Offshore　wind　turbines　(OWTs)　are　subjected　to　long-term　cyclic　loading,　such　as　wind　and　wave　loading,　leading　to　axial-torsional　bidirectional　cyclic　loading　in　the　pile　surrounding　soil.　This　bidirectional　cyclic　loading　results　in　the　cumulative　deformation　of　the　pile　foundation.　The　larger　cumulative　deformation　endangers　the　operational　safety　of　the　wind　turbine　system.　In　China,　offshore　wind　farms　mainly　consist　of　clay　layers　and　their　cyclic　mechanical　characteristics　need　to　be　examined.　Therefore,　a　series　of　bidirectional　cyclic　loading　tests　are　carried　out　by　using　a　hollow　cylindrical　torsional　shear　apparatus　to　investigate　the　effect　of　different　cyclic　stress　levels　on　the　cumulative　strain.　The　results　revealed　that　cumulative　strains　stabilize　as　the　cycles　increase　when　the　cyclic　stress　level　is　less　than　the　critical　cyclic　stress　level.　An　empirical　model　based　on　the　test　results　is　developed　to　reflect　the　cumulative　deformation　characteristic.　In　the　bounding　surface　constitutive　model,　the　plastic　modulus　interpolation　function　is　improved　by　using　the　established　empirical　model,the　effect　of　loading　and　unloading　routes　on　the　variation　of　plastic　modulus　is　investigated.　Furthermore,　a　modified　constitutive　model　is　used　to　predict　the　cumulative　deformation　of　soil　under　the　effect　of　bidirectional　cyclic　loading.　The　predicted　results　agree　well　with　the　findings　achieved　from　the　tests.　©　2024　Elsevier　Ltd