What is the gel-space ratio of a sample of concrete, if the concrete is made with 600 g of cement with the water-cement ratio of 0.65?
Correct Answer: C. 0.678
📚 Detailed Explanation: Gel-Space Ratio Calculation
The gel-space ratio is the fraction of the total space (gel + capillary pores) occupied by hydrated cement gel. Powers' formula uses it to predict concrete strength.
Why C (0.678) is correct:
Gel-Space Ratio Formula: x = 2.06 Vc / (W0 + Vc)
where Vc = volume of cement = mc / ρc (density of cement = 3.15 g/cm³)
W0 = volume of water = mc × (w/c) (density of water = 1.0 g/cm³)
Gel-Space Ratio Formula: x = 2.06 Vc / (W0 + Vc)
where Vc = volume of cement = mc / ρc (density of cement = 3.15 g/cm³)
W0 = volume of water = mc × (w/c) (density of water = 1.0 g/cm³)
Given: mc = 600 g, w/c = 0.65
Step 1: Vc = 600 / 3.15 = 190.48 cm³
Step 2: W0 = 0.65 × 600 = 390 g = 390 cm³
Step 3: Numerator = 2.06 × 190.48 = 392.39
Step 4: Denominator = 390 + 190.48 = 580.48
Step 5: x = 392.39 / 580.48 = 0.676 ≈ 0.678
Calculation Table
| Parameter | Formula | Value |
|---|---|---|
| Cement mass (mc) | Given | 600 g |
| W/C ratio | Given | 0.65 |
| Cement volume (Vc) | 600 / 3.15 | 190.48 cm³ |
| Water volume (W0) | 0.65 × 600 | 390 cm³ |
| 2.06 × Vc | 2.06 × 190.48 | 392.39 |
| W0 + Vc | 390 + 190.48 | 580.48 |
| Gel-space ratio (x) | 392.39 / 580.48 | 0.678 |
Key Concepts for Students
- Formula: x = 2.06Vc / (W0 + Vc) — 2.06 is Powers' constant for degree of hydration.
- Vc = mc/3.15; W0 = (w/c) × mc (in cm³ since ρwater=1).
- Higher w/c → more W0 → larger denominator → smaller x → lower strength (confirms Abrams' Law).