The falling-head test is used for fi ne-grained soils because the fl ow of water through these soils is too slow to get reasonable measurements from the constant-head test. A compacted soil sample or a sample extracted from the fi eld is placed in a metal or acrylic cylinder (Figure ). Porous stones are positioned at the top and bottom faces of the sample to prevent its disintegration and to allow water to percolate through it. Water fl ows through the sample from a standpipe attached to the top of the cylinder. The head of water (h) changes with time as fl ow occurs through the soil. At different times, the head of water.
A falling-head test setup.
is recorded. Let dh be the drop in head over a time period dt. The velocity or rate of head loss in the tube is
and the infl ow of water to the soil is
where a is the cross-sectional area of the tube. We now appeal to Darcy’s law to get the outfl ow:
where A is the cross-sectional area, L is the length of the soil sample, and h is the head of water at any time t. The continuity condition requires that (qz)in 5 (qz)out. Therefore,
By separating the variables (h and t) and integrating between the appropriate limits, the last equation becomes
and the solution for k in the vertical direction is
The hydraulic conductivity is corrected using Equation