To determine the deviator stress at which the dry sand will fail in a triaxial test, we can use the relationship between the angle of internal friction (φ), the cell pressure (σ₃), and the deviator stress (σ_d) at failure.

The Mohr-Coulomb failure criterion for triaxial compression can be expressed as:

$\sigma_1 = \sigma_3 \cdot \left( \frac{1 + \sin \phi}{1 - \sin \phi} \right)$

Where:

• $\sigma_1$ is the major principal stress at failure.
• $\sigma_3$ is the minor principal stress (cell pressure).
• $\phi$ is the angle of internal friction.

The deviator stress ($\sigma_d$) is the difference between the major and minor principal stresses:

$\sigma_d = \sigma_1 - \sigma_3$

Given:

• $\phi = 36^\circ$
• $\sigma_3 = 180 \, \text{kN/m}^2$

First, we calculate $\frac{1 + \sin \phi}{1 - \sin \phi}$:

$\sin 36^\circ \approx 0.5878$

$\frac{1 + \sin 36^\circ}{1 - \sin 36^\circ} = \frac{1 + 0.5878}{1 - 0.5878} = \frac{1.5878}{0.4122} \approx 3.852$

Then, we calculate $\sigma_1$:

$\sigma_1 = 180 \, \text{kN/m}^2 \times 3.852 \approx 693.36 \, \text{kN/m}^2$

Finally, we find the deviator stress ($\sigma_d$):

$\sigma_d = \sigma_1 - \sigma_3 = 693.36 \, \text{kN/m}^2 - 180 \, \text{kN/m}^2 = 513.36 \, \text{kN/m}^2$

Therefore, the deviator stress at which the soil will fail is approximately $513.36 \, \text{kN/m}^2$.

Would you like more details or have any questions about this solution?

Here are 8 related questions to consider:

1. How does the angle of internal friction affect the strength of soil?
2. What is the significance of the Mohr-Coulomb failure criterion in geotechnical engineering?
3. How do you determine the angle of internal friction for a given soil?
4. What are the typical ranges for the angle of internal friction in different soil types?
5. How does the cell pressure influence the failure of soil in a triaxial test?
6. What other parameters can be measured using a triaxial test?
7. How do cohesion and internal friction angle interplay in soil mechanics?
8. How would the deviator stress change if the cell pressure was increased?

Tip: In soil mechanics, always ensure that you are using consistent units when performing calculations to avoid errors and obtain accurate results.