The Critical Gradient calculator computes the hydraulic gradient based on the specific weight of water and the specific weight of the sample.

INSTRUCTIONS: Enter the following:

• (Y) Specific Weight of Sample

Critical Gradient (i_c): The calculator returns the gradient as a real number.

The Math / Science

This is the condition that occurs at a critical upward hydraulic gradient, `i_c`, when the seepage force just balances the buoyant weight of an element of soil. (Shear stresses on the sides of the element are neglected.)

The formula for Critical Gradient is:

   i_c = (Y - Y_w) / Y_w

where:

• Y is the total unit weight, (weight per unit volume). of the sample
• `Y_w` is the unit weight of water

Notes

When the gradient is too great and seepage exits, soil particles may be removed from the area. The critical gradient is the gradient at which flotation of particles begins, `i_c`.

The critical gradient is determined by the in-place unit weight of the soil.  The critical gradient can also be defined as the gradient at which upward drag forces on the soil particles equal the submerged weight of the soil particles.

The critical gradient is dependent on the specific gravity and density of the soil particles and can be defined in terms of specific gravity of solids, `G_s`, void ratio, e, and porosity, nu.