4a lapidario a#3 phase-relationships 2015-2016

7/25/2019 4A Lapidario a#3 Phase-Relationships 2015-2016

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Technological University of the Philippines

1000 Ayala Boulevard, Ermita, Manila

College of Engineering

Civil Engineering Department

CE 410 – 4A

Soil Mechanics, Lec.

Assignment No. 3

Phase-Relationships

LP!DR!", Ronal#o P.

11-0!-11"

#ate of $u%mission& $%ly &&, &'()

Engr. $es%s Ray M. Mansayon

'nstru(tor



1. )or a given soil, s*o+ t*atγ sat =γ d+n γ w

$/'N&

γ sat =W

V

γ sat =W s+W w

V

γ sat =γ d+W w

V

γ sat =γ d+γ w V w

V

γ sat =γ d+γ w (V v−V a )

V

V V =V w ,V a=0

γ sat =γ d+

γ w V v

V

/EE)E γ sat =γ d+nγ w

&. )or a given soil, s*o+ t*at

γ sat =γ d+( e

1+e )γ w

$/'N&

γ sat =W

V

γ sat =W s+W w

V



γ sat =γ d+W w

V

γ sat =γ d+ γ w V w

V v+V s


eV s+V s


V s (1+e )

γ sat =γ d+γ w (V v−V a )

V s (1+e )

V V =V w ,V a=0

γ sat =γ d+ γ w V v

V s (1+e )

γ sat =γ d+γ w( e

1+e )

/EE)Eγ sat =γ d+( e

1+e )γ w

3. )or a given soil, s*o+ t*at

γ d= eS γ w

(1+e ) w

$/'N&

γ d=W s

V

γ d= W w /w

eV s+V s



SAMPLE

γ d= W w

w V s (1+e )

γ d= γ w V w

w V s (1+e )

γ d= γ w SV v

w V s (1+e )

γ d= γ w SeV s

w V s (1+e )

γ d= γ w Se

w (1+e )

/EE)E γ d= eS γ w

(1+e ) w

4. A 0.4m3

moist sam2le *as t*e follo+ing&

Moist mass=711.2kg

Dry mass=623.9 kg

Specific gravity of soil solids=2.68

Estimate&a. Moisture (ontent%. moist density(. #ry densityd. oid atioe. orosity



5'EN&Volume (V) = 0.4 m3

Specific gravity of soil solids (Gs ) = 2.68 oist mass ( ! ) = "##.2 $g %ry mass ( s ) = 623.& $g

E6'E#&w , ρ , e , n , ρd

$/'N&a.

w= M w

M s=

711.2kg−623.9 kg

623.9 kg ; w=0.1399∨13.99

%.

ρ= M

V

=711.2 kg

0.4 m3

7 ρ=1778kg /m

3

(.

ρd= M d

V =

623.9 kg

0.4m3 7 ρd=1559.75 kg /m3

d.

ρd= Gs

1+e ρ w=1559.75

kg

m3=

2.68

1+e (1000 kg

m3 ) 7 e=0.7182

e.

n= e

1+e=

0.7182

1+0.7182; n=0.4180

!. 'n its natural state, moist soil *as a volume of 0.33 ft 3

and +eig*s 38.83 l%. /*e oven-dry

+eig*t of t*e soils is 34.!4 l%. 'fGs=2.67

, (al(ulate t*e moisture (ontent, moist unit +eig*t,

dry unit +eig*t, void ratio, 2orosity, and degree of saturation.



V = 0.33ft3

5'EN&Volume (V) = 0.33 ft 3

'eigt (') = 3&.&3 l*ve+,dry !eigt (' s ) = 34.-4 lSpecific gravity of soil solids (Gs ) = 2.6"

E6'E#&

w , γ , γ d , e , n , S

$/'N&a.

w= M w

M s=

39.93 lb−34.54 lb

34.54 lb ; w=0.1516∨15.61

%.

γ =W

V

=39.93lb

0.33 ft 3

; γ =121lb/ ft 3

(.

γ d=W s

V =

34.54 lb

0.33 ft 3 ; γ d=104.667 kg /m3

d.

γ d= G s

1+e

γ w=104.667 lb

ft 3=

2.67

1+e

(62.4

lb

ft 3

); e=0.5918

e.

n= e

1+e=

0.5918

1+0.5918; n=0.3718

f.

S=w G s

e =

0.1561 (2.67 )0.5918

; S=0.7043

9. /*e moist +eig*t of 0.2 ft 3

of a soil is 3 l%. /*e moisture (ontent and t*e s2e(ifi( gravity of

t*e soil solids are determined in t*e la%oratory to %e 11: and .", res2e(tively.Cal(ulate t*e follo+ing&

a. Moist unit +eig*t (lb / ft 3)

%. #ry unit +eig*t (lb / ft 3)

(. oid atio



SOIL SAMPLE

d. orositye. #egree of $aturation ;:<

f. olume o((u2ied %y +ater (ft 3)

5'EN&Volume (V) = 0.2 ft 3

oist !eigt (') = 23 loisture co+te+t (!) = ##Specific gravity of soil solids (Gs ) = 2."

E6'E#&γ , γ d , e , n , S , V w

$/'N&

a.

γ =W

V =39.93lb

0.33 ft 3 ; γ =115

lb

ft 3

%.

γ d= G s

1+e γ w=γ d=

2.7

1+0.6262 (62.4 lb

ft 3 ); γ d=103.60lb / ft

3

(.

γ =G

s

(1+w )

1+e ( γ w )=115 lbft

3=2.7 (1

+0.11)

1+e (62.4 lb

ft 3

); e=0.6262

d.

n= e

1+e=

0.6262

1+0.6262; n=0.3951

e.

S=w G s

e =

0.11 (2.7 )0.6262

; S=0.4743∨47.43

f.

S=V w

V =0.4743=

V w

0.2; V w=0.09 ft

3

". /*e saturated unit +eig*t of a soil is 19.8 kN /m3

. /*e moisture (ontent of t*e soil is 1".1:.

#etermine t*e follo+ing&



Moist Dry

S = 60%

a. #ry unit +eig*t%. $2e(ifi( gravity of soil solids(. oid atio

5'EN&

Saturated u+it !eigt (γ sat ) = #&.8 $/m3

oisture co+te+t (!) = #".#

E6'E#&γ d , Gs , e

$/'N&a.

γ d= G s

1+e γ w=

2.44

1+0.418 (9.81 kN

m3 ); γ d=16.88

kN

m3

%.

γ sat =Gs+e

1+e γ w=γ sat =

Gs (1+w )

1+e γ w

19.8kN

m3 =

G s (1+0.171 )

1+e (9.81 kN

m3 )

Se=w Gs

(1 ) e=Gs (0.171 ); Gs=2.44

e=0.418

=. /*e unit +eig*t of t*e soil is 95 lb / ft 3

. /*e moisture (ontent of t*is soil is 18. :. >*en t*e

degree of saturation is 90:.#etermine&

a. oid atio%. $2e(ifi( gravity of soil solids(. $aturated unit +eig*t

5'EN&

1+it !eigt (γ ) = &- lft 3

oisture co+te+t(!) = #&.2%egree of Saturatio+(S) = 60

E6'E#&



SOIL SAMPLE

e , Gs , γ s

$/'N&a.

γ =Gs+Se

1+e γ w ;95

lb

ft 3=

G s+0.6e

1+e (62.4 lb

ft 3 )

%.Se=w G s ;0.6 e=0.192G s

Gs= 0.6 e

0.192

*a+ e=0.6912

;%< Gs=2.16

(.

γ sat =Gs+e

1+e γ w ; γ sat =

2.16+0.69121+0.6192 (62.4 lb

ft 3 ); γ sat =105.2

lb

ft 3

8. )or a given soil, t*e follo+ing are given&Gs=2.67

7 moist unit +eig*t, γ =112lb / ft 3

7 and

moisture (ontent, w=10.8 .

#etermine&a. #ry unit +eig*t%. oid atio(. orosityd. #egree of saturation

5'EN&Specific gravity of te soil solid (Gs ) = 2.6"

oist u+it !eigt ( γ ) = ##2 lft 3

oisture co+te+t (!) = #0.8

E6'E#&γ d , e , n , S

$/'N&



SOIL SAMPLE

a.

γ d= G s

1+e γ w ; γ d=

2.67

1+0.6482 (62.4 lb

ft 3 ); γ d=101.09

lb

ft 3

%.

γ =Gs (1+w )

1+e γ w=112

lb

ft

3=

2.67 (1+0.108 )1+e

(62.4

lb

ft

3

); e=0.6482

(.

n= e

1+e=

0.6482

1+0.6482; n=0.3933

d.Se=w G s ; S (0.6482 )=(0.108 )2.67 ; S=44.49

10.efer to ro%lem 8. #etermine t*e +eig*t of +ater, in 2ounds, to %e added 2er (u%i( foot of

soil for&a.=0: degree of saturation%.100: degree of saturation

5'EN&Specific gravity of te soil solid (Gs ) = 2.6"

oist u+it !eigt ( γ ) = ##2 lft 3

oisture co+te+t (!) = #0.8

E6'E#&W w at 80 , W wat 100

$/'N&a.

Se=w G s ; (0.8 )e=0.108 (2.67 )=e=0.3605

γ =Gs+Se

1+e γ w

W

1=2.67+ (0.80 ) (0.3605 )

1+0.3605 (62.4 lb

ft 3 ); W =135.69 lb

W w at 80=135.69 lb−112 lb7

W w at 80=23.69 lb

%.



SOIL SAMPLE

Se=w G s ; (1 ) e=0.108 (2.67 )=e=0.28836

γ sat =Gs+e

1+e γ w

W

1

=2.67+0.28836

1+0.28836 (62.4

lb

ft 3

); W =143.28lb

W w at 100=143.28lb−112lb

W wat 80=31.28 lb

11. /*e moist density of a soil is 1680 kg/m3

. 5iven w=18 andGs=2.73

, determine&

a. #ry density%. orosity(. #egree of saturation

d. Mass of +ater, in kg /m3

, to %e added to rea(* full saturation

5'EN&

ρ=1680kg /m3

w=18

Gs=2.73

E6'E#&γ d , n , S , ρw if S=100

$/'N&

a.γ = ρg

γ =1680 (9.81 )



γ =16480.8 N /m3

γ =Gs (1+w )

1+e (γ w)

16480.8= 2.73 (1+0.18 )1+e

(9810)

e=0.9175

γ d= G s

1+e (γ w)

γ d= 2.73

1+0.9175(9810 ) ; γ d=13966.7797 N /m

3

%.

n= e

1+e

n= 0.9175

1+0.9175; n=0.4785

(.

Se=w Gs

S (0.9175 )=(0.18 ) (2.73 ) ; S=0.5356∨53.56

d.

Se=w Gs



SOIL SAMPLE

(1 ) e= (0.18 ) (2.73 )

e=0.4914

γ =Gs (1+w )

1+e (γ w)

γ =2.73 (1+0.18 )

1+0.4914(9810)

γ =21189.442123 N /m3

γ = ρg

21189.442123= ρ(9.81)

ρ=2159.9839 kg /m3

1. /*e dry density of a soil is 1780kg/m3

. 5ivenGs=2.68

, +*at +ould %e t*e moisture

(ontent of t*e soil +*en saturated?

5'EN&

ρd=1780kg /m3

Gs=2.68

E6'E#&

w , if S=100

$/'N&

)or moisture (ontent,

γ d= ρd g

γ d=1780(9.81)



SOIL SAMPLE

γ d=17461.8 N /m3

γ d= G s

1+e (γ w)

17461.8=2.68

1+e (9810)

e=0.5056

Se=w Gs

1(0.5056)=w(2.68)

w=0.1887

w=18.87

13. /*e 2orosity of a soil is 0.3!. 5ivenGs=2.69

, (al(ulate&

a. $aturated unit +eig*t (kN /m3

)

%. Moisture (ontent +*en moist unit +eig*t ¿17.5 kN /m3

5'EN&

n=0.5

Gs=2.69

E6'E#&

a. γ sat (kN /m3 )

%. w, if γ =17.5 kN /m3



$/'N&

a.

e= n

1+n

e= 0.35

1+0.35

e=0.2593

γ sat =Gs+e

1+e (γ w)

γ sat =2.69+0.2593

1+0.2593(9.81)

γ sat =27.9752 kN /m3

. or moisture co+te+t if γ =17.5 kN /m3

γ =Gs (1+w )

1+e (γ w)

17.5=2.69 (1+w )1+0.2593

(9.81)

w=0.1649

w=16.49



SOIL SAMPLE

14. A saturated soil *as w=23 andGs=2.62

. #etermine its saturated and dry densities in

kg /m3

.

5'EN&

w=23

Gs=2.62

E6'E#&

a. ρsat

%. ρd

$/'N&

a.

γ =γ sat

γ =Gs (1+w )

1+e (γ w )

γ sat =Gs+e

1+e (γ w)

G s (1+w )

1+e (γ w )=

G s+e

1+e (γ w)

G s (1+w )

1+e =

G s+e

1+e

2.62 (1+0.23 )1+e

=2.62+e

1+e

e=0.602 6



SOIL SAMPLE

γ sat =Gs+e

1+e (γ w)

γ sat =2.62+0.6026

1+0.6026(9.81)

γ sat =19.7265 kN /m3

γ sat = ρsat g

19.7265= ρ sat (9.81)

ρsat =2.0108 kg/m3

.

γ d= G s

1+e (γ w)

γ d= 2.62

1+0.6026(9.81)

γ d=16.0378 kN /m3

γ d= ρd g

16.0378= ρ sat (9.81)

ρsat =1.6348 kg/m3

1!. A soil *as e=075, w=21.5 , andGs=2.71

. #etermine&

a. Moist unit +eig*t ;2(f<

%. #ry unit +eig*t (lb / ft 3)

(. #egree of saturation ;:<



5'EN&

e=0.75

w=21.5

Gs=2.71

E6'E#&

a.

ft 3

lb/¿γ ¿

%.

ft 3

lb/¿γ d ¿

(. S

$/'N&

a.

γ =Gs (1+w )

1+e (γ w)

γ =2.71 (1+0.215 )

1+0.75(62.4)

γ =117.4065lb / ft 3

.

γ d= G s

1+e (γ w)

γ d= 2.71

1+0.75(62.4)

γ d=96.6309 lb/ ft 3



SOIL SAMPLE

c.

Se=w Gs

S (0.75)=0.215 (2.71)

S=0.7769

S=77.69

19. /*e soil *as w=18.2 , Gs=2.67

and S=80 . #etermine t*e moist and dry unit

+eig*ts of t*e soil in 2(f.

5'EN&Gs=2.67

w=18.2

S=80

E6'E#&

a. γ

%. γ d

(.

$/'N&

a.

Se=w Gs

0.8(e)=0.182(2.67)

e=0.607 4

γ =Gs (1+w )

1+e (γ w)



SOIL SAMPLE

γ =2.67 (1+0.182 )1+0.6074

(62.4 )

γ =122.515 lb / ft 3

.

γ d= G s

1+e (γ w)

γ d= 2.67

1+0.6074(62.4)

γ d=103.6506 lb/ ft 3

1". /*e moist unit +eig*t of a soil is 112.32lb / ft 3

at a moisture (ontent of 10:. 5iven

Gs=2.7, determine&

a. e

%. $aturated unit +eig*t

5'EN&

γ =112.32lb / ft 3

Gs=2.7

w=10

E6'E#&

a. e

%. γ sat

$/'N&

a.



SOIL SAMPLE

γ =Gs (1+w )

1+e (γ w )

112.32=2.7 (1+0.1 )

1+e (62.4)

e=0.65

.

γ sat =Gs+e

1+e (γ w)

γ sat =2.7+0.651+0.65

(62.4 )

γ sat =126.6909 lb / ft 3

1=. /*e moist unit +eig*ts and degrees of saturation of a soil are given in t*e ta%le.

γ ( pcf ) S ()10!."3 !0

11.9" "!

#etermine&

a. e

%. Gs

5'EN&

γ ( pcf ) S ()

10!."3 !0

11.9" "!

E6'E#&



SOIL SAMPLE

a. e

%. Gs

$/'N&

γ =Gs+Se

1+e ( γ w )

105.73=Gs+0.5e

1+e (62.4 )

Gs−1.194391026 e=105.73

62.4(1 )

112.67=G s+0.75 e

1+e (62.4 )

Gs−1.055608974 e=112.67

62.4(2 )

E@uate ;1< ;<, terefore

Gs=2.6516

e=0.8014

18. efer to t*e ro%lem 1=. #etermine t*e +eig*t of +ater, in l%, t*at +ill %e in 2.5 ft 3

of t*e

soil +*en it is saturated.

5'EN&

V s=2.5 ft 3

+*en saturated

γ ( pcf ) S ()

10!."3 !0



11.9" "!

E6'E#&

W w1 ,

W w2

$/'N&

)or +eig*t of +ater,

γ =Gs+Se

1+e γ w

W w at 50

V s=

Gs+Se

1+e γ w

W w at 50

2.5=

2.6516+0.5 (0.8014 )1+0.8014

(62.4)

W w at 50=264.3271lb

γ =Gs+Se

1+e

γ w

W w at 50

V s=

Gs+Se

1+e γ w

W w at 75

2.5=

2.6516+0.75 (0.8014 )1+0.8014

(62.4)

W w at 75=281.6773lb

4a lapidario a#3 phase-relationships 2015-2016

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