Concrete Mix Design: Breaking Your Mix Design

Editor’s Note: This is the final article in a year-long series that explores the science of concrete to provide a better understanding of mix design. The series was collaboratively written by Paul Ramsburg, technical sales specialist at Sika Corp., and Frank Bowen, business development representative with Rosetta Hardscapes. Click here for the fifth article in the series.

By Frank Bowen and Paul Ramsburg

It’s important to understand the benefits of failure. Henry Ford said, “Failure is simply the opportunity to start again, this time, more intelligently.” The household cleaner “409,” for example, gets its name from how many times it took to get the formula right. And, it took Edison more than 1,000 attempts to perfect the lightbulb before he found his success. Without our ability to overcome and learn from failure, success is unfortunately unobtainable.

It is for this reason we want you to highlight your failures, even elevate them, to enlighten and isolate the key components of the problems you face in creating your perfect mix designs. A mix design should not be expected to perform perfectly after it is designed, since the initial design is simply theoretical.

Batching and testing are necessary to create a final design. Results from failure are better understood when seen in person, not explained through documentation or articles, like this one. We want you to intentionally experiment with your mix designs by changing key variables to understand the constraints of a mix given your specific raw materials. By strategically overdosing or withholding mix components, you should be able to see test results that illuminate the components’ attributes and limits of critical function. Doing so will help you make educated decisions regarding material selection, if needed.

To begin, you need a mix to evaluate. This could be one you recently designed, or one you have used in your plant for years but may not yet know its performance limits. Simply put, we need to know where to draw the line for each key performance criterion the mix is expected to meet. We will also need to create a safety factor based on the testing data we have, so we know to stay within the boundaries we find. After you have found a mix you wish to examine, create a list of specified criteria associated with its performance and keep it close throughout the testing.

For the purpose of this article, let’s use Mix 2 from the 2018 Sept.-Oct. Precast Inc. article, “Concrete Mix Design: Proportioning.” You’ll need to reference the sequencing details and the place-finish-cure plan for this mix while reviewing how to break its constraints.

The shown constraints are the 5,000- to 8,000-psi range for strength, the air content limits for this self-consolidating concrete mix and the slump flow range of 21-24 inches. We also know that the designed air content is 6%, which gives us a target.

The upper limit for air content is 7%, and the lower limit is 4.5%. Additionally, there could be many more constraints we could focus on, such as J-ring testing results, the T-20 test for relative viscosity, initial set penetrometer results or, if this was used in an architectural application, there may be set limits on shade or color produced. You can focus on as many elements as you wish, so long as you keep a close eye on the constants and variables while testing, and always use the scientific method as strictly as possible while undergoing performance testing.

The limits we will address in this article are shown in Table 1. These limits were established by both specifications and plant best practices as detailed below:

• The minimum compressive strength will be specified by the design engineer and should be included on the shop drawings.
• The required compressive strength is an overdesign of the design strength as established by ACI 318, “Building Code Requirements for Structural Concrete and Commentary.”
• The air content may be specified by an agency. For example, a state department of transportation may specify an air range of 4% to 7%. Otherwise, the air content should adhere to recommendations from ACI depending on which freeze/thaw zone in which the product will be installed.
• The range of slump flow for a plant’s SCC mix should be established by the plant itself. Through testing and production evaluation, the plant will determine the lower limit of the spread. This will be the lowest point where the mix is placed with sufficient ease and the product exhibits an acceptable surface appearance. The upper limit will be the point where the mix does not segregate or bleed. Using the standard method for determining visual stability index as outlined in ASTM C1611, “Standard Test Method for Slump Flow of Self-Consolidating Concrete,” the range of spread should result in a VSI of 0-1, though in production a VSI of 2 may be acceptable.

After all the testing data is gathered, we need to look at the average, range, frequency distribution and standard deviation of the results. For an in-depth understanding of these components, reference ACI 214, “Guide to Evaluation of Strength Test Results of Concrete.”

Range

The range is the difference between the upper and lower compressive strength results acquired during testing. The compressive strength results for this mix are:

X₁: 7,200 psi
X₂: 6,900 psi
X₃: 7,500 psi
X₄: 7,800 psi
X₅: 6,850 psi
X₆: 7,400 psi
X₇: 7,200 psi

The range of these seven test results is between 6,850 psi and 7,800 psi.

Average

The average (X), or mean, is calculated by added all the test results and dividing that sum by the total number of test results (n). In this case, the total number of test results is 7.

The equation is:

X = Σ (X_i/n), where:

X = Average or mean
X_i= Each individual test result
n = The total number of test results

X = (7,200 psi + 6,900 psi + 7,500 psi + 7,800 psi + 6,850 psi)/7

= 50,850 psi/7

= 7,264 psi

The average or mean value of these seven test results is 7,264 psi.

Standard deviation

The standard deviation (S or σ) tells us how much the individual results vary as a group. The equation is:

S = √Σ (X_i-X)²/n – 1 , where:

S = Standard deviation
X_i= Each individual test result
X = Average or mean
n = The total number of test results

1. Calculate the deviation of each result from the average (column 2).
2. Square each deviation (column 3).
3. Divide each squared deviation by n-1 (column 4).
4. Find the sum of all the values in column 4. Record this single value as the sum.
5. Find the square root of the sum. Record this value as the standard deviation.

Σ = 682.67 + 22,082.67 + 9,282.67 + 47,882.67 + 28,566 + 3,082.67 + 682.67 = 112,262

S = √112,262 = 335

The standard deviation for these seven test results is 335 psi.

Frequency distribution

Frequency distribution is a helpful way to view test data to show statistical reasoning and predictions for a mix design. It forms what is called a normal distribution curve, or a bell curve. This curve is developed by grouping concrete compressive strength data for a particular mix design. The curve is symmetrical about the average, meaning 50% of the tests will be on either side of the average. The peak of the curve occurs at the average (mean) of the data. The curve is generated from the standard deviation. The greater the spread of the curve, the higher the deviation for the mix.

68% of the area under the bell curve falls within one standard deviation of the mean or average. 95% of the area under the bell curve falls within two standard deviations of the mean or average.

Mix design approval, evaluation and acceptance guidelines

A precast manufacturer, as part of the submittal process, must establish data that demonstrates a proposed mix will produce the required strength for a given project. This can be completed by providing strength data for 10 to 30 consecutive test points or laboratory trial batches in accordance with guidelines in ASTM C192, “Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory.” This includes Three Point Curve trial testing, where a mix design has its w/c ratio varied and the test results are evaluated to determine if they meet the required strength. For example, if your mix design has a target w/c ratio of 0.40, you may make test batches with a 0.38, a 0.40 and a 0.42 w/c ratio.

ACI 318, “Building Code Requirements for Structural Concrete and Commentary,” allows concrete mix revisions that are consistently producing over-strength tests. In order to provide statistically significant data, a sufficient number of tests are required. And as the number and reliability of the tests improve, the required safety factor or over-strength decreases. At least 15 tests (three 4×8 cylinders are required for one Three Point Curve test) are required but 30 tests have become customary. The standard deviation of the results is computed. The required strength must equal the average, plus a safety factor, times the standard deviation as seen here:

σ = Standard deviation
f’cr = Required concrete strength
f’c = Specified concrete strength

• f’c ≤ 5000
• f’cr = f’c + 1.34σ
• f’cr = f’c + 2.33σ – 500

Use the larger value computed

• f’c > 5000
• f’cr = f’c + 1.34σ
• f’cr = 0.90f’c + 2.33σ

Use the larger value computed

The strengths for the mixture shall be reported and must satisfy the following two criteria before the concrete will be considered acceptable for a given project:

• The average of all sets of three consecutive strength tests equal or exceed the specified strength (f’c).
• No single strength test (average of three cylinders) falls below the specified strength (f’c) by more than 500 psi if f’c is 5,000 psi or lower, or falls below f’c by more than 10% if f’c is greater than 5,000 psi.

Be brave and take a risk

Do not be afraid to intentionally break your mix designs to get a better understanding of their limits and the set safety factors they should hold. You understand your mix design better when you discover its abilities and constraints firsthand via calculated experimentation in your laboratory. When you are not in the lab, always remember that a bad batch should never be considered a total loss, as long as it can be considered a lesson. Never waste the opportunity to record as much data as you can when things go wrong at the mixer. That data, since it is not automatically recorded, can be collected only in that moment.

It’s been a great joy engaging the industry at large about mix design issues, techniques and successes over the course of this year with this article series. We hope we have inspired you to take the mix design reins and master your concrete performance.

Paul Ramsburg has worked in the prestressed precast concrete industry since 1988 and is currently a technical sales specialist at Sika Corp.

Frank Bowen, a 2013 Master Precaster graduate, received his M.B.A. from Middle Tennessee State University through the Concrete Industry Management graduate program in 2014 and is a business development representative with Rosetta Hardscapes in Charlevoix, Mich.