The Grade Support Disk is the imaginary circular plane inside the curled slab corresponding to the slab's intersection with the grade's original surface. Absent any live loads, the Grade Support Disk is concentric with the slab's centroid and equates to the imaginary top surface of the displaced grade volume.

Rule 11d: For a plain, crack-free, unloaded slab exhibiting a positive Curl NumberCand having its centroid sunksinches into the grade, the radiusdof the slab's Grade Support Disk will equal 2523 (s/C)½inches.

In last month's column, the center of each of the assumed 6-inch-deep 15x15-foot curled (C50) slab panels sank about s = 0.024 inches into the grade. According to Rule 11d, therefore, the Grade Support Disk under each of the assumed panels must have a radius of 2523(0.024/50)½ = 55 inches, giving each such disk an area of about 66 square feet. Because each 15x15-foot panel covers a total area of 225 square feet, wherever the panels remain unloaded, it can be seen that about 70% of the slab must not be touching the grade at all.

Rule 11e: They might be called slabs on grade, but until they're loaded or cracked, they're really mostly “slabs on air.”

Now a little high school geometry leads to the intimidating but handy:

Rule 11f: For a plain, crack-free, unloaded slab exhibiting a positive Curl NumberCand having its centroid sunksinches into the grade, at any pointzinches from the centroid, the elevationeof the slab's bottom relative to the Grade Support Disk will equal: {3182400 - [31824002-z2C2]½} /C-sinches.

For example, because the corners of the assumed 15x15-foot C50 panels are all z = 127 inches from their centroids, with s equaling 0.024 inches as before, Rule 11f says that an e = 1/10-inch-deep air gap must exist under each corner.

In addition to providing the basis for Rules 11c, 11d, and 11f, the slab's Curl Number C has another very important application:

Rule 11g: The slab's Weightless Shrinkage GradientGequals -t C/ (3182400 +t C) , wheretis the slab's nominal thickness in inches.

Note the value for G will usually be negative, because the slab's total shrinkage typically decreases with depth.

If the curled slab were weightless, then gravity would not deflect its cantilevered edges so as to depress the Curl Number. G would then be a pure measure of the slab's overall change in shrinkage from top to bottom. In the real world, though the effect is small, any lifted edges will indeed be bent down somewhat by their own weight, and the slab's measured C value will be contaminated commensurately. However,

• because most slabs experience very little, if any drying shrinkage at their bottoms,
• because the densities and elastic moduli of most slabs are fairly uniform, and
• because G depends solely upon the overall change in shrinkage through the slab's depth and not upon the particular shape of the shrinkage gradient:

Rule 11h: The Weightless Shrinkage Gradientis an effective gauge of the relative in situ shrinkage experienced by any slab at any time.

* Note that the numerator in the Curl Number equation should be 10608000 S not 6630 S.

Allen Face is the inventor of the F-number system, F-min system, Dipstick, F-Meter, D-Meter, and Screed Rail. He is also an ACI Fellow and a long-time member of ACI Committees 302, 360, and 117.