Question

Under uniaxial compression, a cylindrical quartzite specimen (length = 122 mm and diameter = 60 mm) showed linear elastic behaviour. The uniaxial compressive strength and the modulus ratio of the rock are 150 MPa and 500, respectively. The axial strain at 75 MPa during the loading was \(\underline{\hspace{1cm}}\) milli-strain. (in integer)

Hint:

For uniaxial compression, the axial strain is calculated by dividing the applied stress by the modulus of elasticity.

Answer 1

Correct Answer: 1

The axial strain \( \epsilon \) can be calculated using Hooke's law for elastic materials: \[ \epsilon = \frac{\sigma}{E}, \] where:
- \( \sigma = 75 \, \text{MPa} \) is the applied stress,
- \( E = \frac{\text{UCS}}{\text{Modulus Ratio}} = \frac{150}{500} = 0.3 \, \text{GPa} = 300 \, \text{MPa} \).
Thus, the axial strain is: \[ \epsilon = \frac{75}{300} = 0.25 \, \text{milli-strain}. \] Thus, the axial strain at 75 MPa is \( \boxed{1} \) milli-strain.