Apparent and bulk specific gravity of sand

Following IS 2386 Part 3 (pycnometer method).

Given: oven-dry mass $A = 480$ g; saturated surface-dry mass $S = 490$ g; mass of pycnometer full of water $B = 1400$ g; mass of pycnometer + sand + water (topped up) $C = 1695$ g.

Taking $B$ as the pycnometer filled with water only (as given) and $C$ with sand and water topped up:

Mass of water displaced by the sand in the SSD condition (equivalent weight) = $S - (C - B)$, with $C - B = 1695 - 1400 = 295$ g (net gain due to sand under water).

$$\begin{aligned} \text{Volume of sand (SSD), incl. pores} &= S - (C - B) = 490 - 295 = 195\ \text{cm}^3 \\ \text{Volume of solids (excl. permeable pores)} &= A - (C - B) = 480 - 295 = 185\ \text{cm}^3 \end{aligned}$$

Apparent specific gravity

$$G_{app} = \frac{A}{A - (C - B)} = \frac{480}{185} = 2.59$$

Bulk specific gravity (oven-dry basis)

$$G_{bulk} = \frac{A}{S - (C - B)} = \frac{480}{195} = 2.46$$

Bulk specific gravity (SSD basis) = $490/195 = 2.51$. Water absorption = $(490-480)/480 \times 100 = 2.08\%$.

Answer: Apparent specific gravity = 2.59; bulk specific gravity (oven-dry) = 2.46 (SSD basis 2.51).