02/12/1434

1

3 th

lect

ure

1

5-D

IME

NS

ION

ING

AN

DS

TAB

ILIT

YO

FW

EIR

:

02/12/1434

2

5-D

IME

NS

ION

ING

AN

DS

TAB

ILIT

YO

FW

EIR

:

Wei

ris

subj

ecte

dto

thre

egr

oups

offo

rces

1-D

eriv

ing

For

ces:

Due

tow

ater

thru

stan

daf

fect

sho

rizon

tal

lyon

the

wei

rwal

l

2-S

cour

:Due

tofa

lling

surg

eca

usin

gsc

our

ofth

ebe

dso

ilre

sulti

ngin

asc

our

hole

sat

the

dow

nst

ream

side

ofw

eirf

ound

atio

n.(S

cour

Leng

th).

3-S

eepa

ge:

Due

tope

rcol

atio

nof

wat

erin

the

unde

rlyin

gpe

rm

eabl

eso

ilbe

dca

usin

gbu

oyan

cyof

the

stru

ctur

ean

der

osio

nof

bed

soil

atdo

wn

stre

amsi

deof

foun

datio

n.(P

erco

latio

nLe

ngth

).

4

Flo

wn

et

A n

etw

ork

of s

elec

ted

stre

am li

nes

and

equi

pote

ntia

l lin

es.

SE

EP

AG

E T

HR

OU

GH

PE

RM

EA

BLE

MAT

ER

IAL

See

page

(Per

cola

tion)

Str

eam

line

is s

impl

y th

e pa

th o

f a w

ater

mol

ecul

es fr

om u

pstr

eam

to

dow

nstr

eam

, tot

al h

ead

stea

dily

dec

reas

es a

long

the

stre

am li

ne..

02/12/1434

3

5

Hyd

rau

lic

gra

die

nt

‘ i

‘ be

twee

n A

and

Bis

the

tota

l hea

d lo

ss p

er u

nit l

engt

h.

AB

BA l

TH

TH

i−

=

leng

th A

B, a

long

the

stre

am li

ne

Da

rcy

’s L

aw

Vel

ocity

(v)

of fl

ow i

s pr

opor

tiona

l

To th

e hy

drau

lic g

radi

ent (

i)

v =

ki

Per

mea

bilit

y

•or

hyd

raul

ic c

ondu

ctiv

ity

•un

it of

vel

ocity

(cm

/s)

Wha

t is

the

max

imum

H.G

. al

ong

all t

he s

truc

ture

life

?

6

For

curv

elin

ear

squa

res,

a=b

02/12/1434

4

7

Pip

ing

in

Gra

nu

lar

So

ils

At t

he d

owns

trea

m e

nd o

f fou

ndat

ion,

If i e

xitex

ceed

s th

e cr

itica

l hyd

raul

ic g

radi

ent (

i c),

first

ly th

e so

il gr

ains

at e

xit g

et w

ashe

d aw

ay. T

his

phen

omen

on p

rogr

esse

s to

war

ds

the

dow

nstr

eam

, for

min

g a

free

pas

sage

of w

ater

(“p

ipe”

).

lhi ex

it∆∆

=E

xit h

ydra

ulic

gr

adie

nt

datu

mW

EIR

impe

rvio

us s

trat

a

soil

h

∆h =

tota

l he

ad d

rop

∆l

exitc

pipi

ngii

F=

Typi

cally

5-

10

Fac

tor

of s

afet

y ag

ains

t pip

ing

no s

oil;

all

wat

er

unit

subm

erge

dic

'=

=γ

e1

1G

'

+−=

γ

8

i c>

i

PIP

ING

PH

EN

OM

EN

ON

WIL

L TA

KE

PLA

CE

ciLh

i=

=cih

L=

h 1

=

csa

fei

FL

So,

The

Cre

ep le

ngth

, “th

e sh

orte

st s

trea

m li

ne”,

mus

t not

less

than

L s

afe

to e

nsur

e sa

fety

aga

inst

pip

ing

at D

S o

f the

str

uctu

re fl

oor.

QU

ICK

SA

ND

CO

ND

ITIO

N,

σ v '

= 0

i=i c=

γ‘

σ v '

< 0

The

n,

02/12/1434

5

9

EM

PR

ICA

L D

IME

NS

ION

S:

mt

)7

5.0

5.0(1

−=

max

2)0.1

8.0(H

t−

=

mL

)0.50.3(

1−

=2/)

(5.0

dsw

BL

CL

L−

+=

max

6.0

HC

Lb

s=

AB

BA l

TH

TH

i−

=

10

A-

BL

IGH

’S T

heo

ry :

max

HC

Lb

B= B

ligh’

s co

ef. d

epen

ds o

n th

e so

il ty

pe

Max

. H

ead

diffe

renc

e =

WL

-

WL

us

d

s

CL

-

BL

Whi

ch is

big

ger

vH

act

LL

L

+

=

Per

cola

tio

n

Th

eory

Bli

gh

La

ne

02/12/1434

6

11

BLI

GH

TH

EO

RY:

�

Isus

edin

desi

gnin

gof

impe

rvio

usflo

orfo

rsu

bsu

rfac

eflo

w.

�It

isdi

rect

lyde

pend

ing

onth

epo

ssib

ilitie

sof

perc

olat

ion

inpo

rous

soil

onw

hich

the

floor

(apr

on)

isbu

ilt.

�W

ater

from

upst

ream

perc

olat

esan

dcr

eeps

(or

trav

el)

slow

lyth

roug

hw

eir

base

and

the

subs

oilb

elow

it.

�T

hehe

adlo

stby

the

cree

ping

wat

eris

prop

ortio

nal

toth

edi

stan

ceit

trav

els

(cre

eple

ngth

)al

ong

the

base

ofth

ew

eir

prof

ile.

�T

hecr

eep

leng

thm

ust

bem

ade

asbi

gas

poss

ible

soas

topr

even

tthe

pipi

ngac

tion.

�T

his

can

beac

hiev

edby

prov

idin

gde

epve

rtic

alcu

t-of

fsor

shee

tpile

s

12

Lim

itatio

ns o

f Blig

h's

theo

ry

1.T

his

theo

rym

ade

nodi

stin

ctio

nbe

twee

nho

rizon

tal

and

vert

ical

cree

p.

2.D

idno

tex

plai

nth

eid

eaof

exit

grad

ient

-sa

fety

aga

inst

unde

rmin

ing

cann

otsi

mpl

ybe

obta

ine

db

yco

nsid

erin

ga

flata

vera

gegr

adie

ntbu

tby

keep

ing

this

grad

ient

will

belo

wcr

itica

l.

3.N

odi

stin

ctio

nbe

twee

nou

ter

and

inne

rfa

ces

ofsh

eet

pile

sor

the

inte

rmed

iate

shee

tpile

s,w

here

asfr

omin

vest

igat

ion

itis

clea

r,tha

tth

eou

ter

face

sof

the

end

shee

tpile

sar

em

uch

mor

eef

fect

ive

than

inne

rone

s.

4.Lo

sses

ofhe

addo

esno

ttak

epl

ace

inth

esa

me

prop

ortio

nsas

the

cree

ple

ngth

.A

lso

the

uplif

tpr

essu

redi

strib

utio

nis

not

linea

rbu

tfo

llow

asi

necu

rve.

02/12/1434

7

13

)(

1

sw

HL

LL

L+

+=

)(

21

1t

yt

Lv

++

=2

2)

(t

BL

BL

dsus

+−

=

14

02/12/1434

8

15

)(

2

12

11

ss

ww

HL

LL

LL

L+

++

+=

)(

32

11

ty

yt

Lv

++

+=

32

)(

tB

LB

Lds

us+

−=

usB

L

dsB

L

16

max

HC

LL

L= La

ne’s

coe

f. D

epen

ds o

n th

e so

il ty

pe

Max

. H

ead

diffe

renc

e =

WL

-

WL

us

d

s

CL

-

BL

Whi

ch is

big

ger

vH

act

LL

L

31+

=

B-

LA

NE

’S

Th

eory

:

Lane

con

side

rs th

at th

e ve

rtic

al p

ortio

n of

cre

ep is

mor

e ef

fect

ive

in

resi

stin

g w

ater

flow

in th

e so

il th

an th

e ho

rizon

tal o

ne…

……

.WH

Y?

02/12/1434

9

17

In b

oth

case

s of

BLI

GH

or L

AN

E, t

he a

ctua

l len

gth,

Lac

t,s

houl

d no

t les

s

than

the

theo

retic

al c

reep

leng

th, L

Bor

LL

i-If

L

act=

LB

, the

per

cola

tion

is s

afe.

ii-If

L

act>

LB

, the

per

cola

tion

is m

ore

safe

., ca

lcul

ate

the

mod

ified

' b

C

max

'

HLC

act

b=

iii-

If

Lac

t<

LB

, the

per

cola

tion

is u

nsaf

e, in

crea

seth

e ac

tual

cre

ep le

ngth

DL

Lac

tB

+= If

D <

4m

, ext

ent f

loor

apr

on a

t DS

by D

If D

> 4

m, p

rovi

de s

heet

pile

s

-m

in. d

epth

of e

ach

row

is 2

.0m

and

the

No.

of r

ows

is d

efin

ed a

ccor

ding

to

D

-H

oriz

onta

l dis

tanc

e be

twee

n an

y tw

o ro

ws

not l

ess

than

sum

of i

ts d

epth

s

-S

ides

sho

uld

be c

lose

d

max

'

HLC

act

l=

' lC

18

iii-

If

Lac

t<

LL

, the

per

cola

tion

is u

nsaf

e, in

crea

seth

e ac

tual

cre

ep le

ngth

DL

Lac

tL

+= If

D <

(4/

3 )m

, ext

ent f

loor

apr

on a

t DS

by 3

D

If D

> (

4/3

)m, p

rovi

de s

heet

pile

s p

iles

( m

in. d

epth

of e

ach

row

is 2

.0m

and

the

No.

of r

ows

is d

efin

ed a

ccor

ding

to D

)

US

ING

LA

NE

’S T

HE

OR

Y

02/12/1434

10

19

20

Wha

t is

the

best

pos

ition

for

the

shee

t pile

s an

d w

hy?

02/12/1434

11

21

So

il t

yp

eB

lig

h’s

Co

eff

icie

nt

Cb

La

ne

’sC

oe

ffic

ien

t

CL

Cri

tica

l g

rad

ien

t

i cV

ery

fin

e

sa

nd

/sil

t18

8.5

0.12

Fin

e

s

an

d15

70.

14

Med

ium

san

d6

0.17

Co

arse

sa

nd

125

0.2

Fin

e

g

rav

el

40.

25

Med

ium

gra

ve

l3.

50.

29

Co

arse

gra

ve

l &

co

bb

les

30.

33

Bo

uld

ers

wit

h s

om

e co

bb

les

& g

rave

l5

-9

2.5

0.4

So

ftcl

ay

30.

33

Med

ium

cla

y2

0.5

Har

d

cla

y1.

80.

56

2

Lb

CC

≈

Per

cola

tio

n C

oef

fici

ents

:

22

Com

mon

cau

ses

of w

eir

failu

re in

clud

e:

•Exc

essi

ve a

nd p

rogr

essi

ve d

owns

trea

m e

rosi

on,

both

from

with

in th

e st

ream

and

thro

ugh

late

ral e

rosi

on o

f the

ban

ks.

•Ero

sion

of i

nade

quat

ely

prot

ecte

d ab

utm

ents

.

•Hyd

raul

ic r

emov

al o

f fin

es a

nd o

ther

sup

port

mat

eria

l fro

m

dow

nstr

eam

pro

tect

ion

(gab

ions

and

apr

ons)

res

ultin

g in

ero

sion

of

the

apro

n pr

otec

tion.

•Det

erio

ratio

n of

the

cut

off a

nd s

ubse

quen

t los

s of

con

tain

men

t

•Add

ition

al a

spec

ts s

peci

fic to

con

cret

e, r

ock-

fill o

r st

eel s

truc

ture

s.

02/12/1434

12

23

The

mai

n ca

uses

for

wei

r fa

ilure

incl

ude:

1. P

ipin

gP

ipin

g is

cau

sed

by g

roun

dwat

er s

eepi

ng o

ut o

f the

ban

k fa

ce.

Gra

ins

are

deta

ched

and

ent

rain

ed b

y th

e se

epag

e flo

w a

nd m

ay b

e tr

ansp

orte

d aw

ay f

rom

the

bank

face

by

surf

ace

runo

ff ge

nera

ted

by t

he s

eepa

ge,

if th

ere

is s

uffic

ient

vol

ume

of fl

ow.

2. R

uptu

re o

f flo

or d

ue to

upl

ift:

If th

e w

eigh

t of

the

floor

is in

suffi

cien

t to

resi

st th

e up

lift p

ress

ure,

the

flo

or m

ay b

urst

. Thi

s bu

rstin

g of

the

floor

red

uces

the

effe

ctiv

e le

ngth

of

the

impe

rvio

us fl

oor,

whi

ch w

ill r

esul

ting

incr

easi

ng e

xit

grad

ient

, and

can

cau

se f

ailu

re o

f th

e w

eir.

3. R

uptu

re o

f flo

or d

ue to

suc

tion

caus

ed b

y st

andi

ng w

aves

Hyd

raul

ic ju

mp

form

ed a

t the

dow

nstr

eam

of w

ater

.

24

PR

EC

AU

TIO

NS

AG

AIN

ST

PE

RC

OL

AT

ION

:

1-P

rovi

de

con

cret

e A

PR

ON

eit

her

at

the

US

or

at

the

DS

2-P

rovi

de

cut-

off

wal

ls

3-P

rovi

de

end

cu

t-o

ff

5-P

rovi

de

reve

rsed

filt

er

4-P

rovi

de

con

cret

e b

lock

s

6-P

rovi

de

dra

inag

e p

ipes

7-P

rovi

de

end

sill

8-P

rovi

de

dry

pit

chin

g a

t D

. S.

9-P

rovi

de

pit

chin

g in

mo

rtar

at

U. S

.

02/12/1434

13

25

UP

ST

RE

AM

PR

EC

AU

TIO

N

26

DO

WN

ST

RE

AM

PR

EC

AU

TIO

N

02/12/1434

14

27

bCt 1

bCy

bC1

bCt 2

b

sw C

LL

+

1

sL

wL

1L

Tota

l upl

ift

23 4

56

1’

2’3’

4’

5’ 6’

bCL 1

UP

LIF

T D

IAG

RA

M O

F P

LA

NE

FL

OO

R :

Po

int

Ele

va

tio

nP

oin

tE

lev

ati

on

5’4

’-(L

w+

Ls)

/cb

6’

5’-t

2/cb

=D

S

1’U

S2’

1’-t

1/cb

3’2’

-L1/

cb4

’3’

-y/c

b

Usi

ng B

ligh’

s M

etho

d

28

lCt 1

lCy

lC31

lCt 2

l

sw

C

LL

3+

1

sL

wL

1L

Tota

l upl

ift

23 4

56

1’

2’3’

4’

5’ 6’

lCL 3

1

UP

LIF

T D

IAG

RA

M O

F P

LA

NE

FL

OO

R :

Po

int

Ele

va

tio

nP

oin

tE

lev

ati

on

5’4

’-(L

w+

Ls)

/3cl

6’

5’-t

2/cl

=D

S

1’U

S2’

1’-t

1/cl

3’2’

-L1/

3cl

4’

3’-y

/cl

Usi

ng L

ane’

s M

etho

d

02/12/1434

15

29

bCt 1

bCy 1

bC1

bCt 2

b

sw

C

LL

11

+

b

sw

C

LL

22

+

bCt 3

bC1

bCy

2

3030

UP

LIF

T D

IAG

RA

M O

F F

LO

OR

WIT

H S

HE

ET

PIL

ES

:

Usi

ng

Blig

h’s

Met

ho

d

bCt 1

bCy

bCt 2

bC1

Tota

l upl

ift

sL

wL

bCd 12

02/12/1434

16

31

32

STA

BIL

ITY

OF

FL

OO

R :

Th

e fl

oo

r m

ust

be

stab

le b

y g

ravi

ty.

i.e. T

he

wei

gh

t o

f th

e fl

oo

r at

an

y se

ctio

n

mu

st b

e g

reat

er t

han

th

e u

pw

ard

bu

oya

ncy

fo

rce

“up

lift”

02/12/1434

17

33

1t

Diff

eren

tial u

plift

1h′

1h Tota

l

uplif

t

d

Co

nsi

der

sec

tio

n 1

-1,

Th

e u

pw

ard

lift

ing

fo

rce

is

Th

e d

ow

nw

ard

gra

vity

forc

e is

()

()1

11

ht

hw

w′

+=

=γ γγγ

γ γγγ

dt

wm

γ γγγγ γγγ

+=

1

So

, th

e u

pw

ard

forc

e <

do

wn

war

d fo

rce Ta

ke t1

as m

in. (

0.5

0 -

0.75

m)

()

dt

ht

wm

wγ γγγ

γ γγγγ γγγ

+<

′+

11

1

34

2t

Diff

eren

tial u

plift

2h′

2h

Tota

l

uplif

t

Co

nsi

der

sec

tio

n 2

-2,

Th

e u

pw

ard

lift

ing

fo

rce

is

Th

e d

ow

nw

ard

gra

vity

forc

e is

()

()2

22

ht

hw

w′

+=

=γ γγγ

γ γγγ

()2t

mγ γγγ=

As

crit

ical

; (

)2

22

th

tm

wγ γγγ

γ γγγ=

′+

()

()

wm

wt

hγ γγγ

γ γγγγ γγγ

−=

′2

2

()

()

()1

22

2−′

=−

′=

mw

mwh

ht

γ γγγγ γγγ

γ γγγγ γγγ

As

a fa

cto

r o

f sa

fety

incr

ease

the

wei

gh

t of

flo

or

by

20 –

30 %

()

21

1

22

.*

−′=

mht

γ γγγ

02/12/1434

18

35

bCt 1

bCy

bC1

bCt 2

b

sw C

LL

+

1

sL

wL

1L

Diff

eren

tial u

plift

. h’

23 4

56

1’

2’3’

4’

5’ 6’

bCL 1

Tota

l upl

ift ()

2.1*

12

2−′

=mh

tγ

' 2h m 0.

75 -

50.0(m

in)

1=

t