## Example (4.1): Interaction of two circular rafts

Introduction

In many practical cases, it becomes important to study the interaction of elastic or rigid foundations, which are constructed simultaneously. In this case, there will be interaction of foundations due to the overlapping of stresses through the soil medium, however the structures are not statically connected. The interaction of foundations will cause additional settlements under all foundations.

The conventional solution of this problem assumes that the contact pressure of the foundation is known and distributed linearly on the bottom of it. Accordingly, the soil settlements due to the system of foundations can be easily determined. This assumption may be correct for small foundations, but for big foundations, it is preferred to analysis the foundation as a plate resting on either elastic springs (Winkler’s model) or continuum model. In spite of the simplicity of the first model in application, one cannot consider the effect of neighboring foundations or the influence of additional exterior loads. Thus, because Winkler’s model is based on the contact pressure at any point on the bottom of the foundation is proportional to the deflection at that point, independent of the deflections at the other points. Representation of soil as Continuum model (methodes 4, 5, 6, 7 and 8) enables one to consider the effect of external loads.

The study of interaction between a foundation and another neighboring foundation or an external load has been considered by several authors. Stark (1990) presented an example for the interaction between two rafts. Kany (1972) presented an analysis of a system of rigid foundations. In addition, he presented a solution of system of foundations considering the rigidity of the superstructure using a direct method (Kany 1977). Recently, Kany / El Gendy (1997) and (1999) presented an analysis of system of elastic or rigid foundations on irregular subsoil model using an iterative procedure.

This section presents a general solution for the analysis of system of foundations, elastic or rigid, using the iterative procedure of Kany / El Gendy (1997) and (1999).

Description of the problem

To illustrate the application of the iterative procedure of Kany / El Gendy (1997) for the interactive system of foundations, consider the system of two equal large circular rafts shown in the Figure. The rafts rest on a soil layer of thickness 15 [m]. Each raft has a diameter of 22 [m] and 0.65 [m] thickness. Loading on each raft consists of 24 column loads in which 16 columns loads have P1 = 1250 [kN] and 8 column loads have P2 = 1000 [kN]. The Young’s modulus of the raft material is Eb = 2.6×10 [kN/m ] and Poisson’s ratio is νb = 0.15 [-], while the soil values are Es = 9500 [kN/m] and νs = 0 [-].

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