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You Are Required To Fill in All The Blanks of The Phase Diagrams For All Problems

This document provides solutions to 5 problems related to soil mechanics. Problem 1 involves calculating properties like void ratio, porosity, degree of saturation, dry unit weight, and saturated unit weight for a soil sample. Problem 2 verifies a soil property equation. Problem 3 calculates the water content of a fully saturated soil. Problems 4 and 5 solve additional textbook problems involving calculating soil properties. Diagrams are provided to fill in calculated values.

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164 views5 pages

You Are Required To Fill in All The Blanks of The Phase Diagrams For All Problems

This document provides solutions to 5 problems related to soil mechanics. Problem 1 involves calculating properties like void ratio, porosity, degree of saturation, dry unit weight, and saturated unit weight for a soil sample. Problem 2 verifies a soil property equation. Problem 3 calculates the water content of a fully saturated soil. Problems 4 and 5 solve additional textbook problems involving calculating soil properties. Diagrams are provided to fill in calculated values.

Uploaded by

plmpoi098
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CIVENG 3A03 Assignment #1

Solutions

1. A 0.5 m3 sample of moist soil weights 9.81 kN. The water content is 10%. Assume s =
2.70Mg/m3.
(1) With this information, fill in all blanks in the phase diagram of Fig. 1.

Figure 1

(2) Calculate the void ratio, the porosity, the degree of saturation, the dry unit weight and
the saturated unit weight.

2. Verify the relation =

s + w Sr e

1+ e
(Hint: You may assume Vs=1)

, fill in all the blanks in the phase diagram of Fig. 1.

3. What is the water content of a fully saturated soil with a dry density of 1.70 Mg/m3?
Assume Gs = 2.71.
4. Problem 1.2 in the text.
5. Problem 1.4 in the text.
(You are required to fill in all the blanks of the phase diagrams for all problems).

Solutions:
Q1:
Wt = 9.81kN , Vt = 0.5m3 , water content w = 10%, s = 2.70Mg/m3
Wt = Ws + Ww = Ws + Ws w Ws =

Wt
= 8.92kN
1+ w

Weight of water Ww = Wt Ws = 0.89 kN


W
W
8.92kN
= 0.337 m3
Volume of solids: Vs = s = s =
s s w 2.70 9.81kN / m3
W
0.89
= 0.091 m3
Volume of water: Vw = w =
w 9.81

(1 Mg = 9.81 kN)

Volume of voids: Vv = Vt Vs = 0.5 0.337 = 0.163 m3


Volume of air: Va = 0.072 m3

0.072m3
0.163 m3
0.091m3
0.89 kN
0.5 m

9.81 kN
0.337m

8.92 kN

e=

Vv 0.163
=
= 0.48;
Vs 0.337

Sr =

n=

Vw 0.091
=
= 0.558 = 55.8%
Vv 0.163

Vv 0.163
=
= 0.33
Vt
0.5

d =

Ws 8.92
=
= 17.84 kN / m3
Vt
0.5

sat =

Ws + Vv w 8.92 + 0.163 9.81


=
= 21.04 kN / m3
Vt
0.5

1+e

eSr

Q2: Assuem Vs = 1

Wt s + w S r e
=
Vt
1+ e

Q3: Assume Vs =1
According the defination of void ratio: Vv = eVs = e
Weight of soil particles: Ws = (Gs w ) 1 = d (1 + e)
e=

Gs w

1 =

w (eSr)

2.71 9.81
1 = 0.594
1.70 9.81

For fully saturated soil: Sr = 100%, Vw = Vv

Ws + Vv w Gs w + e w 2.71 + 0.594
=
=
9.81 = 20.33 kN / m3
Vt
1+ e
1 + 0.594

w e

1+e

sat =

(1+e) d = (1)(s)

Q4:

= 1.91 9.81 = 18.74kN / m3 , w = 9.5%, Gs = 2.70 s = Gs w = 26.49kN / m3


e=

s (1 + w)
26.49 1.095
1 =
1 = 0.55

18.74
wGs 2.70 0.095
=
= 46.8%
0.55
e
G +e
2.70 + 0.55
w =
= s
9.81 = 20.57 kN / m3
1+ e
1 + 0.55

Sr =

sat


Q5. M=168 g, Ms=130.5 g, Mw = M - Ms=37.5 g , Gs=2.73,
W=1.65 N, Ws=1.28 N, Ww = W - Ws=0.67 N
1

V = D 2 H = 38 2 76 = 8.62 10 4 mm 3 = 8.62 10 5 m 3
4
4
M
Ms
130.5
Vs = s =
=
= 47.8 cm 3 = 4.78 10 5 m 3
where w = 1g / cm 3
s G s w 2.73 1
Vv=V-Vs=3.84*10-5 m3, Vw =

w=

M w 37.5
=
= 37.5 cm 3 = 3.75 10 5 m 3
w
1

M w 37.5
=
= 28.7%
M s 130.5

Vw 3.75 10 5
=
= 97 .7. %
Vv 3.84 10 5
V v 3.84 10 5
e=
=
= 0.80
Vs 4.78 10 5
Sr =

Ws 1.28 10 3 kN
d =
=
= 14.8 k N / m 3
5
3
V
8.62 10 m
W + Vv w
= 19.2 k N / m 3
sta = s
V
' = sta w = 9.41 k N / m 3
e
e
0.80
water content at saturation: w = w =
=
= 29.3%
s
G s 2.73

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