Overview

In PLAXIS 2D, sheet pile walls are typically modelled using plate elements with the anisotropic elastoplastic plate material model. This article provides a step-by-step method to derive anisotropic plate parameters for sheet pile walls in PLAXIS 2D directly from manufacturer datasheets, using the ArcelorMittal AZ 25 as a worked example. The procedure helps avoid common errors in unit conversion, parameter interpretation, and interlock stiffness assumptions. The same methodology can be applied to other sheet pile sections, including PZ, AZ, AU, and similar hot-rolled or cold-formed profiles.

Why use an anisotropic plate model?

Sheet pile walls behave very stiffly in the longitudinal direction (along the wall), but much more flexibly in the transverse direction due to interlock deformation between adjacent piles. Axial forces are transferred efficiently along the sheet piles, while load transfer between adjacent piles is influenced by the flexibility of the interlocks.

The anisotropic elastoplastic plate model allows this directional behaviour to be represented through separate stiffness and strength parameters in the primary and secondary directions:

• EA₁ represents axial stiffness along the wall axis.
• EA₂ represents axial stiffness across the wall, influenced by interlock behaviour.
• N_p,1,tens and N_p,2,tens represent the corresponding tensile capacities.

This provides a more realistic representation than an isotropic plate model when the behaviour of the sheet pile interlocks influences the structural response.

Required parameters

The anisotropic elastoplastic plate model in PLAXIS 2D requires the following input:

Parameter	Symbol	Description
Unit weight	w	Self-weight per unit length of wall
Primary axial stiffness	EA1	Axial stiffness along the wall axis
Secondary axial stiffness	EA2	Axial stiffness in the transverse direction
Bending stiffness	EI	Out-of-plane flexural stiffness
Plastic bending moment	Mp	Moment capacity at full plastification
Primary plastic tensile force	Np,1,tens	Axial tensile capacity in main direction
Secondary plastic tensile force	Np,2,tens	Axial tensile capacity in transverse direction

Worked example: ArcelorMittal AZ 25

The section properties used below are taken from the publicly available ArcelorMittal AZ 25 sheet pile catalogue, which is used solely as a worked example. The same methodology applies to any sheet pile section for which equivalent section properties are available.

Assumed material properties:

• Young’s modulus for steel E = 210 GPa
• Yield strength fy = 240 MPa (Grade S240GP).

Effect of steel grade

The stiffness parameters EA and EI depend only on the geometry and Young's modulus. However, the plastic capacities depend directly on the yield strength. For the AZ 25 section used in this example:

Steel grade	fy (MPa)	Mp (kNm/m)	Np,1,tens (kN/m)
S240GP	240	690	4,440
S270GP	270	776	4,995
S355GP	355	1,021	6,568

For ArcelorMittal catalogues these values are typically found in the section property tables under the columns A, I_y, W_pl,y and G_w.

Unit weight (w)

The datasheet gives a mass per unit wall area:

G_w = 145 kg/m²

To convert mass per unit area to line load, multiply by gravity and divide by 1000 to obtain kN/m/m.Converting to PLAXIS plate unit weight:

w = G_w [kg/m²] × g [m/s²] / 1000
w = 145 × 9.806 / 1000
w ≈ 1.42 kN/m/m

Primary axial stiffness (EA₁)

The cross-sectional area per metre of wall is:

A = 185 cm²/m = 0.0185 m²/m.

Therefore:

EA₁ = E × A
EA₁ = 210 × 10⁶ [kPa] × 0.0185 [m²/m]
EA₁ ≈ 3.89 × 10⁶ kN/m

Estimating the secondary axial stiffness (EA₂)

The secondary axial stiffness represents load transfer across adjacent sheet piles through the interlocks. Because manufacturers rarely publish interlock stiffness values, this parameter is often estimated during modelling.

Unlike EA₁ and EI, the value of EA₂ is not directly derived from the manufacturer’s section properties. Instead, it must be estimated to represent the mechanical behaviour of the interlocks.

For this worked example, the secondary stiffness is assumed to be:

EA₂ = EA₁ / 20
EA₂ ≈ 1.94 × 10⁵ kN/m

This value has been selected solely to illustrate the calculation procedure and should not be interpreted as a recommended default. The appropriate value depends on the sheet pile system, expected interlock behaviour, project requirements, and any available manufacturer guidance or project-specific calibration.

Where project-specific information or manufacturer recommendations are available, those values should always take precedence over the illustrative assumption used in this example.

Bending stiffness (EI)

The second moment of area is:

I_y = 52,250 cm⁴/m = 5.225 × 10^-4 m⁴/m.

Therefore:

EI = E × I_y
EI = 210 × 10⁶ [kPa] × 5.225 × 10^-4 [m⁴/m]
EI ≈ 1.10 × 10⁵ kNm²/m

Plastic bending moment (M_p)

The plastic section modulus is:

W_pl,y = 2,875 cm³/m = 2.875 × 10^-3 m³/m.

Therefore:

M_p = f_y × W_pl,y
M_p = 240,000 [kPa] × 2.875 × 10^-3 [m³/m]
M_p ≈ 690 kNm/m

Primary plastic tensile force (N_p,1,tens)

N_p,1,tens = f_y × A
N_p,1,tens = 240,000 [kPa] × 0.0185 [m²/m]
N_p,1,tens ≈ 4,440 kN/m

Estimating the secondary plastic tensile force (Nₚ,₂,tens)

The secondary plastic tensile force represents the tensile load transfer that can be mobilised through the sheet pile interlocks.

Where available, the manufacturer's published interlock tensile resistance should be used directly, as it provides a more representative value than assuming a proportion of the steel section capacity.

If manufacturer data is unavailable, a reduced value may be adopted based on engineering judgement. Since the tensile resistance of sheet pile interlocks is typically lower than that of the steel section, the secondary tensile capacity is typically much lower than the primary tensile capacity.

For consistency with this worked example, the value

N_p,2,tens = N_p,1,tens / 20
N_p,2,tens ≈ 222 kN/m

has been adopted solely for illustration.

It should not be interpreted as a recommended default for design.

PLAXIS material dataset

Summary of derived parameters

The table below summarises all derived input values for the ArcelorMittal AZ 25 section:

Table 1. Required input parameters for the anisotropic elastoplastic plate material model in PLAXIS 2D.

Parameter	Value (AZ 25)	Unit
w	1.42	kN/m/m
EA1	3.89 × 106	kN/m
EA2	1.94 × 105	kN/m
EI	1.10 × 105	kN·m²/m
Mp	690	kN·m/m
Np,1,tens	4,440	kN/m
Np,2,tens	222	kN/m

Common mistakes

1. Incorrect conversion of second moment of area: Always check the unit system – values given in cm⁴ must be converted to m⁴.
2. Using elastic section modulus instead of plastic section modulus: The plastic bending moment should be calculated using W_pl,y.
3. Using pile properties instead of wall properties: Ensure the values used are per metre of wall.
4. Using the wrong steel grade: Plastic capacities depend directly on yield strength.
5. Treating the illustrative EA2 value as a recommended default: The EA2 value is illustrative and should be reviewed for each project.