The　lateral　displacement　of　deep　soft　soil　caused　by　large-area　heap　loading　is　a　common　issue　in　engineering　practice,　which　affects　the　stability　of　neighboring　pile　foundations.　This　study　investigates　the　calculation　of　thrust　force　exerted　by　the　flow　of　soft　soil　around　piles　and　its　impact　on　pile　foundations.　The　surrounding　soft　soil　is　considered　a　Bingham　fluid.　An　analytical　formula　for　single　pile　flow　drag　during　the　internal　slip　of　deep　soft　soil　is　derived　based　on　fluid　mechanics　theory　and　the　fluid　characteristics　of　the　Bingham　fluid.　The　traditional　cantilever　pile　approach　is　modified　by　assuming　a　rectangular　distribution　of　flow　drag　along　the　pile　body　and　using　the　matrix　transfer　method.　The　response　of　a　single　pile　body　under　field　heap　loading　conditions　is　then　analyzed,　and　the　results　are　compared　with　the　calculation　results　of　the　traditional　soil　pressure　method　and　field-measured　data　to　validate　the　proposed　calculation　method　for　flow　drag　around　a　pile　in　soft　soil.　Finally,　a　parametric　study　is　conducted　to　analyze　the　effects　of　the　relative　flow　velocity　and　dynamic　viscous　coefficient　of　soft　soil　on　flow　drag.　©　2024　Elsevier　Ltd