Question(3) It is known that the dry mix proportions in laboratory is $\mathrm{C}: \mathrm{W}: \mathrm{S}: \mathrm{G}=$ $1: 0.6: 2.44: 3.9$ . The apparent density of fresh concrete is $\rho_{0}=2350 \mathrm{~kg} / \mathrm{m}^{3}$ . (1) Please calculate the amounts of cement, water, coarse aggregate and fine aggregate for 700 L fresh concrete. (2) In the construction site, the water content of crushed stone is $1.0 \%$ , the water content of sand is $2.5 \%$ . Please calculate the new mix proportion to be used in construction site. (7 points)

Studdy Solution

STEP 1

1. The dry mix proportions are given as Cement (C): Water (W): Sand (S): Gravel (G) = 1: 0.6: 2.44: 3.9.
2. The apparent density of fresh concrete is $\rho_0 = 2350 \, \text{kg/m}^3$ .
3. The volume of fresh concrete required is 700 L (or 0.7 m $^3$ ).
4. The water content of crushed stone is 1.0%.
5. The water content of sand is 2.5%.
6. We need to calculate both the amounts of each component for the given volume and adjust the mix proportions for the construction site.

STEP 2

1. Calculate the total mass of the fresh concrete.
2. Determine the mass of each component based on the dry mix proportions.
3. Adjust the mix proportions for the construction site considering the water content in aggregates.

STEP 3

Calculate the total mass of the fresh concrete.
The volume of fresh concrete is 0.7 m $^3$ . Using the apparent density:
$\text{Total mass} = \rho_0 \times \text{Volume} = 2350 \, \text{kg/m}^3 \times 0.7 \, \text{m}^3 = 1645 \, \text{kg}$

STEP 4

Determine the mass of each component based on the dry mix proportions.
The total proportion sum is $1 + 0.6 + 2.44 + 3.9 = 7.94$ .
Calculate the mass of each component:
- Cement: $\text{Mass of Cement} = \left(\frac{1}{7.94}\right) \times 1645 \, \text{kg}$
- Water: $\text{Mass of Water} = \left(\frac{0.6}{7.94}\right) \times 1645 \, \text{kg}$
- Sand: $\text{Mass of Sand} = \left(\frac{2.44}{7.94}\right) \times 1645 \, \text{kg}$
- Gravel: $\text{Mass of Gravel} = \left(\frac{3.9}{7.94}\right) \times 1645 \, \text{kg}$

STEP 5

Adjust the mix proportions for the construction site considering the water content in aggregates.
Calculate the additional water content:
- Additional water in gravel (1.0% of gravel mass): $\text{Additional Water in Gravel} = 0.01 \times \text{Mass of Gravel}$
- Additional water in sand (2.5% of sand mass): $\text{Additional Water in Sand} = 0.025 \times \text{Mass of Sand}$
Calculate the new water mass:
$\text{New Water Mass} = \text{Mass of Water} - (\text{Additional Water in Gravel} + \text{Additional Water in Sand})$
Calculate the new mix proportions:
- New Cement Proportion: $\text{New Cement Proportion} = \frac{\text{Mass of Cement}}{\text{Total Mass}}$
- New Water Proportion: $\text{New Water Proportion} = \frac{\text{New Water Mass}}{\text{Total Mass}}$
- New Sand Proportion: $\text{New Sand Proportion} = \frac{\text{Mass of Sand}}{\text{Total Mass}}$
- New Gravel Proportion: $\text{New Gravel Proportion} = \frac{\text{Mass of Gravel}}{\text{Total Mass}}$

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