Falling　into　the　framework　of　the　Petrov-Galerkin　finite　element　formulation　with　embedded　discontinuity,　the　assumed　enhanced　strain　(AES)　method　could　simulate　the　structural　localization　phenomenon　and　the　associated　loss　of　bearing　capacity　in　a　way　insensitive　to　mesh　alignment　and　refinement.　For　another　hand,　the　improved　numerical　manifold　method　(INMM)　naturally　excels　at　dealing　with　heterogeneous　problems　such　as　the　soil-rock　mixture　(SRM)　slope　with　embedded　soft　soil　region.　Therefore,　to　simulate　the　shear　band　evolution　in　heterogeneous　slope　more　efficiently,　precisely　and　also　mesh　independently,　this　paper　proposes　to　invoke　the　AES　method　with　the　meshes　of　the　INMM.　Beside,　this　paper　proposes　a　simple　and　efficient　method　to　address　the　constitutive　integration　for　multi-surface　plasticity　induced　by　cutting　the　tensile　part　of　the　Drucker　Prager　model.　Finally,　the　efficiency　and　accuracy　of　the　proposed　approaches　are　tested　on　some　typical　examples　including　heterogeneous　block　and　slope.　©　2022　Elsevier　Ltd