PSI - Issue 78

Christian Salvatori et al. / Procedia Structural Integrity 78 (2026) 1529–1536

1533

Table 1. Mechanical properties and density of the calcium silicate masonry (Guerrini et al., 2021). E [MPa] G [MPa] f t [MPa] f c [MPa] f v0 [MPa] μ [-] f bt [MPa] f bc [MPa]

ρ [kg/m

3 ]

6593

1978

0.28

10.1

0.62

0.71

2.5

19.8

1837

The specimens were subjected to in-plane quasi-static shear-compression tests with increasing target displacements through a horizontal actuator, while two vertical actuators maintained a constant axial load corresponding to an average stress of about σ 0 =0.5 MPa at the top of the piers and ensured double-fixed boundary conditions. Additionally, a restraining system prevented out-of-plane movements of the piers. The testing protocol provided three cycles per displacement increment to investigate stiffness and strength degradation up to sever damage conditions.

3.2. Numerical modeling

The two masonry piers are modeled with their actual geometric dimensions and subjected to double-fixed boundary conditions. The mechanical properties assigned to the masonry reflect the experimental values obtained from the material characterization campaign (Table 1). However, when using the bilinear constitutive laws (Fig. 2a,b), the compressive strength is reduced to 85% of the experimental value, since these models cannot capture the post-peak softening behavior of the material. In contrast, when the multilinear model shown in Fig. 2c is adopted, no reduction is required. In this case, the full compressive strength is used, with a residual strength of αf c =0.4 f c at a strain of μ α ε c =0.35%. The axial-flexural contribution of the strengthening system is explicitly modeled by introducing lumped elements with the elasto-plastic behavior deduced from the J 2 -plasticity theory within the macroelement interfaces. Specifically, four additional elements are placed at the end interfaces to represent the tie-down anchorages (Fig. 3b). The equivalent Young’s modulus, cross -sectional area, and yielding stress of these elements are computed to match the actual axial stiffness and tensile strength of the steel connectors (126000 kN/m and 12.8 kN, respectively, as reported in Guerrini et al., 2021), based on the integration lengths of the end interfaces. The strengthening is irrelevant in the central interface, as double-fixed boundary conditions prevent relative rotations. The shear strength of the piers is defined as the minimum value between two failure criteria, following the provisions of the Italian building code for masonry with regular texture (MIT, 2019): shear sliding over a cracked length ( V u,s ) and stair-stepped diagonal cracking ( V u,d ). Notably, the parameter f v0,lim , which accounts for the tensile failure of units, is assumed equal to the brick tensile strength f bt . The shear strength improvement provided by the OSB panels is implicitly accounted for by assigning increased cohesion and friction coefficients, according to the approach described in previous works (Guerrini et al., 2024). In this case, only the diagonal cracking criterion is activated, as the strengthening system effectively prevents shear sliding failure. Gc t =5 and β = 0.5 are assigned to the shear model of the macroelement. The numerical simulations are carried out by applying the experimental loading protocol in terms of amplitude and number of cycles. Accordingly, a constant vertical load of 101.45 kN is applied at the top of the specimens. 3.3. Numerical results and comparison Numerical results are discussed in terms of hysteresis cycles, namely the horizontal top displacements against the base shear restoring forces, and failure mechanisms. The numerical failure mode of the unstrengthened pier closely reflects the experimental observations (Fig. 4). The pier initially exhibits a rocking response, followed by a sudden drop in strength due to the activation of a shear-sliding mechanism at approximately 0.20% drift. The hysteresis cycles show good agreement with experimental data in terms of elastic stiffness, lateral strength, and energy dissipation. Differences in peak and residual lateral strength are limited to 5.5% and 3.9%, respectively. It is worth noticing that the numerical peak strength is governed by the f v0.lim limitation, making the results highly sensitive to this parameter. Fig. 4a, 4b, and 4c report the numerical response by adopting the constitutive laws depicted in Fig. 2a, 2b, and 2c, respectively. As the compressive strength is not reached during the loading protocol, the results are essentially equivalent across the three models.