Local　site　conditions　may　pose　a　significant　influence　on　the　seismic　responses　of　submarine　pipelines　by　altering　both　the　offshore　motion　propagation　and　soil-structure　interaction　(SSI).　This　paper　aims　to　provide　an　in-depth　understanding　of　the　influence　regularity　of　local　site　conditions　on　the　seismic　performance　of　free-spanning　submarine　pipelines　(FSSPs).　For　this　purpose,　a　suite　of　underwater　shaking　table　tests　were　performed　to　investigate　the　seismic　responses　of　FSSP　subjected　to　the　offshore　spatial　motions　at　three　site　categories.　Response　comparison　factor　(chi　R.ij${\chi　}_{R.ij}$)　is　defined　to　quantify　the　structural　response　discrepancies　caused　by　the　seismic　inputs　at　different　sites.　The　test　results　indicate　that　responses　of　the　studied　model　FSSP　gradually　increase　as　spatial　offshore　motions　at　softer　soil　sites　are　employed　as　inputs;　and　the　values　of　chi　R.ij${\chi　}_{R.ij}$　vary　with　a　maximum　magnitude　of　up　to　40%-60%　for　different　response　indices　when　the　site　soil　changes　from　fine　sand　to　clay.　Subsequently,　the　corresponding　numerical　simulations　are　carried　out　to　reproduce　the　seismic　responses　of　the　test　model.　The　experimental　and　numerical　results　meet　a　good　agreement,　indicating　that　the　developed　numerical　modeling　method　can　accurately　predict　the　seismic　responses　of　FSSPs.　Following　this　verified　modeling　method　and　using　the　p-y　approach　to　address　the　SSI　effect,　fragility　surfaces　of　the　studied　FSSP　are　derived　in　terms　of　PGA　and　site　parameter　VS30${V}_{S30}$　(shear-wave　velocity　in　the　top　30　m　of　the　soil　profile)　via　probabilistic　seismic　demand　analyses.　The　impact　of　local　site　conditions　on　the　seismic　performance　of　the　FSSP　is　quantitatively　examined　by　comparing　the　fragility　curves　corresponding　to　various　VS30${V}_{S30}$.　Furthermore,　a　fast　seismic　damage　assessment　method　is　proposed　for　efficiently　evaluating　the　performance　of　FSSPs　buried　in　various　offshore　soil　conditions.　This　approach　proves　beneficial　for　designers　and　decision-makers,　enabling　accurate　estimation　of　seismic　damage　and　facilitating　the　implementation　of　post-earthquake　maintenance　measures　for　FSSPs.