Interlocking formulation for the assessment of the out-of-plane dynamics of masonry walls interacting with sidewalls

The seismic performance of masonry rocking walls is significantly affected by a complex interaction with orthogonal walls, acting as a restraint to lateral displacements. However, this interaction is often neglected in both research applications and engineering assessments, leading to inaccurate structural assessments. In addition, international technical regulations still lack robust procedures to account for these aspects in structural analyses. This paper proposes an efficient strategy to simulate the dynamic response of rocking walls subjected to out-of-plane ground motions, accounting for the interaction with sidewalls by adopting a friction-resistance formulation previously presented and validated by the authors in the static field. A sliding failure mechanism, characterised by a vertical crack and involving the bed mortar joints of the front-to-lateral walls interlocking interfaces, is assumed. Then, the resistant frictional forces are lumped into a discrete distribution of nonlinear links called “interlocking links”. The paper characterises the different phases of the interlocking links, namely the elastic, plastic, and failure phases. Then, it focuses on the elastic stage, corresponding to the activation of the mechanism, to: (i) prove the existence of a system natural frequency, (ii) evaluate the accuracy of different modelling approaches currently employed in research and engineering practice, and (iii) evaluate the model sensitivity against the number of links and the minimum number of links required to discretise the orthogonal walls. The numerical simulations are performed on a literature benchmark of a building's front wall adopting three different approaches: a Finite Element (FE) model, a Discrete Macro-Element Model (DMEM), and the Rigid Block (RB) model. RB – directly based on an analytical, well-established formulation – is considered the reference solution to evaluate the accuracy of FE’s and DMEM’s predictions. Overall, the comparisons evidenced good agreement between the numerical (FE, DMEM) and analytical (RB) models, with the main limitation observed in the FE model in predicting the near-resonance wall response. Finally, the paper proposes a simple algorithm to establish the minimum number of interlocking links considering the error between natural frequencies and dynamic peaks of the restrained wall compared to a benchmark model. • Proves the existence and evaluates the closed-form expressions of the dynamic properties of the multi-link restrained wall. • Defines and characterises the mechanical phases that the front wall undergoes interacting with sidewalls. • States a criterion to calibrate the stiffness of interlocking links in elastic phase. • Evaluates the minimum number of links needed for accurate predictions.