Axisymmetric Condition
Description:
The other condition that occurs in practical problems is axial symmetry, or the axisymmetric condition, where two stresses are equal. Let us consider a water tank or an oil tank founded on a soil mass, The radial stresses (sr) and circumferential stresses (su) on a cylindrical element of soil directly under the center of the tank are equal because of axial symmetry.
The oil tank will apply a uniform vertical (axial) stress at the soil surface and the soil element will be subjected to an increase in axial stress, Dsz 5 Ds1, and an increase in radial stress, Dsr 5 Dsu 5 Ds3. Will a soil element under the edge of the tank be under an axisymmetric condition? The answer is no, since the stresses at the edge of the tank are all different; there is no symmetry.
Hooke’s law for the axisymmetric condition is
or, in matrix form,
Axisymmetric condition on a soil
element under the center of a tank.
The inverse of Equation gives
Plane strain and axisymmetric stress conditions are ideal conditions. In reality, the stress conditions imposed on soils are much more complicated.