ABSTRACT
The idealization of some problems may lead to the formulation of mathematical models represented in terms of governing equations (i.e. partial differential equations) along with prescribed boundary conditions. In these situations, closed form solutions for the response variables can be obtained by well-established analytical methods either directly by doing the mathematics or by using mathematical packages (i.e. MAPLE). Whenever possible, we try to obtain an analytical solution first as it is ‘exact’ which also provides an insight into the nature of the problem. Additionally, analytical solutions become useful for the verification of the solutions obtained by approximate numerical methods.
In this chapter basic analytical solutions for some simple problems in geomechanics are presented. At a fundamental level, a wide range of such problems reduce to that of deformation and flow of a saturated deformable porous medium subjected to a variety of loading. The problems are chosen from the following: flow of water through non-deformable medium, deformation of soil column, consolidation of a saturated deformable porous medium (decoupled flow and deformation), and flow and deformation in saturated deformable porous medium (coupled flow and deformation). In addition to MATLAB programs, many MAPLE worksheets are also provided at the end of the chapter.
