# Practical Considerations in the Design of Passive Free Piles in Sliding Soil
## 3 Materials and Method
and a passive strength coefficient of \(K_{\rm p}\cong 3\), while the Rankine distribution refers to a ground friction angle of \(\varphi^{\prime}=20^{\circ}\), a cohesion of \(c^{\prime}=100\) kPa, a soil-pile friction angle of \(\delta=0^{\circ}\), a slope inclination of \(\beta=0^{\circ}\) and a passive strength coefficient of \(K_{\rm p}\cong 2\). It can be seen that the maximum net soil pressure does not exceed the passive strength distribution of Lancellotta, with the only exception of a few parts of the Model 2 in which higher passive soil pressures may be mobilised. This may be a consequence of the three-dimensional interaction, as opposed to the plane-strain condition to which the theories in question refer. In conclusion, it was shown that when the design ultimate moment, \(M_{\rm ult,d}\), is attained in the most stressed pile cross-section, the soil passive pressure is reached in a few limited areas of the pile shaft. The synthesis of all the examined models is summarised in Figure 11 in terms of the horizontal pile head displacements, \(d_{y,\rm d}\), able to induce the design yield moment, \(M_{y,\rm d}\), in the most stressed cross-section. For comparison, Figure 12 also shows the horizontal pile head displacements, \(d_{\rm ult,d}\), which cause the design ultimate moment, \(M_{\rm ult,d}\), to be reached in the most stressed cross-section; this latter representation has meaning only if the pile does not fail before in shear. Figure 3:3 Concrete pile 1200 mm in diameter and 2% of longitudinal reinforcement: head displacements \(d_{y,\rm d}\) which induce the design yield moment \(M_{y,\rm d}\) in the most stressed cross-section. Figure 3:4 Mobilisation of the net soil pressures near the design ultimate moment, \(M_{\rm ult,d}\), for the models 1, 2 and 3 of Figure 3:5  
The failure modes of the pile depend primarily on the parameter D/L, i.e., on both the lengths, L, in contact with the stable formation, as well as the lengths, D, in contact with the moving ground. The soil stiffness influences the amount of displacement of the pile head but not the mode of deformation. The data in Figure 11 suggest that the displacements d\({}_{\text{yd}}\) causing yielding in simple bending are relatively small, not exceeding 30 cm. For these levels of displacement, the pile may attain at most the design shear strength, V\({}_{\text{ult,d}}\), especially in the mode of deformation compliant with Model 1. If the shear collapse of the pile does not occur first, pile head displacements, less than 70 cm, occur at the ultimate moment in the most stressed pile section; these displacements depend on both D/L and E\({}_{\text{sup}}\)/E\({}_{\text{inf}}\) (Figure 12). The development of mechanisms BY, B1 and B2, with associated plastic hinges, is less likely to occur in concrete piles if shear failure may occur earlier. In order to clarify this concept, Table 3 reports the ratio between the design shear strength and the design simple-bending strength, V\({}_{\text{ult,d}}\)/M\({}_{\text{ult,d}}\), for concrete piles with different diameters, the cross-section being characterised by a percentage of longitudinal reinforcement between 1% and 2%. A spiral stirrup, \(\mathcal{O}\) 16 mm/180 mm, is assumed to be constant in all cases. What is noticeable is how this ratio tends to decrease as the pile diameter increases, confirming that, under a same kind of kinematics, the shear strength of standard concrete piles can be reached before the simple-bending strength.