So far all the combined aggregate grading techniques we have discussed have been determined almost solely based on the combined grading. The Total Fineness Modulus method and the Coarseness/ Workability chart have adjustments for cement factor, but the cement content isn’t the driving force. The Mix Suitability Factor (MSF) technique, developed by Ken Day in Australia, directly incorporates both the cementitious content of a mix and the air content. This technique is very easy to use as a mix analysis tool, but a little harder to use as a mix design tool.

What I will be presenting here is taken from the 3^{rd} edition of Ken’s book, Concrete Mix Design, Quality Control and Specification. Ken has now released the 4^{th}, and probably final edition of his book. It is available on Amazon at http://www.amazon.com/Concrete-Quality-Control-Specification-Edition/dp/0415504996/ref=sr_1_1?ie=UTF8&qid=1392047055&sr=8-1&keywords=concrete+mix+design+quality+control+and+specification for $171. If you don’t like Amazon check your favorite bookseller.

Introduction: The Mix Suitability Factor (MSF) is an approximation of the workability, or cohesiveness, for a concrete mix. It relies on three values: 1) The modified specific surface of the combined aggregate (SS), 2) the cementitious factor and 3) the air content. The cementitious material and air are considered because, especially at early ages, they act like fine sand. We will go through step-by-step and demonstrate how the MSF is calculated. Please note that this example is for a metric mix expressed in kilograms. When working with a mix in Imperial units per cubic yard, I find it easiest to convert the mix to metric units per cubic meter, then perform Ken’s calculations as shown in his book.

There are three different acronyms referred to in Ken’s book. I actually had a hard time understanding them until I went back to the 2^{nd} edition of his book. They are:

MSF = Mix Suitability Factor = degree of cohesion in a mix

EC = Equivalent Cement Content (there are actually two values for this as will be discussed below)

EWF = Equivalent Water Factor (which has nothing to do with water, really, but has to do with the makeup of the particulate matter in the mix. Again, there will be a discussion of this below.)

Modified Specific Surface: It is widely recognized that as the diameter of particles decreases, the volume decreases faster than the surface area (volume is based on the radius ^ 3, or cubed, and surface area is based on the radius ^2, or squared). In other words, as the particle size of a given volume of material decreases, the total surface area of a constant volume of material will increase. As the surface area goes up, the quantity of cement paste and water required to coat the particle also increases. This is why a mix made with fine sand requires more water than a mix made with coarse sand. The following table shows Ken’s specific surface factors. Based on his experience he has modified the typical factors used for perfect spheres.

A | B | C | D | (B x D)/100 |

Sieve | Modied Specific Surface Factor | Combined % Pass | Indiv % Retained | Mod. Spec Surf Value |

38mm | 1.0 | 100.0 | 0.0 | 0.0 |

19mm | 2.0 | 92.8 | 7.2 | .14 |

9.5mm | 4.0 | 66.4 | 26.4 | 1.0 |

4.75mm | 8.1 | 50 | 16.4 | 1.32 |

2.36mm | 14.9 | 35.2 | 14.8 | 2.20 |

1.18mm | 25.0 | 23.4 | 11.8 | 2.96 |

600 µm | 38.6 | 15.6 | 7.8 | 3.01 |

300 µm | 57.7 | 7.8 | 7.8 | 4.50 |

150 µm | 80.5 | 1.0 | 6.8 | 5.44 |

<150 µm | 104.7 | 1 | 1.0 | 1.08 |

TOTAL | 100.0 | 21.65 |

To get the modified specific surface for a particle size, multiply the individual percent passing for the sieve times the Factor. For this example the Modified Specific Surface is 21.65.

Equivalent cement content: There are various places in the 3^{rd} edition of the book that refer to an adjustment based on Equivalent Cement Content (EC), but this edition doesn’t really explain the concept too well. The 2^{nd} edition of the book has a better explanation. In summary the EC is simply the cumulative weight of the cementitious materials, with each material multiplied times a constant, i.e.

EC = C_{1} + k_{1}C_{2} + k_{2}C_{3}

where C is the weight in kg of each type of cementitious material and k is a constant that typically ranges from 0.8 – 1.2, except that the k value for silica fume ranges from 3-4. Also, there are two values for “k”, depending on if you are talking about the material’s impact on strength or its impact on cohesion. For example, fly ash will typically increase cohesion, but will decrease water demand and so increase strength.

Equivalent Water Factor (EWF): “Equivalent Water Factor” is a bit misleading, since the EWF is not a direct calculation of water content. (Note: I was confused about this for years until I read Ken’s description very carefully, then realized that he explained it properly but I just jumped to a conclusion based on the use of the word “water” in the name.) Instead EWF is a value that relates to the factors contributing to the cohesiveness of the concrete, namely aggregate grading and cementitious content, which in turn affect the water demand. The equation for EWF is:

EWF = SS + 0.025(EC) – 7.5

Mix Suitability Factor: The Mix Suitability Factor is the following:

MSF = SS + 0.025(EC) – 7.5 + 0.25 (% air – 1) or

MSF = EWF + 0.25(%air -1)

MSF = Mix Suitability Factor

SS= modified Specific Surface

EC = Equivalent Cement (in kg)

EWF = Equivalent Water Factor

Ken’s book provides the following comments about various values for the MSF

MSF | Slump, mm | Slump, in | Remarks |

16 | Unusable, too harsh | ||

16-20 | Harsh mixes, only suitable for zero slump concrete under heavy vibration | ||

20-22 | 0-50 | 0-2 | Hard wearing floor slabs, precast products under good external vibration |

22-25 | 50-90 | 2-3.5 | Good structural concrete |

25-27 | 80-100 | 3-4 | Good pumpable concrete. Fine surface finish, Heavily reinforced sections. |

26-28 | 90-120 | 4-5 | Pumpable lightweight concrete |

27-31 | 200+ | 8+ | Flowing superplasticized concrete |

For a more complete discussion of the Mix Suitability Factor please buy the 4^{th} edition of Kens book, available at Amazon at http://www.amazon.com/Concrete-Design-Quality-Control-Specification/dp/0415504996/ref=la_B001H6UN6W_1_1?s=books&ie=UTF8&qid=1393430185&sr=1-1

Not only does his book discuss his mix design method, it also presents information on quality control processes, including the multi-grade, multi-variable CuSum chart, and his thoughts on proper specification of concrete. I strongly recommend it for all students of concrete mix design. Ken has a very good website with several free tools that demonstrate his concepts. His website is at http://www.kenday.id.au/

Designing mixes using the MSF: To create a mix based on the MSF, simply reverse the equation. Select the desired MSF, deduct 7.5 and the appropriate cement and air values, and determine the required Specific Surface. Then calculate the blend of materials necessary to produce the desired specific surface.

One drawback to Ken’s mix design system is that it doesn’t address the impact of the shape of the combined aggregate grading curve. Ken’s system can produce a gap graded mix as easily as a well graded blend. It is up to the user to determine the appropriate blend of materials to obtain an appropriate grading curve.

Estimating Water Demand: While not integral to the Mix Suitability Factor, Ken also presents a method of estimating water demand for a mix design (without regard to the use of admixtures). Again, remember that this technique uses a mix design expressed as kg/cubic meter. For use on Imperial mixes I usually convert the mix to metric, calculate the water demand, then convert the water demand back to Imperial units. Ken’s estimated water demand is calculated as follows (again this is taken from his book).

Factor | Effect on water requirement |

Basic water content | 85 |

Grading effect | +3 x EWF |

Slump effect | + 0.36 x (slump) – 0.0007 x (slump)^2 (slump in mm) |

Entrained air effect | – 5A x 250/(total cementitious in kg) |

Concrete temperature effect (deg. C) | – 0.1 x (temp) + 0.02 x (temp)^2 |

Silt content effect | + [(silt % – 6) x (wt sand)]/300 |

2^{nd} cement/pozzolan |
– Factor k2 x wt of material |

3^{rd} cement/pozzolan |
– Factor k3 x wt of material |

Quantity of cement | + entered factor x amt out of entered range |

SUM | (Sum of above) x water factor = water requirement |

The “water factor” in the last line is an adjustment based on the aggregate particle shape or the use of admixtures. For example, a water reducer might have a water factor of 95% (indicating a 5% reduction in water) while a manufactured sand might increase water demand and so have a water factor of 110%.

Note that the k2 and k3 above are not really defined, but appear to be different (although related to) the k factors for strength and cohesiveness.

Conclusion: Ken has had decades of experience in the concrete industry and his opinions are worthy of consideration. His book is much more complete than what is offered here, so for a better explanation please refer to his book. His technique is very worthy of evaluation for use, but I have had difficulty translating it to use in the field. Of course, there is always the possibility I have misinterpreted parts of his book. Ken never really goes through a step-by-step example using his calculations, which makes it a little difficult to make certain I understand it correctly. If you want to use this technique, I strongly suggest you go to Ken’s website and download the free software he has available. Again, his website is at http://www.kenday.id.au/

In my next blog entry I want to describe the Bolomey curve and how it is used in designing concrete mixes. If you are interested in this approach make certain you read my next entry.

Until next time,

Jay Shilstone

### 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.

## Roberto Torrent says:

Hi, my name is Roberto Torrent and I was leading a team of experts that developed a Mix Design Optimization tool for Holcim. We adopted the MSF concept and formula to assess the elusive cohesiveness (with a numerical value) of a mix. However, we modified it to take into consideration the maximum size of the aggregate (the MSF categorization – from too harsh to flowing – is only valid for MSA=20 mm) and the shape of the particles. Although not perfect in that not always a mix ranked as pumpable behaved like that, particularly when crushed aggregates containing a large quantity of dust were used, it provided at least a good relative indicator. Needless to say, not every concrete engineer will judge the same mix as “pumpable”, particularly if in the fringes of pumpability. So, I have to thank Ken for this useful contribution to the science/art of concrete mix design.