PLANE STRAIN AND AXIAL SYMMETRIC CONDITIONS
Plane Strain Condition:
There are two conditions of stresses and strains that are common in geotechnical engineering. One is the plane strain condition in which the strain in one direction is zero. As an example of a plane strain condition, let us consider an element of soil,
A, behind a retaining wall (Figure). Because the displacement that is likely to occur in the Y direction (Dy) is small compared with the length in this direction, the strain tends to zero; that is, εy 5 Dy/y > 0. We can then assume that soil element A is under a plane strain condition. Since we are considering principal stresses, we will map the X, Y, and Z directions as 3, 2, and 1 directions. In the case of the retaining wall, the Y direction (2 direction) is the zero strain direction, and therefore ε2 5 0 in Equation .
Hooke’s law for a plane strain condition is
Plane strain condition in a soil element
behind a retaining wall.
In matrix form, Equations become
The inverse of Equation gives