Most of the available solutions used to determine the flexibility coefficient, or the modulus of subgrade reaction, assume that the subsoil consists of a homogeneous layer. In reality, the soil consists of different material features in vertical and horizontal directions. In practice, a number of vertical soil profiles defines the soil under the foundation. Each one has multi-layers with different soil materials. Therefore,three-dimensional coefficient of flexibility, or variable modulus of subgrade reaction, must be taken into consideration. Kany (1972) determined the two-dimensional flexibility coefficient for beam foundation by determining flexibility coefficients for the existing boring logs first. Then, by interpolation can obtain the other coefficients outside the boring logs. This example describes the methods that are available in program ELPLA to determine the three-dimensional coefficient of flexibility or variable modulus of subgrade reaction.

Description of the problem

This example is carried out to show the influence of irregular subsoil on the values of settlements, contact pressures and moments. The analysis of the square raft is carried out by the two familiar types of soil models: Winkler's and Continuum models for elastic foundations, besides the analysis of rigid raft on Continuum model, using the following three calculation methods:

Method (3): Variable modulus of subgrade reaction method

Method (7): Modulus of compressibility method

Method (8): Rigid raft on compressible subsoil

A square raft of 10 [m] side is subdivided into 144 square elements as shown in the Figure.

The raft thickness is d = 0.4 [m].