Pole Embedment Calculator (Brinch Hansen): Required Setting Depth for Directly Embedded Poles in Layered Soil
Pole Embedment Calculator (Brinch Hansen): Required Setting Depth for Directly Embedded Poles in Layered Soil
Find how deep to set a directly embedded pole so the soil can resist the overturning load, or check a setting depth you already have. Enter the load, the pole and hole size, the backfill and up to six soil layers with groundwater. The calculator solves the rigid-pole equilibrium, draws the soil reaction and shows every step.
Pole Embedment Calculator
Pick Load example in the toolbar to see a complete case, then change one value at a time. Press the ? beside any input for its meaning and typical values. Click into a soil row, then a soil type in the guide panel, to fill φ, c and γ. Switch to Check an embedment when you already have a setting depth. Report / Save PDF gives you the inputs, both drawings and every calculation step; Clear empties the form for your own data.
What to Enter: Load, Pole, Backfill and Soil
The form follows the order you’d work through a pole foundation: the load from your pole-loading calculation, the pole and hole, then the soil from the borehole log. Both drawings update as you type, so a wrong layer depth or a hole smaller than the pole shows up in red before you calculate.
Which load do I enter?
- Horizontal load P: the unfactored resultant of wind on the pole and conductors, line-angle and dead-end tension, as one force.
- Load factor (OCF): multiplies P to the ultimate load
Puthe soil must resist at failure. The guide lists the NESC 2017 Table 253-1 factors (2.50 Grade B wind, 2.20 Grade C at crossings, 1.75 Grade C elsewhere); check them against the edition and standard you design to. - Load position: either a fixed height above groundline, or an offset below the pole top. With the offset, the load height drops as the pole is set deeper, which is how the pole really behaves.
- Pole length: only needed for the offset option and for the comparison with the 10% rule and the RUS formula.
How do the hole and backfill change the calculation?
Enter the augered or excavated hole diameter for every backfill; it’s drawn on both figures and checked against the pole diameter. What it does to the calculation depends on the backfill:
- Concrete, soil-cement or flowable fill: the backfill bonds with the pole into one shaft, so the effective diameter
Dis the hole diameter and the soil fails around the hole. - Compacted excavated soil or crushed rock:
Dis the pole diameter, and the layer values you enter must describe the soil as compacted around the pole.
What soil data do I need?
- Layers: up to six, top down, each with its bottom depth below groundline. The last layer continues to any depth.
- φ and c: for sand, the drained friction angle with c = 0; for clay under short-term load, the undrained strength
cuwith φ = 0. The quick-fill buttons use mid-range values from ENA C(b)1 Tables B3 to B5. - γ and γsat: bulk unit weight above the water table and saturated weight below it. Leave γsat blank to use γ.
- Soil type: sets the fill pattern in the drawing and the name in the report. The analysis uses only φ, c and γ.
- Groundwater: the highest seasonal level. Below it the calculator uses buoyant weight, which cuts the resistance of granular soil.
The Brinch Hansen Method Behind the Numbers
Brinch Hansen (1961) gave the ultimate lateral earth pressure on a short rigid pile in soil with any combination of friction and cohesion. ENA C(b)1-2006 Appendix B applies it to directly embedded poles: the embedded length rotates about a point zr, soil in front of the pole resists above that point and soil behind it resists below.
What is the ultimate soil reaction at each depth?
Variables
q_z: vertical effective overburden at depth z (kPa), using γ′ = γsat − 9.81 below the water tablec: cohesion of the layer at depth z (kPa);D: effective diameter (m)K_q,z,K_c,z: earth-pressure coefficients for the layer’s φ at relative depth z/D
\( K_c^0 = \left[e^{(\pi/2+\varphi)\tan\varphi}\cos\varphi\tan\left(45^\circ+\dfrac{\varphi}{2}\right) – 1\right]\cot\varphi \)
\( d_c^\infty = 1.58 + 4.09\tan^4\varphi \qquad K_0 = 1 – \sin\varphi \)
\( \alpha_q = \dfrac{K_q^0}{K_q^\infty – K_q^0}\,\dfrac{K_0\sin\varphi}{\sin(45^\circ+\varphi/2)} \qquad \alpha_c = \dfrac{K_c^0}{K_c^\infty – K_c^0}\,2\sin\left(45^\circ+\dfrac{\varphi}{2}\right) \)
These reproduce ENA C(b)1 Tables B1 and B2 exactly, including clay with φ = 0, which the calculator evaluates as the limit at a very small φ.
How is the rotation point and the capacity found?
Variables
e: height of the load above groundline;L: embedment depthz1,z2: depths of the resultants F₁ and F₂- The moment equation (about the load point) fixes
zr; the horizontal balance then gives the ultimate loadHu
The calculator integrates w in 2 mm steps, splitting at every layer boundary, and bisects on L. The required depth is rounded up to the next 0.1 m, and the sizing table lists every 0.1 m step around it. k is the optional ENA calibration: 1.01 for undrained (clay) parameters, 0.60 for drained parameters, or 1.0 for the raw Hansen value.
Where is the largest bending moment in the pole?
The maximum moment sits a little below grade, not at the groundline. Check the pole section at z0.
Worked Example: 45 ft Steel Pole in Clay over Sand
This is the first entry in Load example. Load it and you’ll get the same numbers.
| Pole | 13.72 m (45 ft) steel pole, 0.30 m at groundline |
| Load | P = 8 kN applied 0.61 m below the top, load factor 2.5 → Pu = 20 kN |
| Hole | 0.60 m augered hole, concrete backfill → D = 0.60 m |
| Soil | 0–1.5 m firm clay, cu = 37 kPa, γ = 17 / γsat = 18 kN/m³; below 1.5 m medium dense sand, φ = 33°, γ = 18.5 / γsat = 20 kN/m³ |
| Groundwater | 1.5 m below grade |
| Factors | φs = 1.0, no ENA calibration |
What does the calculator return?
| Quantity | Value |
|---|---|
| Load height above ground at that depth, e | 10.46 m |
| Rotation point, zr | 1.78 m (zr/L = 0.67) |
| F₁ (in front, above zr) | 205.0 kN at z₁ = 1.01 m |
| F₂ (behind, below zr) | 185.0 kN at z₂ = 2.25 m |
| Ultimate capacity, Hu = F₁ − F₂ | 20.0 kN = Pu |
| Groundline moment, Pu·e | 209.2 kN·m |
| Maximum moment in the pole | 212.1 kN·m at z₀ = 0.28 m below grade |
| Layer share of the soil reaction | Clay 41% (all in F₁); sand 59% (governs) |
| Required embedment | 2.65 m (8.70 ft) → set at 2.70 m |
How does the sizing table pick the setting depth?
| L (m) | e (m) | zr (m) | Hu (kN) | Margin | |
|---|---|---|---|---|---|
| 2.50 | 10.61 | 1.66 | 17.1 | −14.3% | fails |
| 2.60 | 10.51 | 1.74 | 19.0 | −5.0% | fails |
| 2.70 | 10.41 | 1.82 | 21.0 | +4.9% | pick |
| 2.80 | 10.31 | 1.90 | 23.1 | +15.5% | ok |
| 2.90 | 10.21 | 1.98 | 25.4 | +26.8% | ok |
“Check this depth in the form” sends 2.70 m to Check mode: utilisation 95.3%, safety factor 2.62 on the unfactored 8 kN load.
Would the 10% + 0.61 m rule have been enough?
What Moves the Embedment Depth Most?
Each row changes one input from the worked example (required depth 2.65 m) and keeps everything else the same.
How sensitive is the depth to backfill, soil, water and load?
| Change | Required L | vs base |
|---|---|---|
| Compacted soil or crushed rock backfill (D = 0.30 m pole) | 3.19 m | +0.54 m |
| Concrete in a 0.75 m / 0.90 m hole | 2.49 m / 2.37 m | −0.16 / −0.28 m |
| Top clay soft, cu = 18 kPa | 3.06 m | +0.41 m |
| Top clay stiff, cu = 75 kPa | 2.26 m | −0.39 m |
| Sand loose (φ = 29°) / dense (φ = 38°) | 2.79 m / 2.50 m | +0.14 / −0.15 m |
| No groundwater / groundwater at the surface | 2.59 m / 2.85 m | −0.06 / +0.20 m |
| Load factor 1.75 (Grade C) / 4.0 | 2.31 m / 3.16 m | −0.34 / +0.51 m |
| ENA drained calibration (× 0.60) | 3.21 m | +0.56 m |
| ENA undrained calibration (× 1.01) | 2.64 m | −0.01 m |
Why Results Differ from Rules of Thumb and Spreadsheets
When your number disagrees with a standard setting depth, an old spreadsheet or another program, check these first.
Which assumptions usually explain the difference?
- Effective diameter: pole diameter or hole diameter. Concrete backfill is the only case where using the hole is justified.
- Overburden: some spreadsheets multiply the current layer’s γ by the full depth and ignore the water table. This calculator adds each layer at its own weight and uses buoyant weight below the water.
- Adequacy check: an “assume a depth, compare moments” check is not the same as Hansen’s equilibrium. In one such workbook, 10.6 ft passed its own check, but solving F₁(e + z₁) = F₂(e + z₂) gives 11.09 ft (111% utilisation at 10.6 ft).
- c–φ soils: Hansen adds the cohesion and friction terms in full. A large c with a large φ in the same layer can overstate capacity; the calculator warns when you enter one.
- Load factor and calibration: a legacy OCF of 4.0 against a modern 2.5 load factor, or ENA’s 0.60 drained factor, change the depth more than any refinement in the method.
Frequently Asked Questions
Why doesn’t a wider concrete hole save more depth?
A wider shaft pushes against more soil, but Hansen’s coefficients depend on z/D, so they fall as D grows at the same depth. The two effects partly cancel: in the worked example, going from a 0.60 m to a 0.90 m hole (50% wider) saves only 0.28 m, about 11%. Concrete’s bigger benefit is that it removes the uncertainty of compaction: in the field tests, flowable fill reached 1,056 kN·m at a shorter embedment than any compacted backfill.
Can I model a ring of compacted backfill around the pole?
Not as a separate ring. With soil or crushed-rock backfill the calculator uses the pole diameter and the layer values you enter. When the hole is much wider than the pole, part of the failure surface runs through the backfill, so the calculator warns you to describe the top layer as placed, not as undisturbed soil.
Does it check how far the pole will lean?
No. Hansen gives the ultimate capacity, the load at which the soil fails. Rotation at working load needs a stiffness-based method; ENA treats it separately, and deflection-based foundation programs cover it. If pole tilt matters for your structures (dead-ends, angle poles, clearance-critical spans), check it separately.
Why does groundwater increase the depth?
Below the water table the soil is buoyed up, so its effective weight drops from about 20 to about 10 kN/m³. Granular resistance is proportional to that overburden, so it roughly halves below the water. Clay under undrained load is barely affected, because its resistance comes from cu. Use the wet-season level; in low-lying sites that is often near the surface.
Why Brinch Hansen and not Broms?
Broms’ method handles either pure sand or pure clay. Brinch Hansen handles soils with both c and φ and lets the resistance vary layer by layer, which matches a real borehole log. In the full-scale field tests above, Broms overpredicted capacity on average (1.22 × measured), while Hansen underpredicted (0.84 × measured). Both had a coefficient of variation of about 0.4, so neither method is precise.
