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9

9.1 Introduction

Connected or semiconnected sheet piles are often used to build continuous walls for water-front structures that range from small waterfront pleasure boat launching facilities to largedock facilities. (See Figure 9.1.) In contrast to the construction of other types of retainingwall, the building of sheet pile walls does not usually require dewatering of the site. Sheetpiles are also used for some temporary structures, such as braced cuts. (See Chapter 10.)The principles of sheet-pile wall design are discussed in the current chapter.

Several types of sheet pile are commonly used in construction: (a) wooden sheetpiles, (b) precast concrete sheet piles, and (c) steel sheet piles. Aluminum sheet piles arealso marketed.

Wooden sheet piles are used only for temporary, light structures that are above thewater table. The most common types are ordinary wooden planks and Wakefield piles.The wooden planks are about in cross section and are driven edgeto edge (Figure 9.2a). Wakefield piles are made by nailing three planks together, withthe middle plank offset by 50 to 75 mm (Figure 9.2b). Wooden planks can also bemilled to form tongue-and-groove piles, as shown in Figure 9.2c. Figure 9.2d showsanother type of wooden sheet pile that has precut grooves. Metal splines are driven intothe grooves of the adjacent sheetings to hold them together after they are sunk into theground.

50 mm 3 300 mm

437

Sheet Pile Walls

Watertable Water table

Sheetpile

Dredge line

Land side

Figure 9.1 Example of waterfront sheet-pile wall

438 Chapter 9: Sheet Pile Walls

Figure 9.2 Various types of wooden and concrete sheet pile

Precast concrete sheet piles are heavy and are designed with reinforcements towithstand the permanent stresses to which the structure will be subjected after con-struction and also to handle the stresses produced during construction. In cross section,these piles are about 500 to 800 mm wide and 150 to 250 mm thick. Figure 9.2e isa schematic diagram of the elevation and the cross section of a reinforced concretesheet pile.

Steel sheet piles in the United States are about 10 to 13 mm thick. Europeansections may be thinner and wider. Sheet-pile sections may be Z, deep arch, low arch, orstraight web sections. The interlocks of the sheet-pile sections are shaped like a thumb-and-finger or ball-and-socket joint for watertight connections. Figure 9.3a is a schematicdiagram of the thumb-and-finger type of interlocking for straight web sections. The ball-and-socket type of interlocking for Z section piles is shown in Figure 9.3b. Figure 9.4shows a sheet pile wall. Table 9.1 lists the properties of the steel sheet pile sectionsproduced by the Bethlehem Steel Corporation. The allowable design flexural stress forthe steel sheet piles is as follows:

Type of steel Allowable stress

ASTM A-328ASTM A-572ASTM A-690

Steel sheet piles are convenient to use because of their resistance to the high driving stressthat is developed when they are being driven into hard soils. Steel sheet piles are also light-weight and reusable.

210 MN>m2

210 MN>m2

170 MN>m2

Wooden Sheet Piles

(a) Planks

Concretegrout

Reinforcement

Elevation

Precast Concrete Sheet Pile

Section

(b) Wakefield piles

(c) Tongue-and-groove piles

(d) Splined piles (e)

(not to scale)

500-800 mm

150-250 mm

9.1 Introduction 439

Figure 9.3 (a) Thumb-and-finger type sheet pileconnection; (b) ball-and-socket type sheet-pileconnection

Table 9.1 Properties of Some Sheet-Pile Sections Produced by Bethlehem Steel Corporation

Section modulus Moment of inertia

Section designation Sketch of section of wall of wall

PZ-40 670.5 3 1026326.4 3 1025

Driving distance 500 mm

409 mm

15.2 mm

12.7 mm

m4,mm3

,m

(c)

(a)

(b)

(Continued)

Figure 9.4 A steel sheet pile wall (Courtesy of N. Sivakugan, James Cook University, Australia )


PZ-35

PZ-27

PZ-22

PSA-31

PSA-23 5.63 3 102612.8 3 1025

Driving distance 406.4 mm

9.53 mm

4.41 3 102610.8 3 1025


12.7 mm

115.2 3 102697 3 1025


228.6 mm

9.53 mm

9.53 mm

251.5 3 1026162.3 3 1025


304.8 mm

9.53 mm

9.53 mm

493.4 3 1026260.5 3 1025


379 mm

15.2 mm

12.7 mm

Table 9.1 (Continued)

Section modulus Moment of inertia

Section designation Sketch of section of wall of wall

m4,mm3

,m

9.2 Construction Methods 441

Anchorrod

Dredge

Originalgroundsurface

Step 1 Step 2

Step 3 Step 4

Backfill

Dredgeline

Backfill

Figure 9.5 Sequence of construction fora backfilled structure

9.2 Construction Methods

Sheet pile walls may be divided into two basic categories: (a) cantilever and (b) anchored.In the construction of sheet pile walls, the sheet pile may be driven into the ground

and then the backfill placed on the land side, or the sheet pile may first be driven into theground and the soil in front of the sheet pile dredged. In either case, the soil used for back-fill behind the sheet pile wall is usually granular. The soil below the dredge line may besandy or clayey. The surface of soil on the water side is referred to as the mud line ordredge line.

Thus, construction methods generally can be divided into two categories (Tsinker,1983):

1. Backfilled structure2. Dredged structure

The sequence of construction for a backfilled structure is as follows (see Figure 9.5):

Step 1. Dredge the in situ soil in front and back of the proposed structure.Step 2. Drive the sheet piles.Step 3. Backfill up to the level of the anchor, and place the anchor system.Step 4. Backfill up to the top of the wall.

For a cantilever type of wall, only Steps 1, 2, and 4 apply. The sequence of constructionfor a dredged structure is as follows (see Figure 9.6):

Step 1. Drive the sheet piles.Step 2. Backfill up to the anchor level, and place the anchor system.Step 3. Backfill up to the top of the wall.Step 4. Dredge the front side of the wall.

With cantilever sheet pile walls, Step 2 is not required.


9.3 Cantilever Sheet Pile Walls

Cantilever sheet pile walls are usually recommended for walls of moderate height—about 6 m or less, measured above the dredge line. In such walls, the sheet piles actas a wide cantilever beam above the dredge line. The basic principles for estimatingnet lateral pressure distribution on a cantilever sheet-pile wall can be explained withthe aid of Figure 9.7. The figure shows the nature of lateral yielding of a cantileverwall penetrating a sand layer below the dredge line. The wall rotates about point O(Figure 9.7a). Because the hydrostatic pressures at any depth from both sides of thewall will cancel each other, we consider only the effective lateral soil pressures. Inzone A, the lateral pressure is just the active pressure from the land side. In zone B,because of the nature of yielding of the wall, there will be active pressure from theland side and passive pressure from the water side. The condition is reversed in zoneC—that is, below the point of rotation, O. The net actual pressure distribution on thewall is like that shown in Figure 9.7b. However, for design purposes, Figure 9.7cshows a simplified version.

Sections 9.4 through 9.7 present the mathematical formulation of the analysis ofcantilever sheet pile walls. Note that, in some waterfront structures, the water level mayfluctuate as the result of tidal effects. Care should be taken in determining the water levelthat will affect the net pressure diagram.

9.4 Cantilever Sheet Piling Penetrating Sandy Soils

To develop the relationships for the proper depth of embedment of sheet piles driveninto a granular soil, examine Figure 9.8a. The soil retained by the sheet piling abovethe dredge line also is sand. The water table is at a depth below the top of the wall.L1

Step 1 Step 2

Step 3 Step 4

Dredge

Originalgroundsurface

Anchorrod

Backfill

Backfill

Figure 9.6 Sequence of constructionfor a dredged structure

9.4 Cantilever Sheet Piling Penetrating Sandy Soils 443

Watertable

Zone A

Zone B

O

Dredgeline

Activepressure Sand

Sand

(a) (b) (c)

Activepressure

Passivepressure

Passivepressure

Activepressure

Zone C

Figure 9.7 Cantilever sheet pile penetrating sand

Watertable

D

Dredge line

Slope:1 vertical:(Kp – Ka)��horizontal

Sand

GBH

(a) (b)

L4

L1

L

L2

L3

L5

F

z

4��3��

2��

1��

�sat��c� = 0

Mmax

Sand�sat��c� = 0

Sand��c� = 0

F�

z�F�

P

zD

C

E

A

Figure 9.8 Cantilever sheet pile penetrating sand: (a) variation of net pressure diagram; (b) variation of moment


Let the effective angle of friction of the sand be The intensity of the active pres-sure at a depth is

(9.1)

where

weight of soil above the water table

Similarly, the active pressure at a depth (i.e., at the level of the dredgeline) is

(9.2)

where .

Note that, at the level of the dredge line, the hydrostatic pressures from both sides ofthe wall are the same magnitude and cancel each other.

To determine the net lateral pressure below the dredge line up to the point of rota-tion, O, as shown in Figure 9.7a, an engineer has to consider the passive pressure actingfrom the left side (the water side) toward the right side (the land side) of the wall and alsothe active pressure acting from the right side toward the left side of the wall. For suchcases, ignoring the hydrostatic pressure from both sides of the wall, the active pressure atdepth z is

(9.3)

Also, the passive pressure at depth z is

(9.4)

where .Combining Eqs. (9.3) and (9.4) yields the net lateral pressure, namely,

(9.5)

where .The net pressure, equals zero at a depth below the dredge line, so

or

(9.6)(z 2 L) 5 L3 5sr2

gr(Kp 2 Ka)

sr2 2 gr(z 2 L) (Kp 2 Ka) 5 0

L3srL 5 L1 1 L2

5 sr2 2 gr(z 2 L) (Kp 2 Ka)

sr 5 sra 2 srp 5 (gL1 1 grL2)Ka 2 gr(z 2 L1 2 L2) (Kp 2 Ka)

Kp 5 Rankine passive pressure coefficient 5 tan2(45 1 fr>2)

srp 5 gr(z 2 L1 2 L2)Kp

sra 5 3gL1 1 grL2 1 gr(z 2 L1 2 L2) 4Ka

gr 5 effective unit weight of soil 5 gsat 2 gw

sr2 5 (gL1 1 grL2)Ka

z 5 L1 1 L2

g 5 unit

Ka 5 Rankine active pressure coefficient 5 tan2(45 2 fr>2)

sr1 5 gL1Ka

z 5 L1

fr.


Equation (9.6) indicates that the slope of the net pressure distribution line DEF is 1 verti-cal to horizontal, so, in the pressure diagram,

(9.7)

At the bottom of the sheet pile, passive pressure, acts from the right toward the leftside, and active pressure acts from the left toward the right side of the sheet pile, so, at

(9.8)

At the same depth,

(9.9)

Hence, the net lateral pressure at the bottom of the sheet pile is

(9.10)

where

(9.11)(9.12)

For the stability of the wall, the principles of statics can now be applied:

and

For the summation of the horizontal forces, we have

or

(9.13)

where of the pressure diagram ACDE.Summing the moment of all the forces about point B yields

(9.14)

From Eq. (9.13),

(9.15)L5 5sr3L4 2 2P

sr3 1 sr4

P(L4 1 z) 2 ¢1

2 L4sr3≤ ¢L4

3≤ 1

1

2L5(sr3 1 sr4) ¢L5

3≤ 5 0

P 5 area

P 2 12sr3L4 1 1

2L5(sr3 1 sr4) 5 0

Area of the pressure diagram ACDE 2 area of EFHB 1 area of FHBG 5 0

S moment of the forces per unit length of wall about point B 5 0

S horizontal forces per unit length of wall 5 0

D 5 L3 1 L4

sr5 5 (gL1 1 grL2)Kp 1 grL3(Kp 2 Ka)

5 sr5 1 grL4(Kp 2 Ka)

5 (gL1 1 grL2)Kp 1 grL3(Kp 2 Ka) 1 grL4(Kp 2 Ka)

srp 2 sra 5 sr4 5 (gL1 1 grL2)Kp 1 grD(Kp 2 Ka)

sra 5 grDKa

srp 5 (gL1 1 grL2 1 grD)Kp

z 5 L 1 D,

srp ,

HB 5 sr3 5 L4(Kp 2 Ka)gr

(Kp 2 Ka)gr


Combining Eqs. (9.7), (9.10), (9.14), and (9.15) and simplifying them further, we obtainthe following fourth-degree equation in terms of

(9.16)

In this equation,

(9.17)

(9.18)

(9.19)

(9.20)

Step-by-Step Procedure for Obtaining the Pressure Diagram

Based on the preceding theory, a step-by-step procedure for obtaining the pressure diagramfor a cantilever sheet pile wall penetrating a granular soil is as follows:

Step 1. Calculate and Step 2. Calculate [Eq. (9.1)] and [Eq. (9.2)]. (Note: and will be given.)Step 3. Calculate [Eq. (9.6)].Step 4. Calculate P.Step 5. Calculate (i.e., the center of pressure for the area ACDE) by taking the

moment about E.Step 6. Calculate [Eq. (9.11)].Step 7. Calculate and [Eqs. (9.17) through (9.20)].Step 8. Solve Eq. (9.16) by trial and error to determine Step 9. Calculate [Eq. (9.10)].

Step 10. Calculate [Eq. (9.7)].Step 11. Obtain from Eq. (9.15).Step 12. Draw a pressure distribution diagram like the one shown in Figure 9.8a.Step 13. Obtain the theoretical depth [see Eq. (9.12)] of penetration as

The actual depth of penetration is increased by about 20 to 30%.

Note that some designers prefer to use a factor of safety on the passive earth pres-sure coefficient at the beginning. In that case, in Step 1,

where of safety (usually between 1.5 and 2).FS 5 factor

Kp(design) 5Kp

FS

L3 1 L4 .

L5

sr3sr4

L4 .A4A1 , A2 , A3 ,

sr5

z

L3

L2L1sr2sr1Kp .Ka

A4 5P(6zsr5 1 4P)

gr2(Kp 2 Ka)2

A3 56P32zgr(Kp 2 Ka) 1 sr54

gr2(Kp 2 Ka)2

A2 58P

gr(Kp 2 Ka)

A1 5sr5

gr(Kp 2 Ka)

L44 1 A1L4

3 2 A2L42 2 A3L4 2 A4 5 0

L4 :


For this type of analysis, follow Steps 1 through 12 with the value of and (instead of ). The actual depth of penetration can now be

determined by adding obtained from Step 3, and obtained from Step 8.

Calculation of Maximum Bending Moment

The nature of the variation of the moment diagram for a cantilever sheet pile wall is shownin Figure 9.8b. The maximum moment will occur between points E and Obtaining themaximum moment per unit length of the wall requires determining the point of zeroshear. For a new axis (with origin at point E) for zero shear,

or

(9.21)

Once the point of zero shear force is determined (point in Figure 9.8a), the mag-nitude of the maximum moment can be obtained as

(9.22)

The necessary profile of the sheet piling is then sized according to the allowable flexuralstress of the sheet pile material, or

(9.23)

where

modulus of the sheet pile required per unit length of the structureflexural stress of the sheet pile

Example 9.1

Figure 9.9 shows a cantilever sheet pile wall penetrating a granular soil. Here, L1 � 2 m,L2 � 3 m, � � 15.9 kN/m3, �sat � 19.33 kN/m3, and �� 32°.

a. What is the theoretical depth of embedment, D?b. For a 30% increase in D, what should be the total length of the sheet piles?c. What should be the minimum section modulus of the sheet piles? Use �all �

172 MN/m2.

Solution

Part aUsing Figure 9.8a for the pressure distribution diagram, one can now prepare the fol-lowing table for a step-by-step calculation.

sall 5 allowable

S 5 section

S 5Mmax

sall

Mmax 5 P(z 1 zr) 2 312 grzr2(Kp 2 Ka) 4 (13)zr

Fs

zr 5Å

2P

(Kp 2 Ka)gr

P 5 12(zr)2(Kp 2 Ka)gr

zr(Mmax)

Fr.

L4 ,L3 ,

KpKp(design)tan2(45 2 fr>2)

Ka 5


Water table

Sand�c� = 0��

Sand�satc� = 0��

Sand�satc� = 0��

L1

L2

D

Dredge line

Figure 9.9 Cantilever sheet-pile wall

Quantity Eq. required no. Equation and calculation

Ka —

Kp —

�1� 9.1 �L1Ka � (15.9)(2)(0.307) � 9.763 kN/m2

�2� 9.2 (�L1 � ��L2)Ka � [(15.9)(2) � (19.33 � 9.81)(3)](0.307) � 18.53 kN/m2

L3 9.6

P —

—

�5� 9.11 (�L1 � ��L2)Kp � ��L3(Kp � Ka) � [(15.9)(2) � (19.33 � 9.81)(3)](3.25)� (19.33 � 9.81)(0.66)(3.25� 0.307) � 214.66 kN/m2

A1 9.17

A2 9.188P

gr(Kp 2 Ka)5

(8) (58.32)

(19.33 2 9.81) (3.25 2 0.307)5 16.65

s5rgr(Kp 2 Ka)

5214.66

(19.33 2 9.81) (3.25 2 0.307)5 7.66

SME

P5

1

58.32C9.763(0.66 1 3 1 2

3) 1 29.289(0.66 1 32)

1 13.151(0.66 1 33) 1 6.115(0.66 3 2

3)S 5 2.23 mz

5 9.763 1 29.289 1 13.151 1 6.115 5 58.32 kN>m

1 (12) (18.53) (0.66)

1 (12) (18.53 2 9.763) (3)5 (1

2) (9.763) (2) 1 (9.763) (3)

12s1rL1 1 s1rL2 1 1

2(s2r 2 s1r)L2 1 12s2rL3

s2rgr(Kp 2 Ka)

518.53

(19.33 2 9.81) (3.25 2 0.307)5 0.66 m

tan2a45 1fr2b 5 tan2a45 1

32

2b 5 3.25


32

2b 5 0.307

9.5 Special Cases for Cantilever Walls Penetrating a Sandy Soil 449

A3 9.19

A4 9.20

L4 9.16 L44 � A1L4

3 � A2L42 � A3L4 � A4 � 0

L44 � 7.66L4

3 � 16.65L42 � 151.93L4 � 230.72 � 0; L4 � 4.8 m

Thus,Dtheory � L3 � L4 � 0.66 � 4.8 � 5.46 m

Part bThe total length of the sheet piles is

L1 � L2 � 1.3(L3 � L4) � 2 � 3 � 1.3(5.46) � 12.1 m

Part cFinally, we have the following table.


z� 9.21

Mmax 9.22

S 9.29 ■Mmax

s all5

209.39 kN # m172 3 103 kN>m2

5 1.217 3 1023 m3>m of wall

5 209.39 kN # m>m

2 c a1

2b (19.33 2 9.81) (2.04)2(3.25 2 0.307) d

2.04

3

P(z 1 zr) 2 c1

2grzr2(Kp 2 Ka) d

zr3

5 (58.32) (2.23 1 2.04)

Ä

2P

(Kp 2 Ka)gr5

Å

(2) (58.32)

(3.25 2 0.307) (19.33 2 9.81)5 2.04 m

5 230.72

P(6zsr5 1 4P)

gr2

(Kp 2 Ka)25

58.323(6) (2.23) (214.66) 1 (4) (58.32) 4

(19.33 2 9.81)2(3.25 2 0.307)2

5 151.93

5(6) (58.32) 3(2) (2.23) (19.33 2 9.81) (3.25 2 0.307) 1 214.664

(19.33 2 9.81)2(3.25 2 0.307)2

6P32zgr(Kp 2 Ka) 1 s5r 4

gr2(Kp 2 Ka)2

9.5 Special Cases for Cantilever Walls Penetrating a Sandy Soil

Sheet Pile Wall with the Absence of Water Table

In the absence of the water table, the net pressure diagram on the cantilever sheet-pile wallwill be as shown in Figure 9.10, which is a modified version of Figure 9.8. In this case,


D

L5

L3

4��3��

2��

Sand��

Sand��

P

z

L4

L

Figure 9.10 Sheet piling penetratinga sandy soil in the absence of thewater table

(9.24)(9.25)

(9.26)

(9.27)

(9.28)

(9.29)

(9.30)

and Eq. (9.16) transforms to

(9.31)

where

(9.32)

(9.33)

(9.34)

(9.35) A r4 5P(6zsr5 1 4P)

g2(Kp 2 Ka)2

A r3 56P32zg(Kp 2 Ka) 1 sr54

g2(Kp 2 Ka)2

A r2 58P

g(Kp 2 Ka)

A r1 5sr5

g(Kp 2 Ka)

L44 1 A r1L4

3 2 A r2L42 2 A r3L4 2 A r4 5 0

z 5 L3 1L

35

LKa

Kp 2 Ka1

L

35

L(2Ka 1 Kp)

3(Kp 2 Ka)

P 5 12sr2L 1 1

2sr2L3

L3 5sr2

g(Kp 2 Ka)5

LKa

(Kp 2 Ka)

sr5 5 gLKp 1 gL3(Kp 2 Ka)

sr4 5 sr5 1 gL4(Kp 2 Ka)

sr3 5 L4(Kp 2 Ka)g sr2 5 gLKa

9.5 Special Cases for Cantilever Walls Penetrating a Sandy Soil 451

Free Cantilever Sheet Piling

Figure 9.11 shows a free cantilever sheet-pile wall penetrating a sandy soil and subjectedto a line load of P per unit length of the wall. For this case,

(9.36)

(9.37)

(9.38)

and

(9.39)

Example 9.2

Redo parts a and b of Example 9.1, assuming the absence of the water table. Use � �15.9 kN/m3 and �� 32°. Note: L � 5 m.

zr 5Å

2P

gr(Kp 2 Ka)

Mmax 5 P(L 1 zr) 2gz93(Kp 2 Ka)

6

L5 5g(Kp 2 Ka)D2 2 2P

2D(Kp 2 Ka)g

D4 2 c8P

g(Kp 2 Ka)dD2 2 c

12PL

g(Kp 2 Ka)dD 2 c

2P

g(Kp 2 Ka)d

2

5 0

Figure 9.11 Free cantilever sheetpiling penetrating a layer of sand

L5

L

P

D��c� = 0

Sand

��3 = �D (Kp – Ka) ��4 = �D (Kp – Ka)


Solution

Part a


Ka —

Kp —

�2� 9.24 �LKa � (15.9)(5)(0.307) � 24.41 kN/m2

L3 9.28

�5� 9.27 �LKp � �L3(Kp � Ka) � (15.9)(5)(3.25) � (15.9)(0.521)(3.25 � 0.307)� 282.76 kN/m2

P 9.29

9.30

A1� 9.32

A2� 9.33

A3� 9.34

A4� 9.35

L4 9.31 L44 � A1�L4

3 � A2�L42 � A3�L4 � A4� � 0

L44 � 6.04L4

3 � 11.52L42 � 90.01L4 � 122.52 � 0; L4 � 4.1 m

Dtheory � L3 � L4 � 0.521 � 4.1 � 4.7 m

Part bTotal length, L � 1.3(Dtheory) � 5 � 1.3(4.7) � 11.11 m ■

9.6 Cantilever Sheet Piling Penetrating Clay

At times, cantilever sheet piles must be driven into a clay layer possessing an undrainedcohesion The net pressure diagram will be somewhat different from thatshown in Figure 9.8a. Figure 9.12 shows a cantilever sheet-pile wall driven into claywith a backfill of granular soil above the level of the dredge line. The water table is at

c(f 5 0).

P(6zs5r 1 4P)

g2(Kp 2 Ka)2 5(67.38) 3(6) (2.188) (282.76) 1 (4) (67.38) 4

(15.9)2(3.25 2 0.307)2 5 122.52

5(6) (67.38) 3(2) (2.188) (15.9) (3.25 2 0.307) 1 282.764

(15.9)2(3.25 2 0.307)2 5 90.01

6P32zg(Kp 2 Ka) 1 sr54

g2(Kp 2 Ka)2

8P

g(Kp 2 Ka)5

(8) (67.38)

(15.9) (3.25 2 0.307)5 11.52

s5rg(Kp 2 Ka)

5282.76

(15.9) (3.25 2 0.307)5 6.04

L(2Ka 2 Kp)

3(Kp 2 Ka)5

53(2) (0.307) 1 3.254

3(3.25 2 0.307)5 2.188 m z

12 s2rL 1 1

2 s2rL3 5 12 s2r (L 1 L3) 5 (1

2) (24.41) (5 1 0.521) 5 67.38 kN>m

LKa

Kp 2 Ka5

(5) (0.307)

3.25 2 0.3075 0.521 m


32

2b 5 3.25


32

2b 5 0.307

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