PSI - Issue 44

Mattia Zizi et al. / Procedia Structural Integrity 44 (2023) 673–680

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Mattia Zizi et al. / Structural Integrity Procedia 00 (2022) 000–000

was considered for both backfill and masonry materials. In such a way, a displacement control analysis in quasi-static conditions was performed. Pictures of the model and of the adopted boundary conditions are shown in Fig. 3.

Fig. 3. Pictures of the FE Model: (a) mesh and (b) boundary conditions.

2.3. Material modelling Masonry elements were simulated by resorting to the macro-modelling technique. The Concrete Damage Plasticity (CDP) material model was used, by assuming an Elastic Modulus E m =16200 MPa and a Poisson’s ratio ν =0.2. Parabolic compressive law according to (Sawko, 1982) and a linear softening in tension in terms of displacements to avoid mesh dependency were considered. Fracture energy G ft was defined according to (Lourenço, 2009), as per Eq.(1). The post-elastic constitutive laws in compression and tension are shown in Fig. 4. ( ) 0.7 0.025 2 ft t G f = ⋅ ⋅ (1)

Fig. 4. Post-elastic constitutive laws in (a) compression and (b) tension assumed for masonry material.

Also, laws for defining the damage evolution in both compression ( d c ) and tension ( d t ) were used to describe the material behavior. In particular, linear relationships were used, where the onset of damage appeared at maximum strength (either in tension or compression) and the maximum value 100% was attained at the maximum inelastic strain (compression) and displacement (tension). For the other parameters, conventional values were adopted, and in particular: i. uniaxial-to-biaxial compressive strength ratio f c0 /f b0 =1.16; ii. dilation angle ψ CDP =10°; iii. Kc =0.667; iv. eccentricity ε =0.1.