Bending Behavior of Double U Sheet Piles 0. Abstract When U-shaped steel sheet piles are used in retaining walls, they are usually installed as double piles, the common interlock being either crimped or welded. Such double U-piles have inclined principal axes. Thus the piles are stressed in oblique (biaxial) bending leading to higher stresses and larger displacements than those calculated using the manufacturers' data. In the worst case stresses and displacements might be twice as high. In Europe several research projects have been carried out to determine how items such as interlock friction, stiffness of the retained ground, walings, and capping beams 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 these piles is that their interlocks are located at the extreme fibers so that they do not have 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 stress distribution is at its maximum. In a retaining wall consisting of single U-piles the interlocks have to allow for full shear force transmission in order for these piles to be fully effective, and obtain their theoretical properties, see figure 1. However, single U sheets cannot fully transfer shear forces and may be capable of attaining only 35% of their theoretical moment of inertia. Several accidents and the results from several measurements on site lead to the conclusion that single U-piles are not fully effective in retaining walls [1]. In order to overcome these problems related to the use of single U-piles, double piles are sometimes used. The common interlock is either welded or crimped in order 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 associated with single sheets, but it does not solve the problem of shear transmission. When drafting the new European design codes (Eurocodes) [2] and the related national application documents a lot of research work was done in order to derive design rules for the bending behavior of double U-piles and the occurrence of oblique bending. The outcome of this research work will be presented in the following.
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 the common interlock welded. On the centroidal axis (x-axis) the center of gravity and the flexural center coincide, but both the y (horizontal) and the z (vertical) axes are not symmetrical axes for the cross-section, see figure 2. The location of the principal 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) between 10 and 21. The cross-section does not change its shape during loading, so the surface loading f, which might represent an earth pressure, may be replaced by an equivalent line load F. Figure 2: Double U-pile
In order to determine the displacement of the centroidal axis at midspan, we have to consider bending around both main axes. This type of bending is called biaxial or oblique bending. First we have to decompose F into two components (F u and F v parallel to uu and vv respectively), see figure 3. Then we separately consider bending 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 load F, see table 3 of [3]: d midspan = 4 5 F L 384 E I (1) Figure 3: Oblique (biaxial) Bending of a Double U-pile
Applied to the principal axes we obtain both displacements: 4 4 5 Fu L 5 Fv L du = (2u) and dv = (2v) 384 E Iv 384 E I I v is the minimum value of the second moment of area (moment of inertia) and I u is its maximum value. Using trigonometry we calculate the vertical components (in z direction) of d u and d v. This yields: u 4 2 2 5 F L & sin (' ) cos (' ) # d = 384 E $ + Iu I! v % " (3) In the manufacturer's catalogue the moment of inertia of the double pile is given around the y-axis: I y. Applying this data and neglecting the occurrence of oblique bending we obtain: d 0 4 5 F L = 384 E I y (4) The ratio d / d 0 depends only on the geometry of the cross-section: 2 d & sin (' ) cos = Iy d $ + Iu % 0 Iv 2 (' ) #! " (5) 2.2 Example Let us consider a double U-pile consisting of two PU32 sheet piles. Cross-sectional data: W = 3840 cm 3, according to the manufacturer's catalogue I u = 423480 cm 4 I v = 36354 cm 4 I y = 86711 cm 4 = I according to the manufacturer's catalogue B = 58.71 cm and H = 24.42 cm, see figure 2 Span length L = 12m, distributed load F = 100 kn/m. 2.2.1 Deflection at midspan By using the manufacturer's data (I y ) for the calculation of deflection, neglecting oblique bending, formula (4) yields:
d0 4 5* (1.0 kn/cm)* (1200 cm) = 2 (384) *(21000 kn/cm )* (86711cm) 4 = 14.8 cm If we take into account oblique bending we use formulas (4) and (5) given above for the determination of the displacement component in z-direction (deflection): 5* ( 1.0 kn/cm)* (1200cm) 2 384* ( 21000 kn/cm ) 2 2 & sin (21 ) cos (21 ) # $ + 31.2 cm 4 cm cm! = % 423480 36354 " 4 d = 4 d / d 0 = 2.1 2.2.2 Design stresses If we consider monoaxial bending only, using the manufacturers' data: Maximum bending moment: M max = F L 2 / 8 = 1800 knm Maximum bending stress: s max = M max / W = 469 MPa If we consider oblique bending the highest stresses appear in points 1 and 2 of the cross-section, see figure 2. In order to obtain the stresses acting in these points we have to add the stresses from bending about the vv and uu axes taking into account the correct signs (tension or compression): M v = F cos(!) L 2 / 8 = 1678.9 knm M u = F sin(!) L 2 / 8 = 649.1 knm max! Mv H Mu B - Iv Iu 1,2 = = 1038 MPa max! 1,2 /! 0 = 2.2 2.3 Conclusion It appears from these two results that the real deflection and the real bending stresses, taking into account oblique bending, are more than twice as high as those predicted by monoaxial bending. Although the reduction of section properties is not as great as occurs with single piles, the theoretical stiffness and strength of the double piles is not accurate. Therefore it is not possible to neglect the effect of oblique bending when calculating the displacements or stresses of double U-piles. Furthermore, it is clear that neglecting oblique bending leads to unsafe designs, both regarding the deformation behavior and the stressing of the retaining structure.
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 extreme cases 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 shear forces, the wall behaves as a monolithic or continuous wall, and oblique bending does not occur. Bending is taking place about the y-axis and thus the 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 the interlocks threaded on site and no other hindrance to oblique bending is effective, 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 in the 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 the effective bending behavior of double U sheet pile walls. The following topics have been covered in this research program:
- 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 soil Presence of a capping beam Presence of a waling Welding of the interlock at the top of the pile Driving the toe of the piling into bedrock Another important element of this European research project is a field test taking place near Rotterdam (The Netherlands) where the bending behaviour of double U-piles during and after excavation is monitored. The outcome of the research project will be presented at an international workshop scheduled for the first quarter 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 the occurrence of oblique bending in a sheet pile wall consisting of double U-piles. In order to transfer the longitudinal shear forces in these interlocks friction forces have to be generated within the interlocks. Installation causes the interlocks to be completely 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 after driving. 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 the sand to fill the void in the interlocks more than 90%, by weight, of the grains had a diameter < 3mm. Two tests were carried out using saturated sands, all the others were 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) which was 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 was vibrated on a vibrating plate. The final density was measured with a standard CPT (Cone Penetration Test).
Figure 5: Steel Tube with Two Welded Interlocks Figure 6 shows the test specimen (length = 1.5m), which was built using two interlocks. The interlocks were threaded and the specimen was driven one meter into the sand using three different vibrators the properties of which were chosen depending on the driving resistance, see figure 7. The driving time varied between one and seventeen minutes. Figure 6: Test Specimen
Figure 7: Vibrodriving of the Test Specimen After driving, the vibrator was dismantled and a frame carrying a hydraulic jack was attached to the fixed interlocks. The test specimen was bolted to the jack. Then the specimen was extracted (about 20mm) with a speed of only 0.01mm/s (quasi static), see figure 8. Both the required extraction force and the relative displacements were measured with a high sampling rate yielding a shear force - interlock slippage diagram, see figure 9. Figure 8: Extraction of the Specimen
Shear force [kn/m'] 100 90 80 70 60 50 40 30 20 Fine sand: Coarse sand: 10 0 0 2 4 6 8 10 12 14 16 18 Interlock slippage [mm] Figure 9: Measured Shear Force - Interlock Slippage Curves At the CRPHT laboratory three tests were carried out to determine the effect of steel on steel interlock friction due to driving imperfections. The sheet piles were prestressed perpendicularly to the interlocks. Then load displacement curves were established 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 was determined by CRPHT via a statistical approach. CRPHT developed a 3D finite element model of the retaining wall using the ANSYS software. The double U piles were modeled using shell elements and the soil was modeled using a subgrade reaction based on Winkler springs, taking into account soil plasticity and the phasing of the excavation works. Friction in the leading interlock was introduced using longitudinal springs the properties of which were in accordance with the correlation determined from the test results. The model also simulated the effect of walings, welding of the interlock and driving into bedrock. About 100 simulations were carried out, using this finite element model, covering various soil conditions, boundary conditions and three different double U sheet piles (small, medium, large). The results in terms of deflections were then compared with the results of calculations using the same subgrade reaction model for the soil but the sheet piling data as given in the manufacturers' catalogues. As a result of these comparisons the reduction coefficients, as given in table 2, have been established.
The CRPHT study shows that friction cannot generate the interlock forces required to allow for full shear force transmission. Figure 10 shows the result of a finite element simulation. In the same diagram we indicate both extreme cases as discussed under 3.1: the shear forces occurring in the interlock if it was fully fixed continuous 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 provides less 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 practice however load reversal often occurs in a retaining structure due to various loadings or 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.
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 reduce these displacements. Figure 12 shows a simplified model of this soil structure interaction. The question is whether the shear forces generated in the shear plane behind the wall are able to prevent the displacements of the piles and thus avoid the occurrence of oblique bending. Figure 12: Shear Plane Acting behind the Wall
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 wall including the soil was meshed, see figure 13. The wall of infinite length was obtained by imposing specific boundary conditions (periodic continuity) in the model. This means that the nodes located in the left plane of the slice are coupled with 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 and saturated conditions were simulated for sands with internal friction angles up to 35. The soil pile interface was considered using the two extreme cases: perfectly smooth and perfectly rough. Figure 15 clearly shows the occurrence of oblique 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 the occurrence of oblique bending. - A concrete capping beam may be an efficient solution to reduce the effect of oblique bending, provided it has been designed to resist the distributed bending moment generated by the piling and it is fully active before loading of the retaining wall, excavation, takes place, see figure 16.
Figure 14: 3D Meshing Figure 15: Occurrence of Oblique (Biaxial) Bending
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, interlocks crimped or welded, leads to a considerable reduction of both the moment of inertia and the section modulus, compared to the theoretical data provided in catalogs. Modern design codes dealing with U sheet piles give reduction factors to allow for oblique bending. Table 1 lists the range of the reduction factors given in the Dutch design manual CUR166 [9] and in the new European design code ENV1993-5 [2]. In both codes several parameters are taken into account when determining the reduction factors.
Table 1: Reduction Factors Given in Design Codes Eurocode ENV 1993-5: Piling Dutch recommandations 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 from situations in the field, table 2 gives a proposal for reduction factors R I for the moment of inertia. The following should be considered when using table 2: Water: Wailing: Weld: Bedrock: Sand: Presence of groundwater during installation and excavation over a substantial part of the height of the wall. Prevents locally horizontal inplane displacement of the wall, welding might be necessary Accordingly designed weld of the interlock at the head of the pile before excavation Driving of the sheet pile toe into bedrock to avoid any lateral inplane displacement of the toe 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 the questions with respect to the criteria listed above. A cautious approach is always recommended when using table 2!
Table 2: Proposal for Moment of Inertia Reduction Factors: Ri Water Wailing Interlock weld at the head Bedrock Sand Ri No No Yes No Yes No Yes not relevant not relevant not relevant No Yes 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 Yes Yes No not relevant not relevant 0,5 Yes No not relevant 0,5 Yes not relevant 0,75 5 Conclusions For retaining walls consisting of double U-piles, with the interlocks crimped or welded, the effect of oblique or biaxial bending leads to a considerable reduction of both the moment of inertia and the section modulus. For a safe design, reduction factors 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, the most important being: presence of groundwater, capping beam, or walers type of ground welding of the interlock threaded on site conditions at the pile toe (driven into bedrock). Modern design codes dealing with U sheet piles give reduction factors for single and double U sheet piles, (the reduction factors for double sheets are given in table 1). A proposal for a set of reduction factors based on the outcome of the research projects presented above is given in table 2.
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, 6 th edition, McGraw-Hill, 1989 [4] Juaristi E.: Influence of interlock friction on the flexural stiffness of a double U steel sheet pile wall, Esch-sur-Alzette, 1998 [5] Vanden Berghe J.F., Holeyman A., Sine B.: Détermination de la loi de comportement de l'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 pile wall, 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