PSI - Issue 44

Micaela Mercuri et al. / Procedia Structural Integrity 44 (2023) 1276–1283 Author name / Structural Integrity Procedia 00 (2022) 000–000

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kinematic mechanisms are analyzed for three different types of vaults, i.e. depressed, barrel and groin vaults, and for six different slenderness ratios.

Nomenclature LDPM lattice discrete particle model c cement-mortar content d 0

minimum stone characteristic size maximum stone characteristic size

d a n f E 0

Fuller coefficient

normal elastic modulus

α

shear-normal coupling parameter

σ t

tensile strength

G t

tensile fracture energy

σ s /σ t

shear-to-tensile strength ratio

n t

softening exponent

σ c0

yielding compressive stress initial hardening modulus final hardening modulus deviatoric strain threshold ratio initial friction coefficient asymptotic friction coefficient transitional strain ratio

H c0 /E 0

H c1 k c0 k c2

μ 0

μ͚

σ N0

transitional stress densification ratio

E d /E 0

2. Lattice discrete modeling of the masonry arches This section presents the numerical analysis of masonry vaulted structures subjected to spreading supports. As already mentioned, the LDPM is adopted for this purpose as it is able to simulate the fracturing behavior of masonry arches and vaults up to their collapse. The geometrical parameters adopted in this study were previously calibrated for the in-plane and out-of-plane behavior of unreinforced masonry (Angiolilli et al. (2020), Mercuri et al. (2020)). More specifically, the stone-to-mortar ratio a/c = 3.4 corresponding to the ratio between the volume of stones and the volume of cement-mortar, and the water-to-mortar ratio w/c = 0.5 were assumed based on the actual masonry composition. The cement-mortar content parameter c=427.5 kg/m 3 was calculated such that the total mass density ρ was equal to 1,800.0 kg/m 3 using the formula: ρ=c(1+w/c+a/c). The stones were assumed to have characteristic size within the range d 0 =33 mm and d a =200 mm in order to simulate the coarse gravel. The Fuller coefficient n f =0.5 was assumed as default parameter since no specific sieve curve was assumed for the preparation of the specimens in the experimental campaign. The identified model parameters are as follows: normal elastic modulus E 0 =1,200 MPa, shear-normal coupling parameter α=0.065, tensile strength σ t =0.3 MPa, tensile fracture energy G t =11 N/m, shear-to tensile strength ratio σ s /σ t =1.25, softening exponent n t =0.2, yielding compressive stress σ c0 =125 MPa, initial hardening modulus H c0 /E 0 =0.4, final hardening modulus H c1 =1, transitional strain ratio k c0 =1.75, deviatoric strain threshold ratio k c1 =1, deviatoric damage parameter k c2 =5, initial friction coefficient μ 0 =0.2, asymptotic friction coefficient μ͚=0, transitional stress σ N0 =42 MPa, densification ratio E d /E 0 =1 and r s =0. Numerical analysis related to three different types of unreinforced masonry vaults are performed, namely groin vaults, barrel vaults and depressed vaults. For each type of vault, six slenderness ratios are analysed, i.e. λ 1 =0.11, λ 2 =0.125, λ 3 =0.15, λ 4 =0.175, λ 5 =0.2, λ 6 =0.225, where λ i =D i /r (i=1,...,6), r=2000 mm is fixed and it represents the mean radius, and D, the thickness, is set equal to 220 mm, 250 mm, 300 mm, 350 mm, 400 mm, 450 mm,