PSI - Issue 44

Valentina Buonocunto et al. / Procedia Structural Integrity 44 (2023) 67–74 Valentina Buonocunto et al. / Structural Integrity Procedia 00 (2022) 000–000

70

4

ultimate axial strain e u = 0.5%. Regarding the tensile behaviour, the Young’s modulus was considered equal to that in compression. The peak tensile strength was assumed to be a deterministic transformation of compressive strength (specifically f t = 0.05 f m ), whereas the tensile fracture energy was deterministically set to G ft = 0.025 N/mm 2 . In the case of irregular masonry, diagonal tension cracking was not considered as shear failure mode, hence only accounting for sliding shear failure and corresponding shear strength at zero confining stress ( f v 0 ).

Table 1. Uncertainty modelling of geometric and material properties

Category

Item

Variable Unit of measure

Value

Distribution

µ

σ

min

max

t

Geometry

Walls

m

0.4

0.6

Discrete

–

–

f m τ 0 E G

MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa

1

2

Lognormal Lognormal Lognormal

1.5

0.35 0.29 0.21

0.018

0.032 1050

0.025

Irregular rubble stone masonry (A2)

690

870

0.33 E 0.05 f m

– – –

– – –

– – –

f t

G ft

N/mm

0.025

f m τ 0 E G

1.4

2.2

Lognormal Lognormal Lognormal

1.80

0.23 0.20 0.17

0.028

0.042 1260

0.035 1080

Cut stone masonry (B2)

900

0.33 E 0.05 f m

– – –

– – –

– – –

Material

f t

G ft

N/mm

0.025

f m τ 0 f v 0

2

3.2

Lognormal Lognormal Lognormal Lognormal

2.60 0.06

0.24 0.35 0.32 0.15

0.04 0.10 1200

0.08 0.19 1620

Regular soft stone masonry (C1)

0.145 1410

E G

0.33 E 0.05 f m

– – –

– – –

– – –

f t

G ft

N/mm

0.025

After uncertainties were modelled, a sample of approximately 1000 buildings for each building sub-typology (defined in terms of masonry type, age of construction, and number of storeys) was randomly generated using an automatic procedure implemented in MATLAB (2020a). Each building was generated according to the assumption of rectangular plan and with an equivalent frame model in which the macro-elements were assimilated to beam elements connected by rigid offsets appropriately sized to take into account the greater or lesser deformability of the nodes, resulting in buildings like that shown in Figure 2. Specifically, the generative procedure was based on Monte Carlo sampling algorithm of RVs and multi-parametric design, according to statistical distributions obtained from CARTIS data for each building sub-typology under study. Floor systems were modelled using equivalent diagonal trusses with appropriate stiffness depending on the type of floor (i.e. deformable, semi-rigid or rigid).