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Bending Behavior of Double U Sheet Piles

0. Abstract

When U-shaped steel sheet piles are used in retaining walls, they are usuallyinstalled as double piles, the common interlock being either crimped or welded.Such double U-piles have inclined principal axes. Thus the piles are stressed inoblique (biaxial) bending leading to higher stresses and larger displacements thanthose calculated using the manufacturers' data. In the worst case stresses anddisplacements might be twice as high.

In Europe several research projects have been carried out to determine how itemssuch as interlock friction, stiffness of the retained ground, walings, and cappingbeams effect the occurrence of oblique bending. The outcome of this research is

outlined in the following article.

1. Introduction

Z-shaped steel sheet piles are generally used in the USA. The advantage of thesepiles is that their interlocks are located at the extreme fibers so that they do nothave to transfer any longitudinal shear stresses as they vanish at the extreme fiber.However, U-pile interlocks are located on the neutral axis, where the shear stressdistribution is at its maximum.

In a retaining wall consisting of single U-piles the interlocks have to allow for fullshear force transmission in order for these piles to be fully effective, and obtaintheir theoretical properties, see figure 1. However, single U sheets cannot fullytransfer shear forces and may be capable of attaining only 35% of their theoreticalmoment of inertia. Several accidents and the results from several measurementson site lead to the conclusion that single U-piles are not fully effective in retainingwalls [1].

In order to overcome these problems related to the use of single U-piles, doublepiles are sometimes used. The common interlock is either welded or crimped inorder to allow for full shear force transmission. Every other interlock still has to be

threaded on site. Therefore the crimping helps to reduce the problems associatedwith single sheets, but it does not solve the problem of shear transmission.

When drafting the new European design codes (Eurocodes) [2] and the relatednational application documents a lot of research work was done in order to derivedesign rules for the bending behavior of double U-piles and the occurrence ofoblique bending. The outcome of this research work will be presented in thefollowing.


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U-Shapes Z-Shapes

Figure 1: Location of Interlocks and Stress Distribution

2. Bending Behavior of a Single Double U-pile

2.1 Theory

We consider a simple beam of span L consisting of a double U-pile with thecommon interlock welded. On the centroidal axis (x-axis) the center of gravity andthe flexural center coincide, but both the y (horizontal) and the z (vertical) axes arenot symmetrical axes for the cross-section, see figure 2. The location of theprincipal axes uu and vv may be determined according to Mohr's formula, see

chapter 5 of [3]. The angle !varies for today's U-piles (width = 600mm) between10 and 21. The cross-section does not change its shape during loading, so thesurface loading f, which might represent an earth pressure, may be replaced by anequivalent line load F.

Figure 2: Double U-pile


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In order to determine the displacement of the centroidal axis at midspan, we haveto consider bending around both main axes. This type of bending is called biaxialor oblique bending. First we have to decompose F into two components (Fuand Fvparallel to uu and vv respectively), see figure 3. Then we separately considerbending around the vv axis (in the uu x plane) and around the uu axis (in the vv

x plane). The usual formula for the deflection at midspan applies for a line loadF, see table 3 of [3]:

(1)

384

IE

LF5d

4

midspan =

Figure 3: Oblique (biaxial) Bending of a Double U-pile


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Applied to the principal axes we obtain both displacements:

(2u)384 v

u

u

IE

LF5d

4

= and (2v)384

IE

LF5d

u

v

v

4

=

Ivis the minimum value of the second moment of area (moment of inertia) and Iuisits maximum value. Using trigonometry we calculate the vertical components (in zdirection) of duand dv. This yields:

(3))()(

384

I

cos

I

sin

E

LF5d

vu

224

!!"

#$$%

&+=

''

In the manufacturer's catalogue the moment of inertia of the double pile is givenaround the y-axis: Iy. Applying this data and neglecting the occurrence of obliquebending we obtain:

(4)

3840

IE

LF5d

y

4

=

The ratio d / d0depends only on the geometry of the cross-section:

(5))()(

0

I

cos

I

sinI

dd

vu

y

22

!!"

#$$%

&+=

''

2.2 Example

Let us consider a double U-pile consisting of two PU32 sheet piles.

Cross-sectional data:W = 3840 cm3, according to the manufacturer's catalogueIu= 423480 cm

4Iv= 36354 cm

4Iy= 86711 cm

4 = I according to the manufacturer's catalogueB = 58.71 cm and H = 24.42 cm, see figure 2Span length L = 12m, distributed load F = 100 kN/m.

2.2.1 Deflection at midspan

By using the manufacturer's data (Iy) for the calculation of deflection, neglectingoblique bending, formula (4) yields:


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cm14.8cm)(86711*)kN/cm(21000

cm)(1200*kN/cm)(1.0*5

42

4

==

*)384(d0

If we take into account oblique bending we use formulas (4) and (5) given abovefor the determination of the displacement component in z-direction (deflection):

cm31.2cm

cos

cm

sin

kN/cm21000(

(1200cm)*kN/cm)1.0(*5d

4

2

4

2

2

4

=!!"

#$$%

& +

=

36354

)21(

423480

)21(

)*384

d / d0 = 2.1

2.2.2 Design stresses

If we consider monoaxial bending only, using the manufacturers' data:

Maximum bending moment: Mmax = F L2/ 8 = 1800 kNm

Maximum bending stress: smax= Mmax / W = 469 MPa

If we consider oblique bending the highest stresses appear in points 1 and 2 of thecross-section, see figure 2. In order to obtain the stresses acting in these pointswe have to add the stresses from bending about the vv and uu axes taking intoaccount the correct signs (tension or compression):

Mv = F cos(!) L2/ 8 = 1678.9 kNm

Mu = F sin(!) L2/ 8 = 649.1 kNm

MPa1038I

BM-

I

HMmax

u

u

v

v

2,1 ==!

2.2/max 02,1 =!!

2.3 Conclusion

It appears from these two results that the real deflection and the real bendingstresses, taking into account oblique bending, are more than twice as high as

those predicted by monoaxial bending. Although the reduction of sectionproperties is not as great as occurs with single piles, the theoretical stiffness andstrength of the double piles is not accurate. Therefore it is not possible to neglectthe effect of oblique bending when calculating the displacements or stresses ofdouble U-piles. Furthermore, it is clear that neglecting oblique bending leads tounsafe designs, both regarding the deformation behavior and the stressing of theretaining structure.


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3. Bending Behavior of a Retaining Wall of Double U-piles

3.1 General

When dealing with the problem of a retaining wall consisting of double U-piles

things become much more complex, see figure 4. First of all the two extremecases which delimit the bending behavior of such a wall should be considered.

- If the interlock to be threaded on site was able to fully transfer the shearforces, the wall behaves as a monolithic or continuous wall, and obliquebending does not occur. Bending is taking place about the y-axis and thusthe manufacturers' data, which is given for the continuous wall, is accurate.

- On the other hand, if no shear force transmission takes place at all in theinterlocks threaded on site and no other hindrance to oblique bending iseffective, the wall behaves as consisting of series of double piles which are

connected as follows in this interlock (two neighboring double piles 1 and 2):

- displacements in y-direction of pile 1 = displacements in y-direction of pile 2,- displacements in z-direction of pile 1 = displacements in z-direction of pile 2,

- displacements in x-direction of pile 1 " displacements in x-direction of pile 2,

See figures 2 and 4

Thus the piles can displace relatively in longitudinal direction in this interlock.Oblique bending occurs and the moment of inertia and section modulus given inthe manufacturer's catalog are not accurate. They are far to optimistic, see 2.3.

Figure 4: Retaining Wall Consisting of Double U-piles

Several research projects have been carried out in Europe to determine theeffective bending behavior of double U sheet pile walls. The following topics havebeen covered in this research program:


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- The effect of friction generated in the interlock to be threaded on site- The changes in bending due to groundwater- The effect the following have on oblique bending:

Stiffness of the retained soilPresence of a capping beam

Presence of a walingWelding of the interlock at the top of the pileDriving the toe of the piling into bedrock

Another important element of this European research project is a field test takingplace near Rotterdam (The Netherlands) where the bending behaviour of doubleU-piles during and after excavation is monitored. The outcome of the researchproject will be presented at an international workshop scheduled for the firstquarter of 2000.

3.2 Friction in the interlocks threaded on site

A research project was carried out by CRPHT [4] and the University of Louvain(UCL) [5] to determine the effect of friction in the leading interlock on theoccurrence of oblique bending in a sheet pile wall consisting of double U-piles. Inorder to transfer the longitudinal shear forces in these interlocks friction forceshave to be generated within the interlocks. Installation causes the interlocks to becompletely or partially filled with soil particles.

At the UCL geotechnical laboratory twelve tests were carried out in order to

determine the longitudinal load displacement behavior of sheet pile interlocks afterdriving. Two different types of sand were used: yellow fine sand (mean diameter =0.18mm) and gray coarse sand (mean diameter = 0.63mm). In order to allow thesand to fill the void in the interlocks more than 90%, by weight, of the grains had adiameter < 3mm. Two tests were carried out using saturated sands, all the otherswere based on dry sands. Interlocks of real U sheet piles were used.

Execution of the tests:

The sand was poured into a steel cylinder (height = 1.5m, diameter = 1.0m) whichwas welded to a base plate. Two clutches were welded to the cylinder, see figure

5. To get the required density of the sand, lose to medium dense, the box wasvibrated on a vibrating plate. The final density was measured with a standard CPT(Cone Penetration Test).


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Figure 5: Steel Tube with Two Welded Interlocks

Figure 6 shows the test specimen (length = 1.5m), which was built using twointerlocks. The interlocks were threaded and the specimen was driven one meterinto the sand using three different vibrators the properties of which were chosendepending on the driving resistance, see figure 7. The driving time variedbetween one and seventeen minutes.

Figure 6: Test Specimen


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Figure 7: Vibrodriving of the Test Specimen

After driving, the vibrator was dismantled and a frame carrying a hydraulic jack wasattached to the fixed interlocks. The test specimen was bolted to the jack. Thenthe specimen was extracted (about 20mm) with a speed of only 0.01mm/s (quasistatic), see figure 8. Both the required extraction force and the relativedisplacements were measured with a high sampling rate yielding a shear force -interlock slippage diagram, see figure 9.

Figure 8: Extraction of the Specimen


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0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18

Interlock slippage [mm]

Shearforce

[kN/m

']

Fine sand:

Coarse sand:

Figure 9: Measured Shear Force - Interlock Slippage Curves

At the CRPHT laboratory three tests were carried out to determine the effect ofsteel on steel interlock friction due to driving imperfections. The sheet piles wereprestressed perpendicularly to the interlocks. Then load displacement curves wereestablished by measuring the force applied in the direction of the interlock and the

longitudinal relative displacement.

From the diagrams a characteristic shear force interlock slippage correlation wasdetermined by CRPHT via a statistical approach. CRPHT developed a 3D finiteelement model of the retaining wall using the ANSYS software. The double U pileswere modeled using shell elements and the soil was modeled using a subgradereaction based on Winkler springs, taking into account soil plasticity and thephasing of the excavation works. Friction in the leading interlock was introducedusing longitudinal springs the properties of which were in accordance with thecorrelation determined from the test results. The model also simulated the effect ofwalings, welding of the interlock and driving into bedrock.

About 100 simulations were carried out, using this finite element model, coveringvarious soil conditions, boundary conditions and three different double U sheetpiles (small, medium, large). The results in terms of deflections were thencompared with the results of calculations using the same subgrade reaction modelfor the soil but the sheet piling data as given in the manufacturers' catalogues. Asa result of these comparisons the reduction coefficients, as given in table 2, havebeen established.


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The CRPHT study shows that friction cannot generate the interlock forces requiredto allow for full shear force transmission. Figure 10 shows the result of a finiteelement simulation. In the same diagram we indicate both extreme cases asdiscussed under 3.1: the shear forces occurring in the interlock if it was fully fixedcontinuous wall, (no oblique bending), and the shear forces equal to zero, in the

case of a fully free interlock. As can be seen the interlock friction does providesless than 30% of the required shear forces.

Figure 10: Shear Forces Acting in the Interlock

So far we have only considered monotone loading behavior in the tests. In practicehowever load reversal often occurs in a retaining structure due to various loadingsor construction phases. Tests carried out at the University of Karlsruhe (Germany)[6] showed that due to quasi static cyclic loading the stiffness of the wall decreased

dramatically, see figure 11.


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Figure 11: Effect of Unloading and Reloading

3.3 Stiffness of the retained soil

When oblique bending occurs, the double U-piles also move parallel to the wall,see figure 16. The stiffness of the soil retained behind the wall tends to reducethese displacements. Figure 12 shows a simplified model of this soil structureinteraction. The question is whether the shear forces generated in the shear planebehind the wall are able to prevent the displacements of the piles and thus avoidthe occurrence of oblique bending.

Figure 12: Shear Plane Acting behind the Wall


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This effect was analyzed at the technical University of Delft (The Netherlands)[7,8]. A 3D finite element model of an infinite retaining wall consisting of double U-piles was developed using the DIANA software. A slice of the retaining wallincluding the soil was meshed, see figure 13. The wall of infinite length wasobtained by imposing specific boundary conditions (periodic continuity) in the

model. This means that the nodes located in the left plane of the slice are coupledwith the nodes in the right plane in a specific way.

Figure 13: Slice of Ground Analyzed

Figure 14 shows the mesh of the worst case: the cantilever wall. Both dry andsaturated conditions were simulated for sands with internal friction angles up to35. The soil pile interface was considered using the two extreme cases:perfectly smooth and perfectly rough. Figure 15 clearly shows the occurrence ofoblique bending: displacements in y-direction (a).

The outcome of both tests are summarized below:

- Even dense sands do not provide enough lateral restraint to prevent theoccurrence of oblique bending.

- A concrete capping beam may be an efficient solution to reduce the effectof oblique bending, provided it has been designed to resist the distributedbending moment generated by the piling and it is fully active beforeloading of the retaining wall, excavation, takes place, see figure 16.


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Figure 16: Effect of a Concrete Capping Beam (Elevation View)

4 Impact of Oblique Bending on Sheet Pile Design

From the above it appears that oblique bending of double U-piles, interlockscrimped or welded, leads to a considerable reduction of both the moment of inertiaand the section modulus, compared to the theoretical data provided in catalogs.Modern design codes dealing with U sheet piles give reduction factors to allow foroblique bending. Table 1lists the range of the reduction factors given in the Dutchdesign manual CUR166 [9] and in the new European design code ENV1993-5 [2].In both codes several parameters are taken into account when determining thereduction factors.


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Table 1: Reduction Factors Given in Design Codes

Eurocode Dutch recommandations

ENV 1993-5: Piling CUR166: Damwandconstructies

Reduction Factor

for the 0.7 - 1.0 0.6 - 1.0

Moment of Inertia

Reduction Factor

for the 0.8 - 1.0 0.7 - 1.0

Section Modulus

Based on the results of laboratory tests in combination with information taken fromsituations in the field, table 2 gives a proposal for reduction factors RI for themoment of inertia. The following should be considered when using table 2:

Water: Presence of groundwater during installation and excavation over asubstantial part of the height of the wall.

Wailing: Prevents locally horizontal inplane displacement of the wall, weldingmight be necessary

Weld: Accordingly designed weld of the interlock at the head of the pilebefore excavation

Bedrock: Driving of the sheet pile toe into bedrock to avoid any lateral inplane

displacement of the toeSand: Granular soil over a substantial part of the driving depth with the

following properties: mean diameter < 3 mm and minimum diameter >0.02 mm

The table should be used by stepping through it from left to right, answering thequestions with respect to the criteria listed above.

A cautious approach is always recommended when using table 2!


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Table 2: Proposal for Moment of Inertia Reduction Factors: Ri

Water Wailing Interlock weld

at the head Bedrock Sand Ri

No 0,5

Yes 0,65

No 0,5

Yes 0,7

No 0,5

Yes 0,65

No 0,5

Yes 0,7

No 0,75

Yes 0,75

No not relevant not relevant not relevant 0,5

No not relevant not relevant 0,5

No not relevant 0,5

Yes not relevant 0,75

Yes

Yes

Yes

No

No

Yes

No

Yes

No

Yes

not relevant

not relevant

not relevant

No

Yes

5 Conclusions

For retaining walls consisting of double U-piles, with the interlocks crimped orwelded, the effect of oblique or biaxial bending leads to a considerable reduction ofboth the moment of inertia and the section modulus. For a safe design, reductionfactors have to be applied to the cross-sectional data given by the manufacturer.The magnitude of the reduction factors depends on a number of parameters, themost important being:

presence of groundwater, capping beam, or walers

type of ground

welding of the interlock threaded on siteconditions at the pile toe (driven into bedrock).

Modern design codes dealing with U sheet piles give reduction factors for singleand double U sheet piles, (the reduction factors for double sheets are given intable 1). A proposal for a set of reduction factors based on the outcome of theresearch projects presented above is given in table 2.


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6 Bibliography

[1] Endley, Snow, Knuckey, Briaud, Lowery: Performance of an anchored sheet pile wall,(ASCE) San Antonio, 1991

[2] CEN: ENV1993-5 Eurocode 3: Design of steel structures, Part 5: Piling, 1997

[3] Young, W.C.: ROARK'S Formulas for Stress & Strain, 6thedition, McGraw-Hill, 1989

[4] Juaristi E.: Influence of interlock friction on the flexural stiffness of a double U steel sheetpile wall, Esch-sur-Alzette, 1998

[5] Vanden Berghe J.F., Holeyman A., Sine B.: Dtermination de la loi de comportement del'interface entre palplanches, Louvain, 1998

[6] Vielsack P., Schmieg H., Wendler W.: Experimentelle Untersuchung zur Hysterese der

Schlossreibung in Spundwandprofilen, Karlsruhe, 1998

[7] Aukema E.J., Joling A.G.: A 3D numerical simulation of oblique bending in a steel sheet pilewall, Delft, 1997

[8] Hockx J.A.W.: Methods to reduce oblique bending in a steel sheet pile wall, Delft, 1998

[9] CUR166: Damwandconstructies, Gouda, 1993

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