Solution to Supplmntay Poblm Chapt Solution. Fomula (.4): g d G + g : E ping th void atio: G d 2.7 9.8 0.56 (56%) 7 mg Fomula (.6): S Fomula (.40): g d E ping at contnt: S m G 0.56 0.5 0. (%) 2.7 + m E ping unit ight: g ( + m ) g d ( + 0.) 7 8.87 kn/m Fomula (.20): g W W g E ping total ight: Wh, 500 cm 500 0 6 m Thfo, Fomula (.7): W 8.87 500 0 6 0.028 kn W ( + m ) W E ping th ight of olid: W W + m 0.028 + 0. 0.0255 kn Intoduction to Soil Mchanic, Fit Edition. Béla Bodó and Colin Jon. 20 John Wily & Son, Ltd. Publihd 20 by John Wily & Son, Ltd. 000992.INDD 6/22/20 4::9 PM
2 Intoduction to Soil Mchanic Fomula (.7): W W + W E ping th ight of at: W W W 0.028 0.0255 0.0028 kn Fomula (.8): W 9.8 0 M E ping th ma of at: Fomula (.46a): a 0 W 0 0.0028 M 0.285 kg 9.8 9.8 + 0 M Rult: olum of ai 25.5 cm 0.56 500 0 0.285 25.5 cm + 0.56 Wight of at 0.0028 kn Ma of at 0.285 kg Altnativ olution fo a : Fomula (.): + v v + Fomula (.9): S v S S v + Fomula (.2): v + a a v + S + a + ( S ) 0.56 500 ( 0.5) 25. cm (A bfo) + 0.56 Solution.2 Fomula (.7): n v v n 0.5 5260 84 cm Fomula (.): + v v 5260 84 49 cm Fomula (.): n n 0.5 0.5 0.58 (5.8%) Th dg of atuation of th and, in it oiginal tat, can no b calculatd fom: mg Fomula (.6): S S 0.5 2.67 0.58 0.744 (74.4%) 000992.INDD 2 6/22/20 4:: PM
Solution to Supplmntay Poblm: Chapt Th volum of at in th and, in it oiginal tat, i calculatd fom: Fomula (.9): S v S v 0.744 84 70 cm Whn th oil i fully atuatd, thn S, that i o v v Th addd volum of at ( d ) i, thfo, givn by: d v 70 84 70 47 cm Th ight ( d W ) of addd at i givn by: Fomula (.2): g δ W δ Ma of at addd d W g d 9.8 (47 0 6 ) 462 0 6 kn 0 462 0 9.8 6 0.47 kg Rult: Wight of at addd 0.00462 kn Ma of at addd 0.47 kg Altnativ olution: Initial moitu contnt: m 5% oid atio: 5.8% olum of olid: 49 cm Fomula (.4): G Fomula (.): W g g G S g 2.67 9.8 26.2 kn/m W g 26.2 (49 0 6 ) 0.0896 kn Final at contnt ( m 2 ) aft atuation ( S ) i givn by: Fomula (.6): m 2 G 0.58 2.67 0.205 (20.5%) Chang in at contnt: d m m 2 m 0.205 05 0.055 (5.5%) Wight of addd at ( d W ) i calculatd fom: Fomula (.5a): d m 2 δ W W d W d m W 0.055 0.0896 0.0046 (a bfo) 2 000992.INDD 6/22/20 4::5 PM
4 Intoduction to Soil Mchanic Solution. G ( G Fomula (.4): g + g ) mg Fomula (.6): Dg of atuation: S 2.65 9.8 0.86 8.69 ( ) 0.5 2.65 0.86 0.46 Thfo, at fill 46.% of th void. + Fomula (.4): S S + 0.86 000 0.46 + 0.86 640.6 cm 640.6 0 6 m W Fomula (.2): g W g 9.8 (640.6 0 6 ) 0.00628 kn 0 W 0 0.00628 It ma M 0.64 kg 9.8 9.8 Rult: a) Pcntag of void filld ith at 46.%. b) Wight of at in th void 6.28 0 kn c) Ma of at in th void 0.64 kg Solution.4 G + S Fomula (.8): g + g Wh S. Subtituting: G m S + g S m g + nn mg S + S m + ( + ms ) m( + ) + m g m + S g (.59) mg n 2. Subtitut: and + + S n into fomula (.59): n + m g m mg S S g n + m mg g m S ( n) S g 000992.INDD 4 6/22/20 4:4: PM
Solution to Supplmntay Poblm: Chapt 5 Canclling m and S : g ( + m) ( n) G g (.60). Fo atuatd oil S and mg n Fom hich, m ( ng ) n at atuation. Subtitut thi into fomula (.60): g at + n ( n ) G ng g ( ) ( ) ( ) ng+ n ( n ) G ng g Cancl ( n ) G g at [( n ) G + n ] g (.6) 4. Subtitut S into (.59) to gt: + m g at m + g (.62) 5. Fo dy oil S 0 and m 0. Subtitut G g d n g + n ( ) ng n+ n g n into (.8): n Canclling n in th dnominato: g d ( n ) G g (.6) 6. Fom (.6): g at ( n ) G g + n g g d Fom hich, g d g at n g (.64) n 7. Fo ubmgd oil S mg n } Fom (.): g g at g + m Uing (.59): g m ( ) + + m ( + ) m g g g + m m m ( + ) m g 000992.INDD 5 6/22/20 4:4:58 PM
6 Intoduction to Soil Mchanic Canclling tm m : ( m) ( + ) m (.65) 8. E p g at fom (.64): g at g d n g Thfo, g ( g d + n g ) g g d + n g g And, g g d ( n ) g (.66) Solution.5 a) Calibation: M 2 4.99 kg M 0.58 kg M.9 kg c 2000 cm 2 0 m Th dy ma dnity of and i givn by: M2 M M 4.99.9 0.58 60 kg/m 2 0 b) Tt: M 4 2.574 kg m 9% M 5 2.2 kg Ma of and in th hol: M M 2 M M 5 4.99 0.58 2.2 2.09 kg M 2.09 olum of hol: ρ 60. 0 - m M Ma dnity of oil: 4 2.574 980 kg/m. 0 Ma dy dnity: d ρ + m 980 + 0.9 664 kg/m Bulk dy dnity: g d 664 9.8 0 6.2 kg/m 000992.INDD 6 6/22/20 4:5:9 PM
Solution to Supplmntay Poblm: Chapt 7 Solution.6 a) Stp : Fo th void atio at th mot dn tat, p max fom (.47): D 00 max max min D 00 ma x D 00 min max D Fom hich, max 00 D 00 D 00 max min Stp 2: Th volum of olid i givn by: Fomula (.2): Fomula (.): m ρ G g/cm D 00 min 40 0.52 0 00 40 00 M G ρ 0.96 0.6 0.66 00 0 7594 cm 2.66 Stp : Th volum of void i givn by fomula.5, in gnal a: v Stp 4: By fomula (.), th total volum i: v + Stp 5: Tabulating th calculation fo th volum: Tabl.5 v (cm ) v + (cm ) max 0.66 0.66 7594 2482 2482 + 7594 62406 0.52 0.52 7594 9549 9549 + 7594 574 min 0. 0. 7594 654 654 + 7594 49248 b) Dg of atuation i S 0.8, hnc fom (.6) in gnal: S m G 0.8 2.66 0. Tabl.6 m % max 0.66 0 0.66 9.8 0.52 0 0.52 5.6 min 0. 0 0. 9. 000992.INDD 7 6/22/20 4:5:2 PM
8 Intoduction to Soil Mchanic c) Dg of atuation i S, hnc fom (.42) in gnal: g at G + + g 2.66 + + 9.8 Tabl.7 (2.66 + ) 9.8 + g at (kn/m ) max 0.66 2.57.66 9.6 0.52.20.52 20.5 min 0. 29.4. 22.2 Solution.7 Givn: W 48.5 kn 2.5 m G 2.7 S Unit ight, g at W 48.5 9.4 kn/m 2.5 G + E ping th void atio fom fomula (.42): g at + 9.4 ( + ) 2.7 + 0.98 0.72 9.8.98 +.98 2.7 + 0.72 0.98 0.75 Wat contnt fom fomula (.6): m G 0.75 0.27 2.7 g Wight of olid fom fomula (.7): W + Wm 48.5.27 8.2 kn Wight of at fom fomula (.7): W W W 48.5 8.2 0. kn W 0. Thfo, th volum of at: 9.8.05 m 000992.INDD 8 6/22/20 4:5:50 PM
Solution to Supplmntay Poblm: Chapt 9 Solution.8 a) Soil in-itu : m W W 8. kn g 8. kn/m W W S 6 kn g d 6 kn/m Wight of at: W W W 8. 6 2. kn W Wat contnt: m W 2. 6 0. Th void atio i pd fom (.9): ( + mg ). 2.66 9.8 0.6 8. Th volum of ai i givn by (.46): a + W 0.6.6 2. 9.8 0.7 m Th pcntag of ai void i givn by (.49): a P a 00 0.7 7.% Compactd oil Stp : Conid th am ight of oil, compactd to dy dnity 8.2 kn/ m at m.% Givn: W 8. kn W 6 kn m 0. 2? W 2. kn g d2 8.2 kn 2 Stp 2: Fom (.40): g d2 + m g ( + m) g. 8.2 20.6 kn/m 2 d2. 2.66 9.8 Stp : 2 0.4 20.6 W Stp 4: Fom (.44): G ( + ) 2 W.4 6 2 G 2.66 9. 0.88 m 2 Fom (.45): + 2 2 2 Stp 5: a2 + W 0.4 0.88 2. 2.4 9.8 0.052 m a2 Thfo, P a2 00 5.2 0.88 5.9 % 2 000992.INDD 9 6/22/20 4:6:08 PM
0 Intoduction to Soil Mchanic Summay: A W 8. kn ( m ) of oil i compactd into a volum of 0.88 m, th:. oid atio dca fom 6.% to 4.%. 2. Pcntag of ai dca fom 7.% to 5.9%. b) olum of oil xcavatd 40000 4 0 4 m olum aft compaction: 0.88 4.0 4.52 0 4 m But, th volum of th mbankmnt i givn by: Ax Wh, A 2 m 2, x lngth of mbankmnt Hnc, x A.52 0 2 4 29 m 2.9 km Solution.9 a) Fom (.40): g ( + m ) g d.2 6 7.9 kn/m mg b) Fom (.6): S G S m 0.49 4.08 0.2 Fom (.8): g G + S + g G ( + ) S ( + ) 7.9 9.8 0.49 Equating: G 4.08 ( + ) 7.9 9.8 0.49 4.08.82 +.82 0.49.82 2.75 0.66 E ping: 2.75.82 Hnc, G 4.08 0.66 2.7 G + Fom (.42): g at + g 2.7 + 0.66 9.8 9.9 kn/m.66 Solution.0. Total ight: W g 7.9 0.5 2.69 kn 2. Wight of olid: W + Wm 2.69.2 Wight of at: W W W 0.29 kn 2.40 kn. olum of olid: + 0.5.66 0.09 m W 0.29 olum of at: 0.029 m 9.8 olum of void: v 0.66 0.09 0.06 m 000992.INDD 0 6/22/20 4:6:40 PM
Solution to Supplmntay Poblm: Chapt Solution. M Fom (.57): G M + M M 42 42 + 92 289 2.75 2 Fom (.58): m M G M M G 2 59 285 92 2.75 2.75 908.25 720.5 0.26 (26%) olum of at: m M 0.26 42 07 cm M olum of olid: G 42 50 cm 2.75 Fo fully atuatd oil: S and a 0 v Total volum thfo: + 50 + 07 257 cm Not: All oth oil chaactitic can no b dtmind fom: M 59 g M 42 g 257 cm G 2.75 Bulk ma dnity (.20): M 59 2.02 g/cm 257 Bulk unit ight (.2): g 9.8 9.8 2.02 9.8 kn/m Dy ma dnity (.25): d M 42.6 g/cm 257 Dy unit ight (.27): g d 9.8 d 9.8.6 5.7 kn/m M Ma dnity of olid (.2): 42 50 2.75 g/cm (G ) Unit ight of olid (.4): g 9.8 9.8 2.75 27 kn/m v oid atio (.05): 07 50 0.7 Pooity (.6): n v 07 257 0.42 Satuatd ma dnity (.28): M + ρ M v + at 2.02 g/cm 42 + 07 257 000992.INDD 6/22/20 4:7:04 PM
2 Intoduction to Soil Mchanic Satuatd unit ight (.29): g at 9.8 at 9.8 2.02 9.8 kn/m Chck fo atuation (.8): S 07 0.7 50 v Not: a) Th pcific gavity can b dtmind alo by a ga ja o a dnity bottl. Th pycnomt fomula a applicabl to th contain. Gla plat Ja Rubb topp Gla topp ith cntal bo fo caping ai Ga ja Dnity bottl b) Fomula (.56) to (.58) can b pntd in diffnt fom, dpnding on th ay th ma a maud duing th tt. Mau th ma in tp: Stp : Figu.27 m ma of pycnomt Stp 2: m 2 ma of pycnomt + oil Stp : m ma of pycnomt + oil + at Stp 4: m 4 ma of pycnomt + at G In th tm: M ( m m4) G m2 m G m m m m ( ) ( ) 4 2 M G m m m G ( ) 4 By compaion: m M p m 2 m M m 2 M p + M m m 2 M 2 M p M m M 2 m 4 m M 0 m 4 M m m 4 M 2 M c) Th fomula a applicabl to both atuatd and patially atuatd oil, a long a dy matial i placd into th contain. d) Fo patially atuatd oil a i unknon and cannot b divd fom Figu.26. Fo thi aon only G, m, and can b calculatd. S Exampl.9. ) Fo fully atuatd oil a 0, hnc th nti ang of oil chaactitic can b divd, a in Poblm.. 000992.INDD 2 6/22/20 4:7:7 PM