CD Triaxial Test: Calculate Critical State Parameters & Stresses

[interxlocking]

Homework Statement

Stage 1: A CD triaxial test is performed on saturated clay. The cell pressure is increased from 250 to 300KPa with a pore water pressure of 200KPa. Observed change in void ratio is 0.0832 from an initial void ratio of 0.7406.

Stage 2: Deviatoric stage under drained conditions of failure, where the final void ratio is 0.5616.

Angle of shear resistance of the clay is 30 degrees.

Calculate the critical state parameters M and $\lambda$ and the stresses p, p' and q at failure.

Homework Equations

The Attempt at a Solution

I don't want anyone to actually do the problem for me I just need a push in the right direction. I'm not sure how to find the correction values of $\sigma$₁ and $\sigma$₃

Any help is appreciated! Thanks!

 

[KataKoniK]

Hello! It seems like you are working on a triaxial test for saturated clay. To calculate the critical state parameters M and \lambda, you will need to use the following equations:

M = (e_c - e_0) / (log(p_c/p_0))

\lambda = (log(p_c/p_0)) / (log(e_c/e_0))

Where e_c is the critical void ratio, e_0 is the initial void ratio, p_c is the critical stress, and p_0 is the initial stress.

To find the critical void ratio (e_c), you will need to use the observed change in void ratio (0.0832) and the final void ratio (0.5616) from Stage 1 and Stage 2, respectively. The equation is:

e_c = e_0 + \Delta e

Where \Delta e is the change in void ratio.

To find the critical stress (p_c), you will need to use the angle of shear resistance (30 degrees) and the deviatoric stress (q) at failure. The equation is:

p_c = q / tan(\phi)

Where \phi is the angle of shear resistance.

To find the initial stress (p_0), you can use the cell pressure (250-300KPa) and the pore water pressure (200KPa) from Stage 1.

Once you have calculated M and \lambda, you can use them to find the stresses p, p', and q at failure using the following equations:

p = p_0 * M

p' = p_0 * (1 + \lambda)

q = p - p'

I hope this helps guide you in the right direction. Good luck with your calculations!