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A novel scheme to apply constitutive (continuum) soil models to the mechanical modelling of soil-structure interfaces is presented. Opposite to existing approaches, all normal stress components of the interface depend directly on the normal stress components of the adjacent continuum. This allows to satisfy boundary conditions not only for the continuum but also for the interface. Interface models based on Hypoplasticity with intergranular strain extension and on Sanisand (version of 2004) are formulated. They are implemented in the framework of a mortar contact discretisation technique in a finite element code, which is available for download. A numerical differentiation scheme is used to secure consistent derivatives of contact forces with respect to displacement. The performance of the proposed interface models is evaluated by comparison with data from (cyclic) simple interface shear tests and an existing (hypoplastic) interface model proposed by Stutz et al. (2016). Subsequently, a large-scale cyclic interface shear test with complex geometry is simulated using the different interface models. It is concluded that only the novel interface formulation allows to appropriately consider the boundary conditions of the large-scale interface shear test in the interface.