rigid retaining wall

7/29/2019 rigid retaining wall

1/11

Foundation Engineering

Foundation Engineering

Prof. Mesut Pervizpour

Earth Retaining StructuresFlexible Retaining Walls:

Anchored sheet pile wallsBraced excavationsSlurr wallsStability of open cuts

For NAVFAC and other online manuals

1

(including Army Corps of Eng, & FHWA)http://www.vulcanhammer.net/download/

Lecture Outline

HCantilever sheetpile wall (H < 3m)Design of:

Cantilever Sheet Pile Walls

Anchored Sheet Pile Walls

Braced Excavation

Anchored sheetpile (H > 3m) H

Anchor

Slurry Walls

er Braced Excavation(H > 3m)

2


2/11

Cantilever Sheet Pile Wall:H

Cantilever sheetpile wall (H < 3m)

Used as a temporary or long term retaining structure

o a ona suppor no rac ng or anc or

Resistance by passive support of soil in the front (& flexural stiffness

of the wall)

Applications include: waterfront, bridge abutment, cellular cofferdam, cut-off walls in

levees, dams, etc. Material: Steel, reinforced concrete, wood, aluminum, fiber lass, etc.

Major issue: excessive corrosion

Design approach: Use equilibrium (Moment)conditions to determine necessary depth ofem e men an e requ re sec on proper y o ewall

Construction: driven

in to ground using

pile-driving (hammer

or vibration)

methods. Several ata time to assure

3

alignment

Cantilever Sheet Pile Wall Design: Classical lateral earth pressure theories

Drained strength parameters, effective

If multilayer soil with clay, use total stressconditions for short term clay behavior

iav: seepage pressure per volume

stresses

Assumption: Active in the back, passive

in the front of the wallPivot

Rotation

wCB

dba

dbauu

2

2

Include the pore water and seepage

pressure effects ww

dba

dbadbaP

2

22

2

1

. .

ww

da

daadP

2

ddbbdbaa 223322

wavdba

i 2

3

2dazw

ai

dbaw

23Resultant PWP = 0

Use

auB B

AwB

da

dau

2

2

da

Pw

uB Ba

b

effectivestresses

4d zw

w

C

zwC

D

d


3/11

Cantilever Sheet Pile Wall Design:

Lateral Earth Pressure Distribution in Sand

Theoretical Earth PressureDistribution for Sands

Actual Earth PressureDistribution for Sands

Simplified Earth PressureDistribution for Sands

H

Sand Sand Sand

Active

Passive

a

p

a

Passive

Activep p

5


Lateral Earth Pressure Distribution in Sand - Procedure

Use Rankine or Coulomb for Ka and Kp for each soil layer reduce

Kp by FS = 1.5 2.0 Kp = Kp/ FS


Sand

A

raw ac ve pressure s r u on , ge a

Slope of CD slope : (Kp Ka)

Locate point C by plotting a line with slope from B (or set

Ra

H

a p , p = p- a

a = pa/(Kp Ka)

Use equilibrium conditions 1) Fx = 0, 2) Mbottom = 0

pa BCa

Y-z

RP

y

x a P P

22

Yp

zppRR pppPP ''

DE

F

z RP

Plug in expression: Ra + RP RP = 0

Ra + (pP+ pP) (z / 2) pP (Y / 2) = 0

p

6

pp

ACAp

pp

RYpz

'

2

pp = (Kp Ka) Y

pp = H Kp + (Kp Ka)(a+Y)


4/11




A

bottom =

have a cubic polynomial in Y, Obtain Y in conjunction

with expression of pp calculated for a trial value of Y.

w =

Depth of embedment D is: D = a + Ypa B

Ca

-RP

a

y

Approximate Values for D:

DE

F

z RP

(N for last 0.3m)

r

(relative density) (depth)

0 45 10 Very looseLoose 2.0 H1.5 H

pppp

7

11 3031 50Over 50

Medium denseDense

Very dense

1.25 H1.0 H0.75 H



Sand

pa BC

Ra

ya

D

E

RP

RM of R

p

due to blue area.RRp

Mo = 0 = Ra (Y + y) + M of Rp M of RpY-z

z

pp

Fpp

M of Rp due to pink area.

RaNet Moment : M(Rp) M(Rp)

M(Rp) = (pp+pp)(z/2)(z/3) = (pp+pp)(z2/6)

O

RP Y + y

M(Rp) = pp (Y/2)(Y/3) = pp(Y2/6)

Mo = 0 = Ra (Y + y) + (pp+pp)(z2/6) pp(Y

2/6)

C = (Kp Ka)

8

RpRp RP

0'32''

6'

ypRpC

YCp

RYp

Y pap

a

p

a

p

a

pp = (Kp Ka) YIf no GWT: pp = H Kp + (Kp Ka)(a+Y)


5/11

Cantilever Sheet Pile Wall Design:Lateral Earth Pressure Distribution in Sand General Expression

RRRRR R1

R

Sand

H

hw = H

2

1

2

1wa hKR

R3

paa

RAH hwwaw2

23 '21

wa hHKR

4Y-z

z

P

RP

D ap

a

KK

pR

'2

2

4

pp pp

'

wwaa hHhKp '

0'32''

6'

23

ypRpC

YCp

yRY

pY pa

p

a

p

a

p

aap

apa

KK

pa

'

9

aYKhDHKKhp awppwp '''


Obtain sheet ile t e b solvin for its section modulus thru M :

Max. moment at V=0: Mo = Mmax Divide the Maximum moment by the allowable

section modulus

Select appropriate sheet pile section from tables RAa

RP1

3

1max

xRxyRM pa

V = 0 Ra = Rp1

V = 0M = Mmax

3

max

xRxyRM aa

3

2max

xyRM a

Fx = 0 Ra = R 1

aapp R

xxKKR

2'

1

R2

a

aKK

RyRM

'

2

3

2

max

10

ap

a

KKx

'


6/11


Summar rocedure:

Calculate active pressure diagram in backfill and obtain paCalculate slope C = (Kp Ka) , note Kp may be the reduced valueCalculate distance a = / K K

Calculate Ra and y (or ybar)

Calculate pp (use estimated D): aYKhDHKKhp awppwp '''

Calculate Y:

Repeat calculation by updated D.

0'32''

6'

23

ypRpC

YCp

yRY

pY pa

p

a

p

a

p

a

nce o ta ne na , aven t app e yet: FS = .

Calculate Mmax:

a

a

RyRM

'

22max

Determine section modulus and select sheet pile.ap

11


Simplified Earth PressureDistribution Layered Sand

a

p

p

12


7/11


a era ar ressure s r u on o an ever ee e a s n a

Active and Passive stresses for cohesive soils are:

aaa KcKz 2 ppp KcKz 2

Undrained conditions (c = cu or su, and = 0 Ka = Kp = 1) should be used for

s or erm s a y ana ys s

Lon term stabilit anal sis should be based on the drained stren th arameters

(c = c, and = )

13


Lateral Earth Pressure Distribution in Clays

Simplified Earth PressureDistribution short term

Simplified Earth PressureDistribution long term

H

Hc

H

Hc

a a

su -

p p

p

4su + H

c2

14

ere c s e cr ca e g :a

cK

Note: if backfill granular, then use granulardistribution for backfill segment!


8/11

Cantilever Sheet Pile Wall Design:Short-termLateral Earth Pressure Distribution in Cohesive Soils

HcCLAY

Granular

Ra

eH=q q= eHpay

Ray

p

D

p

D

4su - eH4su + eH

p

=2 - =2qu + q4su - eH

4su + eH

p

=2 - =2qu + q

Immediately after consolidation: c = 0.5qu

, = 0

Establish ressure distribution, and solve

15


Short-termLateral Earth Pressure Distribution in Cohesive Soils

H

Granulare erm ne z rom x=

Ra + [ Rp Rp] = 0

and [ Rp Rp] =

a

CLAY

eH=q

R

pay

= c-q + c+q . z c-q = cz c-q

Ra + 4cz (4c-q)D = 0

RDqc a4

Rpz

Dc4

Calculate moment about bottom Mo=0

4su - eH4su + eH

=2qu - q=2qu + q

032

82

4

cDqcyDRa

08

24

2

2 cz

DRDc3

a

Substitute expression for z & obtain:

0418

242

2

2

aa RDqcc

yDRDqc

16

Obtain solution by trial & error and increase D by 20-40%


9/11

Cantilever Sheet Pile Wall Design:Short-termLateral Earth Pressure Distribution in Cohesive Soils

Granular Obtain Mmax at V = 0

xcR 4F =0

Ra

H

y qcR

xa

4

V=0

x

2

4max

xxqcyxRM a

max

qc

Ry

qc

RRM aaa

42

1

4max

17

Cantilever Sheet Pile Wall Design Example:

a) Embedment depth D (note use DSF = 1.3D) Sand

A

max

RaH=15 = 135pcf

= 32oCalculate:= 32o

Ka=Kp=Pa= Hka

C= (Kp-Ka)=pa B

Oa

Y-zRP

y

= 132.4pcfo

D

a= Pa/C =

Ra = Pa H + Pa a =

Find , use Mo :y

pp

DE

F

z RP

pp

=

= 30o

3

2

2

1

32

1 aaPa

HHPyR aaa

Ka=Kp=

'22.7 yAssume Y, calculate pp and iterate for Y:

appp KaYKaYHKp ''' 0'32'

21

'6

'

2 23

ypRR

Yy

RYR

Y paa

aa

pppFor Y = 17.5

Assumed Y 12 15 18 17.5 17.4

Pp 9433 10003 10563 10470 10451

18

Calculated Y -2355 -1391 374 17 -50


10/11

Cantilever Sheet Pile Wall Design Example (cont.):Use Y = D = Y + a = Ddesign =

Mmax :

xyRM a

2max

aRx '

2

ap

19

Cantilever Sheet Pile Wall Design Example:

a) Embedment depth D (note use DSF = 1.3D)max

HH=16.5

= 101pcf

Granular

6.6pa1

R1

R2a

CLAY

eH=q

Rp

y == 32o9.9

=Ka=Kp= pa2

R3

Rpz

DD

= 0C = 982pcf

4su - eH4su + eH

=2qu - q=2qu + q

20


11/11

Cantilever Sheet Pile Wall Design Example, (cont.):

Calculate depth of embedment D:

044

1

3

824

22

aa RDqcc

cyDRDqc

R

Calculate Maximum Moment:

qcx a

4

2

4max

xxqcyxRM a

21

rigid retaining wall

Documents