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Advanced Foundation Engineering     

2013 

Prof.T.G. Sitharam Indian Institute of Science, Bangalore 

 

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CHAPTER 5: SHEET PILE WALL 

5.1 INTRODUCTION 

5.2 CANTILEVER SHEET PILE WALL 

Case 1: Cantilever sheet pile embedded in granular soil.  

Case 2: Cantilever sheet pile wall embedded in cohesive soil.  

5.3 ANCHORED BULKHEAD 

5.3.1 Free‐Earth Support Method 

Case 1: Anchored bulkhead driven into granular soil.  

Case 2:Anchored bulkhead embedded in cohesive soil 

5.3.2 Fixed Earth Support Method 

5.4 Lateral Earth Pressures on Braced Sheeting   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Chapter 5

Sheet Pile Wall

5.1 Introduction

A series of sheet piles driven into the ground side by side, form a continuous vertical

wall which is referred to as a sheet pile wall. A sheet pile wall acts as a retaining wall but

unlike the RCC or masonry rigid retaining walls, it is light in weight and flexible.

The sheet piles used are of timber, reinforced concrete or steel depending on the

provision made for achieving stability. Sheet pile walls are of three types:

1) Cantilever sheet piling

2) Anchored sheet piling

3) Braced sheeting

Sheet pile walls are used in

1. Light weight construction when the bearing stratum is poor for supporting the

heavier RCC or masonry retaining wall.

2. For temporarily retaining earthfills in some construction activities and

3. Water front structures.

A bulk head is a sheet pile wall used as a water front structure backed up by ground

and finds wide application in docks and harbours. A cofferdam is a reasonably watertight

enclosure, usually temporary, built around a working area in the midst of water for the

purpose of excluding water from that enclosed area during construction. Sheet pile walls can

be employed in the construction of cofferdams.

It has already been mentioned that sheet piles can be of timber, RCC or steel. Timber

sheet piling is suitable only for short spans, where lateral loads are light and are commonly

used in the form of braced sheeting in temporary construction activities. Timber sheet piles

have to be used below permanent water level; otherwise they have to be pretreated with

preservatives to prevent rotting due to alternate wetting and drying. Reinforced cement

concrete sheet piles are precast. They are designed to withstand the permanent stresses

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induced during service and handling stresses during construction. They are usually provided

with tongue and groove joints. They have the disadvantages of being heavy and bulky,

requiring heavier equipment during handling and driving. Steel sheet piling is usually the best

choice because of the following advantages:

1) light weight,

2) can be reused several times,

3) can resist high driving stresses,

4) lesser deformation of joints during driving,

5) easier to increase the pile length and

6) longer service life.

5.2 Cantilever Sheet Pile Wall

A Cantilever sheet pile wall derives its stability entirely from the lateral resistance of

the soil into which it is driven and requires sufficient embedment in soil. It is therefore

economical only for moderate heights of earthfill to be retained for which the depth of

embedment required is not too large. In the following analysis two specific cases have been

considered.

Case 1) Cantilever sheet pile embedded in granular soil.

From experimental investigations it is found that, the earth pressure developed tend to

cause rotation of the wall about a pivot (point c) below the dredge level as shown in Fig

5.1(a) and the probable earth pressure distribution will be as shown in Fig5.1(b). But the

conventional design of cantilever sheet pile wall is based on the simplified pressure

distribution shown in Fig5.1(c).

In the Fig 5.2, H is the height of fill above dredge line and D is the depth of

embedment. Assuming that the properties of soil are the same above and below the dredge

line, we make the following computations.

Active earth pressure intensity at dredge level, towards back of wall, 𝑝 ₁ = 𝐾 𝛾𝐻.

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Fig 5.1: Analysis of cantilever sheet pile wall embedded in granular soil

Fig. 5.2: Pressure distribution diagram in the case of cantilever sheet pile wall in granular soil

Letobe the point at which the net pressure intensity becomes zero, and is at a depth ‘a’

below the dredge line. Then, at point o we have

𝐾 𝛾𝑎 − (𝑝 ₁ + 𝐾 𝛾a) =0 .·. 𝑎 = ₁( ) …..(5.1)

Net passive pressure intensity at base of wall, towards front of wall 𝑝 ₁ = 𝐾 − 𝐾 𝛾𝑌 ....(5.2)

Net passive pressure intensity at base of wall towards back of wall, 𝑝 ₂ = 𝐾 𝛾(𝐻 + 𝑎 + 𝑌) − 𝐾 𝛾(a+Y) ….(5.3)

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Let Ra denote the resultant active earth pressure on back of wall. Let it act at a distance of 𝑦

from point o.

Applying the condition ∑ 𝐻 =0 𝑅 + ½ 𝑝 ₁ + 𝑝 ₂ 𝑍 − ½𝑝 ₁𝑌 = 0 …..(5.4)

Taking moments about base ‘b’ and applying the condition∑ 𝑀 = 0,

𝑅 (�̅�+Y)+½(𝑝 ₁ + 𝑝 ₂)𝑍. − ½𝑝 ₁𝑌. = 0 …..(5.5)

Value of ‘a’ can be obtained from Equation (5.1). Equations (5.2) and (5.3) express 𝑝 ₁ and 𝑝 ₂ in terms of ‘Y’.Equation (5.4) is used to express ‘Z’ in terms of ‘Y’.

After substituting the values of Ra,𝑦 and the expression for 𝑝 ₁, 𝑝 ₂ and Z in Eq (5.5),

we get a fourth degree equation in ‘Y’, solving which the value of ‘Y’ is obtained.

Then D=a+Y …….(5.6)

To account for the differences between the assumed and actual pressure distributions

as well as uncertainties in evaluating soil parameters, a factor of safety ‘F’ is applied to𝐾 ,

i.e, is used in place of𝐾 . Usually ‘F’ is taken between 1.5 and 2. Alternatively the value

of ‘D’ obtained by Equation(5.6) is increased by 20% to 40%.

Approximate Analysis

In the approximate analysis the active pressure distribution on back of wall and

passive pressure distribution on front of wall is assumed to extend upto bottom of wall. The

passive pressure on back of wall below point c is also assumed to act at bottom of wall.

Fig. 5.3: Cantilever sheet pile wall: approximate analysis

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Taking moments about b, for equilibrium ΣM=0

i.e. ½𝐾 𝛾𝐷. 𝐷. − ½𝐾 𝛾(𝐻 + 𝐷). (𝐻 + 𝐷) ( ) = 0

[𝐾 𝛾𝐷 − 𝐾 𝛾(𝐻 + 𝐷) ] = 0

We thus get a cubic equation in D, solving which the depth of embedment is obtained.

Case 2) Cantilever sheet pile wall embedded in cohesive soil.

In the Fig 5.4, H is the height of wall above dredge line and D is the depth of

embedment. The soil is considered to be purely cohesive (ϕ = 0) both above and below the

dredge line. At any depth z below the surface of fill, the active pressure intensity is given by 𝑝 = 𝛾z cot ² ∝ −2c cot ∝

= γz-2c (∵∝ =45°for ϕ= 0)

At a,z = 0 ⟹ 𝑝 = −2c

At d, z=H ⟹ 𝑝 = 𝛾𝐻 − 2c = 𝑞 − 2c

where q denotes the effective vertical pressure at dredge line level, behind the wall.

Net passive pressure intensity at d, towards front of wall

= [0 (tan ² ∝) + 2𝑐 tan ∝] − [𝑞 cot ² ∝ −2𝑐 cot ∝] = [2c]-[q-2c]

= 4c-q(∵∝= 45°for ϕ=0)

Net passive pressure intensity at b, towards back of wall

= [(q+γD)tan ² ∝ +2𝑐 tan ∝] − [𝛾𝐷 cot ² ∝ −2𝑐 cot ∝] =q+γD+2c-γD+2c

=4c+q

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Fig 5.4: Cantilever sheet pile wall in cohesive soil

In the earth pressure distribution diagram shown in Fig 5.4, the net passive pressure

diagram is shown shaded. Let Ra denote resultant active pressure on back of wall acting at a

distance 𝑦 above dredge line level.

Applying the condition ∑H=0 for equilibrium, we get 𝑅 + ½(4𝑐 − 𝑞 + 4𝑐 + 𝑞)ℎ − (4𝑐 − 𝑞)𝐷 = 0 ….. (5.7)

Taking moments about bottom b and applying the condition ∑M=0 for equilibrium, we get

𝑅 (�̅� + 𝐷) + ½(4𝐶 − 𝑞 + 4𝐶 + 𝑞)ℎ. − (4𝐶 − 𝑞)𝐷. = 0 …..(5.8)

Equation (5.7) is used to express h in terms of D. and then substituted in Eq (5.8).

Then it contains only one unknown D and can be solved for D. The value of D obtained is

increased by 20% to 40% to account for uncertainties. Alternatively C is replaced by C/F

where the factor of safety is taken from 3 to 4.

Note: Many times it is desirable to drive the sheet pile into cohesive soil and then backfill

with a freely draining granular soil. In such conditions the active pressure diagram above the

dredge level will be for the granular fill as shown in fig 5.5. But for this, the analysis is the

same as that for the case shown in fig 5.4.

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Fig. 5.5: Cantilever sheet pile wall embedded in cohesive soil but with granular fill

5.3 Anchored Bulkhead

Anchored bulkhead is a water-front structure backed up by ground. The use of anchor

rod helps in reduction of lateral deflection and depth of penetration. In case of walls with

large height more than one anchor can be provided. The stability of an anchored bulkhead

depends on;

(1) Relative stiffness of sheet piling

(2) Depth of penetration

(3) The relative compressibility of soil and

(4) Amount of yield of anchor

The two methods commonly used in the design of anchored bulkheads are

(1) Free earth support method and

(2) Fixed earth support method.

The following discussions deal with the two problems involved in the design of anchored

bulkhead

(1) Determining the depth of embedment, and

(2) Force in anchor rod.

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5.3.1 Free-Earth Support Method

The method is based on the following assumptions.

(a) The sheet pile is perfectly rigid as compared to the surrounding soil.

(b) There is no lateral movement at the rod level. The sheet pile is free to rotate about

the point of wall at which anchor rod is provided. This assumption is satisfied only if

the sheet pile is driven to a shallow depth in soil.

(c) The active and passive earth pressures can be computed using Rankine's theory.

Case (1) Anchored bulkhead driven into granular soil.

The simplified pressure distribution diagram for this case is shown in Fig 5.6.Active pressure

intensity at dredge line level, acting towards back of wall, 𝑃 ₁ = 𝐾 𝛾ℎ₁ + 𝐾 𝛾′ℎ₂ …… 5.9

Let the net pressure intensity be zero at point ‘c’ which is at a depth ‘a’ below dredge line.

Then 𝐾 𝛾′𝑎 − 𝑃 ₁ + 𝐾 𝛾′𝑎 = 0

Fig 5.6: Anchored bulkhead embedded in granular soil

.·. a= ₁( ) ….. (5.10)

Net passive pressure intensity at bottom of wall, acting towards front of wall,

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𝑝 = 𝐾 𝛾 𝑌 − 𝐾 𝛾 𝑌 = 𝐾 − 𝐾 𝛾 𝑌 …..(5.11)

Let𝑅 =resultant active pressure acting at distance y₁ below the anchor rod level 𝑅 =resultant net passive pressure acting at distance y₂ below the anchor rod level.

Taking moments about anchor rod level and applying the condition ∑M=0, we have 𝑅 𝑌 -𝑅 𝑌₁=0 .….(5.12)

But𝑅 =½(𝐾 -𝐾 )𝛾′𝑌 and𝑦 =h+a+⅔Y

Substituting in Equation (5.12), we get

½(𝐾 -𝐾 )𝛾′𝑌 (ℎ + 𝑎 +⅔𝑌) − 𝑅 𝑌 = 0

¹ 𝑌³ + ¹( ) 𝑌² − 𝑅 𝑌 = 0 …..(5.13)

From Equation (5.10) ‘a’ is evaluated.

Substituting the value of ‘a’ in Equation (5.13), and then solving it,Y is obtained. Then

D=Y+a.

The value of D thus obtained is increased by 20 to 40% or is used in place of𝐾 ,

where factor of safety F is taken from 1.5 to 2. To find the force in the anchor rod, we apply

the condition ∑H=0.

𝐹 + 𝑅 − 𝑅 = 0

.·. 𝐹 = 𝑅 − 𝑅 ..… (5.14)

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Case (2) Anchored bulkhead embedded in cohesive soil

Fig. 5.7: Anchored bulkhead embedded in cohesive soil

Fig 5.7 shows the earth pressure distribution for bulkhead with cohesive soil below

the dredge line and granular fill above it.

Active pressure intensity at dredge line level acting on back of wall, 𝑝 ₁ = 𝐾 𝛾ℎ₁ + 𝐾 ₂𝛾 ℎ₂ ..…(5.15)

Net passive pressure intensity at dredge level, acting on front of wall,

𝑝 ₁ = (0 + 2𝑐) − (𝑞 − 2𝑐) = (4𝑐 − 𝑞) …..(5.16)

Let Ra be the resultant active pressure acting at distance 𝑦₁ from anchor rod level and 𝑅 the

resultant net passive pressure acting at distance 𝑦 from anchor rod level.Taking moments

about anchor rod level and applying the condition ∑M=0, we get

(4c-q)D. (h+ ) -𝑅 𝑦₁=0

i.e.,( )

D² + (4c-q)hD - 𝑅 𝑦₁=0 ..…(5.17)

Solving the above equation D is obtained. To find the force in the anchor rod we apply the

condition ∑H=0

𝑅 + 𝐹 − 𝑅 =0

.·. 𝐹 = 𝑅 − 𝑅 .…. (5.18)

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The value of D obtained from Equation (5.17) is increased by 20 to 40% to cover the

uncertainties.

5.3.2 Fixed Earth Support Method

When an anchored bulkhead is driven to a considerable depth, its lower portion will

be practically fixed in position and it slowly acts as a vertical propped cantilever. The

deflected shape or the elastic line of the anchored bulkhead is likely to be as shown in Fig 5.8

(a). Fig 5.8(b) shows the assumed earth pressure distribution for an anchored bulkhead

embedded in granular soil.

The fixity is over the length ‘cb’ which remains straight and vertical. ‘c’ is the point

of contra-flexure. Let it be at distance y below the dredge line. To simplify the analysis,

pressure diagram below the point ‘c’ is replaced by a force Rb acting at ‘e’.

Fig. 5.8: Anchored bulkhead with fixed earth support

There are two approaches for analysis of bulkheads with fixed earth support.

(1) Elastic line method and

(2) Equivalent beam method

In the elastic line method, the distance Y is first estimated and Rb is evaluated. The

bending moment diagram is drawn and the tangential deviation of ‘e’ with respect to ‘f’ (at

anchored rod level) is computed. The distance Y is then suitably revised to reduce the

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deviation. The process is repeated until the computed tangential deviation of ‘e’ becomes

zero. The method is time consuming. Because of this the equivalent beam method which

represents a simplification of the elastic line method and requires much less time and labour with

only little sacrifice in accuracy is generally preferred.

Fig. 5.9: Variation of y with φ

The equivalent beam method as given by H. Blum (1931) is discussed here. In this method the

distance ‘y’ of point of contra flexure ‘c’ below dredge line is a function of ɸ and can be

obtained from Fig 5.9, drawn for granular soil.

A hinge is assumed at the point of contra flexure ‘c’, and the two parts ‘bc’ and ‘ca’ are

treated as two independent spans. The upper part ‘ca’ is treated as simply supported beam with

overhanging end. Further it is assumed that ‘be’=0.2Y

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Fig. 5.10: Equivalent beam method

Referring to fig 5.10(a),

Active earth pressure intensity at dredge level, acting on back of wall, 𝑝 = 𝐾 𝛾ℎ + 𝐾 𝛾 ℎ ….(5.19)

To find ‘a’, we have,

𝐾 𝛾 𝑎 − (𝐾 𝛾 𝑎 + 𝑝 ) = 0

. .̇ a = ( ) …..(5.20)

‘y’ is found from Fig 5.9 and the active pressure intensity 𝑝 at point c, is given by 𝑝(a − 𝑦) = 𝑝a

i.e 𝑝 = (a − 𝑦) …..(5.21)

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Considering free body diagram of portion ‘ca’ and taking moments about ‘f’ (anchor rod

level) and applying the condition ΣM=0, we can evaluate the force 𝑅

Net passive pressure intensity at ‘b’, acting on front of wall, 𝑝 = 𝐾 𝛾′(𝑌 − a) − 𝐾 𝛾′(𝑌 − a) ……(5.22)

Considering free body diagram of portion ‘bc’, taking moments about ‘e’ and applying

the condition ΣM=0, we can find the distance (Y-y) and hence Y.

Finally D=1.2Y

The value of D thus obtained is increased by 20 to 40% to cover the uncertainties.

5.4Lateral Earth Pressures on Braced Sheeting

In strutted excavations sheet piles are

used to retain the soil on the sides. The sheet

piles are held in position by means of wales and

struts as shown in Fig 5.11. The pressure

distributions on the sheet piles are difficult to be

determined theoretically. Based on actual

measurements in field, Terzaghi and Peck, and

Tschebotariaff have proposed empirical pressure

distribution diagrams shown in Fig 5.12 and Fig

5.13 for sands and clays respectively. It is found

that it is better to estimate using both the

methods and use the one that is more critical.

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Fig 5.12: Earth pressure distribution diagrams on braced sheeting in sand proposed by Terzaghi & Peck (a,b) &Tschebotariaff (c)

Fig. 5.13:

Earth pressure distribution diagrams on braced sheeting in clay proposed by Terzaghi &

Peck (a) &Tschebotariaff (b,c)