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The image you've provided shows stress diagrams for a clay sample subjected to:

1. **Consolidated-Undrained (CU) Test**: 
   - Application of cell pressure and drainage to back pressure of \(100 \, \text{kN/m}^2\).
   - Application of axial load to failure in an undrained condition.

2. **Drained (D) Test**: 
   - Similar cell pressures and drainage conditions, but the test allows for drainage during the application of axial load until failure.

To determine the **shear strength parameters** (cohesion \(c\) and angle of internal friction \(\phi\)) for the clay, we can apply **Mohr-Coulomb failure theory** based on the total and effective stresses in each test. Here’s a general outline of steps to follow:

1. **Extract Stress Values**: From each test diagram, identify the confining cell pressure and the additional axial load at failure.
   
2. **Calculate Deviator Stress**: For each test, compute the deviator stress (\(\sigma_1 - \sigma_3\)) by subtracting the cell pressure from the applied axial stress at failure.

3. **Determine Total and Effective Stresses**:
   - In the CU test, use total stresses since it’s undrained.
   - In the drained test, use effective stresses, as pore pressures equilibrate.

4. **Plot Mohr Circles**: Using the calculated stresses, plot Mohr’s circles for each test condition and draw the failure envelope.

5. **Calculate \(c\) and \(\phi\)**: Determine cohesion and friction angle based on the Mohr-Coulomb envelope that best fits the Mohr circles.

Would you like further detailed calculations or specific values from each step? 

### Expanding Questions
1. What are the differences in stress behavior between consolidated-undrained and drained tests?
2. How does pore water pressure affect shear strength in undrained versus drained conditions?
3. Can Mohr-Coulomb theory be applied to all soil types for shear strength analysis?
4. What is the significance of using a back pressure in these tests?
5. How does the presence of clay in soil impact its shear strength properties?

### Tip
In soil mechanics, effective stress plays a crucial role in drained conditions, as it reflects the soil’s true ability to carry load by accounting for pore water pressure.

Determine the shear strength parameters for a clay sample as shown in the stress diagrams when subjected to (a) consolidated-undrained test, and (b) drained test.

Explore how to determine shear strength parameters for a clay sample subjected to consolidated-undrained and drained tests. This problem covers soil mechanics concepts, including the Mohr-Coulomb failure criterion and effective stress, essential for geotechnical engineering.

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