Chapter 2 Solutions to Exercises - Wiley: · PDF fileChapter 2 Solutions to Exercises...
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Smith’s Elements of Soil Mechanics. 9 th Edition Ian Smith Published by Wiley ISBN-13: 978-0470673393 http://www.wiley.com/go/smith/soil Chapter 2 Solutions to Exercises Exercise 2.1 4 7 . 12 4 2 2 × = = π πd a = 126.7 mm 2 4 76 4 2 2 × = = π πD A = 4536 mm 2 × × × = 254 508 ln 6 . 19 4536 152 7 . 126 1 k = 0.150 mm/sec × × × = 127 254 ln 4 . 19 4536 152 7 . 126 2 k = 0.152 mm/sec Average k = 0.151 mm/sec
Transcript of Chapter 2 Solutions to Exercises - Wiley: · PDF fileChapter 2 Solutions to Exercises...
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Chapter 2 Solutions to Exercises Exercise 2.1
47.12
4
22 ×==ππda = 126.7 mm2
476
4
22 ×==ππDA = 4536 mm2
⎟⎠
⎞⎜⎝
⎛××
×=
254508ln
6.1945361527.126
1k = 0.150 mm/sec
⎟⎠
⎞⎜⎝
⎛××
×=
127254ln
4.1945361527.126
2k = 0.152 mm/sec
Average k = 0.151 mm/sec
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.2
455
4
22 ×==ππDA = 2375.8 mm2
4008.2375615010400 3
××
××==
tAhQlk = 10.5 mm/sec = 1.05 × 10-2 mm/sec
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.3 z2 = (12.5 – 1.95) – 1.36 = 9.19 m z1 = (12.5 – 1.95) – 1.625 = 8.925 m q = 850 kg/min = 0.85 m3/min = 0.85 × 60 m3/hr = 51 m3/hr
( )2122
1
2ln
zzr
rqk
−
⎟⎠⎞⎜
⎝⎛
=π
( )
( )22 925.819.92.15
4.30ln51
−
×=π
= 2.34 m/hr = 2.34 ÷ 3600 m/sec = 6.7 × 10-4 m/sec k ≈ 2
1001.0 D× ⇒ 01.010
kD ≈ ≈ 0.26 mm
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.4
Length of flow path through sample, L = 250200150 22 =+ mm Difference in head between inlet and outlet of sample, h h = 250 + 150 + 20 – 100 = 320 mm
2503202500)6010(5 ××××
==LktAhQ = 9 × 106 mm3
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.5
i) 45.0145.0
1 −=
−=
nne = 0.818
818.1154.2
11 −=
+
−=
eGi s
c = 0.85
ii) 37.0137.0
1 −=
−=
nne = 0.587
587.154.1
11=
+
−=
eGi s
c = 0.97
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.6 At point of collapse, 3.67 m of clay (γ = 17.6 kN/m3) is balanced by upward water pressure, u i.e. u = 3.67 × 17.6 = 645.5 kPa ⇒ Height that water would rise to in stand-pipe, h
h = 105.64
=w
uγ
= 6.45 m above top of sand
7.63 m
11.3 - 7.63 = 3.67 m
11.3 m CLAY
SAND
Smith’s Elements of Soil Mechanics. 9th Edition Ian Smith
Published by Wiley ISBN-13: 978-0470673393
http://www.wiley.com/go/smith/soil
Exercise 2.7
kx = H1k1 +H2k2 +H3k3H
1!0.3+ 2!0.2+3!0.11+ 2+3
=16= 0.167
kz =H
H1
k1+H2
k2+H3
k3
610.3
+20.2
+30.1
= 0.138
kxkz=0.1670.138
=1.22
