The angle between the directions of the failure and the major principal plane, is equal to

ANS:D - 45° + half of the angle of shearing resistance.

1. 45°: This component represents the angle between the major principal plane and the horizontal axis on a Mohr's circle diagram. It's a fixed value that accounts for the orientation of the major principal plane.
2. Half of the angle of shearing resistance: The angle of shearing resistance (often denoted as φ) is a fundamental parameter in soil mechanics that represents the inclination of the failure plane to the major principal plane. By taking half of this angle, we effectively calculate the deviation from the major principal plane to the failure plane.

When we add 45° to half of the angle of shearing resistance, we are essentially determining the total angle between the failure plane and the major principal plane. This calculation accounts for the combined effects of the inherent orientation of the major principal plane and the deviation caused by the shearing resistance of the soil. In summary, "45° + half of the angle of shearing resistance" provides a method for estimating the angle between the directions of the failure plane and the major principal plane, which is a crucial aspect of analyzing soil behavior and stability.