Solutions to Supplementary Problems

Transcription

1 Solution to Supplmntay Poblm Chapt Solution. Fomula (.4): g d G + g : E ping th void atio: G d (56%) 7 mg Fomula (.6): S Fomula (.40): g d E ping at contnt: S m G (%) m E ping unit ight: g ( + m ) g d ( + 0.) kn/m Fomula (.20): g W W g E ping total ight: Wh, 500 cm m Thfo, Fomula (.7): W kn W ( + m ) W E ping th ight of olid: W W + m kn Intoduction to Soil Mchanic, Fit Edition. Béla Bodó and Colin Jon. 20 John Wily & Son, Ltd. Publihd 20 by John Wily & Son, Ltd INDD 6/22/20 4::9 PM

2 2 Intoduction to Soil Mchanic Fomula (.7): W W + W E ping th ight of at: W W W kn Fomula (.8): W M E ping th ma of at: Fomula (.46a): a 0 W M kg M Rult: olum of ai 25.5 cm cm Wight of at kn Ma of at kg Altnativ olution fo a : Fomula (.): + v v + Fomula (.9): S v S S v + Fomula (.2): v + a a v + S + a + ( S ) ( 0.5) 25. cm (A bfo) Solution.2 Fomula (.7): n v v n cm Fomula (.): + v v cm Fomula (.): n n (5.8%) Th dg of atuation of th and, in it oiginal tat, can no b calculatd fom: mg Fomula (.6): S S (74.4%) INDD 2 6/22/20 4:: PM

3 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 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 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 ( ) kn kg Rult: Wight of at addd 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 kn/m W g 26.2 ( ) kn Final at contnt ( m 2 ) aft atuation ( S ) i givn by: Fomula (.6): m 2 G (20.5%) Chang in at contnt: d m m 2 m (5.5%) Wight of addd at ( d W ) i calculatd fom: Fomula (.5a): d m 2 δ W W d W d m W (a bfo) INDD 6/22/20 4::5 PM

4 4 Intoduction to Soil Mchanic Solution. G ( G Fomula (.4): g + g ) mg Fomula (.6): Dg of atuation: S ( ) Thfo, at fill 46.% of th void. + Fomula (.4): S S cm m W Fomula (.2): g W g 9.8 ( ) kn 0 W It ma M 0.64 kg Rult: a) Pcntag of void filld ith at 46.%. b) Wight of at in th void 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 INDD 4 6/22/20 4:4: PM

5 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 INDD 5 6/22/20 4:4:58 PM

6 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 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 kg/m 2 0 b) Tt: M kg m 9% M kg Ma of and in th hol: M M 2 M M kg M 2.09 olum of hol: ρ m M Ma dnity of oil: kg/m. 0 Ma dy dnity: d ρ + m kg/m Bulk dy dnity: g d kg/m INDD 6 6/22/20 4:5:9 PM

7 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 M G ρ 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 min b) Dg of atuation i S 0.8, hnc fom (.6) in gnal: S m G Tabl.6 m % max min INDD 7 6/22/20 4:5:2 PM

8 8 Intoduction to Soil Mchanic c) Dg of atuation i S, hnc fom (.42) in gnal: g at G + + g Tabl.7 ( ) g at (kn/m ) max min Solution.7 Givn: W 48.5 kn 2.5 m G 2.7 S Unit ight, g at W kn/m 2.5 G + E ping th void atio fom fomula (.42): g at ( + ) Wat contnt fom fomula (.6): m G g Wight of olid fom fomula (.7): W + Wm kn Wight of at fom fomula (.7): W W W kn W 0. Thfo, th volum of at: m INDD 8 6/22/20 4:5:50 PM

9 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 kn W Wat contnt: m W Th void atio i pd fom (.9): ( + mg ) Th volum of ai i givn by (.46): a + W m Th pcntag of ai void i givn by (.49): a P a % 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 kn/m 2 d Stp : W Stp 4: Fom (.44): G ( + ) 2 W G m 2 Fom (.45): Stp 5: a2 + W m a2 Thfo, P a % INDD 9 6/22/20 4:6:08 PM

10 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 m olum aft compaction: m But, th volum of th mbankmnt i givn by: Ax Wh, A 2 m 2, x lngth of mbankmnt Hnc, x A m 2.9 km Solution.9 a) Fom (.40): g ( + m ) g d kn/m mg b) Fom (.6): S G S m Fom (.8): g G + S + g G ( + ) S ( + ) Equating: G 4.08 ( + ) E ping: Hnc, G G + Fom (.42): g at + g kn/m.66 Solution.0. Total ight: W g kn 2. Wight of olid: W + Wm Wight of at: W W W 0.29 kn 2.40 kn. olum of olid: m W 0.29 olum of at: m 9.8 olum of void: v m INDD 0 6/22/20 4:6:40 PM

11 Solution to Supplmntay Poblm: Chapt Solution. M Fom (.57): G M + M M Fom (.58): m M G M M G (26%) olum of at: m M cm M olum of olid: G cm 2.75 Fo fully atuatd oil: S and a 0 v Total volum thfo: 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 g/cm 257 Bulk unit ight (.2): g kn/m Dy ma dnity (.25): d M 42.6 g/cm 257 Dy unit ight (.27): g d 9.8 d kn/m M Ma dnity of olid (.2): g/cm (G ) Unit ight of olid (.4): g kn/m v oid atio (.05): Pooity (.6): n v Satuatd ma dnity (.28): M + ρ M v + at 2.02 g/cm INDD 6/22/20 4:7:04 PM

12 2 Intoduction to Soil Mchanic Satuatd unit ight (.29): g at 9.8 at kn/m Chck fo atuation (.8): S 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 INDD 2 6/22/20 4:7:7 PM