Unreinforced masonry walls with irregular opening layouts: reliability of equivalent-frame modelling for seismic vulnerability assessment

Equivalent-frame modelling for the estimate of in-plane seismic vulnerability of masonry wall is endorsed by international codes. However, in presence of irregular layouts of openings, the definition of equivalent-frame becomes non-unique and may lead to epistemic modelling errors. The aim of this paper is to develop a simplified tool to estimate such errors as functions of the level or geometric irregularity. Four types of irregularity are considered and quantified by geometric indexes. Nonlinear static analyses are carried out through an equivalent-frame model and a nonlinear finite-element model. It is assumed that both models are exact for perfectly-regular walls, while in presence of irregularities only the continuum approach is able to correctly predict the vulnerability, so that the difference between the two results can be taken as a measure of the error of the equivalent frame. A regular wall is taken as case study and both numerical models are calibrated on experimental data. The four typologies of irregularity are introduced separately, each in steps of increasing magnitude. The results show that the equivalent frame approach is usually not safety-preserving and may be affected by a significant error. A tentative global measure of irregularity, weighting the average effects of each irregularity type, is proposed. The resulting simplified relationship between irregularity level and expected error can be used to define a confidence factor on the modelling, which penalizes the application of the equivalent frame in case of irregular walls. Eventually, an applicability limit of the equivalent-frame model might be set.