A Non Linear Fractal Model for the Analysis of Pile Foundations

"In the paper a non linear model for the analysis of the pile response to the axial loads is presented. The study aims to find a general analytical solution concerning the pile-soil interaction modeled by means of the method of the load transfer curves. It makes use of a criterion based on the plastic and on the hardening work locally done by the shear stresses and due to the current elastic shortening of the shaft. Then a specific solution, denoted fractal model, is found applying recurrent relations that link the shaft shear stresses and the tip normal stresses to the pile settlements. These relations are based on that one proposed by Kondner in modeling the soil samples response in the triaxial tests and then used by Chin in the inverse slope method in estimating the pile capacity by the load test results. The comparison between the model predictions and the load tests measures validate the fractal model.INTRODUCTIONThe behavior of the axially loaded piles is known to be characterized by a highly non linear trend caused by the onset of plastic and irreversible deformations in the soil starting just from the first load levels. With the purpose to reach a deeper understanding of the pile-soil interaction, the influence of the soil inelastic properties on the distribution of the axial loads and of the vertical displacements is investigated. The research starts analyzing the behavior of an infinitesimal length of a pile embedded in a non linear homogeneous soil. That initial study leads to a criterion based on the plastic and on the hardening work locally done by the shear stresses and that allows to find the axial loads as a function of the elastic shortenings of the shaft. The relation that links the pile axial load to the elastic strain of the pile material is then used. That allows to find the vertical displacements and the axial loads as function of the depth in a parametric form in which the tip settlement acts as an independent parameter. The method of the load transfer curves is used and the effects of the pile technology are included in the soil constitutive relations. The analysis is then extended to the non-homogenous soils in a very effective way. The solution is applied taking as constitutive relations of the pile-soil interface the one proposed by Kondner to analyze the soil triaxial tests and by Chin to interpolate the pile response measured in the load tests."