The influence of the vertical component of ground motion on the probabilistic treatment of the rocking response of free-standing blocks

The influence of the vertical component of ground motion is investigated forassessing the distribution of the seismic response of unanchored rigid blocks.Multiple stripes of site-hazard-consistent ground motions are employed for cal-culating the seismic response of rigid rocking blocks with and without the inclu-sionoftheverticalcomponent.Thecomparisonoftheresultingresponseisbeingmade both for single records and full suites, employing a paired record versus anensemble-statistics comparison, respectively. It is shown that on a single recordbasis,theverticalcomponentmayhaveanon-negligiblebuthighlyvariableinflu-ence on the rocking response, sometimes detrimental, sometimes beneficial.Still, when considering any large ensemble of records, the effect becomes statis-tically insignificant, except for the very specific case of rocking uplift for stockyblocks. To this end, for cases where the appearance of uplift is associated withdamage, closed-form expressions are proposed to modify the lognormal fragilityfunction of rocking initiation given the block slenderness and the ratio of thepeak vertical over the peak horizontal ground acceleration.