Chapter 8
Elastic Solutions in Geomechanics
8.1 Introduction
Many of the elastic solutions for problems in geomechanics were solved in the
later part of nineteenth century, and they were usually solved not for geotechnical
engineering applications, but to answer basic questions about elasticity and behaviour
of elastic bodies. Some special problems that hold a fundamental position in relation
to elastic solutions in geotechnical engineering are presented in this chapter. With
one exception, all the problems presented involve a point load. This point load is a
finite force applied at a point (on a surface of zero area). Due to stress singularities,
the point load problems involve limiting procedures. Solutions of the problems of
Kelvin, Boussinesq, Flamant Cerrutti and Mindlin related to point load are discussed
in this chapter.
The classical problem of Kelvin involves a point load acting in the interior of
infinite elastic body. The Kelvin’s solution has found many applications in engineering. This is useful for the analysis of screw plate in which the plate is embedded
in an infinite elastic body and the screw plate can be represented by an assumed
load distribution. The classical problem of Boussinesq dealing with a normal force
applied at the plane boundary of a semi-infinite solid has found practical application
in the study of the distribution of foundation pressures, contact stresses and in other
problems of soil mechanics.
Of all the above problems discussed in this chapter, the most useful in geomechanics is the Boussinesq’s solution. The Flamant’s problem uses Boussinesq’s solution together with the principle of superposition to solve for a stress field for a line
load acting on the surface of the half-space. The Flamant problem has many applications in determining the stress and displacement fields below continuous strip
footings, embankments and retaining wall foundations. The fundamental solution of
Cerrutti for horizontal load acting at the surface of the elastic half-space has found
applications for stress and displacement fields in geotechnical engineering dealing
with lateral loads at the ground surface. Examples include single or group of piles
subjected to horizontal lateral load at the ground line. The fundamental solution by
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
T. G. Sitharam and L. Govindaraju, Theory of Elasticity,
https://doi.org/10.1007/978-981-33-4650-5_8
261
Elastic Solutions in Geomechanics
8.1 Introduction
Many of the elastic solutions for problems in geomechanics were solved in the
later part of nineteenth century, and they were usually solved not for geotechnical
engineering applications, but to answer basic questions about elasticity and behaviour
of elastic bodies. Some special problems that hold a fundamental position in relation
to elastic solutions in geotechnical engineering are presented in this chapter. With
one exception, all the problems presented involve a point load. This point load is a
finite force applied at a point (on a surface of zero area). Due to stress singularities,
the point load problems involve limiting procedures. Solutions of the problems of
Kelvin, Boussinesq, Flamant Cerrutti and Mindlin related to point load are discussed
in this chapter.
The classical problem of Kelvin involves a point load acting in the interior of
infinite elastic body. The Kelvin’s solution has found many applications in engineering. This is useful for the analysis of screw plate in which the plate is embedded
in an infinite elastic body and the screw plate can be represented by an assumed
load distribution. The classical problem of Boussinesq dealing with a normal force
applied at the plane boundary of a semi-infinite solid has found practical application
in the study of the distribution of foundation pressures, contact stresses and in other
problems of soil mechanics.
Of all the above problems discussed in this chapter, the most useful in geomechanics is the Boussinesq’s solution. The Flamant’s problem uses Boussinesq’s solution together with the principle of superposition to solve for a stress field for a line
load acting on the surface of the half-space. The Flamant problem has many applications in determining the stress and displacement fields below continuous strip
footings, embankments and retaining wall foundations. The fundamental solution of
Cerrutti for horizontal load acting at the surface of the elastic half-space has found
applications for stress and displacement fields in geotechnical engineering dealing
with lateral loads at the ground surface. Examples include single or group of piles
subjected to horizontal lateral load at the ground line. The fundamental solution by
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
T. G. Sitharam and L. Govindaraju, Theory of Elasticity,
https://doi.org/10.1007/978-981-33-4650-5_8
261