Abstract :
[en] In 1920 Prandtl published an analytical solution for the bearing capacity of a maximum strip load on a weightless infinite half-space, based on a sliding soil part, with three sliding zones, which is nowadays called the Prandtl wedge. This solution was extended by Reissner in 1924 with a surrounding surcharge. Keverling Buisman (1940) , and many researchers after him, extended the Prandtl-Reissner formula for the soil weight, but this part can be neglected for the deep pile foundations. It was Terzaghi (1943) who wrote the formula with bearing capacity factors and Meyerhof (1953) who started to write this formula with both inclination factors and shape factors.
Because of the this development for shallow foundations , many researchers thought that failure of a pile tip in a deep sand layer will also show a Prandtl-wedge type of failure and that the stresses on the pile tip are constant and depend only on the shape factor, the friction angle of the soil and the vertical effective stress near the pile tip ( ), so not on the shape and size of the pile tip. This means that a Cone Penetration Test gives the average stress of a real pile and can in principle be used without a reduction for calculating the bearing capacity of a pile, just as Boonstra (1940) showed with his field test and just as the method of Van Mierlo & Koppejan (1952) assume and also many more recent predicting models do.
The problem is that many researchers (Jardine et al, 2005, Lehane et al, 2005, Clausen et al, 2005) and recent field tests show that bearing capacity design based on unreduced Cone Penetration Test data are more than 30% too high (Van Tol et al. , 1994, 2010, 2012). Therefore all this has been modelled and studied, as far as possible, with Finite Element Modelling (Plaxis 2D axial-symmetric) .
Many remarkable results were found. The shape and size of the pile tip did not matter indeed. But the currently used surcharge shape factor is incorrect. There is also no Prandtl-wedge type of failure at the pile tip, but a zone of plasticity, but still the surcharge bearing capacity factor of Reissner is correct. Also the stresses below the pile tip are not constant, but higher near the centre of the pile.
Additional calculations show that the pile shaft friction does not influence the stresses at the pile tip, but the normal stresses of the pile tip do influence the shear stresses along the shaft.
