Example (5.2): Rigidity of irregular raft on irregular subsoil


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 problem

A general numerical example is carried out to show the applicability of system rigidity analysis, which proposed by El Gendy (1998), to find the rigid thickness of rafts of any shape considering re-entrant corner and opening within the rafts.

In one case the raft carries many types of external loads; concentrated loads, distributed load, line load and moments in x-and y-direction as shown in The Figure. The raft parameters are Young's modulus Eb = 2×10 [kN/m] and Poisson's ratio νb = 0.25. The level of foundation is df = 2.7 [m].