Concrete Mix Design: Adjusting for Fly Ash
This guide demonstrates how to adjust a standard concrete control mix when introducing 30% fly ash into the cementitious material. The calculation utilizes the cementing efficiency factor (K-factor) method and maintains the original coarse-to-fine aggregate ratio to ensure consistent workability.
1. Initial Data (Control Mix)
First, we define the properties of the baseline control mix designed for a 28-day Target Mean Strength (TMS) of 35 MPa:
- Water (W1): 200 kg/m3
- Cement (C1): 378 kg/m3
- Fine Aggregate (FA1): 678 kg/m3
- Coarse Aggregate (CA1): 1155 kg/m3
The wet density of the control mix (D1) is the sum of these components: 2411 kg/m3.
The ratio of Coarse to Fine Aggregate is: CA1 / FA1 = 1155 / 678 ≈ 1.7035.
2. Calculating New Water Content
The introduction of fly ash allows for a water reduction of 15 kg/m3 to achieve the same workability.
- New Water Content (W2): 200 – 15 = 185 kg/m3
3. Calculating Cement and Fly Ash Content
To achieve the same 28-day TMS, the effective water-to-cement ratio must remain constant. We use a K-factor of 0.3 for the fly ash.
Original water-to-cement ratio: W1 / C1 = 200 / 378 ≈ 0.5291
For the new mix with fly ash (F) and new cement content (C2), the equivalent cement equation is:
W2 / (C2 + 0.3F) = 0.5291
185 / (C2 + 0.3F) = 0.5291
C2 + 0.3F = 349.65 kg/m3
Given that fly ash constitutes 30% of the total cementitious material (T), we can set F = 0.30T and C2 = 0.70T. Substituting these into our equation:
0.70T + 0.3(0.30T) = 349.65
0.70T + 0.09T = 349.65
0.79T = 349.65
Total Cementitious Material (T) = 442.59 kg/m3
- Fly Ash Content (F): 0.30 × 442.59 = 132.78 kg/m3
- New Cement Content (C2): 0.70 × 442.59 = 309.81 kg/m3
4. Calculating Aggregate Content
The new mix has a reduction in wet density of 40 kg/m3 due to the fly ash and reduced water.
- New Target Wet Density (D2): 2411 – 40 = 2371 kg/m3
Subtracting the water and cementitious materials from the new density gives us the total mass available for aggregates:
Total Aggregates = 2371 – (185 + 309.81 + 132.78)
FA2 + CA2 = 1743.41 kg/m3
Applying our previously calculated aggregate ratio (CA = 1.7035 × FA) to the total aggregate mass:
FA2 + (1.7035 × FA2) = 1743.41
FA2 × 2.7035 = 1743.41
FA2 = 1743.41 / 2.7035 = 644.87 kg/m3
And the coarse aggregate is simply the remainder:
CA2 = 1743.41 – 644.87 = 1098.54 kg/m3
Final Trial Mix Proportions
| Material | Calculated Content |
|---|---|
| Water Content | 185 kg/m3 |
| Cement Content | 309.81 kg/m3 |
| Fly Ash Content | 132.78 kg/m3 |
| Fine Aggregate Content | 644.87 kg/m3 |
| Coarse Aggregate Content | 1098.54 kg/m3 |
