In drained Direct Shear (DS) test, how to find soil stress path to reach failure(i.e. CSL)?

Sure, here are the steps to find the soil stress path to reach failure (i.e., Critical State Line, CSL) in a drained Direct Shear (DS) test:

1. Perform the Direct Shear Test: The first step is to perform the Direct Shear test on the soil sample under drained conditions. This involves applying a normal load to the soil sample and then shearing it at a constant rate. The shear stress and normal stress at failure are recorded.

2. Plot the Mohr Circle: The next step is to plot the Mohr Circle using the shear stress and normal stress at failure. The Mohr Circle is a graphical representation of the stress state at a point in soil. The x-axis represents the normal stress, and the y-axis represents the shear stress.

3. Determine the Failure Envelope: The failure envelope is a line that best fits the Mohr Circles. This line represents the shear stress versus normal stress relationship for the soil at failure.

4. Find the Intersection with the CSL: The Critical State Line (CSL) is a line that represents the state at which soil shears without volume change. The intersection of the failure envelope with the CSL represents the stress path to reach failure.

5. Plot the Stress Path: The stress path is a line from the origin to the point of intersection with the CSL. This path represents the changes in stress state in the soil as it is sheared to failure.

Remember, the exact location of the CSL and the shape of the stress path can vary depending on the specific characteristics of the soil, including its consolidation history and the type of loading applied.