From the calculated design force required to tie back the sheet pile wall determine the minimum tie rod size using clause 7.2.3 of EN1993-5.

The first assumption to be made is whether tie rod connections to the wall will be articulated or fixed. Articulated connections will minimise any bending that may be introduced to the tie rod due to settlement if fill material or perhaps misalignment during installation. EN1993-5 allows for this by applying a factor to the thread capacity – 0.6 for fixed connections and 0.9 for articulated connections, this factor is given the nomenclature of ‘kt

EN1993-5 states

kt may be given in the National Annex. The recommended value for kt is kt = 0,6. This is motivated for cases where possible bending in the anchor as an effect of actions is not made explicit. Only in cases where the structural detailing of the location where the anchor rod is joined to the wall is such that bending moments are avoided at that location, the recommended value for kt may be chosen as kt = 0,9”.

Tables given in the Anker Schroeder brochure can be used for easy reference, as a conservative design it is recommended to use a kt factor of 0.6 combined with articulation.

Min. Thread Size

From Table 2 Grade ASDO500, with kt = 0.6

Select M100/76 bar –

Thread size = M100 Metric thread (major diameter 100mm)
Shaft Size = 76mm dia
fy = 500N/mm2
fua = 660N/mm2

Design tensile resistance Ftt,Rd = 2,216kN > 2,200kN OK

Check elongation under axial characteristic loading

 

 

Where Elastic Modulus = 205kN/m2
Hint – if the elongation is too great try a larger diameter of a lesser grade

Check Serviceability Limit State – Clause 7.2.4 EN1993-5

The required additional check for serviceability in this example is already implied in the resistance check FRd < FEd as a kt factor of 0.6 has been used, however it is performed here for information.

     where As is the lesser of shaft area or thread area

Consider corrosion resistance – for robustness and simplicity in handling and installation use sacrificial steel.

Corrosion Protection = sacrificial steel

The tie bar is split into zones as per the diagram below – The corrosion rate assumed for each zone depends on local conditions, or the guidance given in EN1993-5 can be considered. The rates given below are for example only.

Zone 1 Splash zone = 3.75mm (from table 4.2 EN1993-5)

Therefore allow 3.75mm per side

Minimum thread size = M100
Thread size with corrosion allowance = 100 + (3.75 x 2) = 107.5mm

Nearest standard metric thread = M110 ∴ Use M110 at anchor head
Resulting corrosion allowance = 110-100 = 5mm per side

Minimum shaft size = 75mm
Shaft size with corrosion allowance = 75 + (3.75 x 2) = 82.5mm
A shaft size of 83mm is possible but for this example a standard bar diameter is chosen.
Smallest standard shaft diameter for M110 thread = 85mm

∴ Use 85mm diameter shaft

Resulting corrosion allowance = 85 - 75 = 5mm per side

Hint – to reduce exposure of the thread to the splash zone, and hence reduce corrosion loss, the anchor connection to the front wall can be made to the inside of the sheet pile pan, eg



In this case the corrosion rates for Zone 2 could be used thus reducing the shaft diameter.

 

Zone 2 Directly behind wall = 2.0mm (assumed)

Therefore allow 2.0mm per side

Minimum shaft size = 75mm
Shaft size with corrosion allowance = 75 + (2.0 x 2) = 79mm
However shaft is already 85mm from Zone one check

∴ Use 85mm diameter shaft for zone 2

Resulting corrosion allowance = 85 - 75 = 5mm per side

 

Zone 3 Compacted fill, non aggressive = 0.6mm (from table 4.1 EN1993-5)

NB Table 4.1 EN1993-5 allows corrosion rates for non-compacted fills to be halved for compacted fills. For conservatism this is ignored in this example.

Therefore allow 1.2mm per side

Minimum thread size = M100
Thread size with corrosion allowance = 100 + (1.2 x 2) = 102.4mm
Nearest standard metric thread = M105

∴ Use M105 Thread

Resulting corrosion allowance = 105 - 100 = 2.5mm per side

Minimum shaft size = 75mm
Shaft size with corrosion allowance = 75 + (1.2 x 2) = 77.4mm
Nearest standard shaft diameter = 80mm

∴ Use 80mm diameter shaft

Resulting corrosion allowance = 80 - 75 = 2.5mm per side

Note : although increasing the diameter of the tie bar will increase its unit weight (by 8% in the above example) and hence cost it should be remembered that this is only a raw material increase and typically no extra labour or machining is required. This means that the economics of using sacrificial steel are very favourable in comparison to coatings or wrappings and have the additional advantage that it cannot be damaged during installation.

Hint – depending upon the size of the project it may be more economic to standardise the thread and shaft size along the whole anchor. Generally speaking only large projects (where the total anchor tonnage > 200t) benefit from mixing diameters of shafts within the same anchor.

 

Final Specification
As a minimum the following information is required in order to specify the tie rods correctly.

Tie Rods : Grade 500 - M110/85, M100/80
with articulated connections, turnbuckles and length as indicated on drawing
Minimum design resistance, Ft,Rd = 2,200kN
kt = 0.6 (in accordance with EN1993-5)
fy = 500N/mm2
fua = 660 N/mm2
Corrosion protection = sacrificial steel to all bars and components as indicated