Geotech IV 6 Seepage and Flow Net

7/30/2019 Geotech IV 6 Seepage and Flow Net

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Geotechnical EngineeringLecture

Civil Engineering Term IV

Prof. Kazunori Tabe, Ph.D.

Civil Engineering Section

School of Engineering and TechnologySharda University

Source: http://starb.on.coocan.jp/
http://starb.on.coocan.jp/gallery/p127/index0.htmlhttp://starb.cool.ne.jp/daily/daily2.html


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Lecture Note !

LMS (read in campus only)

Search: kazunori tabe Click lecture note 1, 2, 3, 4 and 5

Sanjay (Rm#501)


3/113

Geotechnical Engineering-SyllabusLecture Contents

1. Syllabus and Introduction (4 hrs)

2. Soil Classification (4hrs)

3. Phase Diagram (4 hrs)4. Permeability of Soils (4 hrs)

5. Effective Stress (4 hrs)

6. Seepage and Flow Nets (4 hrs)

7. Soil Compaction (4hrs)

8. Consolidation and Settlements (4hrs)

9. Shear Strength (4hrs)

10. Slope Stability (4hrs)


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Geotechnical EngineeringTerm Periods and coverage

To Mid Term Exam1. 10th Jan,-14th Jan.

2. 17th Jan. 21st Jan.

3. 24th Jan. 28th Jan.

4. 31st

Jan. 4th

Feb.5. 7th Feb. 11st Feb.

6. 14th Feb. 18th Feb.

7. 21st Feb. 25th Feb.

8. 28th Feb. 4th Mar.

9. 9th Mar. 16th Mar.

Expected coverage:

Introduction (4 hrs),

Soil Classification(4hrs),

Phase Diagram (4 hrs),

Permeability of Soils (4 hrs),

Effective Stress (4 hrs),

Seepage and Flow Nets (4 hrs)

To End Term Exam

1. 21st Mar.-25th Mar.

2. 28th Mar. 1st Apr.

3. 4th Apr. 8th Apr.

4. 11st

Apr. 15th

Apr.5. 18th Apr. 22nd Apr.

6. 25th Apr. 29th Apr.

7. 2nd May 6th May

8. 9th May 16th May

Expected coverage:

Soil Compaction (4 hrs),

Consolidation and Settlement (4hrs),

Shear Strength and Triaxial Tests (4hrs)

Slope Stability (4 hrs)


5/113

What we learned in Geotech

lecture

Clay Atterberg Limit Tests

Soil ClassificationSystem

Phase Diagram

Permeability

Sand

Sieve Analysis

Soil ClassificationSystem

Phase Diagram

Permeability

Soils as constructionmaterials

Clay Water doesnt

move throughclay very well.

Sand

Water movesthrough sandquite well.

Clay Effective Stress

(Fluctuation of WT)

More practical?

Sand

Effective Stress(Fluctuation of WT)

More practical?

MassVolume Relationship StressVolume Relationship


6/113

6. Seepage and Flow Net (1/4)

http://starb.cool.ne.jp/daily/daily0.html


7/113

Geotechnical Engineering -Syllabus

6. Seepage and Flow Nets

Learning Objectives;

Gain an understanding of seepage pressure andits role in causing the quick condition

Gain an understanding of Darcy's law. An ability to draw flow nets and determine the

water head at a given point and the water flowrate

An ability to calculate critical hydraulic gradientand factor of safety against quick condition,

Etc.

Source: jan.ucc.nau.edu

1. Introduction (4 hrs)

2. Soil Classification (4hrs)

3. Phase Diagram (4 hrs)

4. Permeability of Soils (4 hrs)

5. Effective Stress (4 hrs)6. Seepage and Flow Nets (4

hrs)

7. Soil Compaction (4hrs)

8. Consolidation andSettlements (4hrs)

9. Shear Strength (4hrs)

10. Slope Stability (4hrs)


8/113

Core Test Page P.148-154 (esp. p.154)

P.173-199 P. 173-175 (Theory: Laplaces Equation->flow lines and

equipotential lines)

Flow Net

P. 175-180 (flow lines and equipotential lines form Flow

Nets, Use of Flow Nets) P. 180-183 (Method for obtaining Flow Nets)

P. 183-189 (flow and soil condition)

P. 190-199 (Examples and Problems)


9/113

2D Flow-Laplaces Equation

(p.173-175) The flow of water into an element in a

saturated soil

)dim2(

,0

arg

arg

f lowensionalfor

papertheofplanethetolarperpendicudirectionytheinvelocitythev

z

hdirectionverticaltheingradienthydraulicthei

directionverticaltheinvelocityedischofcomponentthev

x

hdirectionhorizontaltheingradienthydraulicthei

directionhorizontaltheinvelocityedischofcomponentthev

planethistolarperpendiculengththedy

papertheofplanetheindirectionverticalthedz

papertheofplanetheindirectionhorizontalthedx

y

z

z

x

x


10/113


(p.173-175)

dzdxdyz

vdxdyvdxdzdy

x

vdzdyvtimeunitinelementtheleavesthatwaterofamountThe

dxdyvdzdyvtimeunitinelementtheenteringwaterofamountThe

zz

xx

zx


11/113


(p.173-175)

)1.7(0sin0

0

.:

dxdzdycez

v

x

v

ordxdyvdzdyvdzdxdyz

vdxdyvdxdzdy

x

vdzdyv

timewithconditionanyinchangenobecanthereflowstatesteadytheIn

dzdxdyz

vdxdyvdxdzdy

x



zx

zxz

zx

x

zz

xx

zx


12/113


(p.173-175)

)2.7(0

;

hom'min

)1.7(0sin0

0

.:

2

2

2

2

z

h

x

h

typermeabilitorespectwithisotropysoilthat

andogeneousissoilthethatandlawsDarcyofvaliditythethatgAssu

dxdzdycez

v

x

v

ordxdyvdzdyvdzdxdyz

vdxdyvdxdzdy

x

vdzdyv


dzdxdyz

vdxdyvdxdzdyx



zx

zxz

zx

x

zzxx

zx


13/113


(p.173-175)

.

.int)2(

.

.2')1(

)2.7(0

;

hom'min

)1.7(0sin0

0

.:

2

2

2

2

equalisheadpotentialtotalthewherespojoining

linesarelinesialequipotenttheandf lowofdirectiontheindicatelinesFlow

linesialequipotentsetothertheandlinesf lowtheasknowniscurvesofsetOne

othereachtoorthogonalcurvesofsetsyieldsEquationsLaplacetheofsolutiongeneralThe

zh

xh

typermeabilitorespectwithisotropysoilthat

andogeneousissoilthethatandlawsDarcyofvaliditythethatgAssu

dxdzdycez

v

x

v

ordxdyvdzdyvdzdxdyzvdxdyvdxdzdy

xvdzdyv


dzdxdyz

vdxdyvdxdzdy

x



zx

zxz

zx

x

zz

xx

zx


14/113

Flow Nets (p.175-180) h=2.25-0.25=2m

Flow lines

a-b, c-d, e-f, etc.

The flow path of water in a pervious

medium Equipotential lines

The points on the flow lines where thetotal head or total head loss is thesame

Flow lines and Equipotential lines formFlow Net .

Numbers of flow lines and equipotential lines It is inconvenient to draw too many of

these lines in a flow net.

Flow lines have to cross equipotentiallines orthogonally.


15/113

Use of Flow Net (p.176-180)

)3.7(1;1;1

;sec

,.,'

3

3

332

2

221

1

11

ab

hkqa

b

hkqa

b

hkq

tiontheofplanethetolarperpendicu

widthunitperf lowtheSokiAflowofratelawsDarcyFrom


16/113


1

,""

3&2

2&1

)3.7(1;1;1

;sec

,.,'

3

3

2

2

1

1

32

21

3

3

332

2

221

1

11

b

a

b

a

b

a

squareselementaryasdrawnarenetflowainfieldsallIf

hhlinesialequipotentsameField

qqchannelf lowsameField

ab

hkqa

b

hkqa

b

hkq


widthunitperflowtheSokiAf lowofratelawsDarcyFrom


17/113


dd

d

n

Hkq

n

Hh

dropsialequipotentofnandf lowtheduringlossheadtotaltheisHIf

hkq

equalbealsowillf ieldeachacrosslossheadtheandequalbewillf ieldeachthroughflowofquantityThe

hhhh

qqqq

EqinaboveallSubstitute

b

a

b

a

b

a

squareselementaryasdrawnarenetflowainf ieldsallIf

hhlinesialequipotentsameField

qqchannelf lowsameField

ab

hkqa

b

hkqa

b

hkq


widthunitperf lowtheSokiAflowofratelawsDarcyFrom

,#,

.

,3.7.

1

,""

3&2

2&1

)3.7(1;1;1

;sec

,.,'

321

321

3

3

2

2

1

1

32

21

3

3

332

2

221

1

11


18/113


)6.7(

)(

)5.7(

,#

n

n

nkHq

netf lowinsquareselementarynotaref ieldsallnb

aIf

n

nkHnqq

islengthunitperchannelsf lowallthroughqf lowofrateThenisnetf lowainchannelsf lowoftheIf

d

f

d

f

f

f


19/113


Uplift pressure (p.179)

Exit gradient and piping (p.179)

Pore-water pressure determination (p.180)


20/113


21/113

Graphical method Upstream ground surface AB is an

equipotential line, since at every point onAB, the total head is constant and equal to

2m (pressure head=2.25m; elevationhead=-0.25m, for the datum shown)

Method for obtaining Flow Nets(p.180-183)


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Similarly, CD is an equipotential line withtotal head equal to 0m at every point on it(pressure head=0.25m and elevationhead=-0.25m)



23/113





From point A, water flows down the sheetpile on the upstream side, touched the tip ofthe sheet pile E and moves up on thedownstream face EC. Thus, AEC is a flowline.



24/113





From point A, water flows down the sheetpile on the upstream side, touched the tip ofthe sheet pile E and moves up on thedownstream face EC. Thus, AEC is a flowline.

FG is a flow line, since water must flowalong the impermeable surface and cannotpenetrate the impermeable layer.



25/113

Confined flowFlow space was completely defined by the 4boundary conditions and flow itself was limitedto this space.

Unconfined flowThe flow space is not fully defined.

Flow Net Conditions (p. 183-189)

Confined & Unconfined (p.183-186)


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Flow Net Conditions (p. 183-189)Unconfined (Homogeneous and Isotropic) (p.183-186)

The upstream slope AC is a boundary equipotential line (=H), since at everypoint on it, the total head is constant.

The discharge surface FH is a boundary equipotential line with zero total head.

The top flow line would begin at point C.

The exact flow path of the water is not known. However, at every point on thetop line, the pressure head is zero (=atmospheric pressure). Therefore, the totalhead is simply equal to the elevation head.


27/113

Flow Net Conditions (p. 183-189)Unconfined (Homogeneous and Isotropic) (p.183-186)

There must be equal vertical intervals H between the points of intersection ofsuccessive equipotential lines with top flow line. (Kozeny, Casagrande)

Casagrande , A. (1937) Seepage Through Dams, reprinted in the Boston Society of Civil Engineers,Contributions to Soil Mechanics, 1925-1940. This reference quated J.S. Kozenys aproach.


28/113

Flow Net Conditions (p. 183-189)

Anisotropic ->P.186-188

Nonhomogeneous->p.188-189


29/113

Thank you.Source: http://starb.on.coocan.jp/
http://starb.on.coocan.jp/daily/daily0.html


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Geotechnical EngineeringLectureCivil Engineering Term IV


Civil Engineering Section

School of Engineering and TechnologySharda University



31/113




32/113

Seepage and Flow Nets

What is seepage pressure? Why is it important toGeotechnical engineering?

Seepage pressure is the pressure due to viscousfriction exerted by the water flowing through soilpores. Seepage pressure can increase or decreasethe effective stress in a soil mass.

When seepage pressure acts against gravity, quick

sand condition occurs. This is important in the stability analysis of earth

structures subjected to the action of seepage.


33/113

What are the applications of flow net? What are the characteristics offlow net?

Flow nets are used to determine hydrostatic pressure,

seepage pressure, and exit gradient under 2D or 3D flowconditions. A flow net is made up of flow lines and equipotential lines,

where they meet at right angles to each other and formapproximately square elements.

Flow lines are the path along which the water travels from

upstream to downstream in permeable saturated soil. Theequipotential lines represent lines along which the total headis constant. The quantity of water flowing through each flowchannel is the same as well as the potential drop occurringbetween two successive equipotential lines.

Seepage and Flow Nets


34/113

Seepage and Flow Net calculation 1

A new building with deepbasement is proposed to construct

over a site. The boring data showsa thin layer of impervious clay isencountered 15m below theground water table, which is twofeet below grade. Ignoring thepressure of sheeting to support

the excavation, determine themaximum depth of excavationwithout the danger of blow out ifthe saturated unit weight of thesandy soil is 1900 kg/m3.

15m 1900kg/m3 1000kg/m3

1900kg/m3


35/113


15m 1900kg/m3 1000kg/m3

1900kg/m3

DHP

DP

layerofbottomtheonpressureupwardandDownward

Step

wwup

wsoildown

:

:1


36/113


15m 1900kg/m3 1000kg/m3

1900kg/m3

mH

D

DHD

PPwhenoccursoutblow

excavationofDepth

Step

DHPDP


Step

soil

ww

wwwsoil

updown

wwup

wsoildown

89.7

:

:2

:

:1


37/113


15m 1900kg/m3 1000kg/m3

1900kg/m3

.8:

89.7

:

:2

:

:1

mthangreaterisexcavationofdepththeifoccursoutBlowAnswer

mH

D

DHD

PPwhenoccursoutblow

excavationofDepth

StepDHP

DP


Step

soil

ww

wwwsoil

updown

wwup

wsoildown


38/113

Water is flowing through two types of soils, gravel andsand, under a constant head with an area of 20 cm2.Determine:

Seepage pressures and piezometric head at point A.

If 35% of the excess seepage pressure is lost as waterflows upward through gravel, what is the seepagepressufre and piezometric head at point B?

What is the quantity of water flowing through thegravel if its hydraulic conductivity is 2.6m/day?

What is the hydraulic conductivity of the sand?


20cm

15cm

10cm


39/113


20cm

15cm

10cm

220

6.2,20,15,10

:

cmAday

mkcmHcmHcmH

Given

gravelwsandgravel


40/113


20cm

15cm

10cm

cmHHHH

cmHHH

BpoatheadcpiezometriandpressureseepageeDeter

cmHHHH

cmHH

ApoatheadcpiezometriandpressureseepageeDeter

Step

cmA

day

mkcmHcmHcmH

Given

grave lwpiezoApiezoB

wseepageAseepageB

wsandgravelpiezoA

wseepageA

gravelwsandgravel

28102035.04535.0

132035.02035.0

:intmin

45101520

20

:intmin

:1

20

6.2,20,15,10

:

..

..

.

.

2


41/113


20cm

15cm

10cm day

cmAikq

H

Hi

gravelinratef lowCalculate

Step

gravelgravel

gravel

wgravel

3

36952070.0260

70.0

10

2035.035.0

:

:2


42/113


20cm

15cm

10cm

87.015

2035.0135.01

:

:

:3

sand

wsand

H

Hi

layersandthroughgradienthydraulic

sandtheoftyconductivihydraulicCalculate

Step


43/113


20cm

15cm

10cm

daym

daycm

Aiqk

layersgravelandsandthroughplacetakesf lowsameThe

Step

sand

sand 12.22122087.0

3695

:4


44/113

Water is flowing through the soil layers shown below.Determine the total stress, effective stress, and water pressure at point A and point B.


1800 kg/m31.3 cm/s

2000 kg/m30.6 cm/s

12m

9m

12m


45/113


1800 kg/m31.3 cm/s

2000 kg/m30.6 cm/s

12m

9m

12m

32322

1311

1000,sec

6.0,2000,12

21,sec

3.1,1800,21:

m

kgcmk

m

kgmL

mHcm

km

kgmLGiven

w

w


46/113


1800 kg/m31.3 cm/s

2000 kg/m30.6 cm/s

12m

9m

12m

mhmhhh

hhce

hh

hcmhcm

L

hi

L

hi

where

AikAik

layersoileachforlostheadwatereDeter

Step

m

kgcmk

m

kgmL

mHcm

km

kgmLGiven

w

w

3.5,7.6128.0

12)129()12912(sin

8.012sec6.021sec3.1

,

:

:min

:1

1000,sec

6.0,2000,12

21,sec

3.1,1800,21:

1222

21

21

21

2

22

1

11

222111

32322

1311


47/113


1800 kg/m31.3 cm/s

2000 kg/m30.6 cm/s

12m

9m

12m

2

2

22211

2

211

211

498001200061800

12000121000

61800122000211800

:int,,

221001570037800

157003.5211000

37800211800

:int,,

:2

m

kg

m

kgHu

m

kgLL

BpoatstresseffectiveandpressurewaterporestresstotalCalculate

m

kg

m

kghLu

m

kgL

ApoatstresseffectiveandpressurewaterporestresstotalCalculate

Step

wwB

B

wA

A


48/113

What is the seepage flow rate, per unit width,under the concrete dam shown below?


23m

10m

15m

3m

0.01 cm/s

0.0000001 cm/s


49/113



50/113


mwidthcm

kmHmHGiven sandww 1,sec

01.0,3,10: 21


51/113


mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

ww

sandww

7310

:

:1

1,sec

01.0,3,10:

21

21


52/113


day

mcm

N

NHkq

damconcretetheunderratef lowSeepage

Step

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

f

sand

ww

sandww

33

21

21

23sec

5.2621008

370001.0

:

:2

7310

:

:1

1,sec

01.0,3,10:


53/113



54/113

Geotechnical EngineeringLectureCivil Engineering Term IV


Civil Engineering SectionSchool of Engineering and Technology

Sharda University



55/113




56/113

Draw a flow net for sheet pile shownbelow:

What is the piezometric head above thedatum at point A and B?

What is the flow rate below the sheet pilein cubic meter per day if the structure is150 m wide?


3m

12m

10m

23m

=0.0000001 cm/s


57/113


3m

12m

10m

23m

=0.0000001 cm/s


58/113


mwidthcm

kmHmHGivensandww

150,

sec

01.0,3,10: 21


59/113


mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

ww

sandww

875.08

7

7310

:

:1

150,sec

01.0,3,10:

21

21


60/113


mhHH

BpoatheadcPiezometri

mhHH

ApoatheadcPiezometri

headcPiezometri

Step

mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

wB

wA

d

ww

sandww

1.405.4875.08.6108.6

:int

7.86875.8875.05.1105.1

:int

:

:2

875.08

7

7310

:

:1

150,sec

01.0,3,10:

2

1

21

21


61/113


day

m

daycm

mcm

widthN

N

Hkq

damthethroughrateFlow

Step

mhHH

BpoatheadcPiezometri

mhHH


headcPiezometri

Step

mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

f

sand

wB

wA

d

ww

sandww

3

2

1

21

21

45361508

4

7

sec246060

100sec01.0

:

:3

1.405.4875.08.6108.6

:int

7.86875.8875.05.1105.1

:int

:

:2

875.08

7

7310

:

:1

150,sec

01.0,3,10:


62/113

Calculate the factor of safety against downstream heave for the sheetpile shown below. The saturated unit weight of the soil is 2000 kg/m3.

Reference: Alam Singh, Modern Geotechnical Engineering, 3rd Ed.CBS, pp. 202-204.


3m

10m

15m

6m


63/113

Calculate the factor of safety against downstream heave for the sheetpile shown below. The saturated unit weight of the soil is 2000 kg/m3.


3m

10m

15m

6m


64/113


mDmHmHm

kg

m

kg

Given

wwsandw 6,3,10,2000,1000

:

2133


65/113


m

HH

H

mHHH

zoneheavethebelowheadAverage

Step

mDmHmHm

kg

m

kg

Given

avg

ww

wwsandw

74.22

76

7.17

6

3

2

6

7.1

6

3

7310

:

:1

6,3,10,2000,1000

:

21

2133


66/113


46.06

74.2

:

:2

74.22

76

7.176

3

2

6

7.1

6

3

7310

:

:1

6,3,10,2000,1000

:

21

2133

D

Hi

gradienthydraulicAverage

Step

mHH

H

mHHH


Step

mDmHmHm

kg

m

kg

Given

avg

avg

avg

ww

wwsandw


67/113


17.2

100046.0

1000

100010002000

:

:3

46.06

74.2

:

:2

74.22

76

7.17

6

3

2

6

7.1

6

3

7310

:

:1

6,3,10,2000,1000

:

3

21

2133

wavg

s

wsand

avg

avg

avg

ww

wwsandw

i

F

m

kg

heavedownstreamagainstsafetyofFactor

Step

D

Hi

gradienthydraulicAverage

Step

m

HH

H

mHHH


Step

mDmHmHm

kg

m

kg

Given


68/113

Draw a flow net for the sheet pile structureshown below.Compute the quantity of flow in cubic meter

per day.What is the head at point A & B?


12m

10m

23m

3m


69/113


12m

10m

23m

3m


70/113


mwidthcm

kmHmH

Given

ww 1,sec

05.0,3,10

:

21


71/113


mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmH

Given

d

ww

ww

7.010

7

7310

:

:1

1,sec05.0,3,10

:

21

21


72/113


mhHHmhh

mhHHmhh

datumtheaboveheadcPiezometri

Step

mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmH

Given

BwBB

AwAA

d

ww

ww

33.467.510,67.57.01.81.8

67.833.110,33.17.09.19.1

:

:2

7.010

7

7310

:

:1

1,sec

05.0,3,10

:

1

1

21

21


73/113


day

m

daycm

mcmwidth

N

HNkq

structurethebelowrateFlow

Step

mhHHmhh

mhHHmhh

datumtheaboveheadcPiezometri

Step

mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmH

Given

d

f

BwBB

AwAA

d

ww

ww

3

1

1

21

21

2.151110

57sec246060

100sec05.0

:

:3

33.467.510,67.57.01.81.8

67.833.110,33.17.09.19.1

:

:2

7.010

7

7310

:

:1

1,sec

05.0,3,10

:


74/113

For the sheet pile shown below, using a flownet:

What is the piezometric head above the groundlevel at point A and B?

What is the flow rate below the structure incubic meter per day if the structure is100 m wide?

What is the factor of safety against down

stream heave if the saturated unit weight ofsand is 1800 kg/m3?

Reference: Alam Singh, Modern GeotechnicalEngineering, 3rd Ed. CBS, pp. 202-204.


12m

10m

23m


75/113


12m

10m

23m P1 P2

A B


76/113


mDm

kg

m

kg

cmkmwidthmHmHGiven

wsand

sandww

12,1000,1800

sec01.0,100,0,10:

33

21

P1 P2

A B


77/113


mN

Hh

mHHH

dropsheadCalculate

Step

mDm

kg

m

kg

cmkmwidthmHmHGiven

d

ww

wsand

sandww

25.18

10

10010

:

:1

12,1000,1800

sec01.0,100,0,10:

21

33

21

P1 P2

A B


78/113


mhHHBpoatheadcPiezometri

mhHH


headcPiezometri

Step

mN

Hh

mHHH

dropsheadCalculate

Step

mDm

kg

m

kg

cmkmwidthmHmHGiven

wB

wA

d

ww

wsand

sandww

75.125.16.6106.6:int

375.825.13.1103.1

:int

:

:2

25.18

1010010

:

:1

12,1000,1800

sec01.0,100,0,10:

1

1

21

33

21

P1 P2

A B


79/113


day

m

daycm

mcmwidth

N

NHkq


Step

d

f

sand

3

43201008

410

sec246060

100sec01.0

:

:3

P1 P2

A B


80/113


:

:4

43201008

410

sec246060

100sec01.0

:

:3

3

heavestreamdownagainstsafetyofFactor

Step

day

m

daycm

mcmwidth

N

NHkq


Step

d

f

sand

P1 P2

A B


81/113


mPP

H

mhHP

mhHP

zoneheavethebelowheadaverageheavestreamdownagainstsafetyofFactor

Step

day

m

daycm

mcmwidth

N

NHkq


Step

avg

w

w

d

f

sand

875.32

75.25

2

75.225.18.5108.5

525.10.4100.4

:

:4

43201008

410

sec246060

100sec01.0

:

:3

21

12

11

3

P1 P2

A B


82/113


32.012

875.3

875.32

75.25

2

75.225.18.5108.5

525.10.4100.4

:

:4

43201008

410

sec246060

100sec01.0

:

:3

21

12

11

3

D

Hi

gradienthydraulicaverage

mPP

H

mhHP

mhHP

zoneheavethebelowheadaverage


Step

day

m

daycm

mcmwidth

N

NHkq


Step

avg

avg

avg

w

w

d

f

sand

P1 P2

A B


83/113


5.2

100032.0

800

80010001800

32.012

875.3

875.32

75.25

2

75.225.18.5108.5

525.10.4100.4

:

:4

43201008

410

sec246060

100sec01.0

:

:3

3

21

12

11

3

wavg

s

wsand

avg

avg

avg

w

w

d

f

sand

i

F

m

kg

heavedownstreamagainstsafetyofFactor

D

Hi

gradienthydraulicaverage

mPP

H

mhHP

mhHP

zoneheavethebelowheadaverage


Step

day

m

daycm

mcmwidth

N

NHkq


Step

P1 P2

A B


84/113



85/113

Geotechnical EngineeringLecture

Civil Engineering Term IV


Civil Engineering SectionSchool of Engineering and Technology

Sharda University



86/113




87/113

For the hydraulic structure shownbelow:

What is the piezometric head above thedatum at point A, B, and C?

What is the flow rate below the

structure in cubic feet per day if thestructure is 100 m wide?


3m

30m

12m

15m


88/113


3m

30m

12m

15m


89/113


mwidthcm

kmHmHGiven ww 100,sec

01.0,3,12: 21


90/113


7.069.013

9

9312

:

:1

100,sec

01.0,3,12:

21

21

d

ww

ww

N

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven


91/113


mhHCmhh

mhHBmhh

mhHAmhh

datumtheaboveheadcpiezometriCalculate

Step

N

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

CwC

BwB

AwA

d

ww

ww

58.442.712,42.77.06.106.10

68.632.512,32.57.06.76.7

09.1191.012,91.07.03.13.1

:

:2

7.069.013

9

9312

:

:1

100,

sec

01.0,3,12:

1

1

1

21

21


92/113


day

m

daycm

mcmwidth

N

NHkq

structurethebelowratef lowCalculate

Step

mhHCmhh

mhHBmhh

mhHAmhh


Step

N

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

f

CwC

BwB

AwA

d

ww

ww

3

1

1

1

21

21

2392610013

49

sec246060

100sec01.0

:

:3

58.442.712,42.77.06.106.10

68.632.512,32.57.06.76.7

09.1191.012,91.07.03.13.1

:

:2

7.069.013

9

9312

:

:1

100,sec

01.0,3,12:


93/113

Draw a flow net below the dam shownbelow:

What is the piezometric head above thedatum at point A, B, and C?

What is the flow rate between the dam incubic feet per day if the structure is 1000m wide?


3m

7.5m

25m

12m


94/113


3m

7.5m

25m

12m


95/113


mwidthcm

kmHmHGivensandww

1000,sec

02.0,3,5.7:21


96/113


mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

ww

sandww

5.09

5.4

5.435.7

:

:1

1000,sec

02.0,3,5.7:

21

21


97/113


mhHH

mhHH

mhHH


Step

mN

Hh

mHHH

dropsheadCalculateStep

mwidthcm

kmHmHGiven

wC

wB

wA

d

ww

sandww

45.45.01.65.71.6

9.35.02.75.72.7

65.65.07.15.77.1

:

:2

5.09

5.4

5.435.7

::1

1000,sec

02.0,3,5.7:

1

1

1

21

21


98/113


day

m

daycm

mcmwidth

N

NHkq


Step

mhHH

mhHH

mhHH


Step

mN

Hh

mHHH

dropsheadCalculate

Step

mwidthcm

kmHmHGiven

d

f

wC

wB

wA

d

ww

sandww

3

1

1

1

21

21

3456010009

45.4

sec246060

100sec02.0

:

:3

45.45.01.65.71.6

9.35.02.75.72.7

65.65.07.15.77.1

:

:2

5.09

5.4

5.435.7

:

:1

1000,sec

02.0,3,5.7:

Seepage through an Earth Dam on


99/113

Seepage through an Earth Dam onImpervious Base

Das,B.M. Principles of Geotechnical Engineering, 6th Ed. Thomson, pp. 215-216

Alam Singh Modern Geotechnical Engineering , third edition, CBS Publishers &Distributors PVT. Ltd.

C. Venkatramaiah Geotechnical Engineering, revised third edition, New AgeInternational Publishers

Dr. K.R. Arora Soil Mechanics and Foundation Engineering, StandardPublishers Distributors

)sin)(tan( widthLkq soil

2

2

2

2

sincoscos

wHddL


100/113


For the earth dam shown below,using a flow net:

What is the piezometric head atpoint A, B, and C?What is the flow rate throughthe dam in cubic meter per dayif the dam is 600 m wide?


What is the piezometric head atpoint a, B, and C?

10m12m10m

3m

10m


101/113



What is the piezometric head atpoint a, B, and C?

10m12m10m

3m

10m


102/113


mhmdmdmd

cmkmwidthmHGiven

dam

soilw

13310,10,12,10

,sec

00004.0,500,10:

321


103/113


m

HddL

md

mHdh

damtheexistwillwaterthewhereeDeter

Step

mhmdmdmd

cmkmwidthmHGiven

w

wdam

dam

soilw

8.11.52sin

10

1.52cos

58.26

1.52cos

58.26

sincoscos

58.26)3.0(101210

75.729.1

10tan

,1.521013tantan

:min

:1

13310,10,12,10

,sec

00004.0,500,10:

2

2

2

2

2

2

2

2

1

1

1

321


104/113


mHCpoatheadcPiezometri

mhHHBpoatheadcPiezometri

mhHHApoatheadcPiezometri

headcPiezometri

Step

C

B

A

0:int

4.271.07.10107.10:int

29.971.00.1100.1:int

:

:2


105/113


day

m

daycm

mcmwidthLkq

damthethroughrateflowtheeertomethodSecond

day

m

daycm

mcmwidth

N

NHkq


Step

soil

d

f

3

3

5.311.52sin1.52tan5008.1sec246060

100sec00004.0)sin)(tan(

:mindet

)2(

3750014

310

sec246060

100sec00004.0

:

)1(

:3


106/113


23m23m 30m

6m

6m18m

Draw a flow net in the earth damshown below. Compute the quantityof flow in cubic meter per daythrough the dam using twomethods.What is the head at point A & B?


107/113


23m23m 30m

6m

6m18m


108/113


mhmLmLmLmh

cmkmHmHGiven

dam

soilww

24618,23,30,23,6

,sec00007.0,6,18:

321

21


109/113


mHHdd

L

mxLxd

mHh

x

mHLh

damtheexistwillwaterthewhereeDeter

Step

mhmLmLmLmh

cmkmHmHGiven

ww

wdam

wdam

dam

soilww

9.18.43sin

618

8.43cos

7.56

8.43cos

7.56

sincoscos

7.56)5.123.05.12(7.17307.17)3.0(

7.178.43tan

624

8.43tan

5.1296.0

6188.43tan

,8.432324tantan

:min

:1

24618,23,30,23,6

,sec

00007.0,6,18:

2

2

2

2

2

2

21

2

2

2

2

1

1

1

321

21


110/113


mN

HhmHHH

dropsheadCalculate

Step

d

ww 6.020

12,12618

:

:2

21


111/113


mH

mhHH

headcPiezometri

Step

m

N

HhmHHH

dropsheadCalculate

Step

B

A

d

ww

0

84.96.09.2126.3

:

:3

6.0

20

12,12618

:

:2

21


112/113


day

m

daycm

mcmwidthLkq

damthethroughf lowcalculatetomethodsSecond

daym

daycmmcmwidth

NNHkq

mwidth


Step

soil

d

f

soil

3

3

08.08.43sin8.43tan19.1sec246060

100sec00007.0)sin)(tan(

:

)2(

11.0120312sec246060

100sec00007.0

1

:

)1(

:4


113/113


Geotech IV 6 Seepage and Flow Net

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Transcript of Geotech IV 6 Seepage and Flow Net