Retaining wall analysis and design according to aci

retaining wall

1. DESIGN OF REINFORCED
CONCRETE RETAINING WALL
Dr. ZainorizuanMohdJaini
Faculty of Civil and Environmental Engneering
UniversitiTunHussein OnnMalaysia
86400 ParitRaja, BatuPahat, Johor, Malaysia
Semester 2 2017/2018

2. Introduction
2
❑Retainingwallsareusuallybuilttoholdbacksoilmass.
❑Retainingwallsarestructuresthatareconstructedtoretailsoil
oranysuchmaterialswhichareunabletostandverticallyby
themselves.
❑Theyarealsoprovidedtomaintainthegroundsattwodifferent
levels.
❑Typesofretainingwall:
-Gravitywall
-Cantileverwall
-Counterfortwall
-Buttresswall
-Pilingwall(CBP)
-Anchoredwall

3. Introduction
3

4. Introduction
4
Gravity Retaining Wall
Cantilever
Retaining Wall
Counterfortand Buttressed
Retaining Wall

5. Introduction
5
No. Type Descriptions
1Gravity wallStabilityisprovidedbytheweightofthe
concreteinthewall.
2Cantilever wallWallactsasaverticalcantilever.
Stabilityisprovidedbytheweightof
structureandearthonaninnerbaseor
theweightofthestructureonlywhen
thebaseisconstructedexternally.
3Counterfort
and buttress
wall
Theslabissupportedonthethreesides
bythebaseandcounterfortorbuttress.
Stabilityisprovidedbytheweightofthe
structureinthecaseofbuttressandby
theweightofstructureandearthonthe
baseinthecounterfortwall.

6. Design Consideration
6
❑Component:
Steel reinforcement
50mm weep hole
@ 1-2m
Frostline
Drainage mat with
filter fabric
Porous backfill
50mm minimum
cover
Perforated drainpipe
sloped to drain away
from the wall
75mm minimum
cover

7. Design Consideration
7
❑Typicalsize:

8. Design Consideration
❑Designprocedure(cantileverretainingwall):
−Assumeabreathforthebaseis0.75ofthewallheight.The
preliminarythicknessforthewallandbasesectioncanbe
assumed.
−Calculatethehorizontalpressureonthewall.Then,
consideringallforces,checkstabilityagainstoverturning
andtheverticalpressureunderthebaseofthewall.
8Horizontal
pressure
Net pressure
Pressure
Inner footingouter footing
Pressure on the wall
and base

9. Design Consideration
−Calculateandchecktheresistancetosliding.Useγ
f=1.4
tothehorizontalloadsfortheoverturningandslidingcheck.
Themaximumverticalpressureiscalculatedusingservice
loadandshouldnotexceedsafebearingpressure.
−Reinforcedconcretedesignforthewallisconductedby
usingtheultimateload.Forthewallandearthpressure,use
γ
f=1.4.
−Surchargeifpresentmaybeclassedaseitherdeador
imposedloaddependingonitsnature.
−Forthewall,calculateshearforceandmomentscausedby
thehorizontalearthpressure.
−Designtheverticalmomentsteelfortheinnerfaceand
checktheshearstresses.
9

10. Design Consideration
−Minimumsecondarysteelisprovidedinthehorizontal
directionfortheinnerfaceandbothverticallyand
horizontallyfortheouterface.
−Thenetmomentduetoearthpressureonthetopand
bottomfacesoftheinnerfootingcausestensioninthetop
andreinforcementisdesignedforthisposition.
−Themomentduetoearthpressurecausestensioninthe
bottomfaceoftheouterfooting.
10

11. Earth Pressure
11
Ground pressure (passive)
or subsoil reaction
Active earth
pressure
behind wall
–wedge or
retained
earth plus
any
hydrostatic
pressurePassive earth pressure in
front of wall
Mass of wall acts downward

12. Earth Pressure
❑Activesoilpressure:
−Twocasesknownascohesionlesssoilsuchassandand
cohesivesoilsuchasclay.
−Theactivesoilpressureisduetothelevelofbackfill.
−Ifthereisasurchargeofw.kN/m
2
onthesoilbehindthewall,
thisisequivalenttoanadditionalsoildepthof
where:
wissurchargeinkN/m
2
γisthedensityofsoilinkN/m
3
12w
z

=

13. Earth Pressure
−Forcohesionlesssoil(c=0),thepressureatanydepth,zis
givenby:
where:isthedensityofsoiland isthefrictionangle.
Meanwhile,theforceonthewallofheightH1is:
−Forcohesivesoil( ),thepressureatanydepth,zis
givenby:
Thisexpressiongivesnegativevalueneartopofthewall.In
practice,avaluefortheactivesoilpressureis< .
131sin
1sin
z



−
=
+ 2
11
1sin
0.5
1sin
PH



−
=
+   0= ()2zc=− 0.25z

14. Earth Pressure
❑Verticalpressureunderthebase:
−Theverticalpressureunderthebaseincalculatedforthe
serviceload.
−Foracantileverwall,1mlengthofwallwithbasedwidthbis
consider;thentheareaandmodulusofsectionarea:
−Thesumofthemomentofallverticalforcesaboutthe
centerofthebaseandactivepressureonthewallis:
−Thepassiveearthpressureinfrontofthebasehasbeen
neglected.Themaximumpressureis:
14( )( )
11/ 2 / 3M W x b P H= − − 2 2 3
1 m m ; /6 mA b b Z b=  = = max
WM
P
AZ
=

This should not exceed the
safe bearing pressure on
the soil

15. Stability
❑Wallstability
−Theverticalloadsaremadeupoftheweightofthewalland
base,andtheweightofthebackfillonthebase.Frontfillon
theouterbasecanbeneglected.
−Surchargewouldneedtobeincludedifpresent.
−Thecriticalconditionforoverturningiswhenamaximum
horizontalforceactswithminimumverticalload.
15
Overturning
about its toe
Slidingalong
the base
Bearing
capacity
failureof
supporting
base
*Excessivesettlementmayoccurifweaksoillayer
*islocatedbelowthefoundationwithin1.5times
*foundationwidth

16. Stability
−Toguardagainstfailurebyoverturning,itisusualtoapply
conservativefactorsofsafetytotheforceandloads.
−Ifthecentreofgravityoftheseloadsisxfromthetoeofthe
wall,thestabilizingmomentisΣWxwithpartialsafetyfactor
isγ
f=0.9.
−Theoverturningmomentduetotheactiveearthpressureis
1.1P
1(H
1/3)withadversepartialsafetyfactorγ
f=1.1.
−Theunfavourableeffectsofthevariablesurchargeloading
aremultipliedbythepartialsafetyfactorofγ
f=1.5.
−Thestabilizingmomentfrompassiveearthpressurehas
beenneglected.
−Forthewalltosatisfytherequirementofstability:
161
1
3
f
H
Wx P

 



17. Stability
❑Resistancetosliding
−Cohesionlesssoil:ThefrictionRbetweenthebaseandthe
soilisμΣMwhereμisthecoefficientoffrictionbetweenthe
baseandthesoil(μ=tanø).Thepassiveearthforceagainst
thefrontofthewallfromadepthH
2soilis:
−Cohesivesoils:TheadhesionRbetweenthebaseandthe
soilisβ
bwhereβistheadhesioninkN/m
2
.Thepassive
earthpressureis .
−Anibcanbeaddedtoincreasetheresistancetosliding
throughpassiveearthpressure.
−Forthewalltobesafeagainstsliding, where
H
kisthehorizontalactiveearthpressureonwall
172
22
1sin
0.5
1sin
PH



+
=
− 2
2 2 20.5 2P H cH=+ 1.0
k f kGH

18. Detailing
18
❑Reinforcementarrangement:

19. Detailing
19
❑Reinforcementarrangement:

20. Design of Retaining Wall
20
Example 5.1:
Cantilever Retaining Wall

21. Example 5.1
❑CantileverretainingwallsasinFigure1supportabankofearth
4.5mheight.Thesoilbehindthewalliswell-drainedsandwith
thefollowingproperties:
-Density,γ
soil=2000kg/m
3
=20kN/m
3
-Angleofinternalfriction,ø=30
o
Thematerialunderthewallhasasafebearingpressureof
110kN/m
2
.Thecoefficientoffrictionbetweenthebaseandthe
soilis0.45.
Designthewallusinggrade30concreteandgrade500
reinforcement.
21

22. Example 5.1
22P1
H
2
P2
98.15 kN/m
2
59.73 kN/m
2
2200800
400
400
4500
600
3400
134.2 kN
B
C
1700

23. Example 5.1
❑Checkwallstability
Earthpressure,
For1mlengthofwall,
Horizontalload
❑Maximumsoilpressure
The base properties area
Modulus
Maximum soil pressure at toe is:
231sin 1sin30
20(4.9)
1sin 1sin30
z



−−
==
++ 2
32.34kN/m= ( )()0.532.34 4.9 79.23kN== 2
3.41m (width) 3.4 m=  = 22
99.6kN/m 110kN/m (OK) 23
3.4/6=1.93m= 2
max
271.4 129.4191.22
99.6kN/m
3.4 1.93
WM
P
AZ
  −
= + = + =

24. Example 5.1
24
Load
Horizontal load
(kN)
Distance from
C (m)
Moment about
C (kNm)
Active
pressure
79.23 1/3(4.9) = 1.63 -129.41
Vertical load
(kN)
Distance from
B (m)
Moment about
B (kNm)
Wall
0.5 (0.3+0.4)4.5 x 25 = 39.4-0.7 -27.58
Footing 0.4 x 3.4 x 25 = 34 0 0
Backfill 2.2 x 4.5 x 20 = 198 0.6 118.8
Total 271.4 91.22

25. Example 5.1
❑Checkstabilityandoverturning
ThestabilitymomentaboutthetoeAofthewallforapartial
safetyfactorγ
f=1.0is:
1
91.22+(271.4x1.7)=552.6kNm
1
Theoverturningmomentforapartialsafetyfactorγ
f=1.4is:
1
1.4x129.41=181.2kNm
1
Thestabilityofthewallisadequate
25

26. Example 5.1
❑Checkresistancetosliding
Theforcesresistingslidingarethefrictionunderthebaseand
thepassiveresistanceforadepthofearth:
Passive force,
Friction force = 0.45 x 271.4 = 122.13kN
Total friction force = 10.8 + 122.13 = 132.9kN
Sliding force = 79.23 x 1.4 = 110.9kN
The resistance to sliding is satisfactory
262
22
1sin
0.5
1sin
PH



+
=
− ()()()
2
0.520 0.6 3 10.8==

27. Example 5.1
❑Wallreinforcement:
Pressureatthebaseofthewall,
Shearforce
Moment
1
UseC
nom=40mm;Ø
bar=20mm
2721sin
20(4.5)(0.33) 29.7kN/m
1sin
z



−
= = =
+ 6
22
153.3410
1.18 1.27
1000(360)
M
bd

= = 
Use Z = 0.95d( )
6
2153.3410
1031mm/m
0.86 0.87(500)0.95360
s
yk
M
A
fz

= = =

Use H20-250 (A
s= 1260mm
2
/m)( )() 1.350.529.7 4.5 90.2kN== ()()
11
90.2 4.5 0.4 153.34kNm
32

= + =

 ()40030.520 360d mm= −− =

28. Example 5.1
❑Innerfootingreinforcement:
Shearforce,
Moment,
28( )( )
2.2
1.3519834 602.2 0.52.225.6
3.4
   
= + −  −  
    6
22
117.510
0.90 1.27
1000(360)
M
bd

= = 
Use Z=0.95d( )
6
2117.510
790mm/m
0.86 0.87(500)0.95360
s
yk
M
A
fz

= = =

Use H20-300 (A
s= 1050mm
2
/m) 1.35198 21.1131.431.1 79.56kN= + − − = ( )( ) ( ) 1.35198 21.11321.10.2 31.10.7330.2= + − + − + 117.5kNm=

29. Example 5.1
❑Outerfootingreinforcement:
Shearforce,
Moment,
29( )( )
0.8
1.35 90.30.8 0.50.89.3 34
3.4
  
=  +   − 
   6
22
68.410
0.52 1.27
1000(360)
M
bd

= = 
Use Z=0.95d( )
6
268.410
457mm/m
0.86 0.87(500)0.95360
s
yk
M
A
fz

= = =

Use H16-300 (A
s= 670mm
2
/m) 1.3572.23.727.7 92.10kN= + − = ( )( ) ()( ) 1.3572.27.2 0.40.2 3.722/30.8 0.2= − + + + 68.4kNm=

30. Design of Retaining Wall
30
Example 5.2:
Cantilever Retaining Wall
(Include Surcharge Loading)

31. Example 5.2
❑Designacantileverretainingwalltosupportabankofearth
3.5mheight.Thetopsurfaceishorizontalbehindthewallbutit
issubjectedtoadeadloadsurchargein15kN/m
2
.Thesoil
behindthewalliswell-drainedsandwiththefollowing
properties:
-Density,γ
soil=1800kg/m
3
=18kN/m
3
-Angleofinternalfriction,φ=30
o
Thematerialunderthewallhasasafebearingpressureof
100kN/m
2
.Thecoefficientoffrictionbetweenthebaseandthe
soilis0.50.
DesignthewallusinggradeC30concreteandgrade500
reinforcement.
31

32. Example 5.2
32

33. Example 5.2
❑Checkwallstability
Consider1mlengthofthewall.Thesurchargeisequivalentto
anadditionalheightof15kN/m
2
/18kNm
3
=0.85.
Therefore,totalheightofthesoil=3.5+0.25+0.85=4.6m
Earthpressure,
Atz=0.85m,ρ=5kN/m
2
Atz=4.6m,ρ=27kN/m
2
❑Maximumsoilpressure
The base properties area
Modulus
331sin 1sin30
20()
1sin 1sin30
zz



−−
==
++ ()( )
2
17.6 0.333 5.87kN/mzz== 2
2.851m (width) 2.85 m=  = 23
2.85/6=1.35m=

34. Example 5.2
34
Load
Horizontal load
(kN)
Distance from
C (m)
Moment about
C (kNm)
Active
pressure
5 x 3.75 = 18.75
0.5 x 22 x 3.75 = 41.25
1.875
1.25
-35.08
-51.56
Total 59.98 -86.64
Vertical load
(kN)
Distance from
B (m)
Moment about
B (kNm)
Wall 4.1 x 0.25 x 25 = 25.6 -0.5 -12.8
Footing2.85 x 0.25 x 25 = 17.81 0 0
Backfill1.8 x 3.5 x 17.6 = 110.88 0.525 58.21
Surcharge 15 x 1.8 = 27 0.525 14.18
Total 181.29 59.59

35. Example 5.2
Maximumsoilpressureatserviceload:
❑Checkstabilityandoverturning
ThestabilitymomentaboutthetoeAofthewallforapartial
safetyfactorγ
f=0.9is:
1
59.59+[181.29x(2.85/2)]=317.9x0.9=286.11kNm
1
Theoverturningmomentforapartialsafetyfactorγ
f=1.1is:
1
1.1x86.64=95.3kNm1
Thestabilityofthewallisadequate
3522
83.76kN/m 110kN/m (OK) 2
max
181.29 86.6759.59
83.76kN/m
2.85 1.35
WM
P
AZ
  −
= + = + =

36. Example 5.1
❑Checkresistancetosliding
Theforcesresistingslidingarethefrictionunderthebaseand
thepassiveresistanceforadepthofearthof850mmtothetop
ofthebase.
Passive force,
Friction force = 0.45 x 181.29 = 81.58kN
Total friction force = 19.51 + 81.85 = 101.36kN
Sliding force = 1.4 x 59.98 = 83.97kN
The resistance to sliding is satisfactory
362
22
1sin
0.5
1sin
PH



+
=
− ()( )()
2
0.518 0.85 3 19.51==