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[15 points] a laboratory sample of sand is formed inside a mold of 0.4 cubic meters. it took 711.2 kg of wet sand (dry mass of sand

Sagot :

The following are the values:-

(a)Water content (W%)  = 13.99%

(b) Total unit weight (Υ[tex]_{t}[/tex]) = 1778 kg/m³

(c) Dry unit weight (Y[tex]_{d}[/tex]) = 1559.75 kg/m³

(d) Void ratio (e)  = 0.718

(e) Porosity (n) = 0.417

Volume of mold (V[tex]_{t}[/tex]) = 0.4 m³

Dry mass of sand (W[tex]_{s}[/tex]) = 623.9 kg

Wet mass of sand (W[tex]_{t}[/tex]) = 711.2 kg

Specific Gravity (G[tex]_{s}[/tex]) = 2.68

1) Water content (W%)

Water content (W%) = [tex]\frac{W_{w} }{W_{s} }[/tex] × [tex]100[/tex]

Water content (W%) = [tex]\frac{711.2 - 623.9}{623.9}[/tex] × [tex]100[/tex]

Water content (W%) = 13.99%

2) Total unit weight (Υ[tex]_{t}[/tex])

Total unit weight (Υ[tex]_{t}[/tex]) = [tex]\frac{W_{t} }{V_{t} }=\frac{711.2}{0.4}[/tex]

Total unit weight (Υ[tex]_{t}[/tex]) = 1778 kg/m³

3) Dry unit weight (Y[tex]_{d}[/tex])

Dry unit weight (Y[tex]_{d}[/tex]) = [tex]\frac{W_{s} }{V_{t} }=\frac{623.9}{0.4}[/tex]

Dry unit weight (Y[tex]_{d}[/tex]) = 1559.75 kg/m³

4) Void ratio(e)

Solid unit weight (Y[tex]_{s}[/tex]) = [tex]\frac{W_{s} }{V_{s} }[/tex]

Or

G[tex]_{s}[/tex] = [tex]\frac{Y_{s} }{Y_{w} }[/tex] ⇒ Y[tex]_{s}[/tex] = G[tex]_{s}[/tex]Y[tex]_{w}[/tex]

Y[tex]_{s}[/tex] = 2.68 × [tex]\frac{10^{-3} }{(10^{-2})^{3} }\frac{kg}{m}[/tex] = 2680 kg/m³

Now,

Void Ratio (e) = [tex]\frac{Y_{s} }{Yd}-1[/tex]

Void Ratio (e) = [tex]\frac{2680}{1559.72}-1[/tex]

Void Ratio (e) = 0.718

5) Porosity (n)

Porosity (n) = [tex]\frac{e}{1+e}[/tex]

Porosity (n) = [tex]\frac{0.718}{1+0.718}[/tex]

Porosity (n) = 0.417

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A laboratory sample of sand is formed inside a mold of 0.4 cubic meters. It took 711.2 kg of wet sand (dry mass of sand = 623.9 kg) to fill the mold. Assuming the specific gravity of the solid is 2.68, compute the:

(a)Water content (W%)  

(b) Total unit weight (Υ[tex]_{t}[/tex])

(c) Dry unit weight (Y[tex]_{d}[/tex])

(d) Void ratio (e)

(e) Porosity (n)