Walls with different support conditions at the base and more than one row of anchors

Walls with more than one row of anchors can be calculated as described above by using iden- tical boundary conditions. Establishing the embedment depth is carried out via the force or deformation boundary condition at the base of the wall according to section 6.5.

It should be pointed out that owing to the static indeterminacy , the analytical solution involves considerably more work when more than one row of anchors is employed. Nomograms for calculating both simply supported and fully fixed walls with two rows of anchors can be found in the literature (H OFFMANN, 1977) together with accompanying explanations.

It is worthwhile employing a computer for sheet piling structures with more than one row of anchors. Design programs speci fically for foundations calculate the required embedment length automatically depending on the chosen support conditions for the section. Any frame program can be used to calculate the embedment length by means of iteration.

For the purposes of preliminary design, several rows of anchors can be approximated to one row.

Impact driving

Impact driving involves driving the sheet piles into the ground with a succession of hammer-blows (as the follow picture shows). A timber driving cap is usually placed between the hammer and the sheet pile. We distinguish between slow- and rapid-action systems. Slow-action plant such as drop hammers and diesel hammers is primarily used in cohesive soils so that the ensuing pore water pressure has time to dissipate between the individual blows. In a drop hammer, a weight is lifted mechanically and then allowed to fall from a height h. Modern drop hammers operate hydraulically. The number of blows can be set as required between 24 and 32 blows per minute. The drop height of a diesel hammer is determined by the explosion of a diesel fuel/air mixture in a cylinder. Depending on the type of hammer, the weight is either allowed to drop freely onto the driving cap or instead the weight can be braked on its upward travel by an air buffer and then accelerated on its downward travel by a spring. Using this latter technique, 60–100 blows per minute are possible, whereas with the non-accelerated hammer the figure is only 36–60 blows per minute. Rapid-action hammers are characterised by their high number of blows per minute: between 100 and 400. However, the driving weight is correspondingly lighter. Rapid-action hammers are driven by compressed air and the weight is accelerated as it falls.

The head of the sheet pile can be overstressed during impact driving if the hammer is too small or the resistance of the ground is too great. Possible remedies are to strengthen the head or use a larger hammer. In the case of a high ground resistance, excessive driving force or an incorrectly attached driving cap, the pile can buckle below the point of impact. To avoid this, use thicker sections or loosen the ground beforehand.

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Modelling the sheet pile wall

The HOESCH 1605 sheet pile wall section is discretised with 3-node beam elements assuming a quadratic displacement. A linear elastic behaviour is assumed for the sheet pile wall. Using the section properties from appendix A, we get the following system parameters:

E = 2.1 · 108 kN/m2
A = 1.363 · 10-2 m2/m
I = 2.8 · 10-4 m4/m
E = 1.05 kN/m/m

=> EA = 2 862 300 kN/m; EI = 58 800kNm2/m

The sheet pile/soil boundary surface is discretised with interface elements. The wall friction angle for the steel/soil boundary surface is given as δ =2ϕ/3. In order to achieve a realistic bond between base of wall and body of soil, the interface elements are extended 2 m into the body of soil. However, δ = ϕ applies for these interface elements.

Using FEM for the design of sheet piling structures

Possibilities and limitations

Like analytical methods of computation, FEM involves modelling errors due to deviations of the physical-mathematical equivalent problem from the initial problem plus data errors due to deviations in the chosen values of the initial parameters of the finite element model from the real values. And like other discretisation methods, FEM also involves procedural errors (numerical errors) due to the deviation of the solution of the discretised problem from the solution of the continuum problem plus rounding errors due to the deviation of the solution with exact numerical values from the solution with approximated numerical values (computer arithmetic).

Recommendations regarding the use of FEM in geotechnics

Since 1991 the “Numerics in Geotechnics” working group has published four sets of recommendations (in German only) for the use of FEM in geotechnics:
• Set 1 – General recommendations for modelling (Meißner, 1991)
• Set 2 – Modelling recommendations for underground tunnels (Meißner, 1996)
• Set 3 – Modelling recommendations for excavations (Meißner, 2002)
• Set 4 – Recommendations for material models for soils, modelling for serviceability analyses, stability and groundwater (Schanz, 2006)

In EAB recommendation R 103, W EISSENBACH (2003) speaks about the use of FEM within the scope of the new DIN 1054. Further recommendations regarding modelling can also be found in P OTTS ET AL. (2002). A description of various sources of errors and corresponding error effects when using FEM in geotechnics is given, for example, in (HÜGEL 2004/2005). Recommendations for reducing procedural errors can be obtained from general textbooks on FEM, especially for non-linear problems, e.g. in (W RIGGERS, 2001) or (BAT H E , 2002).

Impact driving

Impact driving involves driving the sheet piles into the ground with a succession of hammer- blows (as the follow picture shows). A timber driving cap is usually placed between the hammer and the sheet pile. We distinguish between slow- and rapid-action systems. Slow-action plant such as drop hammers and diesel hammers is primarily used in cohesive soils so that the ensuing pore water pressure has time to dissipate between the individual blows. In a drop hammer, a weight is lifted mechanically and then allowed to fall from a height h. Modern drop hammers operate hydraulically. The number of blows can be set as required between 24 and 32 blows per minute. The drop height of a diesel hammer is determined by the explosion of a diesel fuel/air mixture in a cylinder. Depending on the type of hammer, the weight is either allowed to drop freely onto the driving cap or instead the weight can be braked on its upward travel by an air buffer and then accelerated on its downward travel by a spring. Using this latter technique, 60–100 blows per minute are possible, whereas with the non-accelerated hammer the figure is only 36–60 blows per minute. Rapid-action hammers are characterised by their high number of blows per minute: between 100 and 400. However, the driving weight is correspondingly lighter. Rapid-action hammers are driven by compressed air and the weight is accelerated as it falls.

The head of the sheet pile can be overstressed during impact driving if the hammer is too small or the resistance of the ground is too great. Possible remedies are to strengthen the head or use a larger hammer. In the case of a high ground resistance, excessive driving force or an incorrectly attached driving cap, the pile can buckle below the point of impact. To avoid this, use thicker sections or loosen the ground beforehand.

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Anchor-sheet Pile Construction Details

The hinged connection of an anchor to a trough-type sheet pile wall is carried out on the centre- of-gravity axis in the trough, especially on walls with interlocks. In the case of combined sheet pile walls, the web of the loadbearing pile offers the best connection options. The connection via a capping beam at the top of the sheet pile wall is another option primarily suited to smaller tension piles and lightweight sheet pile walls. With threaded anchors there is the additional option of a connection with a washer plate, hinged splice plate and nut. In order to avoid having to install an anchor at every trough, a horizontal waling of steel or reinforced concrete can be provided to spread the load. This should be positioned on the land side in the case of quay structures, and on the excavation side in the case of excavation enclosures in order to guarantee easy removal.

Anchors can be installed before or after erecting the sheet pile wall. Maintaining the intended position of the anchor, which is necessary to achieve an accurate connection, is easier to estab- lish when installing the anchors afterwards. Anchor piles can be driven through an opening cut in the sheet pile wall, for instance. The follow pictures show possible anchor-sheet pile connection details.

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Advice on the use of FEM for retaining walls

2D/3D problem

Retaining wall structures are generally simulated with 2D equivalent models for FEM purposes (which is, of course, not possible with distinctly 3D problems such as the corners of excavations). Resolved structures such as struts, anchors, staggered sheet pile walls or bearing pile walls can be taken into account approximately in the 2D equivalent model but assuming equivalent stiffnesses related to a 1 m length of wall. Every individual case must be checked to ensure that the equivalent structure does not exhibit any unrealistic properties. Examples of this are: 2D equivalent anchors may not relieve the earth pressure acting on the retaining wall, 2D equivalent walls for staggered sheet pile walls may not be impermeable at the level of the staggered pile ends, 2D equivalent walls for bearing pile walls may not mobilise any unrealistically large passive earth pressures. It is not always clear whether all the deformations and stresses calculated with the 2D equivalent model are on the safe side; see (HÜGEL , 2004), for example. Examples of complex 3D analyses of sheet piling structures can be found in (BOLEY ET AL., 2004) and (M ARDFELDT, 2006).

Generalisation of the subsoil

Soil strata and groundwater conditions should be generalised in the finite element model depending on the database. However, when doing so, it must be ensured that the mechanical and hydraulic behaviour of the finite element model is comparable with the initial problem.

Subsoil segment and boundary conditions

The size of the subsoil segment should be specified such that the boundaries do not have any signi ficant effect on the deformations at the point of load transfer or such that the boundary conditions are known. Estimates of the dimensions necessary can be found in (MEISSNER, 2002) for the case of excavations.

Geometric non-linearity

Retaining wall structures are generally designed to be so stiff that finite element analyses may be based on geometric linearity. In the case of a yielding earth resistance and/or yielding anchorage, comparative analyses can be used to check whether geometric non-linearity needs to be taken into consideration.

Vibratory Driving

Vibratory driving is based on the harmonic excitation of the sheet pile. This causes a redis-tribution of the soil and reduces the friction between soil and sheet pile, also the toe resistance. Local liquefaction of the soil may also take place at the boundary layer between sheet pile and soil, and this also leads to a decrease in the driving resistance. One advantage of vibration is that the same plant can be used for driving and also for extracting sheet piles.

The harmonic excitation is generated by eccentric weights in the vibrator (as the follow picture shows). The isolator prevents the oscillations being transmitted to the pile-driving plant as the eccentric weights rotate. The sheet pile is loaded by a static force due to the self-weight of the vibrator and, if necessary, by an additional leader-guided prestressing force. The maximum centrifugal force Fd is

Fd = muruΩ2

In this equation, mu is the mass of the eccentric weights, ru is the distance of the centre of gravity of the eccentric weights to the point of rotation, and Ω is the exciter frequency. The product of mu and ru is also known as a static moment.

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Vibrators can be mounted on the head of the sheet pile, suspended from an excavator or crane or also guided by leaders. Vibrators are driven hydraulically and with modern vibrators it is possible, for a constant centrifugal force, to adjust the frequency, and hence the static moment, to suit the soil properties in order to achieve optimum driving progress.

The acceleration and braking of the eccentric weights is critical in vibratory driving because in doing so they pass through the low frequencies and thus excite the natural frequencies of buildings (approx. 1–5 Hz) and suspendedfloors (approx. 8–15 Hz). These days, vibrators are therefore in the position of being able to accept the maximum r.p.m. initially and then generate a variable (from zero to maximum) imbalance moment by rotating the eccentric weights. Further- more, there are systems that permit online monitoring of the oscillation velocities at measuring points close by. The vibrator operator, in conjunction with variable imbalance, is therefore in the position of being able to react to unacceptably high oscillation velocities by changing the imbalance amplitude or frequency.