Introduction

The foundation is considered as rigid, elastic or flexible, depends on the ratio between the rigidity of the foundation and the soil. The oldest work for the analysis of foundation rigidity is that of * Borowicka *(1939). He analyzed the problem of distribution of contact stress under uniformly loaded strip and circular rigid foundations resting on semi-infinite elastic mass.

After *Borowicka*’s analysis, many authors introduced formulae to find the foundation rigidity for plates resting on different subsoil models. For examples, *Gorbunov*/ *Posadov * (1959) introduced formula for an elastic solid medium. *Cheung*/ *Zienkiewicz * (1965) introduced formulae for Winkler springs and isotropic elastic half space model. *Vlazov*/ *Leontiv * (1966) introduced formula for a two-parameter elastic medium. A good review for those formulae may be found in * Selvadurai *(1979).

Lately, based on great number of comparative computations for the modulus of compressibility method, *Graßhoff *(1987) proposed various degrees of system rigidity between foundation and the soil until case of practical rigidity using Equation (5.2). The equation still used in many national standard specifications such as German standard (*DIN *4018) and Egyptian Code of Practice (*ECP *196-1995).

Description of the problem

Ribbed raft may be used for many structures have heavy loads or large spans, if a flat level for the first floor is not required. Consequently, concrete is reduced. Such structures are silos and elevated tanks. In spite of this type of foundation has many disadvantages if used in normally buildings, still used by many designers. Such disadvantages are the raft needs deep foundation level under the ground surface, fill material on the foundation to make a flat level and an additional slab on the fill material to construct the first floor. The use of the ribbed raft relates to the simplicity of analysis by hand calculations.

First, both of the two rafts with and without ribs are clearly saves and correct, but there is still a question, whose one of the two types is more rigid? To answer this question the following example is presented. Consider the foundation of an elevated tank may be designed for both types of foundations. The foundation has the dimensions of 20 [m] × 20 [m], transmits equal loads for all 25 columns, each of 1000 [kN]. The loads give average contact pressure on soil *q _{av}* = 62.5 [kN/m]. Columns are equally spaced, 4 [m] apart, in each direction as shown in the Figure.