Mortar for 10 m³ brickwork (1:4) numerical

Given: brickwork volume $= 10\ \text{m}^3$; brick size 57 mm x 115 mm x 240 mm (actual size, without mortar); mortar joint $= 10$ mm; mortar 1:4 (cement : sand).

Step 1: Size of brick with mortar

$$(0.25 \times 0.125 \times 0.067) = 0.002094\ \text{m}^3$$

Step 2: Number of bricks

$$N = \frac{10}{0.002094} = 4776.1 \approx 4777\ \text{bricks}$$

Step 3: Volume of bricks without mortar

$$4777 \times 0.24 \times 0.115 \times 0.057 = 7.515\ \text{m}^3$$

Step 4: Wet volume of mortar

$$10 - 7.515 = 2.485\ \text{m}^3$$

Step 5: Dry volume of mortar (add 27% for dry bulk, voids in sand, wastage and shrinkage)

$$2.485 \times 1.27 = 3.156\ \text{m}^3$$

Step 6: Cement and sand for 1:4 (sum of ratio $= 5$)

$$\text{Cement} = \frac{1}{5} \times 3.156 = 0.631\ \text{m}^3 = 909\ \text{kg} \approx 18.2\ \text{bags (50 kg, 0.0347 m}^3\text{ each)}$$ $$\text{Sand} = \frac{4}{5} \times 3.156 = 2.525\ \text{m}^3$$

Answer: Mortar required for 10 m³ brickwork = 2.49 m³ (wet) or 3.16 m³ (dry); this needs about 0.631 m³ cement (18.2 bags) and 2.53 m³ sand; bricks = 4777 nos.