PSI - Issue 78

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

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Fig. 4. Hysteretic cycles of the bare pier using the (a) Penna et al. (2014), (b) Bracchi et al. (2021), and (c) multilinear material models. Experimental and numerical responses in gray and black, respectively.

The numerical simulation of the retrofitted pier also shows good agreement with the experimental results (Fig. 5), with a minor discrepancy of about 2% in the peak lateral strength estimation across the three constitutive models adopted for the axial-flexural response of the interfaces. Experimentally, the timber frame effectively inhibited the shear-sliding mechanism, allowing the pier to reach its flexural capacity. This resulted in pronounced toe-crushing at the base, which progressively reduced the effective dimensions of the pier, leading to lateral strength degradation and the development of a diagonal crack at around 0.80% drift, ultimately causing shear failure at 2% drift. All the adopted material models for the axial-flexural interfaces successfully capture the extensive masonry plasticization. Nevertheless, the cyclic response is significantly influenced by the choice of constitutive law. More specifically, the bilinear model with parallel-elastic unloading (Fig. 4b) provides a better representation of damage accumulation compared to the recentering unloading (Fig. 4a). However, the plastic plateau limits the accuracy of the formulation. Conversely, the multilinear model successfully reproduces the lateral strength degradation associated with toe crushing, up to the onset of the diagonal crack observed during the experimental test, which ultimately led to shear failure of the specimen. This crack is a consequence of the reduction in the effective dimensions of the pier due to severe damage, a phenomenon that cannot be properly captured through this macroelement model. Notably, previous studies proved that stripe and full fiber discretizations with the material model of Fig. 2a yield almost overlapping results (Salvatori et al., 2025a), with minor discrepancies due to the approximations involved in the analytical integration procedure (Penna et al., 2014).

Fig. 5. Hysteretic cycles of the retrofitted pier using the (a) Penna et al. (2014), (b) Bracchi et al. (2021), and (c) multilinear material models. Experimental and numerical responses in gray and black, respectively.