The standard method of measuring the specific gravity of solids (ASTM D854) uses a calibrated glass flask known as a pycnometer, as shown in Figure 4.6. The pycnometer is first filled with water and set on a balance to find its mass. Then, it is refilled with a known mass of dry soil plus water so

Question

The standard method of measuring the specific gravity of solids (ASTM D854) uses a calibrated glass flask known as a $pycnometer$ , as shown in Figure 4.6. The pycnometer is first filled with water and set on a balance to find its mass. Then, it is refilled with a known mass of dry soil plus water so the total volume is the same as before. Again, its mass is determined. From this data, we can compute $G_{s}$ .

Using this technique on a certain soil sample, we have obtained the following data:

Mass of soil = 81.8 g

Moisture content of soil = 11 .2%

Mass of pycnometer+water = 327.12 g

Mass of pycnometer+soil+water = 373.18 g

Volume of pycnometer = 250.00 ml

Compute $G_{s}$ for this soil.

Using this technique on a certain soil sample, we have obtained the following data:

Mass of soil = 81.8 g

Moisture content of soil = 11 .2%

Mass of pycnometer+water = 327.12 g

Mass of pycnometer+soil+water = 373.18 g

Volume of pycnometer = 250.00 ml

Compute [latex]G_{s}[/latex] for this soil.

Accepted Answer

[latex]\left(M_{w}\right) _{A}=V\rho _{w}=\left(250.00 ml\right) \left(1 g/ml\right) =250.00 g[/latex]

[latex]M_{p}=M_{A} - \left(M_{w}\right) _{A}=327.12 g - 250.00 g=77.12 g[/latex]

[latex]\left(M_{s}\right) _{B}=\frac{M}{1 + w} =\frac{81.8 g}{1 + 0.112} =73.56 g[/latex]

[latex]\left(M_{w}\right) _{B}=373.18 g - 77.12 g - 73.56 g=222.50 g[/latex]

[latex]\left(V_{w}\right) _{B}=\frac{\left(M_{w}\right) _{B}}{\rho _{w}} =\frac{222.50 g}{1 g/ml} =222.50 ml[/latex]

[latex]\left(V_{s}\right) _{B}=250.00 ml - 222.50 ml=27.50 ml[/latex]

[latex]G_{s}=\frac{M_{s}}{V_{s}\rho _{w}} =\frac{73.56 g}{\left(27.50 ml\right) \left(1 g/ml\right) } =2.67[/latex]

Note: A real laboratory specific gravity test also considers various correction factors to account for the density of water as a function of temperature and other variables. For simplicity. we have not considered these factors here.

Question 4.3: The standard method of measuring the specific gravity of sol...

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