Deflection is the check that governs most buried flexible pipe designs. This worked example takes a realistic scenario all the way through so you can see exactly where each number comes from — and reproduce it in the AS2566 calculator. If you want the theory behind the soil modulus that dominates the result, read The E′ Soil Modulus Problem in AS2566 first. For where deflection design (Part 1) stops and installation (Part 2) begins, see AS2566.1 vs AS2566.2.
The design scenario
A DN315 PE100 (HDPE) gravity sewer laid in a trench beneath a sealed local road, at 1.5 m cover, with a T44 design vehicle. The embedment is a compacted sand/gravel; the native trench wall is a softer silty clay.
| Parameter | Symbol | Value | Source |
|---|---|---|---|
| Pipe outside diameter | De | 315 mm | PE100 DN315 (PN16, SDR11) |
| Wall thickness | t | 30.1 mm | SDR11 solid wall |
| Ring-bending stiffness | SDL | 3,800 N/m/m | Product stiffness class |
| Cover to crown | H | 1.5 m | Design |
| Soil unit weight | γ | 18 kN/m³ | Cl. 4.3 |
| Live load (T44, dispersed) | wq | 20.5 kPa | Cl. 4 / Fig. 4.1 at 1.5 m |
| Bedding factor | K | 0.1 | Cl. 5.2 (default) |
| Embedment modulus | E′e | 5 MPa | Table 3.2 — sand/gravel, D 85% |
| Native soil modulus | E′n | 3 MPa | Geotechnical (silty clay) |
| Trench width at pipe | B | 0.80 m | Design |
Step 1 — Vertical load on the pipe
The total design pressure at the pipe crown, w, is the sum of the earth load and the dispersed live load. For a standard trench installation, AS2566.1 permits a prism earth load (Cl. 4.3):
Adding the dispersed T44 live load of 20.5 kPa (there is no additional surcharge in this case):
Step 2 — Effective soil modulus E′
The embedment value from Table 3.2 is E′e = 5 MPa. But the native trench wall here is softer than the embedment (E′n = 3 MPa < E′e), so the effective modulus is reduced by the Leonhardt correction factor ζ (Cl. 3.4.3). This is the step most hand calculations skip — and it is unconservative to skip it when the native soil is soft.
B/De = 0.80 / 0.315 = 2.54E′n/E′e = 3 / 5 = 0.60The soft native soil pulls the effective modulus down from 5 MPa to 3.0 MPa — a 40% reduction that flows straight into the deflection result. Assuming E′ = E′e = 5 MPa here would under-predict deflection by roughly a third.
Step 3 — Deflection (modified Iowa formula)
With load and effective modulus in hand, apply the modified Iowa formula from AS2566.1 Eq. 5.2(2). Note that w is converted from kPa to MPa (÷ 1000) to match the units of the denominator:
Notice the denominator: the soil term (0.1827) is six times the pipe-stiffness term (0.0304). Even for this relatively stiff SDR11 wall, the soil is doing most of the work — which is the whole reason installation quality is a structural variable, not a construction nicety.
Step 4 — Check against the allowable limit
AS2566.1 Table 2.1 gives a design allowable deflection of 7.5% for solid-wall PE. Utilisation is the calculated deflection divided by the limit:
At 30% utilisation, deflection passes comfortably. That is typical — for a well-embedded flexible pipe at modest cover, deflection is rarely the binding constraint. The checks that more often govern are ring-bending strain and buckling.
Step 5 — Ring-bending strain (companion check)
Deflection rarely travels alone. As the ring deflects, the pipe wall bends, and AS2566.1 checks the resulting strain against an allowable value (Eq. 5.3.1). The shape factor Df relates deflection to peak wall strain:
Combined-loading interaction (Eq. 5.3.3) then confirms the pair together: (2.23/7.5)² + (0.76/4.0)² = 0.13 ≤ 1.0 ✓. Buckling under external pressure is a separate limit state — the calculator checks it too, and we cover it in a dedicated article (Buckling under AS2566.1, in preparation).
Common mistakes this example avoids
- Skipping the Leonhardt correction. Using E′e directly when the native soil is softer over-states the soil support and under-states deflection. Always check ζ when E′n < E′e.
- Unit slips in the Iowa formula. w must be in MPa (÷ 1000 from kPa) against the 0.061·E′ term. A missed conversion changes the answer by a factor of 1000.
- Optimistic compaction. Select E′e for the compaction you can actually guarantee and inspect on site — not the best-case value. Here, 5 MPa reflects a realistic D 85%.
- Stopping at deflection. Deflection passing does not mean the design passes. Strain and buckling frequently govern, especially for thinner walls.
Summary
- Total load w = 47.5 kPa (27.0 earth + 20.5 live).
- Effective soil modulus E′ = 3.00 MPa after the Leonhardt ζ = 0.599 correction.
- Deflection Δy/D = 2.23% vs 7.5% allowable → 30% utilisation, pass.
- Ring-bending strain εb = 0.76% vs 4.0% allowable → 19% utilisation, pass.
- The soil term dominates the Iowa denominator — E′, and therefore compaction, is the controlling design variable.
Open the calculator and enter these inputs to reproduce every figure above, with the full working shown for each step.
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