Sequence-aware Damage Accumulation Function for light damage in masonry walls under repeated, nonidentical earthquakes

Abstract Decades of induced seismicity in Groningen have exposed unreinforced clay masonry to frequent, shallow, small-to-moderate earthquakes. Conventional, event-centric vulnerability assessments largely ignore the cumulative effects of repeated shaking and therefore under-predict visible (light, crack-based) damage. We propose a sequence-aware Damage Accumulation Function (DAF) that advances a measured crack-based state Ψ across arbitrary PGV histories by separating similar-intensity repetitions (small increments) from events that set a new maximum (disproportionate jumps). The method integrates (i) earlier full-scale wall and spandrel experiments with high-resolution digital image correlation to quantify crack initiation, widening and extension; (ii) earlier calibrated nonlinear time-history analyses of Groningen-type motions using the Engineering Masonry Model; and (iii) a semi-empirical surrogate linking ∆Ψ to PGV and typological parameters with heteroskedastic, PGV-dependent uncertainty whose incremental contribution decays with sequence position. Applied to historical records and hypothetical futures, DAF results indicate that repeated low-intensity events meaningfully affect accumulation (≈10–20% additional ∆Ψ for same-intensity repeats), while a record-high PGV produces a marked jump. Regional analyses yield exceedance maps that differ from single-event fragility, especially at the edges with low but repeated PGV values and enable decision-facing metrics such as “damage hastening.” The formulation is intended for DS1/early DS2 crack damage of in-plane URM walls and uses PGV as the intensity measure. The DAF provides an interpretable, probabilistic complement to standard fragility where history and repetition govern light-damage progression.