Now that we have finished discussing particle packing techniques (although there is still a lot more to say about the subject) we can turn our attention to the more common combined aggregate grading techniques used in designing concrete mixes. As has been previously discussed, even though particle packing and voids techniques are more directly associated with concrete performance, combined aggregate grading techniques are easier to calculate with minimal testing and they approximate the results of the particle packing technique. For the next couple of months I want to talk about some different combined grading approaches and the strengths and limitations of each. However, before we talk about the combined grading techniques, I think it would be helpful to review how to calculate a combined aggregate grading.

When discussing combined aggregate grading there is really only one major philosophical topic to be discussed – are we calculating aggregate percentages based on weight or volume? If you are working with aggregates of different densities, the difference between the weight and volume methods can be significant. While I know many respected people in the industry who insist on calculating aggregate percentages based on weight, my father and I settled on calculating it based on volume for the following reasons:

- The concrete doesn’t care about the weights of materials, just the volume they occupy (there are a few exceptions to this rule but they primarily relate to segregation potential)
- Using volume lets you compare combined gradings of material combinations using differing densities
- If you use the volumetric method you can also perform a combined grading analysis including cementitious materials, water and air. This is a big help for paste analysis.

How do you calculate the volume percentages of aggregates?

- Calculate the volume of each aggregate,
- Add the volumes together to get the total aggregate volume.

I have always calculated the percentages based on the saturated, surface dry density of the aggregates, but I know that Europeans prefer to use the oven dry density of the aggregates, then adjust for absorption. Since we aren’t talking about “rocket science” here, I don’t think the difference is really significant unless you have highly absorptive aggregates, such as pumice or lightweight aggregate. (There are also some other approximations we are making, but I will discuss those later on.)

For example:

- Volume = weight / density, or
- Volume = weight / (specific gravity x density of water)

You lucky people who use metric can ignore the density of water, since it has a density of 1 kg / liter. The U.S. uses 62.4 lbs/cubic foot as the density of water. The examples with numbers are as follows:

- Imperial volume = 1800 lbs / (2.62 sp.g. x 62.4 lbs/cft) = 11.01 cubic feet
- Metric volume = 880 kg / 2620 kg/cubic meter = 0.336 cubic meters

Next you add the volumes together (1), then divide each aggregate volume by the total volume to get the % of total aggregate volume (2). Here is an example in Imperial units:

Material | Weight | Density | Volume | % of aggregate (2) |

1” stone (25mm) | 1400 lbs | / (2.64 x 62.4) | 8.50 cubic ft. | 46.5% |

3/8” stone (9.5mm) | 400 lbs | / (2.64 x 62.4) | 2.43 cubic ft. | 13.3% |

Concrete sand | 1200 lbs | / (2.62 x 62.4) | 7.34 cubic ft. | 40.2% |

TOTAL | 18.27 cu. ft. (1) | 100% |

Next you multiply the percentage of each aggregate volume (1) times the % passing each sieve (2) to get the individual percent passing for each aggregate (3), then add those percents passing to get the total percent passing (4). Here is an example using 2 aggregates:

Sieve | CA-%Pass | FA-%Pass | CA-Pass | FA-Pass | Combined |

% Agg | 63.5% (1a) | 36.5% (1b) | 100% | ||

1-1/2″ | 100 (2a) | 100 (2b) | 63.5 (3a) | 36.5 (3b) | 100 (4) |

1″ | 97 | 100 | 61.6 | 36.5 | 98.1 |

3/4″ | 65 | 100 | 41.28 | 36.5 | 77.78 |

1/2″ | 43 | 100 | 27.31 | 36.5 | 63.81 |

3/8″ | 15 | 100 | 9.53 | 36.5 | 46.03 |

#4 | 8 | 98 | 5.08 | 35.77 | 40.85 |

#8 | 1 | 92 | .64 | 33.58 | 34.22 |

#16 | 0 | 68 | 0 | 24.82 | 24.82 |

#30 | 0 | 45 | 0 | 16.43 | 16.43 |

#50 | 0 | 18 | 0 | 6.57 | 6.57 |

#100 | 0 | 8 | 0 | 2.92 | 2.92 |

#200 | 0 | 1 | 0 | .37 | .37 |

For the sand grading you have to make certain you include the 100% passing for all the sieves above the normal sand sieves. If you are missing a % passing for a coarse aggregate (such as the 3/8” sieve for a 1” nominal stone) you must include some value, whether by interpolation or by guess. This also applies if you have a coarse aggregate grading that jumps from the percent passing the #8 (2.36mm) sieve to the #200 (75µm) sieve. You can’t just put zeros in to substitute for missing values. You should either use the % passing the %200 sieve in the interim sieves or change the % passing the #200 to zero.

The end result is a combined gradation for all the aggregates. This can be converted to cumulative % retained or individual % retained for further analysis.

When creating a combined grading that includes the paste there are two changes that need to be made. First, the air doesn’t have weight, so you go determine the volume and add it to the volumes of the other materials. Secondly, since water and air don’t have a particle size, my father and I created a fictitious “Fluid” sieve and declared that water and air pass the Fluid sieve and are retained on the Pan. This way you can get a volume of total Fluids (including air) as part of the combined grading calculation. Since an increase in water or air (within certain limitations) will reduce concrete performance (except for freeze-thaw durability) we treat them the same.

Now, here are a couple of “gotchas” (really they are just assumptions and shortcuts):

- A gradation is based on weight, but we are treating it as a volume – We have assumed that for a given material the density of all the different particle sizes will be the same.
- We don’t take into consideration particle shape and texture and don’t know how they will impact voids or workability – You are right. For each particle size if there is a problem with angular shape or rough texture we will eventually need to revise our recommendation for combined grading, but that comes later.
- Air isn’t really a fluid – No, but it acts like one for most of our purposes. It enhances workability, it reduces strength and it doesn’t have a particle size (except at the nano level)

If this has gotten too confusing, leave a comment and I will create a spreadsheet documenting the process.

In the coming weeks we will talk about combined grading approaches to mix designs and the specifications that are used for each technique. If you have anything in particular you would like to discuss, drop me a line. (If you know anything about the Feret combined grading technique, please let me know if you would be interested in writing a guest blog entry on it.)

Until next time,

Jay Shilstone

P.S. I am now offering consulting services primarily oriented toward concrete and precast producers and their quality control programs. If you are interested in hiring me, go to www.commandalkon.com/jayshilstone.asp.

### About Jay Shilstone

I am a concrete technologist for Command Alkon, Inc. and have been in the concrete industry for over 35 years. For 28 of those years I have been working on quality control software for the concrete industry. I am a Fellow of the American Concrete Institute and a member of multiple ACI, ASTM and NRMCA committees. I look forward to talking about concrete mix design and quality control with everyone.

## Matt Gawelko says:

Jay,

Great topic! You pick them well. I have wrestled with the question of calculating combined gradation percentages based upon volume vs. mass since the first time I created my first spreadsheet which performs these exact calculations. A quick back story, I once had a college professor named David Mays who, like all other professors my engineering curriculum, would hand back an assignment or a test covered in red ink if I did not have a unit of measure alongside my actual number calculations. He forced us to show all units of measurement as well as unit conversions using dimensional analysis. If there was a number floating around on my page without a unit next to it, there was going to be red ink. There was no sliding anything by him. His was the first course where I couldn’t BS my way through with a good grade based upon my natural interest in the subject matter. I had to buckle down and truly challenge myself to be successful. It was the toughest “B” I’ve ever earned.

David’s rigid approach changed my thought process. It took me from understanding mathematics to understanding applied mathematics and laid the foundation for what some call “engineering judgment.”

Back to the subject at hand. My engineering judgment screams out to me that even though percentages have no units of measure, we must use percent by mass when calculating combined gradation percent passing for no other reason than consistency of calculation. As you mentioned, in the case that you assume all materials have the same relative density, it wouldn’t matter. I don’t think it would really even matter if we were talking about two materials with specific gravities of say, 2.60 and 2.62 due to the inherent variability in human testing and measurement. But say we’re dealing with two different materials having specific gravities of 2.62 and 2.76- which happens to be the specific gravities of the two materials that I’m most used to. My thought process leads me down the line of how the yield of the concrete mixture as well as the subsequent value for the customer and cost of production may be affected. Pennies are dollars.

I am really enjoying your Concrete Mix Design: Art and Science blog series. I read every one (sometimes twice) and I am learning a lot. I look forward to future topics.

MG

## JayShilstone says:

I understand your desire to use percent by mass, but if we do that we can’t consider the impact of paste on the combined grading. Yes, we are mixing apples and oranges, but I think that the limited degree of accuracy we need allows us to do so.