# How to Calculate Polymer and Fibers in GFRC Concrete Countertops

## How to Calculate Polymer Dose for GFRC

The minimum effective dose of polymer solids in GFRC is 6% by weight of cementitious material. Polymer is most often in a liquid form, so the calculations to figure the right amount of liquid polymer require knowledge about the solids content of the liquid polymer. Most commercial GFRC polymer is about 50% solids (two widely used brands have 51% solids and 47% solids). If we use an example of polymer with 50% solids, half of the weight of the liquid is polymer solids, and the other half is water. And this water counts as part of the mix water used in the GFRC.

Graphical breakdown of a commercial GFRC polymer with 51% solids content
I will step through the calculations since this gets a bit complicated.

Let’s start with a typical commercial GFRC mix design that will make 10 sq ft of ¾” thick backer for GFRC:

• Sand: 33.4 lb
• 6% Polymer at 51% solids: 3.9 lb
• Water (.32 w/c): 8.8 lb
• Portland Cement (80%): 26.7 lb
• Pozzolan (20%): 6.7 lb
• 3% AR Glass Fibers: 2.5 lb (3% of total weight of non-fiber materials)
• Total weight per batch 82.0 lb

This mix design has 33.4 lb of sand and 33.4 lb (26.7+6.7) of total cementitious material. All admixtures (polymer solids, pigments, superplasticizer, etc.) are dosed based on the total cementitious material weight.

A 6% polymer solids dose means we need 33.4 lb * 0.06 (or 6%) = 2.0 lb of polymer solids (not liquid polymer). To calculate how much liquid polymer (what is poured out of the bucket) is needed, perform this calculation:

2.0 lb polymer solids / 0.51 (or 51% solids content) = 3.9 lb of liquid polymer

If you think about it, about half of the liquid polymer is water and the other half is solids, so about 2 lb of solids is contained in about 4 lb of liquid polymer.

Now to calculate the mix water:

1. Calculate the total amount of water needed: 33.4 lb cementitious * 0.32 = 10.7 lb of water
2. However, some of that water comes from the liquid polymer. So now we need to calculate how much water will come from the polymer we’re adding. We’ve already calculated that 3.9 lb of liquid polymer is needed, and that contains 2.0 lb of polymer solids, leaving 1.9 lb of water being contributed by the liquid polymer. (3.9 – 2.0 = 1.9)
3. Now subtract that water from the total amount needed. 10.7 lb – 1.9 lb = 8.8 lb water to add.

Changing the w/c ratio alters only how much water we must batch out (more or less than 8.8 lb), it does not change the amount of liquid polymer needed.

## How to Calculate Fiber Load for GFRC

Unlike other admixtures, fibers are not dosed based on dry cementitious weight. A 3% fiber load means there are 3 lb of fibers added to 97 lb of non-fiber material to make 100 lb of GFRC backer. The minimum effective fiber load for GFRC is 3%.

We first have to determine how much non-fiber material we have. Adding up our ingredients (everything but the fibers), we have:

33.4 lb sand + 26.7 lb cement + 6.7 lb pozzolan + 3.9 lb liquid polymer + 8.8 lb water = 79.5 lb of non-fiber material

So rather than having 97 lb of material, we have 79.5 lb of material. We can use ratios to find the amount of fibers to add:

• In English: 79.5 lb is to 97 lb as (unknown fiber quantity) is to 3 lb.
• In mathematical terms: 79.5 / 97 = x / 3.

To find x, just multiply both sides by 3 to cancel out the 3 on the right.

79.5 / 97 * 3 = 2.458 lb of fibers needed. (Rounded up to 2.5 in the example above.)

The total amount of backer would be 79.5 lb + 2.5 lb = 82.0 lb.

## Another Way to Calculate GFRC Mixes

These calculations are complex but essential for correct GFRC mix design. I’ve included them to give you a full understanding of GFRC mix calculations. It is easier to present GFRC mixes in 10 sq ft batches, which you can then multiply by the number of 10 sq ft units you have.

For example, if you need to make 52 sq ft of GFRC, you can simply multiply your 10 sq ft batch by 5.2. Alternatively, I have a GFRC mix calculator that allows you to enter only the square footage (or meters), and it prints a batch report. ## How to Check Your GFRC Mix Design for Correctness

There are GFRC mix designs being published for concrete countertops that do not contain adequate amounts of polymer and fibers. But how do you know if you’re simply presented with a mix in terms of “use this many pounds of each ingredient”? Here is how to back-calculate the percentages, using 2 examples.

Example 1: Liquid Polymer

Suppose you were given the following mix design:

• Cement: 23.5 lb
• Pozzolan: 2.6 lb
• Sand: 21.5 lb
• Water: 7 lb
• Liquid polymer (50% solids): 1.5 lb
• Glass Fiber: 1 lb

To determine the polymer content:

1. Add up your cementitious content: 23.5 lb + 2.6 lb = 26.1 lb. (Note that this mix has more cementitious material than sand, and it is supposed to have 1 to 1 cement to sand.)
2. Determine the amount of polymer solids: 1.5 lb * 0.5 (50%) = 0.75 lb
3. Divide polymer solids by cementitous: 0.75 lb / 26.1 lb = 2.9% polymer solids

This is far below the 6% required for GFRC!

To determine the fiber content:

1. Add up all your materials including the fibers: 23.5 + 2.6 + 21.5 + 7 + 1.5 + 1 = 57.1 lb
2. Divide your fiber weight by the total weight: 1 lb / 57.1 lb = 1.8% fibers

This is far below the required fiber minimum of 3%! It is over 33% less!

Example 2: Dry Polymer

Suppose you were given the following mix design:

• Cement: 30 lb
• Sand: 30 lb
• Water: 9 lb
• Dry polymer (100% solids): 0.45 lb
• Glass Fiber: 1.8 lb

To determine the polymer content:

1. Take your cementitious content: 30 lb.
2. Take your polymer solids:  0.45 lb
3. Divide polymer solids by cementitous: 0.45 lb / 30 lb = 1.5% polymer solids

Again, far below the 6% required for GFRC! This is 1/4 of the amount you need! Unless the publisher of this mix advocates 7-day wet curing, this will result in weak, brittle GFRC.

To determine the fiber content:

1. Add up all your materials including the fibers: 30 + 30 + 9 + 0.45 + 1.8 = 71.25 lb
2. Divide your fiber weight by the total weight: 1.8 lb / 71.25 lb = 2.5% fibers

Again, this is below the required minimum fiber dose of 3%.

## Conclusion

Even if you never actually do the formulas because you’re using a mix calculator or a 10 sq ft batch method, it is important to understand the following points:

• The minimum effective dose of polymer solids in GFRC is 6%.
• Polymer dose is calculated by weight of cementitious materials.
• The minimum effective fiber load for GFRC is 3%.
• A 3% fiber load means there are 3 lb of fibers added to 97 lb of non-fiber material to make 100 lb of GFRC backer.

Know how to double-check these proportions, and you’ll steer clear of GFRC mix problems.

Purchase polymer and fibers in the CCI online store.

Purchase the GFRC Mix Calculator for concrete countertops.