UPDATE 2014-01-14: The attached .zip file now contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
The purpose of this worksheet is to calculate the combined aggregate gradation after blending (combining) two or more different aggregates. Combining aggregates is required when an aggregate gradation is specified that is different than the aggregate supplier's stock gradations. In my work as a consulting civil engineer, I most often see combined aggregate gradations when I review contractor submittals for concrete mix designs, aggregate base, and miscellaneous engineered aggregates.
This worksheet contains two examples. The first example is for a concrete mix design that I reviewed a few years ago and contains two aggregates that were combined to make the coarse aggregate. As part of reviewing the submittal, I created an Excel spreadsheet to check the aggregate supplier's calculation for the combined aggregate gradation and that spreadsheet is the basis for this worksheet. The second example is from a sample calculation I found on the internet that combines five aggregates, three gravels and two sands.
The combined aggregate gradation algorithm proceeds as follows:
Step 0 (Data) — Individual aggregate gradations are described in terms of percent of aggregate by weight passing each in a series of standard sieves. This is the raw data from the submittal. Sieves must be listed from largest to smallest, which is the normal convention.
Step 1 — The percents passing data for each aggregate is converted to percent retained on each sieve. This is accomplished with the program function Ret(P).
Step 2 — The combined aggregate gradation (in terms of percent retained on each sieve) is calculated by prorating the percents retained results for the individual aggregates.
Step 3 — The calculated percents retained for the blended aggregate is converted back to percents passing, which is the combined aggregate gradation that the submittal will show. This is accomplished with the program function Pass(R).
The method used in this worksheet is flexible and can be resized and modified to fit project requirements. This worksheet and its two examples are based on several ASTM standards, but other standards can be used. U.S. Standard Test Sieves are covered in ASTM E 11. Aggregate gradations are specified in various ASTM standards, such as ASTM C 33 for concrete aggregate, ASTM C 144 for masonry mortar aggregate, ASTM D 1241 for soil-aggregate subbase, base, and surface course, etc.
ASTM E 11, Table 1, Nominal Dimensions, Permissible Variations for Wire Cloth of Standard Test Sieves (U.S.A.) Standard Series, lists 56 standard sieves ranging in size from 125 mm (5" nominal) down to 20 μm (No. 635, 0.0008" nominal). Most aggregates I deal with have particle sizes in the range of 50 mm (2" nominal) to 75 μm (No. 200, 0.0029"). There are 42 sieves that cover this range, but most gradations are reported using less than a dozen sieves.