A 500 g sample of dry soil was used for a combined sieve and hydrometer analysis (152 H type hydrometer). The soil mass passing through the 75 μ sieve = 120 g. Hydrometer analysis was carried out on a mass of 40 g that passed through the 75 μ sieve. The average temperature recorded during the test

Question

A 500 g sample of dry soil was used for a combined sieve and hydrometer analysis (152 H type hydrometer). The soil mass passing through the 75 μ sieve = 120 g. Hydrometer analysis was carried out on a mass of 40 g that passed through the 75 μ sieve. The average temperature recorded during the test was 30°C.

Given: [latex]\left.G_{s}=2.55, C_{m} ext { (meniscus } ight)=0.50, C_{o}=+2.5, \mu=8.15 imes 10^{-3}[/latex] poises.

The actual hydrometer reading [latex]R_{a}=15.00[/latex] after a lapse of 120 min after the start of the test. Determine the particle size D and percent finer [latex]P^{\prime} \% ext { and } P \%[/latex].

Accepted Answer

From Eq. (3.29)

[latex]L=16.3-0.1641 R[/latex] (3.29)

[latex]L=16.3-0.1641 R[/latex]

where, [latex]R=R_{a}+C_{m}=15.0+0.5=15.5[/latex]

[latex]L=16.3-0.1641 imes 15.5=13.757[/latex]

From Eq. (3.24)

[latex]D=\sqrt{\frac{30 \mu}{\left(G_{s}-1 ight) \gamma_{w}}} \sqrt{\frac{L}{t}}=K \sqrt{\frac{L}{t}}[/latex] (3.24)

[latex]D=\sqrt{\frac{30 imes 8.15 imes 10^{-6}}{2.55-1}} imes \sqrt{\frac{13.757}{120}}=0.0043 mm[/latex]

From Eq. (3.32)

[latex]P^{\prime}=\frac{C_{s g} R_{c}}{M_{s}} imes 100[/latex]

Percent finer, [latex]P^{\prime} \%=\frac{C_{s g} R_{c}}{M_{s}} imes 100[/latex]

From Table 3.7, [latex]C_{s g}=1.02 ext { for } G_{s}=2.55[/latex]

From Table 3.6, [latex]C_{T}=+3.8 ext { for } T=30^{\circ} C[/latex]

Now, [latex]R_{c}=R_{a}-C_{o}+C_{T}=15-2.5+3.8=16.3[/latex]

Now, [latex]P^{\prime}=\frac{1.02 imes 16.3}{40} imes 100=41.57 \%[/latex]

[latex]P \%=41.57 imes \frac{120}{500} \approx 10 \%[/latex]

Table 3.6 Temperature correction factors [latex]C_{T}[/latex]
Temp °C	[latex]C_{T}[/latex]	Temp °C	[latex]C_{T}[/latex]
15	-1.1	23	0.7
16	-0.9	24	1
17	-0.7	25	1.3
18	-0.5	26	1.65
19	-0.3	27	2
20	0	28	2.5
21	0.2	29	3.05
22	0.4	30	3.8

Table 3.7 Correction factors [latex]C_{s g}[/latex] for unit weight of solids
[latex]G_{s}[/latex] of soil solids	Correction factor [latex]C_{s g}[/latex]	[latex]G_{s}[/latex] of soil solids	Correction factor [latex]C_{s g}[/latex]
2.85	0.96	2.65	1.00
2.80	0.97	2.60	1.01
2.75	0.98	2.55	1.02
2.70	0.99	2.50	1.04

Question 3.11: A 500 g sample of dry soil was used for a combined sieve and...

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