## Example (4.4): interaction of two square rafts constructed side by side

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

Settlement joints are usually used in the foundation when the intensity of loads on it differs considerably from area to another. In such case, the foundation may be divided corresponding to its load intensity to avoid cracks. Settlement joint is constructed by making a complete separated joint in the foundation or a hinged joint. If the foundation has a separated joint, each part will settle independently but it will be interaction between parts of the foundation through the subsoil. In the other case of hinged joint, there will be transmission of shearing forces between connection parts.

This example is carried out to examine the interaction of two rafts considering settlement joint. Consider two equal square rafts I and II will be constructed side by side. Each raft has a side of 12 [m] and 0.5 [m] thickness. Raft I is subject to a uniform load of 400 [kN/m2], while raft II carries a uniform load of 200 [kN/m2].