# Concept of Stress and strain

### Stress and Strains:

All stresses, which are applied to a rock mass can be resolved into three mutually perpendicular directions. These directions are called ”axes of stress” and their magnitude is expressed as greatest, intermediate, and least. When the magnitude of stresses for each axis is equal, the stresses are said to be hydrostatic. Under such stresses only the volume of the rock changes while its shape remains the same. When the stresses are unbalanced, a deformational force operates, which changes the shape of the rock.

Application of stresses produces a ”strain”. The distribution of strain along the principal stress axes gives rise to strain axes. These strain axes are as follows.

- Axis of Least Strain: The axis of greatest stress is the axis of greatest compression. Hence it is regarded as the ”axis of least strain”.
- Axis of Intermediate Strain: The axis of intermediate stress becomes the ”axis of intermediate strains”.

### Strain Ellipsoid:

The strain ellipsoid in an imaginary figure. It is produced when a sphere of homogeneous rock is subjected to deforming stress. In this ellipsoid, the orientation of strain axes is shown in Fig ; below.

Most sections through the ellipsoid are ellipse. Two of the sections, however, are circles whose diameters are ”a.c” and ”b.d” Fig;.

Along the circular sections, the surface of the ellipsoid and the sphere coincides. It means that along these sections no change in shape has taken place. Along all other sections, however, the shape has been distorted.

In the segment ‘b.e.c’ of the ellipsoid the strain has produced elongation, while in the segment ‘a.e.b’, the strain has caused shortening. The plane of circular cross-section ‘bd’ lies between these two segments. This is a surface of shear because the distribution of stress on either side of it is in the opposite directions. Thus there are two shear planes, which pass through the strain ellipsoid. These shear planes become the surface of rupture when the compressional strength of the rock has been exceeded.

In the strain ellipsoid, the axis of the greatest strain indicates the direction of elongation. If the tension fractures form, they develop parallel to the plane that contains the least and intermediate strain axes. It means tension fractures form at right angles to the greatest axis of the strain ellipsoid.

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