach on a model representative of a complex masonry building. The structure is inspired by the school “P. Capuzi” in Visso (MC, Italy), proposed as one of the benchmark structures in the “URM nonlinear modelling—Benchmark project” funded by the Italian Department of Civil Protection within the context of the ReLUIS projects. The 2-stories building is characterized by an irregular T-shaped plan and load-bearing walls consisting of two-leaf stone masonry with a rather regular bond scheme. The school was severely damaged by the seismic sequence that hit Central Italy in 2016/2017 and essentially exhibited a global in-plane box-type response, with a clear evidence of cracks concentrated in piers and spandrels. The availability of an accurate survey of the crack extension represents a precious and rare reference to firstly address in the paper the rules to be adopted in the EF models for the definition of the structural elements geometry. Then, the comparison of results is made with a twofold aim: firstly, by setting the models adopting shared and consistent modelling assumptions across the SWs; secondly, by investigating the sensitivity of the seismic response to some common epistemic and modelling uncertainties (namely: the adoption of various EF idealization rules for walls, the out-of-plane contribution of piers, the flange effect). In both cases, results are post-processed to define reference values of the achievable dispersion. The comparison is carried out in relation to a wide set of parameters, namely: global parameters (e.g. dynamic properties, pushover curves and equivalent bilinear curves); synthetic parameters of the structural safety (i.e. the maximum acceleration compatible with the ultimate limit state); the damage pattern simulated by SWs.

Numerical Simulation of Unreinforced Masonry Buildings with Timber Diaphragms

Though flexible diaphragms play a role in the seismic behaviour of unreinforced masonry buildings, the effect of the connections between floors and walls is rarely discussed or explicitly modelled when simulating the response of such buildings. These flexible diaphragms are most commonly timber floors made of planks and beams, which are supported on recesses in the masonry walls and can slide when the friction resistance is reached. Using equivalent frame models, we capture the effects of both the diaphragm stiffness and the finite strength of wall-to-diaphragm connections on the seismic behaviour of unreinforced masonry buildings. To do this, we use a newly developed macro-element able to simulate both in-plane and out-of-plane behaviour of the masonry walls and non-linear springs to simulate wall-to-wall and wall-to-diaphragm connections. As an unretrofitted case study, we model a building on a shake table, which developed large in-plane and out-of-plane displacements. We then simulate three retrofit interventions: Retrofitted diaphragms, connections, and diaphragms and connections. We show that strengthening the diaphragm alone is ineffective when the friction capacity of the wall-to-diaphragm connection is exceeded. This also means that modelling an unstrengthened wall-to-diaphragm connection as having infinite stiffness and strength leads to unrealistic box-type behaviour. This is particularly important if the equivalent frame model should capture both global in-plane and local out-of-plane failure modes.