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

El Arabi / El Gendy (2001) examined the structural analysis and design of the three common foundation systems: raft, grid and isolated footings. They carried out the examination to evaluate the different types of structural systems in order to decide the most suitable ones for a specific situation. Here, an example is chosen from the above study with some modifications.

Consider the foundation system shown in the Figure, which may be designed as raft or grid. The raft dimensions are 30.5 [m] × 30.5 [m] while the overall grid dimensions are 33.0 [m] × 33.0 [m], with a constant strip width in both directions. The foundation carries 49 column loads, which are equally spaced, 5.0 [m] apart, in each direction. Column loads and the arrangement of columns are shown also in the Figure.