# Practical Considerations in the Design of Passive Free Piles in Sliding Soil
## 2 The Numerical Models  
In order to investigate the interaction process of a free-head concrete single-pile bored in a sliding ground, a finite element model of translational landslide is proposed. A layer of uniform soil, with a thickness of D, can slide over a stable one along a sliding surface inclined with an angle, \(\beta\). The reinforced concrete pile has a constant diameter, d, and extends for a length, L, inside the stable soil, for a total pile length of D + L. Displacements are imposed on the upper layer in steps, along a direction parallel to the sliding surface. Slope reinforcement using free-head vertical single piles involves a model mesh in which the pile is not influenced by the presence of adjacent piles. Therefore, in order to avoid the development of any arch effect between the piles, both the transversal and the longitudinal symmetry planes are located at sufficiently long distances of more than 4 and 6 diameters of pile, respectively [23]. Three different geometries have been studied in order to highlight the failure modes outlined by [3]: Model 1 should fail based on failure mode BY, Model 2 should fail based on failure mode B2, and Model 3 should fail based on failure mode B1 (Figure 2). The synthesis of the geometries of the numerical models considered is reported in Table 1.  
The slip surface between the two soil blocks and the separation surface between the pile and the ground are modelled with the aid of interface elements, in order to create localised discontinuities and to favour the relative displacement between the pile and the ground. These elements of virtual thickness are characterised by both normal and tangential stiffness and by shear strength. To reproduce the different parts of the model, three-dimensional brick elements implemented in MIDAS FEA NX 2021 v1.1 code have been used. These elements have several advantages, including a more stable numerical performance and a reduction in the number of degrees of freedom (three degrees per node). In MIDAS, pile modelling is also supported via the virtual beam function, which allows a quick representation of the stress diagrams in the pile, as well as the displacements of the pile axis. Figure 1: Failure modes of a flexible free-head pile, D + L in length, interacting with a translational landslide of thickness D.  
It is necessary to adopt two different constraint conditions: in the first phase, hinges are applied only at the base of the model, whereas at the lateral boundaries displacements are blocked along both the axes X and Y, so that only the compression of the mesh is allowed to occur along the vertical axis, Z. In the second phase, hinges are applied both to the base and to the sides of the underlying stable formation, while on the sides of the above unstable formation the displacement is blocked only along the Y axis, while it is allowed along the slip plane direction, in terms of displacement vectors U\({}_{\text{xx}}\) with components along Z and X. In the first phase of the analysis, the initial state of equilibrium is sought (Figure 3a): the soil parameters are attributed to the whole model, including the elements schematising the pile, and a homogeneous compression of the model is carried out under the gravity. In the next phase (Figure 3b), the concrete properties are assigned to the pile elements and then displacements U\({}_{\text{xx}}\) are applied in steps until the calculation process converges.