Principles of Geotechnical Engineering
SI Version 8th Edition Das Solutions Manual
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41 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
7.1 From the figure: α α α sin cos tan length loss head = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = S S i q = k i A = (k)(sin α)(4.2 cos α)(1) k = 4.8 × 10-3 cm/sec = 4.8 × 10-5 m/sec /hr/m m 10 7.54 3 2× ≈ = ° ° × = /hr/m m 0.0754 )(3600) 6 cos )(4.2 6 )(sin 10 (4.8 3 m/hr to change to 5 q 7.2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = α cos S h i /sec/m m 10 1.29 3 4× = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = 14) cos 2 ( 30 14 cos 2.75 10 0.075 1) cos ( cos m/sec 2 1 α α H S h k kiA q
Chapter 7
2 Aht QL k
7.3 a. cm/sec 10 3.96 3× = = = sec) cm)(300 )(50 cm (176.71 cm) )(30 cm (350 2
b. ki v e e v v s = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ; 1 cm/sec 0.0174 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 61 0 61 0 1 cm 30 cm 50 00396) (0 1 e e ki v s
7.4 )(60) (31.67)( (160)(15) 0.062 ; h Aht QL k = = h = 20.37 cm
1 10 h h At aL k cm/sec 10 2.75 -4 × =
log 60) 64)(8 (19 (0.25)(15) 303) 2 ( log 303 2 10 2
7.5 a. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ × = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 20
1 log10 2.303 h h At aL k ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝
⎛
42 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
40
=
⎜
⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ × = 2 2 10 40 log 0.00122 40 log 60)
h
⎜
⎠ ⎞ ⎜ ⎝ ⎛ = 2 1 log10 303 2 h h At aL k cm/sec 0.00402 cm/min 0.241 18.5 41 log 10 16 50 0.97 2.303) ( 10 = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × × = 2 -12 m 10 4.13 × = × ⋅ × × = = 3 3 2 3 5 N/m 10 9.789 ) s/m N 10 m/sec)(1.005 10 4.02 ( w k K
b. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2 η
⎟ ⎟ ⎠ ⎞
⎜
(19.64)(6 (0.25)(15) 2.303) ( 0.000275 h h
2 = 23.82 cm 7.6 a. ⎟ ⎟ ⎠ ⎞
⎜ ⎝ ⎛ ⎟
γ
43 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. b. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2 1 log10 2.303 h h At aL k ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × × = 2 10 41 log 7 16 50 0.97 2.303) ( cm/min 0.241 h h2 = 23.5 cm 7.7 From Eq. (7.15) and Table 7.2 for T = 28 ° C: 3 10 7.49 ° ° ° ° × = = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ) 009 )(0 832 (0 C T 20 C T 20 k k C C η η cm/sec 7.8 Eq. (7.31): 0.0747 0.1471 0.48 1 0.48 62 0 1 62 0 0.03 or , 1 1 3 3 2 2 3 2 1 3 1 2 1 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = + + = k e e e e k k k2 = 0.015 cm/sec 7.9 e = emax – (emax – emin)Dr = 0.68 – (0.68 – 0.42)(0.52) = 0.544 Eq. (7.32): 7825 0 3 2 10 1 4622 2 (cm/sec) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = e e D k cm/sec 0.1 = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 7825 0 3 2 544 0 1 0.544 4) (0 4622) 2 ( 7.10 e1 = emax – (emax – emin)Dr = 0.72 – (0.72 – 0.46)(0.8) = 0.512 e2 = 0.72 – (0.72 – 0.46)(0.67) = 0.545 0.1047 0.0887 0.545 1 0.545 0.512 1 512 0 0.006 or , 1 1 3 3 2 2 3 2 1 3 1 2 1 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = + + = k e e e e k k
44 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. k2 = 7.08 × 10-3 cm/sec 7.11 0.562 0.36 1 36 0 1 0.36; 1 1 1 1 = = = = n n e n 0.923 0.48 1 48 0 0.48; 2 2 = = = e n Eq. (7.31): 3 3 1 2 2 1 1 3 1 1 2 3 2 1 2 562 0 0.923 923 1 1.562 (0.072) 1 1 1 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎟⎛ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = e e e e k e e e e k k k2 = 0.259 cm/sec
γd(field) = Rγd(max) = (0.9)(16) = 14.4 kN/m3 0.839 1 14.4 2.7)(9.81) ( 1 field) ( = = = d w s G e γ γ cm/sec 0.732 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 32 2 6 0 3 2.32 10 6 0 3 23) (0 1) 3 ( 839 0 1 0.839 35 mm) )( ( 1 35 (cm/sec) : (7.34) Eq. D C e e k u 7.13 Sieve no. Opening (cm) Percent passing Fraction between two consecutive sieves (%) 30 40 60 100 200 0.06 0.0425 0.02 0.015 0.0075 100 73 59 23 0 { 27 { 14 { 36 { 23 .93 550 0425 0 06 0 27 40 and 30 Nos. sieve between fraction For 595 0 404 0 595 0 404 0 = × = × ⎭ ⎬ ⎫ si li i D D f
7.12
45 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. .21 514 02 0 0425 0 14 60 and 40 Nos. sieve between fraction For 595 0 404 0 595 0 404 0 = × = × ⎭ ⎬ ⎫ si li i D D f .71 2127 015 0 02 0 36 100 and 60 Nos. sieve between fraction For 595 0 404 0 595 0 404 0 = × = × ⎭ ⎬ ⎫ si li i D D f .35 2306 0075 0 015 0 23 200 and 100 Nos. sieve between fraction For 595 0 404 0 595 0 404 0 = × = × ⎭ ⎬ ⎫ si li i D D f 0.0182 2306.35 2127.71 514.21 550.93 100 100% 595 0 404 0 ∑ = + + + = × ∑ si li D D cm/sec 0.0219 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × = 0.68 1 0.68 7.5 1 )(0.0182) 10 (1.99 3 2 2 4 k 7.14 n n n e e e e e e e e k k ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 2 1 1 2 2 2 1 1 2 1 1 1 1 1 n ⎟ ⎠ ⎞ ⎜ ⎝ ⎟⎛ ⎠ ⎞ ⎜ ⎝ ⎛ = × × 1.6 0.95 1.95 2.6 10 0.91 10 0.2 6 6 ; 0.1648 = 0.593 n 3.45 0.593 log 1648 0 log = = n ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 1 1 1 1 e e C k n ; cm/sec 10 4.655 0.95 95) 0 )(1 10 2 (0 7 45 3 6 × = + × = C cm/sec 10 3.08 7× = × ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ) 10 4.655 ( 2.1 1 1 7 45 3 3 k 7.15 Eq. (7.37): log k = A′ log e + B′ 2.9 log(1.6) log(0.95) ) 10 log(0.91 ) 10 log(0.2 log log log log 6 6 2 1 2 1 = × × = = ′ e e k k A 634 6 95) log(0 9 2 ) 10 2 log(0 log log 6 1 1 = × = ′ ′ e A k B log (k3) = (2.9)log(1.1) – 6.634 = –6.514
46 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. k3 = 3.062 × 10-7 cm/sec 7.16 ....) ( 1 2 2 1 1 ) eq ( + + = H k H k H k H cm/sec 10 7.042 2)] )( 10 (3.5 )(1) 10 2.8 ( )(1) [(10 4 1 3 5 2 4 ) eq ( × = × + × + = H k cm/sec 10 5.95 10 3.5 2 10 2.8 1 10 1 4 5 5 2 4 2 2 1 1 ) eq ( × = × + × + = + + = k H k H H kV 118.35 = × × = 5 3 ) eq ( ) eq ( 10 95 5 10 042 7 V H k k 7.17 kiA q = 08 0 125 150 160 = = i 250 = q m3/day A = 2×500 = 1000 m2 3.125 = = = (0.08)(1000) 250 iA q k m/day CRITICAL THINKING PROBLEM 7.C.1 a. 3 4 2 3 3 3 2 2 1 1 ) eq ( 10 1.076 10 3.9 20 10 4.2 20 10 5 20 60 × = × + × + × = + + = k H k H k H H k v cm/sec 0.149 ) (15 4 60 47 (0.001076) 2 ) eq ( = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = iA k q v cm3/sec = 536.4 cm3/hr
b. x = 0 mm
Z = –220 mm; 690 = + = 220 470
mm
mm 470 = = + = 220 690 Z u h
x = 200 mm
Z = –220 mm
( 436.29
u γ mm
x = 400 mm
Z = –220 mm 2 2 )
Therefore,
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w u γ
w
γ
1 1 ) eq ( i k i k v = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 20 Δ (0.005) 60 47 (0.001076) H
mm 33.71 cm 3.371 Δ = = H
w
Therefore, mm 436.29 = = 71 33 470 h 656.29 = = 220)
eq
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 20 Δ 042) (0 60 47 001076) (0 H mm 4 cm 0.4 Δ = = H
( i k i k v =
w
mm 432.29 = = 4 .29 436 h 652.29 = = 220) ( 29 432
u γ mm
x = 600 mm
c. The variation of heads with distance is shown in the following figure.
48 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
mm 3 3 ) eq ( i k i k v = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 20 Δ (0.00039) 60 47 (0.001076) H mm 432.24 cm 43.224 Δ = = H Therefore, mm 0 ≈ = 24 432 29 432 h 220 = = 220) ( 0 w u γ mm
Z = –220
d. 000843 0 60 47 001076) (0 ) eq ( = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = i k v v cm/sec
Soil I: 0.00168 = = 5 0 000843 0 s v cm/sec
Soil II: 0.0014 = = 0.6 0.000843 s v cm/sec
Soil III: 0.00255 = = 0.33 0.000843 s v cm/sec
These values are plotted in the figure on the previous page.
e. Height of water column is equal to the piezometric or pressure head at a point. Therefore, height of water in A = pressure head at x = 200 mm = 656.29 mm
height of water in B = pressure head at x = 400 mm = 652.29 mm
49 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. n v v s
=
50 © 2014 Cengage Learning. All rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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to lose sight of it, until it reaches home in safety, or it will run great risk of being changed.
After spending two or three days longer at Genoa, I engaged for my passage in a felucca to Leghorn, and what is singular, it had the same name, the Divine Providence, as the one I had so lately sailed in from Nice. A great number of vessels of this kind are continually passing from hence to Leghorn, and the felucca men, if they have an idea of any one being about to undertake the voyage, are extremely troublesome in pestering him, as he passes along the streets, to sail with them, and will even fish the servants at his hotel, to gain intelligence of his intended proceedings. In arranging the point of fare with them, it is necessary to be very cautious, as they will ask four times the usual rate.
I agreed for twelve francs, the sum which the master of the felucca had found out, that I had paid for my passage from Nice; it cost me, however, half as much more in gratuities, and other expenses, and I had afterward the mortification to find, that other passengers had secured the same accommodations, for only five francs each.
About six o’clock on the evening of Saturday, March the 11th, the captain came to apprize me that the vessel was waiting. On getting on board there was very little wind, so that throughout the night, we were obliged to make use of our oars as well as sails; at day-break a breeze sprang up from the eastward, which obliged us to turn back for fifteen miles, towards Porto Fino, where we anchored at ten o’clock, and went on shore to a miserable auberge.
Among our passengers were two French gentlemen who were friends, but of very opposite characters; the one was volatile, and thoughtless, and talked of proceeding to Naples, and offering his services to the patriot army, the other who, we understood, had been a merchant, was sedate and thoughtful, so that, I dare say, pounds, shillings, and pence might have been read in his face. The lively one amused us, not a little, with his eccentricity; he spoke of having a mistress at Genoa, whom he had engaged to marry that very morning, but he stated that the present was not the first time of his
having proved faithless to her, and seemed to exult in her disappointment; it, however, appeared in the sequel that he could not reconcile himself to give her up, for after we entered Porto Fino, he began to repent, and earnestly solicit his friend to return to Genoa with him, offering to pay all expenses; at length, the other acceded to his wishes, and they left us, which was to myself a source of considerable regret as I lost, at least, one amusing companion, whose language I could understand, and had no one left with whom I could converse. In order to get back to Genoa, these gentlemen had to pull five or six miles, in the midst of a heavy rain, and in an open boat, in a contrary direction, until they reached the new road making between Genoa and Spezzia.
This road when completed, will be an incalculable advantage to the communications with the southern parts of Italy; the old road to Florence, over the mountains, being a very indirect one; although an expensive undertaking, there is little doubt but that this will be compensated, as many thousands, who in order to reach southern Italy, now go by sea to Lerici and Leghorn, will then prefer the journey by land; and in the event of an equally good communication being formed between Genoa and Nice, a strong inducement will be offered to the traveller, to enter this country by that route, particularly in the winter season. This has been partially effected under the auspices of Bonaparte; the present Sardinian government, however, are not disposed to carry it forward, as they are naturally jealous of affording their neighbours, the French, so easy an access into the heart of their country.
Throughout the remainder of this, and part of the next day, the weather continued unfavourable, and we made no attempt to leave Porto Fino; however, in the afternoon of the latter we sailed, but in the evening it fell calm, and we took to our oars throughout the night; about noon, on the following day, a light and favourable air sprang up, which soon increased to a moderate breeze; about three o’clock we arrived at the entrance of the Gulf of Spezzia, where to my great concern, notwithstanding I said every thing to induce him to push on as the wind was fair, the captain persisted in coming to an anchor,
