ANS:D - directional angles

In a purely cohesive soil, the critical center (also known as the critical failure surface) typically lies at the intersection of the following two lines:.

Perpendicular drawn at 2/3rd slope from the toe to the locus of the center: This is often referred to as the "drainage line" or "pore water pressure line. " It represents the line along which pore water pressure is dissipated during shear.

The locus of the center: This is essentially the centerline of the potential failure surface and represents the critical path along which the soil may slide.

So, the critical center in a purely cohesive soil is at the intersection of these two lines. This concept is part of Rankine's earth pressure theory, which is used to analyze the stability of slopes in cohesive soils. Point Q is found at a distance H downwards from the toe and 4.5H horizontally away as shown in the diagram. As, for purely cohesive soil the centre of the critical slip circle is P, so it is taken to lie at the intersection of directional angles α and β.