Unit 1 sheet pile-converted
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Nov 16, 2018
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About This Presentation
For Sheet pile concept to understand
Slide Content
ADVANCE FOUNDATION
ENGINEERING
by
D.Nigitha
National Institute of Technology, Trichy.
ENGINEERING
by
D.Nigitha
National Institute of Technology, Trichy.
SYLLABUS
Sheetpilestructures-cantileversheetpilewallsingranularand
cohesivesoils-Anchoredbulkheads-Freeearthsupportandfixed
earthsupportmethods-Anchors.
Sheetpilestructures-cantileversheetpilewallsingranularand
cohesivesoils-Anchoredbulkheads-Freeearthsupportandfixed
earthsupportmethods-Anchors.
SHEET PILE STRUCTURE
SHEET PILE STRUCTURE
INTRODUCTION
Sheetpilewallsareretainingwallsconstructed
toretainearth,wateroranyotherfillmaterial.
Thesewallsarethinnerinsectionas
comparedtomasonrywalls.
Asheetpilewallconsistofaseriesofsheetpiles
drivensidebysideintotheground,thusforming
acontinuousverticalwallforthepurposeof
retaininganearthbank.
Example:
Wanttobuildastructureinthesea(waterfront
structures)wecanusesheetpilestoretainseawater
fromflowingtotherequiredarea,andthenwithdraw
thewaterconfinedbetweensheetpilesand
therebybuildtherequiredstructures,finallyremove
sheetpilesbecausetherefunctionswereend.
INTRODUCTION
Sheetpilewallsareretainingwallsconstructed
toretainearth,wateroranyotherfillmaterial.
Thesewallsarethinnerinsectionas
comparedtomasonrywalls.
Asheetpilewallconsistofaseriesofsheetpiles
drivensidebysideintotheground,thusforming
acontinuousverticalwallforthepurposeof
retaininganearthbank.
Example:
Wanttobuildastructureinthesea(waterfront
structures)wecanusesheetpilestoretainseawater
fromflowingtotherequiredarea,andthenwithdraw
thewaterconfinedbetweensheetpilesand
therebybuildtherequiredstructures,finallyremove
sheetpilesbecausetherefunctionswereend.
SHEET PILE STRUCTURE
USES
Water front structures, for example, in building wharfs, quays, and
piers
Building diversion dams, such as cofferdams
River bank protection
Retaining the sides of cuts made in earth
Temporary construction
Light weight construction where sub-soil is poor for supporting a retaining
wall.
USES
Water front structures, for example, in building wharfs, quays, and
piers
Building diversion dams, such as cofferdams
River bank protection
Retaining the sides of cuts made in earth
Temporary construction
Light weight construction where sub-soil is poor for supporting a retaining
wall.
SHEET PILE STRUCTURE
SHEET PILE CAN BE OF
Timber
•Timber sheet piling is used for short spans, light lateral loads, and commonly for
temporary structures in the form of braced sheeting .
•Wooden sheet piles may be considered permanent if they are permanently under
water,or if they are impregnated with preservatives.
Reinforced concrete
•Concrete sheet piles are precast members, usually with a tongue and groove joint,
designed to with the permanent stresses during service and the handling stresses
during construction.
•They are heavy and bulky, and require heavier equipment to drive and handle.
Steel
•Steel sheet piling is the most common type because it is resistant to high diving
stresses, light weight, can be used several times, long service, easier to increase
the pile length.
SHEET PILE CAN BE OF
Timber
•Timber sheet piling is used for short spans, light lateral loads, and commonly for
temporary structures in the form of braced sheeting .
•Wooden sheet piles may be considered permanent if they are permanently under
water,or if they are impregnated with preservatives.
Reinforced concrete
•Concrete sheet piles are precast members, usually with a tongue and groove joint,
designed to with the permanent stresses during service and the handling stresses
during construction.
•They are heavy and bulky, and require heavier equipment to drive and handle.
Steel
•Steel sheet piling is the most common type because it is resistant to high diving
stresses, light weight, can be used several times, long service, easier to increase
the pile length.
SHEET PILE STRUCTURE
Sheet piles in Basement
.
Section of Sheet Pile
Sheet piles in Basement
.
Section of Sheet Pile
SHEET PILE STRUCTURE
.
.
SHEET PILE STRUCTURE
ADVANTAGES
1. Provides high resistance to driving stresses.
2. Light weight.
3. Can be reused on several projects.
4. Long service life above or below water with modest protection.
5. Easy to adapt the pile length by either welding or bolting.
6. Joints are less apt to deform during driving
ADVANTAGES
1. Provides high resistance to driving stresses.
2. Light weight.
3. Can be reused on several projects.
4. Long service life above or below water with modest protection.
5. Easy to adapt the pile length by either welding or bolting.
6. Joints are less apt to deform during driving
SHEET PILE STRUCTURE
TYPES
Cantilever sheet piling
Anchored sheet piling
TYPES
Cantilever sheet piling
Anchored sheet piling
CANTILEVER SHEET PILEs
CANTILEVER SHEET PILEs
Cantileversheetpilewallsareusuallyusedasfloodwallorasearthretaining
wallswithlowwallheights(3to5m0rless).
Becausecantileverwallsderivetheirsupportsolelyfromthefoundation
soils.,theymaybeinstalledinrelativelycloseproximitytoexistingstructure
Cantileversheetpilesarefurtherdividedintotwotypes:
Freecantileversheetpiles
Cantileversheetpiles
Cantileversheetpilewallsareusuallyusedasfloodwallorasearthretaining
wallswithlowwallheights(3to5m0rless).
Becausecantileverwallsderivetheirsupportsolelyfromthefoundation
soils.,theymaybeinstalledinrelativelycloseproximitytoexistingstructure
Cantileversheetpilesarefurtherdividedintotwotypes:
Freecantileversheetpiles
Cantileversheetpiles
CANTILEVER SHEET PILEs
FreeCantileverSheetPile
▪TheSheetpilesubjectedtoconcentrated
horizontalloadatitstop.
▪Nobackfillabovethedredgeline.
▪Itderivesitsstabilityfromthelateral
passiveresistanceofthesoilbelowthe
dredgelinewhereitisdriven.
Cantileversheetpiles
▪Itretainsbackfillatahigherlevelonone
side.
▪Thestabilityisentirelyfromthelateral
passiveresistanceofthesoilwherethe
sheetpileisdriven,likethatofafree
cantileversheetpile.
FreeCantileverSheetPile
▪TheSheetpilesubjectedtoconcentrated
horizontalloadatitstop.
▪Nobackfillabovethedredgeline.
▪Itderivesitsstabilityfromthelateral
passiveresistanceofthesoilbelowthe
dredgelinewhereitisdriven.
Cantileversheetpiles
▪Itretainsbackfillatahigherlevelonone
side.
▪Thestabilityisentirelyfromthelateral
passiveresistanceofthesoilwherethe
sheetpileisdriven,likethatofafree
cantileversheetpile.
CANTILEVER SHEET PILEs
Failure modes of Cantilever sheet piles
Failure modes of Cantilever sheet piles
CANTILEVER SHEET PILEs
Elastic Line and Straining Actions
Elastic Line and Straining Actions
CANTILEVER SHEET PILEs
Equilibrium of Cantilever Sheet Piles
ForEquilibrium,themomentoftheactiveand
passivepressureonaboutthepointofreactionR
mustbalance.
σ??????= 0.0
Thedepthcalculatesshouldbeincreasedbyatleast
20%toallowextralengthtodevelopthepassive
pressureR.
Equilibrium of Cantilever Sheet Piles
ForEquilibrium,themomentoftheactiveand
passivepressureonaboutthepointofreactionR
mustbalance.
σ??????= 0.0
Thedepthcalculatesshouldbeincreasedbyatleast
20%toallowextralengthtodevelopthepassive
pressureR.
FREE CANTILEVER SHEET PILE
The free cantilever sheet pile rotate about a point O below the dredge line. The actual Pressure
Distribution is shown in Figure 1
The passive resistance of the soil on the left side is idealized as a right angle triangle
AOE.
The distributed pressure acting on the right side below the pivot O is replaced as concentrated load P 1
acting at a point O.
Free Cantilever Sheet Pile Analysis
The free cantilever sheet pile rotate about a point O below the dredge line. The actual Pressure
Distribution is shown in Figure 1
The passive resistance of the soil on the left side is idealized as a right angle triangle
AOE.
The distributed pressure acting on the right side below the pivot O is replaced as concentrated load P 1
acting at a point O.
Free Cantilever Sheet Pile Analysis
FREE CANTILEVER SHEET PILEs
FREE CANTILEVER SHEET PILE
Moment:
By Equilibrium, the moment of all the forces about O must be equal to Zero.
Mo = F(h+d) –[
�
�
d (K
p–K
a) d] x d/3 = 0
Where
F is the horizontal force
H is the height of the wall above the dredge line
D is the depth of embedment.
The above equation can be solved for d. The actual depth to be provided is generally taken as
1.2d
Bending Moment
The bending moment at depth x below the dredge level is given by,
Mx = F(h+d) –
????????????
�
??????
(K
p–K
a)
For Maximum bending moment,
??????????????????
????????????
= 0
Free Cantilever Sheet Pile Analysis
Moment:
By Equilibrium, the moment of all the forces about O must be equal to Zero.
Mo = F(h+d) –[
�
�
d (K
p–K
a) d] x d/3 = 0
Where
F is the horizontal force
H is the height of the wall above the dredge line
D is the depth of embedment.
The above equation can be solved for d. The actual depth to be provided is generally taken as
1.2d
Bending Moment
The bending moment at depth x below the dredge level is given by,
Mx = F(h+d) –
????????????
�
??????
(K
p–K
a)
For Maximum bending moment,
??????????????????
????????????
= 0
Free Cantilever Sheet Pile Analysis
FREE CANTILEVER SHEET PILE WALLS
F -
(K
p–Ka)
6
3??????
2
= 0
X =
2??????
(K
p–Ka)
The Maximum Bending Moment is obtained by substituting the value of x inMx.
The section Modulus of the sheet pile can then be determined as
S =
M
max
??????�
Where
??????�= allowable bending stress
The bending moment diagram is shown in the previous figure.
F -
(K
p–Ka)
6
3??????
2
= 0
X =
2??????
(K
p–Ka)
The Maximum Bending Moment is obtained by substituting the value of x inMx.
The section Modulus of the sheet pile can then be determined as
S =
M
max
??????�
Where
??????�= allowable bending stress
The bending moment diagram is shown in the previous figure.
CANTILEVER SHEET PILEs IN
GRANULAR SOIL
GRANULAR SOIL
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The Figure (a) shows the cantilever sheet pile in a cohessionless soil deposits.
The pile rotates about the point O’ as shown in figure.
The pressure above O is passive in the front and active on the back side.
The pressure below the point O’ will be reverse i.e., there is active pressure in the
front and passive on the back side.
The Figure (b) shows the actual pressure distribution.
The Figure (a) shows the cantilever sheet pile in a cohessionless soil deposits.
The pile rotates about the point O’ as shown in figure.
The pressure above O is passive in the front and active on the back side.
The pressure below the point O’ will be reverse i.e., there is active pressure in the
front and passive on the back side.
The Figure (b) shows the actual pressure distribution.
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The analysis taking actual pressure distribution is quite complicated, so the pressure
distribution is generally simplified as shown in below figure.
As shown in figure the pressure will be Zero at the point O’.
The pressure diagram BCO1 shows the active pressure.
The analysis taking actual pressure distribution is quite complicated, so the pressure
distribution is generally simplified as shown in below figure.
As shown in figure the pressure will be Zero at the point O’.
The pressure diagram BCO1 shows the active pressure.
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The pressure at the dredge level is given by
P
1 = hKa
The depth a of Point O1 of Zero Pressure is given by,
P
1−a(K
p–Ka)= 0
a =
P
1
(K
p–Ka)
The total active pressure above point O1 be P
1 acting at a height of �
1above O1.
The passive pressure is given by the diagram O1EO. The passive pressure intensity at the
bottom tip A can be expressed as
P
2= (K
p–Ka)(d-a)
P
2= (K
p–Ka)b
Where b = d-a , in which d is the depth of point A below the dredge level.
The pressure at the dredge level is given by
P
1 = hKa
The depth a of Point O1 of Zero Pressure is given by,
P
1−a(K
p–Ka)= 0
a =
P
1
(K
p–Ka)
The total active pressure above point O1 be P
1 acting at a height of �
1above O1.
The passive pressure is given by the diagram O1EO. The passive pressure intensity at the
bottom tip A can be expressed as
P
2= (K
p–Ka)(d-a)
P
2= (K
p–Ka)b
Where b = d-a , in which d is the depth of point A below the dredge level.
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The Passive pressure is indicated by the diagram OAF on the back side. The intensity of
pressure at the tip A is given by,
P
3= (h + d)K
p–dKa
From the equation of equilibrium in the horizontal direction,
P
1+ P
3 -P
2= 0
The total pressure P
3 and P
2can be expressed as follows :
P
1 +
�
�
m (P
2+ P
3)-
�
�
??????(P
2) b = 0
The equivalence of areas has been taken as shown in below figure:
The Passive pressure is indicated by the diagram OAF on the back side. The intensity of
pressure at the tip A is given by,
P
3= (h + d)K
p–dKa
From the equation of equilibrium in the horizontal direction,
P
1+ P
3 -P
2= 0
The total pressure P
3 and P
2can be expressed as follows :
P
1 +
�
�
m (P
2+ P
3)-
�
�
??????(P
2) b = 0
The equivalence of areas has been taken as shown in below figure:
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The height of the point E above the tip A is taken as m .
M =
1
2
p
2b−p1
1
2
(P
2+p
3)
M =
p
2b−2p1
P
2+p
3
Taking moments of all the forces about A,
P
1 (b+�
�) -
�
�
p
2b−(b/3) +
�
�
m(P
2+p
3)x m/3 = 0
Substituting the value of m from before equation,
P
1 (b+�
�) -
p
2b
2
??????
+
P
2+p
3
??????
[
p
2b−2p1
P
2+p
3
�
= 0
The height of the point E above the tip A is taken as m .
M =
1
2
p
2b−p1
1
2
(P
2+p
3)
M =
p
2b−2p1
P
2+p
3
Taking moments of all the forces about A,
P
1 (b+�
�) -
�
�
p
2b−(b/3) +
�
�
m(P
2+p
3)x m/3 = 0
Substituting the value of m from before equation,
P
1 (b+�
�) -
p
2b
2
??????
+
P
2+p
3
??????
[
p
2b−2p1
P
2+p
3
�
= 0
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
The above equation can be written as,
b
4
+ C
1b
3
–C
2b
2
–C
3b –C
4 = 0
Where
C
1=
P4
(K
p–Ka)
C
2=
8P
1
(K
p–Ka)
C
3 =
6P
1[2(K
p–Ka)??????1+p4]
(K
p–Ka)2
C
4 =
(??????1p4)6+4P
1
(K
p–Ka)2
In which
P4 = hKp+(K
p–Ka)a
By trial and error method b can be determined. The value of d is equal to (b + a).
The depth d is a factor of safety of unity.
The required depth (D) is usually taken as 1.2d to 1.4d.
D = 1.2d to 1.4d.
The above equation can be written as,
b
4
+ C
1b
3
–C
2b
2
–C
3b –C
4 = 0
Where
C
1=
P4
(K
p–Ka)
C
2=
8P
1
(K
p–Ka)
C
3 =
6P
1[2(K
p–Ka)??????1+p4]
(K
p–Ka)2
C
4 =
(??????1p4)6+4P
1
(K
p–Ka)2
In which
P4 = hKp+(K
p–Ka)a
By trial and error method b can be determined. The value of d is equal to (b + a).
The depth d is a factor of safety of unity.
The required depth (D) is usually taken as 1.2d to 1.4d.
D = 1.2d to 1.4d.
CANTILEVER SHEET PILE WALLS IN GRANULAR SOILS
CANTILEVER SHEET PILEs IN
COHESIVE SOIL
COHESIVE SOIL
CANTILEVER SHEET PILE WALLS IN COHESIVE SOILS
The cantilever sheet pile penetrating clay below the dredge level. The backfill is of
cohessionless soil (C=0).
Then the bulk unit weight of the backfill material and clay will be respectively γ
1and
γ.Thecohesioninterceptofclayisc.
The cantilever sheet pile penetrating clay below the dredge level. The backfill is of
cohessionless soil (C=0).
Then the bulk unit weight of the backfill material and clay will be respectively γ
1and
γ.Thecohesioninterceptofclayisc.
CANTILEVER SHEET PILE WALLS IN COHESIVE SOILS
The pressure P
1 at the dredge line on the back side is given by
P
1= 1hk
a1
Below the dredge line but above the point of rotation O, the passive pressure acts from left
to right and the active pressure acts from right to left. Therefore, the pressure at depth Z
below the dredge level is given by
P
2= p
p–p
a
P
2= (K
pZ + 2C??????
??????) –[ Ka( Z + h) –2C ??????
??????]
For ∅=0; K
p= k
a= 1
Then Finally the value of P
2,
P
2= 4C -h
Likewise the pressure P
3from right to left is given by
P
3= (K
p(h+d)+ 2CK
p) –[ Kad –2C K
a]
For ∅=0; K
p= k
a= 1
Then Finally the value of P
3,
P
3= 4C + h
The pressure P
1 at the dredge line on the back side is given by
P
1= 1hk
a1
Below the dredge line but above the point of rotation O, the passive pressure acts from left
to right and the active pressure acts from right to left. Therefore, the pressure at depth Z
below the dredge level is given by
P
2= p
p–p
a
P
2= (K
pZ + 2C??????
??????) –[ Ka( Z + h) –2C ??????
??????]
For ∅=0; K
p= k
a= 1
Then Finally the value of P
2,
P
2= 4C -h
Likewise the pressure P
3from right to left is given by
P
3= (K
p(h+d)+ 2CK
p) –[ Kad –2C K
a]
For ∅=0; K
p= k
a= 1
Then Finally the value of P
3,
P
3= 4C + h
CANTILEVER SHEET PILE WALLS IN COHESIVE SOILS
From equilibrium in the horizontal direction, considering equivalent areas as in
P
1–[p
2x d] + [p
2+ p
3] x m/2 = 0
P
1–[(4C -h)x d] + [8c] x m/2 = 0
M =
(4C−h)xd−??????�
�??????
Taking moments of all the forces about A,
P
1 (�
�+ d )-(4C−h)xdx d/2 + ½ x 8c x m x m/3 = 0
Substitute the value of m in the above equation.
Then the equation can be written in the form of
d
2
(4c -h) –2 P
1d -
??????
�
(��??????��+??????
�
)
�??????+??????
= 0
The above equation is solved for d. The actual depth D is kept 40% to 60% more.
D = 1.2d to 1.4d.
From equilibrium in the horizontal direction, considering equivalent areas as in
P
1–[p
2x d] + [p
2+ p
3] x m/2 = 0
P
1–[(4C -h)x d] + [8c] x m/2 = 0
M =
(4C−h)xd−??????�
�??????
Taking moments of all the forces about A,
P
1 (�
�+ d )-(4C−h)xdx d/2 + ½ x 8c x m x m/3 = 0
Substitute the value of m in the above equation.
Then the equation can be written in the form of
d
2
(4c -h) –2 P
1d -
??????
�
(��??????��+??????
�
)
�??????+??????
= 0
The above equation is solved for d. The actual depth D is kept 40% to 60% more.
D = 1.2d to 1.4d.
ANCHORED SHEET PILES
ANCHORED SHEET PILES
Anchoredsheetpilesareheldabovethedrivendepthbyanchorsprovidedatasuitable
level.
Theanchorprovideforceforthestabilityofthesheetpile,inadditiontothelateralpassive
resistanceofthesoilintowhichsheetpilesaredriven
Theanchoredsheetpilesarealsooftwotypes:
Free-Earth Support
Fixed-Earth Support
Free-EarthSupport
Ananchoredsheetpileissaidtobefreeearthsupportwhenthedepthofembedmentis
smallandthepilerotatesatitsbottomtip.
Thenthereisnopointofcontraflexureinthepile.
Fixed-EarthSupport
Ananchoredpilehasafixedearthsupportwhenthedepthofembedmentisverylarge.
Thebottomtipofthepileisfixedagainstrotations.
Thereischangeinthecurvatureofthepile,andhenceaninflexionpointoccurs.
Anchoredsheetpilesareheldabovethedrivendepthbyanchorsprovidedatasuitable
level.
Theanchorprovideforceforthestabilityofthesheetpile,inadditiontothelateralpassive
resistanceofthesoilintowhichsheetpilesaredriven
Theanchoredsheetpilesarealsooftwotypes:
Free-Earth Support
Fixed-Earth Support
Free-EarthSupport
Ananchoredsheetpileissaidtobefreeearthsupportwhenthedepthofembedmentis
smallandthepilerotatesatitsbottomtip.
Thenthereisnopointofcontraflexureinthepile.
Fixed-EarthSupport
Ananchoredpilehasafixedearthsupportwhenthedepthofembedmentisverylarge.
Thebottomtipofthepileisfixedagainstrotations.
Thereischangeinthecurvatureofthepile,andhenceaninflexionpointoccurs.
ANCHORED SHEET PILES
ANCHORED SHEET PILEs WITH FREE EARTH
SUPPORT
SUPPORT
ANCHORED SHEET PILE in FREE EARTH SUPPORT
Inthismethod,thesoilisassumedasasimplysupport(pinsupport)attheendofsheet
pile,andalsothewallissimplysupportedfromitsupperedgebyanchor.
Sothedeflectionofsheetpilewillbesimilartothedeflectionofsimplysupported
beamasshowninthefollowingfigure:
Inthismethod,thesoilisassumedasasimplysupport(pinsupport)attheendofsheet
pile,andalsothewallissimplysupportedfromitsupperedgebyanchor.
Sothedeflectionofsheetpilewillbesimilartothedeflectionofsimplysupported
beamasshowninthefollowingfigure:
ANCHORED SHEET PILE WITH FREE EARTH SUPPORT
Thestabilityofthepileismainlydependupontheanchorforceinadditiontothatupon
thepassiveearthpressure.
Theembedmentdepthissmallwhenitcomparedtothecantileversheetpile.
So,inthismethodthelengthofthepileisreduced.Also,theadditionalcostofanchoris
tobeconsideredwhilejudgingtheeconomyofthetwotypeofconstruction.
Theequationforthedepthdarederivedseparatelyforthecohessionlessand
cohesivesoil.
Thestabilityofthepileismainlydependupontheanchorforceinadditiontothatupon
thepassiveearthpressure.
Theembedmentdepthissmallwhenitcomparedtothecantileversheetpile.
So,inthismethodthelengthofthepileisreduced.Also,theadditionalcostofanchoris
tobeconsideredwhilejudgingtheeconomyofthetwotypeofconstruction.
Theequationforthedepthdarederivedseparatelyforthecohessionlessand
cohesivesoil.
FREE EARTH SUPPORT IN COHESIONLESS SOIL
ANCHORED SHEET PILE in cohessionless soil
The force acting on the pile, assuming that the material above and below the dredge
line is cohessionless.
From Equilibrium,
T + P
2–P
3= 0
Where T is the tension force in the anchor.
The depth a to the point of zero pressure can be determined as under.
K
a(h+a) -K
pa= 0
a(K
p-K
a) = (K
ah)
a=
K
ah
K
p−Ka
Therefore, P
2= ½ P
2b = ½(K
p-K
a) b
2
Where, P
2= (K
p-K
a) b
The force acting on the pile, assuming that the material above and below the dredge
line is cohessionless.
From Equilibrium,
T + P
2–P
3= 0
Where T is the tension force in the anchor.
The depth a to the point of zero pressure can be determined as under.
K
a(h+a) -K
pa= 0
a(K
p-K
a) = (K
ah)
a=
K
ah
K
p−Ka
Therefore, P
2= ½ P
2b = ½(K
p-K
a) b
2
Where, P
2= (K
p-K
a) b
ANCHORED SHEET PILE in cohessionless soil
Taking moments of all the forces about anchor point M,
P
1(a+ h-e-�
�) -P
2 (h-e+a+2b/3) = 0
Substituting the value of P
2 in above equation
Finally the equation can be written as,
b3 (Kp-Ka) /3 + b2 (Kp-Ka) /2 (g+a) -P1f = 0
b3 +1.5b2 (g+a) -
3P1f
(Kp−Ka)
then f= a+ h-e-�
1; g= h-e
Then d is determined as
d = b+a.
The actual depth D is taken equal to 1.2 to 1.4 times d.
The force in anchor rod can be obtained from the equation as
T = P
1–P
2
The value of P1 and P2 are obtained from pressure diagram.
Taking moments of all the forces about anchor point M,
P
1(a+ h-e-�
�) -P
2 (h-e+a+2b/3) = 0
Substituting the value of P
2 in above equation
Finally the equation can be written as,
b3 (Kp-Ka) /3 + b2 (Kp-Ka) /2 (g+a) -P1f = 0
b3 +1.5b2 (g+a) -
3P1f
(Kp−Ka)
then f= a+ h-e-�
1; g= h-e
Then d is determined as
d = b+a.
The actual depth D is taken equal to 1.2 to 1.4 times d.
The force in anchor rod can be obtained from the equation as
T = P
1–P
2
The value of P1 and P2 are obtained from pressure diagram.
ANCHORED SHEET PILE in cohessionless soil
ANCHORED SHEET PILE in cohessionless soil
The Net Pressure Distribution Diagram :
The Net Pressure Distribution Diagram :
FREE EARTH SUPPORT IN COHESIVE SOIL
ANCHORED SHEET PILE in cohesive soil
Theanchoredsheetpileisdriveninclay,buthasthebackfillofcohessionless,granular
material.
Thepressuredistributionabovethedredgelineissameasthatinthecaseof
cohessionlesssoil.
Theanchoredsheetpileisdriveninclay,buthasthebackfillofcohessionless,granular
material.
Thepressuredistributionabovethedredgelineissameasthatinthecaseof
cohessionlesssoil.
ANCHORED SHEET PILE in cohesive soil
The pressure distribution above the dredge line is same as that in the case of
cohessionless soil. However , below the dredge line , the pressure is given by
P
2= (K
pZ + 2c??????
??????) -[K
p(Z+h) -2c??????
�]
Therefore, Kp= Ka= 1 ( For ∅= 0)
P
2 = 2c + 2c -h = 4c -h
From Equilibrium cases, T = P
1–P
2
T = P
1–P
2x d
Taking the moments of all forces about M,
P
1x f -P
2d (g +d/2) = 0
Substitute P2 value in above equation
P
1x f -(4c -h)d (g +d/2) = 0
d
2
+ 2gd -
�??????
�
??????
�??????−??????
The value of d is determined. The actual depth D provided is 20 to 40 % more than d.
The pressure distribution above the dredge line is same as that in the case of
cohessionless soil. However , below the dredge line , the pressure is given by
P
2= (K
pZ + 2c??????
??????) -[K
p(Z+h) -2c??????
�]
Therefore, Kp= Ka= 1 ( For ∅= 0)
P
2 = 2c + 2c -h = 4c -h
From Equilibrium cases, T = P
1–P
2
T = P
1–P
2x d
Taking the moments of all forces about M,
P
1x f -P
2d (g +d/2) = 0
Substitute P2 value in above equation
P
1x f -(4c -h)d (g +d/2) = 0
d
2
+ 2gd -
�??????
�
??????
�??????−??????
The value of d is determined. The actual depth D provided is 20 to 40 % more than d.
ANCHORED SHEET PILE in cohesive soil
ANCHORED SHEET PILE in cohesive soil
ANCHORED SHEET PILEs WITH FIXED-EARTH
SUPPORT
SUPPORT
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
The figure shows the deflected shape of an anchored sheet pile with fixed –earth support.
The figure shows the deflected shape of an anchored sheet pile with fixed –earth support.
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
TheelasticlinechangesitscurvatureattheinflexionpointI.
Thesoilintowhichthesheetisdrivenexertsalargelinechangesitscurvatureatthe
inflexionpointI.
Thesoilintowhichthesheetisdrivenexertsalargerestraintonthelowerpartofthepile
andcausesachangeincurvature.
Blumgaveamathematicalrelationshipbetween(i/h)and∅,whereIisthedepthofthe
pointofinflexionIbelowthedredgelevelandhistheheightofsheetpileabovethedredge
level.ThusinflectionpointIislocated.
TheelasticlinechangesitscurvatureattheinflexionpointI.
Thesoilintowhichthesheetisdrivenexertsalargelinechangesitscurvatureatthe
inflexionpointI.
Thesoilintowhichthesheetisdrivenexertsalargerestraintonthelowerpartofthepile
andcausesachangeincurvature.
Blumgaveamathematicalrelationshipbetween(i/h)and∅,whereIisthedepthofthe
pointofinflexionIbelowthedredgelevelandhistheheightofsheetpileabovethedredge
level.ThusinflectionpointIislocated.
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
Infigure,thelowerportionofthepressureontherightsideisreplacedbyaconcentrated
forceRkatpointK.
ThemagnitudeofRkisinitiallyunknown,butitisdeterminedfromtheequation
whenthemomentsaretakenaboutK.
Oncethedepthisfound,Rkcanbedeterminedfromtheequilibriumequationinthe
horizontaldirection.
AnEquivalent-beammethodisused.Itisassumedthatthesheetisabeamwhich
issimplysupportedattheanchorpointMandfixedatthelowerendK.
Thefigure(b)showsthebendingmomentdiagram.
ThebendingmomentisZeroattheinflexionpointI.Theoretically,thelowerpart
IKofthepilecanberemovedandtheshearforcecanbereplacedbyareactionR1.
TheSimplysupportedbeamBIisshowninfigure.
Infigure,thelowerportionofthepressureontherightsideisreplacedbyaconcentrated
forceRkatpointK.
ThemagnitudeofRkisinitiallyunknown,butitisdeterminedfromtheequation
whenthemomentsaretakenaboutK.
Oncethedepthisfound,Rkcanbedeterminedfromtheequilibriumequationinthe
horizontaldirection.
AnEquivalent-beammethodisused.Itisassumedthatthesheetisabeamwhich
issimplysupportedattheanchorpointMandfixedatthelowerendK.
Thefigure(b)showsthebendingmomentdiagram.
ThebendingmomentisZeroattheinflexionpointI.Theoretically,thelowerpart
IKofthepilecanberemovedandtheshearforcecanbereplacedbyareactionR1.
TheSimplysupportedbeamBIisshowninfigure.
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
The following procedure is used for the analysis of the sheet pile with fixed-earth support,
using equivalent beam method.
(a) Upper Beam BI
Determine the Pressure P1 at the dredge level.
Estimate the angle of shearing resistance ∅of the soil.
Determine the distance I of the point of inflexion .
Determine the distance a of the point of zero pressure from the equation.
a=
P
1
(Kp−Ka)
Determine the pressure P
0at the point of inflexion from the relation,
P
0 =
P
1
�
( a –i)
Determine the reaction R1 for the beam IB by taking moments about the point M of
anchor of all the force acting on IB. ( Shown in above figure)
The following procedure is used for the analysis of the sheet pile with fixed-earth support,
using equivalent beam method.
(a) Upper Beam BI
Determine the Pressure P1 at the dredge level.
Estimate the angle of shearing resistance ∅of the soil.
Determine the distance I of the point of inflexion .
Determine the distance a of the point of zero pressure from the equation.
a=
P
1
(Kp−Ka)
Determine the pressure P
0at the point of inflexion from the relation,
P
0 =
P
1
�
( a –i)
Determine the reaction R1 for the beam IB by taking moments about the point M of
anchor of all the force acting on IB. ( Shown in above figure)
ANCHORED SHEET WITH FIXED-EARTH SUPPORT
Lower Beam IK
Determine the pressure P2 from the relation
P
2 = (K
p-K
a) (d-a)
Determine the distance (d-a) by taking moments of all the forces on the beam IK about K.
The reaction R1 on the lower beam is equal and opposite to the upper beam.
Calculate d from pressure equation and hence find D = 1.2d.
Determine the tension T in anchor by considering the equilibrium of beam IB. Thus
T = P
1–R
1
Where P1 = total force due to pressure on IB
Lower Beam IK
Determine the pressure P2 from the relation
P
2 = (K
p-K
a) (d-a)
Determine the distance (d-a) by taking moments of all the forces on the beam IK about K.
The reaction R1 on the lower beam is equal and opposite to the upper beam.
Calculate d from pressure equation and hence find D = 1.2d.
Determine the tension T in anchor by considering the equilibrium of beam IB. Thus
T = P
1–R
1
Where P1 = total force due to pressure on IB
ANCHOR DESIGN
DESIGN OF ANCHORs
The anchor used in sheet pile walls are of the following types:
Anchor plates and beams
Tie Backs
Vertical Anchor piles
Anchor beams supported by batter piles.
The anchor used in sheet pile walls are of the following types:
Anchor plates and beams
Tie Backs
Vertical Anchor piles
Anchor beams supported by batter piles.
DESIGN OF ANCHORs
The design of anchor plates and beams:
Anchor plates and beams are made of cast-concrete blocks. A horizontal beam is placed at
the front face of the sheet pile, and a tie rod is attached to it.
The other end of the tie rod is connected to an anchor plates or a beam. As shown in below
figure.
Anchor Pile
Batter Pile
The design of anchor plates and beams:
Anchor plates and beams are made of cast-concrete blocks. A horizontal beam is placed at
the front face of the sheet pile, and a tie rod is attached to it.
The other end of the tie rod is connected to an anchor plates or a beam. As shown in below
figure.
Anchor Pile
Batter Pile
DESIGN OF ANCHORs
Theresistanceofferedbyananchorplateorabeamisderivedfromthepassive
resistanceofthesoilinfrontoftheplate.
Forfullpassiveresistancetodevelop,theanchorplatemustbelocatedinZone
CDE.
Tenggavethefollowingequationsfortheultimateresistanceofanchorplatesin
granularsoilslocatedatornearthegroundsurface.
LetBbethelengthoftheanchorperpendiculartothecrosssectionandlethbethe
heightoftheanchor.
Theresistanceofferedbyananchorplateorabeamisderivedfromthepassive
resistanceofthesoilinfrontoftheplate.
Forfullpassiveresistancetodevelop,theanchorplatemustbelocatedinZone
CDE.
Tenggavethefollowingequationsfortheultimateresistanceofanchorplatesin
granularsoilslocatedatornearthegroundsurface.
LetBbethelengthoftheanchorperpendiculartothecrosssectionandlethbethe
heightoftheanchor.
DESIGN OF ANCHORs
(a) For continuous plates or beams with B/h > 5, the ultimate resistance is given by
P
u= B (P
p-P
a)
P
u = (1/2H
2
K
p)-(1/2H
2
K
a)
Where H is the depth of the lower face of the anchor beam from the ground surface.
(b) For plates or beams with B/h < 5, the ultimate resistance is given by,
P
u= B (P
p-P
a) + ½K
0 (??????
??????+??????
�) H
3
tan∅
Where K0 = coefficient of earth at rest (= 0.40)
P
u=
??????
�
??????
�
(K
p-K
a) + 1/3K
0 (??????
??????+??????
�) H
3
tan∅
The allowable resistance is taken as
P
a=
P
u
??????�
Where FS = Factor of Safety
The centre –to –centre spacing of anchors is obtained from the relation.
S =
P
a
�
Where T= Tension in sheet pile per unit length as obtained from the analysis of anchored
sheet pile.
(a) For continuous plates or beams with B/h > 5, the ultimate resistance is given by
P
u= B (P
p-P
a)
P
u = (1/2H
2
K
p)-(1/2H
2
K
a)
Where H is the depth of the lower face of the anchor beam from the ground surface.
(b) For plates or beams with B/h < 5, the ultimate resistance is given by,
P
u= B (P
p-P
a) + ½K
0 (??????
??????+??????
�) H
3
tan∅
Where K0 = coefficient of earth at rest (= 0.40)
P
u=
??????
�
??????
�
(K
p-K
a) + 1/3K
0 (??????
??????+??????
�) H
3
tan∅
The allowable resistance is taken as
P
a=
P
u
??????�
Where FS = Factor of Safety
The centre –to –centre spacing of anchors is obtained from the relation.
S =
P
a
�
Where T= Tension in sheet pile per unit length as obtained from the analysis of anchored
sheet pile.
THANK YOU
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