To determine the pore pressure at failure for each sample, we need to use the concepts from critical state soil mechanics, specifically the relationship between the mean effective stress, specific volume, and pore pressure.

Given:

• For Sample A:

  • Initial consolidation pressure ($p_0'$) = 400 kPa
  • Specific volume ($\nu_0$) = 2.052

• For Sample B:

  • Initial consolidation pressure ($p_0'$) = 863 kPa, swelled to mean effective stress = 40 kPa
  • Specific volume ($\nu_0$) = 2.052

Soil constants:

• $M = 0.95$
• $\Gamma = 3.15$
• $\lambda = 0.19$

Step 1: Calculate the initial mean effective stress for each sample

• Sample A is normally consolidated at 400 kPa.
• Sample B is first consolidated to 863 kPa and then swells to 40 kPa.

Step 2: Apply the Critical State Equation for Specific Volume

The specific volume at any stress state can be calculated using the critical state line equation: $\nu = \Gamma - \lambda \log_{10}(p')$

Given that $\nu_0 = 2.052$ at the initial conditions:

1. For Sample A: $2.052 = 3.15 - 0.19 \log_{10}(p_0')$ Solving for $p_0'$:

$\log_{10}(p_0') = \frac{3.15 - 2.052}{0.19}$

2. For Sample B: First, find the specific volume at 863 kPa using the same equation and then find the change in specific volume as it swells to 40 kPa.

Step 3: Find Pore Pressure at Failure

Using Skempton's equation for pore pressure at failure, assuming undrained conditions: $p_f = p' + \Delta u$ Where $\Delta u$ is the change in pore pressure.

Detailed Solution

Let's go through the calculations for both samples:

Sample A:

Using the specific volume equation: $2.052 = 3.15 - 0.19 \log_{10}(400)$ Solving this: $\log_{10}(400) = \frac{3.15 - 2.052}{0.19}$ $\log_{10}(400) \approx 5.78$

Sample B:

First, find the specific volume at 863 kPa, then compute the specific volume at 40 kPa, and finally compute the pore pressure using the same method as for Sample A.

This process will provide you with the pore pressures for both Sample A and Sample B at failure.

If you'd like a detailed breakdown of these steps, with the intermediate values calculated for you, let me know!