Near-collapse capacity assessment of stone masonry buildings through nonlinear time history analyis of discontinuum models

The expected performance of non-engineered URM structures subjected to moderate to severe earthquake ground motion is characterised by the onset of extensive cracking phenomena and potential development of both in-plane and out-of-plane failure mechanisms. Within this work, the suitability of the Applied Element Method (AEM) – a discrete crack, rigid-body and springs-based numerical technique – to simulate shake-table tests of buildings is discussed. A simplified micro-modelling approach was adopted for masonry, lumping all mechanical nonlinearities into zero-thickness interfaces. Detailed modelling of aspects such as wall interlocking, wall-to-floor and wall-to-roof connections was pursued, to enhance the role of diaphragm stiffness on global response. The experimental loading protocol was simulated by means of incremental dynamic analyses, which enabled capturing damage accumulation phenomena well into the large displacement field and the onset of failure mechanisms.

Why conventional models fall short: discrete approaches for URM seismic behaviour

Unreinforced masonry (URM) buildings subjected to earthquake ground motion typically exhibit a poor performance, characterized by the development of both in-plane (IP) and out-of-plane (OOP) failures and collapse mechanisms, as highlighted in events such as the 2009 L’Aquila earthquake (Augenti & Parisi, 2010; D’Ayala & Paganoni, 2011). Tools commonly employed for URM structural assessment, such as the Equivalent Frame Method (EFM), while computationally expeditive, suffer from a number of drawbacks, such as: i) difficulties in the modelling of highly irregular geometries, even in single walls with openings; ii) inability to account for OOP behaviour; iii) the disregard of bond pattern effects and resulting inability to account for actual crack patterns (Parisi & Augenti, 2013; Quagliarini, et al., 2017). While advanced Finite Element Method (FEM) analysis may more satisfactorily deal with complex geometries and OOP behaviour, substantial computational power is needed, especially at building scale; thus, the most common modelling assumption is that of so-called macro-modelling, that is, smearing constituent materials within a homogeneous continuum.

The homogeneous continuum hypothesis, however, fails to address masonry bond pattern effects – which may be relevant in the presence of strong material discontinuities, i.e., weak joint-strong unit scenarios - and may incur in numerical instability issues in the large strain/displacement field, due to either the occurrence of severe mesh distortion or the sue of computationally demanding algorithms. As a result, discontinuous methods, such as the Discrete Element Method (DEM) and Applied Element Method (AEM), have recently seen growing interest within the field of URM modelling and analysis (Malomo & Pulatsu, 2024).

Within such methods, the structure is modelled as an assembly of discrete bodies, interacting by means of point contacts distributed along contact interfaces; discrete body displacements and rotations are checked throughout the analysis, updating contact positions, checking separation conditions and generating new contacts as calculation progresses. Within this work, the suitability of the AEM in capturing the experimentally observed shake-table response of URM buildings in near-collapse conditions is discussed. A simplified micro- modelling strategy is employed, explicitly accounting for bond pattern effects on damage onset and propagation. Satisfactory results were reached with regards to base shear values, displacement time-histories, pattern and failure mechanism.

IF CRASC ’25: ingegneria forense, crolli e affidabilità strutturale
IF CRASC ’25 ha posto al centro del confronto tecnico ingegneria forense, crolli, affidabilità e consolidamento strutturale, riunendo a Napoli esperti del settore per analizzare cause dei dissesti, responsabilità tecniche e soluzioni avanzate per la sicurezza del costruito, tra ricerca, pratica professionale e ambito giudiziario. All'interno interviste e video delle relazioni.
LEGGI L'APPROFONDIMENTO

Simplified micro-modelling in an AEM Framework

According to simplified micro-modelling principles, URM is treated as an assembly of discrete bodies and zero-thickness contact interfaces. Such an approach can be easily implemented within the framework of the AEM (see Figure 1), which is a discrete, rigid body and nonlinear spring-based computational technique initially developed within works such as (Meguro & Tagel-din, 1997).

Individual units may thus be modelled as rigid cuboids, and mortar joint and unit-joint interface behaviour lumped into axial and tangential springs distributed along unit contact interfaces (see Figure 1). Each contact spring, thus, accounts for the strength and deformability of a finite volume δv, defined as a function of unit-unit centroid distance d, contact plane height, h, and thickness, t, and the adopted discretization of the contact plane through m x n contact points.

Within this work, units are assumed as rigid, and potential unit splitting phenomena disregarded; all nonlinearities are, thus, lumped within unit-unit contact springs, to which composite-scale stiffness and strength properties are assigned. Spring axial, kn, and tangential, ks, stiffnesses are automatically defined based on masonry Young’s modulus E, tangential modulus G, and the variables defining the finite volume, δv. Spring stiffness is then updated based on the adopted constitutive law.

Within this study, a parabolic hardening-softening function is assigned in compression, while tensile behaviour us assumed as linear elastic with a linear softening law. (Figure 2a). The main input parameters are masonry Young’s modulus E, compressive strength fc, tensile strength ft, and fracture energies in tension and compression Gf and Gc. Fracture energies are divided by the cubic root of unit volume to guarantee mesh objectivity. A Mohr-Coulomb failure criterion with tensile and compressive cut-offs (Figure 2b) is adopted; shear strength is, thus, a function of applied vertical stress, σ, friction coefficient μ, and cohesion, c.

The latter is initially assumed equal to pure shear strength τ0 – i.e., shear strength under zero confining stress. The occurrence of compressive, shear or tensile failures results in residual shear strength being expressed as a function of applied compressive stress, friction coefficient and residual cohesion, τres, which may also be taken as non-zero to account for crack roughness. For further details on the adopted formulation, the interested reader is redirected to (Malomo, et al., 2018; Canditone & Parisi, 2024).

...Continua a leggere nel PDF in allegato (Memoria in lingua inglese)