Question

A triaxial test on a sandstone sample is conducted at a confining pressure of 10 MPa. The elastic axial and volumetric strains at axial stress of 50 MPa are recorded to be \( 4.2 \times 10^{-3} \) and \( 2.0 \times 10^{-3} \) respectively. The modulus of elasticity, in GPa, and Poisson’s ratio of the sample, respectively are closest to:

• A. 5.11, 0.35
• B. 10.22, 0.35
• C. 5.11, 0.17
• D. 10.22, 0.17

Hint:

To find Modulus of Elasticity and Poisson’s ratio in triaxial tests, use the relations for axial and volumetric strains carefully. The relationship between stress, strain, and material constants is crucial for accurate calculations.

Answer 1

The Correct Option is B

Step 1: Using the relationship for Modulus of Elasticity and Poisson’s Ratio. 
The axial strain \(\varepsilon_a\) and volumetric strain \(\varepsilon_v\) are related to the stress and material properties as follows: \[ \varepsilon_a = \frac{\sigma_a}{E} - \nu \frac{\sigma_v}{E} \] Where \(\sigma_a\) and \(\sigma_v\) are axial and volumetric stresses, \(\nu\) is Poisson’s ratio, and \(E\) is the modulus of elasticity. 
Step 2: Calculate Modulus of Elasticity.
From the given data, solve for the modulus of elasticity and Poisson’s ratio using the strain-stress relations. \[ E \approx 10.22 \, {GPa}, \quad \nu \approx 0.35 \]