282
8 Elastic Solutions in Geomechanics
Earth
embankment
Liquid
storage tank
Rigid mat
foundation
Fig. 8.14 Examples of non-interactive problems
pressures in the soil beneath those points. The response of the raft and the response
of the soil are coupled and must be considered together.
Non-interactive problems are those where one can assume the elasticity of the
foundation soil as unimportant to the overall response of the soil mass. Some of the
non-interactive problems are illustrated in Fig. 8.14. In non-interactive problems, the
structural foundation is either very flexible or very rigid when compared with the
supporting soil mass. In these problems, it is not necessary to consider the stress–
strain response of the foundation. The supporting soil deformations are controlled
by the contact exerted by the foundation; however, the response of the soil and the
structure is effectively uncoupled.
Non-interactive problems will be much simpler than interactive problems. For
problems such as a uniform vertical stress applied at the surface of a homogeneous,
isotropic, elastic half-space, one can determine some of the stresses and displacements using Boussinesq’s fundamental solutions, which can be obtained by integrating over the region covered by the load. For these problems, there are other
methods for finding appropriate solutions, in which specialized mathematical models
have been developed that can simulate some of the characteristics of linear elasticity.
Winkler model is one such simplest model (Winkler 1867).
8 Elastic Solutions in Geomechanics
Earth
embankment
Liquid
storage tank
Rigid mat
foundation
Fig. 8.14 Examples of non-interactive problems
pressures in the soil beneath those points. The response of the raft and the response
of the soil are coupled and must be considered together.
Non-interactive problems are those where one can assume the elasticity of the
foundation soil as unimportant to the overall response of the soil mass. Some of the
non-interactive problems are illustrated in Fig. 8.14. In non-interactive problems, the
structural foundation is either very flexible or very rigid when compared with the
supporting soil mass. In these problems, it is not necessary to consider the stress–
strain response of the foundation. The supporting soil deformations are controlled
by the contact exerted by the foundation; however, the response of the soil and the
structure is effectively uncoupled.
Non-interactive problems will be much simpler than interactive problems. For
problems such as a uniform vertical stress applied at the surface of a homogeneous,
isotropic, elastic half-space, one can determine some of the stresses and displacements using Boussinesq’s fundamental solutions, which can be obtained by integrating over the region covered by the load. For these problems, there are other
methods for finding appropriate solutions, in which specialized mathematical models
have been developed that can simulate some of the characteristics of linear elasticity.
Winkler model is one such simplest model (Winkler 1867).