| Application | PLAXIS 3D |
| Version | All supported versions |
| Date created | 11 September 2026 |
| Date modified | 11 September 2026 |
| Original author | Vasileios Basas - Technical Support Group |
| Keywords | PLAXIS, PLAXIS 3D, secant pile wall, orthotropic plate, isotropic plate, plate stiffness, retaining wall |
1. Notation and Terminology
This workflow uses primary/secondary terminology consistently. The secondary pile is the reinforced hard pile that primarily resists the vertical retaining-wall bending action. The primary pile is the lower-stiffness pile, typically soft or firm, between secondary piles. The formula notation below uses descriptive subscripts to avoid ambiguity.
| Symbol | Meaning |
|---|---|
| Dsec | Diameter of the secondary/hard/reinforced pile. |
| Dprim | Diameter of the primary/soft or firm/weaker pile. |
| Esec | Young’s modulus assigned to the secondary pile material for the relevant analysis stage. |
| Eprim | Young’s modulus assigned to the primary pile material. |
| Isec = πDsec4/64 | Second moment of area of the secondary pile section. |
| Iprim = πDprim4/64 | Second moment of area of the primary pile section. |
| s | Centre-to-centre spacing between secondary piles. |
| deq | Equivalent plate thickness selected for PLAXIS input. The examples below use deq = Dsec. |
2. Estimating E1 — Vertical Bending Stiffness
The E1 formulation is the CIRIA C760 flexural rigidity expression rewritten in the orthotropic plate format required by PLAXIS 3D. It preserves the established vertical bending stiffness based on the secondary piles. EI1 per unit width = Esec · Isec / s PLAXIS plate input uses E and d, from which the plate bending stiffness per unit width is EI = E·d3/12. After selecting the equivalent thickness, back-calculate E1 as: E1 = 12 · Esec · Isec / (s · deq3) If the selected equivalent thickness is deq = Dsec, then: E1 = 3π · Esec · Dsec / (16s)
Thickness choice: Other equivalent thickness choices are possible. The selected deq must be used consistently for E1, E2, and the associated PLAXIS plate material definition. The bending stiffness is matched by back-calculating E, but the associated axial stiffness EA will vary with the chosen thickness.
3. Construction Stage and Long-Term Reductions
If the design basis requires construction-stage or long-term stiffness reductions, apply the relevant reduction to Esec before calculating E1. For example, CIRIA C760 Section 4.2.3, Key Point 9, provides commonly used reductions for reinforced concrete wall stiffness in soil-structure interaction analysis.
| Analysis stage | Example Esec multiplier | Comment |
|---|---|---|
| Short-term construction, SLS | 0.7 E0 | Apply before computing E1 if this is the project design basis. |
| Long-term, SLS | 0.5 E0 | Apply before computing E1 if this is the project design basis. |
| ULS, all stages | 1.0 E0 | Use full rigidity where required by the applicable design basis. |
Design-standard caveat: The values above are included to show how the calculation is applied. Users should verify the applicable design standard, project specification, and latest published guidance before applying stiffness reduction factors in design.
4. Estimating E2 — Horizontal Bending Stiffness
The E2 formulation is not contained in CIRIA C760. It is proposed as a practical engineering approximation for orthotropic PLAXIS 3D plate modelling. In 2D plane-strain analysis, horizontal bending along the wall is not normally represented. In 3D, however, direction-2 bending may influence behaviour at corners, re-entrant geometry, and changes in alignment.
Figure 3. Conceptual load paths governing vertical and horizontal bending stiffness in a secant pile wall.
A conservative lower-bound estimate for horizontal bending stiffness may be obtained by assuming that the weaker primary piles govern the effective response along the wall. This is not a rigorous homogenisation result; it is an engineering approximation intended to avoid unconservative overestimation of stiffness in direction 2. EI2 per unit width ≈ Eprim · Iprim / s E2 = 12 · Eprim · Iprim / (s · deq3)
Recommended sensitivity range: For critical applications, vary E2 between a conservative primary-pile lower-bound estimate and a higher stiffness justified by composite action, calibration, or comparison with explicit pile modelling. The selected value should reflect the assumed degree of interaction between adjacent primary and secondary piles.
5. Remaining Orthotropic Plate Parameters
5.1 Poisson’s Ratio ν12
For typical concrete materials, ν is often close to 0.20. A stiffness-weighted estimate can be used if distinct values are available: ν12 = (Eprim · νprim + Esec · νsec) / (Eprim + Esec) For many retaining-wall applications, ν12 ≈ 0.20 is sufficient because the global response is much more sensitive to bending stiffness than to the exact Poisson’s ratio.
5.2 Shear Stiffnesses G12, G13, and G23
There is no generally accepted simple procedure for deriving equivalent orthotropic shear stiffnesses for a secant pile wall from first principles. The following options should be treated as engineering estimates:
| Option | Expression | Use |
|---|---|---|
| A — secondary-pile based | G12 = G13 = G23 = Esec / [2(1 + νsec)] | Less conservative; often sufficient where global response is dominated by bending. |
| B — primary-pile based | G12 = G13 = G23 = Eprim / [2(1 + νprim)] | Conservative lower-bound estimate; useful where the primary pile material may control shear transfer. |
Numerical stability check: For very low-stiffness soil-cement primary piles, a primary-pile based shear stiffness may become very small. If this causes numerical difficulties, apply a practical lower bound and perform a sensitivity study rather than relying on one shear-stiffness value.
6. Summary of PLAXIS 3D Input Parameters
| Parameter | Expression | Basis | Notes |
|---|---|---|---|
| d | deq, commonly Dsec | Chosen | Choose first and use consistently. |
| E1 | 12·Esec·Isec / (s·deq3) | C760-based vertical bending | Apply project-specific reductions to Esec where required. |
| E2 | 12·Eprim·Iprim / (s·deq3) | Engineering approximation | Conservative lower-bound estimate; sensitivity study recommended. |
| ν12 | ≈ 0.20 or stiffness-weighted value | Engineering estimate | Usually low sensitivity in retaining wall deformation problems. |
| G12, G13, G23 | Option A or Option B | User judgement | No rigorous simple basis; check sensitivity if shear response is important. |
7. Worked Example — Hard/Firm Secant Pile Wall
The following example illustrates the calculation for a typical hard/firm secant pile wall at a construction SLS stage. The example uses deq = Dsec and applies a 0.7 reduction to the secondary pile modulus before calculating E1.
| Input parameter | Value | Notes |
|---|---|---|
| Dsec | 0.600 m | Secondary/hard pile diameter. |
| Dprim | 0.600 m | Primary/firm pile diameter. |
| s | 0.550 m | Centre-to-centre spacing between secondary piles. |
| E0 | 30,000,000 kN/m2 | Uncracked concrete modulus. |
| Esec | 21,000,000 kN/m2 | 0.7 × E0 for construction SLS in this example. |
| Eprim | 5,000,000 kN/m2 | Firm primary pile material. |
| νsec = νprim | 0.20 | Typical concrete value. |
| deq | 0.600 m | = Dsec. |
Section properties: Isec = Iprim = π × 0.64 / 64 = 6.362 × 10−3 m4 per pile
Vertical bending stiffness: EI1 = 21,000,000 × 6.362×10−3 / 0.550 = 242,835 kNm2/m E1 = 12 × 242,835 / 0.63 = 11,241,000 kN/m2 ≈ 11.2 GPa
Horizontal bending stiffness, conservative lower bound: EI2 = 5,000,000 × 6.362×10−3 / 0.550 = 57,836 kNm2/m E2 = 12 × 57,836 / 0.63 = 2,678,000 kN/m2 ≈ 2.7 GPa
In this example, E1/E2 ≈ 4.2. An isotropic plate calibrated to E1 would therefore assign approximately four times the horizontal bending stiffness represented by this conservative lower-bound E2 estimate.
| PLAXIS input | Value | Unit | Confidence / basis |
|---|---|---|---|
| d | 0.600 | m | Chosen geometric value. |
| E1 | 11,241,000 | kN/m2 | High; derived from vertical bending stiffness. |
| E2 | 2,678,000 | kN/m2 | Moderate; conservative lower-bound estimate. |
| E1/E2 | 4.2 | — | Informative stiffness contrast. |
| ν12 | 0.200 | — | Typical concrete value. |
| G12 | 2,083,333 | kN/m2 | Option B; sensitivity study recommended. |
| G13 | 2,083,333 | kN/m2 | Option B; sensitivity study recommended. |
| G23 | 2,083,333 | kN/m2 | Option B; sensitivity study recommended. |
8. Practical Implementation Checks in PLAXIS 3D
8.1 Local Axis Orientation
PLAXIS 3D assigns local axes to plate elements based on geometry. Direction 1 is not guaranteed to align with the vertical pile axis. Before interpreting results, activate the local axes display and confirm that direction 1 and direction 2 correspond to the intended vertical and horizontal directions. If the axes are swapped, either swap E1 and E2 in the material definition or adjust the plate orientation.
Critical check: Incorrect local axis orientation is one of the most likely sources of error when using anisotropic plates. This check should be treated as mandatory before comparing results or drawing design conclusions.
8.2 When to Perform a Sensitivity Study
- The wall has significant curvature in plan, corners, re-entrant geometry, or changes in alignment.
- The stiffness contrast Esec/Eprim is high, especially for hard/soft walls with soil-cement primary piles.
- The model output includes significant in-plane shear forces in the plate.
- The wall has combined retaining and load-bearing function, or carries significant vertical loading.
- The selected E2 value materially affects deformation, prop loads, or force distribution in the design assessment.
8.3 Validation Against Explicit Pile Modelling
Where greater confidence is required, compare wall deflections and global force redistribution against a simplified explicit model, such as embedded beam rows representing the secondary piles or selected volume-pile checks. The comparison should focus on global behaviour rather than one-to-one agreement in local pile forces, because the orthotropic plate model is a smeared continuum approximation.
9. Implementation Checklist
- Select the equivalent plate thickness deq and use it consistently.
- Compute Isec and Iprim from the selected pile diameters.
- Compute E1 from the secondary-pile vertical bending stiffness.
- Compute E2 from the primary-pile lower-bound horizontal bending stiffness, unless a higher value is justified by calibration or composite-action assumptions.
- Assign ν12, usually close to 0.20 for concrete materials.
- Select shear stiffnesses using Option A or Option B, then run sensitivity studies when shear response is relevant.
- Verify local axis orientation in PLAXIS 3D before interpreting results.
- Document the assumptions used for E2, G values, and any project-specific stiffness reductions.
10. References
- Gaba, A., Hardy, S., Doughty, L., Powrie, W. and Selemetas, D. (2017). CIRIA C760 — Guidance on Embedded Retaining Wall Design. CIRIA, London.
- PLAXIS 3D Reference Manual. Bentley Systems.
- Timoshenko, S.P. and Woinowsky-Krieger, S. (1959). Theory of Plates and Shells. 2nd ed. McGraw-Hill.
- Reddy, J.N. (2006). Theory and Analysis of Elastic Plates and Shells. 2nd ed. Taylor & Francis.
- Potts, D.M. and Zdravković, L. (2001). Finite Element Analysis in Geotechnical Engineering: Application. Thomas Telford, London.
- EN 1997-1:2004. Eurocode 7: Geotechnical design — Part 1: General rules.