PSI - Issue 78

Giuseppina Uva et al. / Procedia Structural Integrity 78 (2026) 1048–1055

1050

Table 1. Structural materials identified in the bridge, with indication of the position and label assigned.

Structural materials

Position

Label

Stone and lime mortar masonry

Piers, spandrel walls, abutments, parapets

Masonry 1

Stone and concrete mortar masonry

Arch cornice

Masonry 2

Bricks and concrete mortar masonry

Vaults

Masonry 3

Waste soil-like material obtained from excavation of foundations

Infill above vaults and between spandrel walls

Infill

The mechanical properties of materials in terms of density, Young’s modulus, Poisson’ ratio, internal friction angle and cohesion have been measured by laboratory and in situ tests and are summarized in Table 2. The design acceleration spectra to be used for the seismic analyses of the case study have been determined according to the Italian Building Code for the Limit State of Life Safety, assuming a Design Working Life of 50 years and a Use Class III. The literature about the bridge indicates that the soil type is “A” and the topographic category is “T1”.

Table 2 - Mechanical parameters for the four materials of the Bridge provided by literature.

Uniaxial Tensile Strength , [MPa]

Uniaxial Compressive Strength , [MPa]

Material

Friction Angle Φ [°]

Cohesion c [MPa]

Infill

20

0.05

0.070

0.143

Masonry 1

61

0.58

0.299

4.485

Masonry 2

61

0.58

0.299

4.485

Masonry 3

55

0.35

0.221

2.220

3. Definition of calibrated simplified FE numerical models In the elastic field, all the materials of the numerical models of the bridge are considered as homogeneous, isotropic continuum, with the following parameters (mass; Young modulus; tangential modulus; Poisson coefficient): - Infill: Ρ = 1800 kg/m 3 ; E = 1000 MPa; G = 416.67 MPa; υ = 0.2; - Masonry 1: P= 2200 kg/m 3 ; E = 10000 MPa; G = 4166.7 MPa; υ = 0.2; - Masonry 2: = 2200 kg/m 3 ; E = 12000 MPa; G = 5000 MPa; υ = 0.2; - Masonry 3: = 1800 kg/m 3 ; E = 10000 MPa; G = 4166.7 MPa; υ = 0.2. The post-elastic response is modelled by using the Concrete Damage Plasticity (hereafter CDP) Model, a continuum model with damage available in the Abaqus material Library (Dessault, 2011), that allows to model at the macro scale the effects of the cracking process in concrete-like materials, albeit with appropriate simplifications. It is being widely used in recent literature for modelling the behaviour of masonry structures because of its ease of handling without requiring the use of complex tools such as user-defined subroutines (Rainone et al, 2023). For the compressive skeleton curve, to consider the effects of micro-cracks under small load increments and model the damage development, a multi-linear stress-strain law characterized by hardening and softening is adopted. Regarding the damage model in compression, CDP assumes that failure is governed by a crushing mechanism related to the compressive inelastic strain ̃ � �� , as a function of the actual compressive stress state � . The tensile constitutive relation has been implemented with some adaptions with respect to the standard CDP Abaqus model, modifying the skeleton curve according to a bilinear branch with a higher initial stiffness until the