Example (5.1): Rigidity of simple square raft


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 (ECP196-1995).

Description of problem

For comparison with complex foundation rigidity problems, no solution is yet available. Therefore, for judgment on the analysis of El Gendy (1998) to find the system rigidity of foundation, consider the simple example of raft foundation shown in Figure (5.2). The raft has dimensions of 12 [m] × 12 [m] and carries four symmetrical and equal loads, each of P = 9000 [kN]. The raft rests on a homogenous soil layer of thickness 20 [m]. The Young’s modulus of the raft and soil materials are Eb = 2×10 [kN/m] and Es = 10000 [kN/m], respectively. Poisson's ratio of the raft material is ν= 0.15.