Eurocode 7 Sheet Pile Design: A Free Online Calculator

Published 1 September 2026 · 🇷🇴 Română

Why this calculation is different

Most retaining wall calculations answer "how much does the soil push?" A cantilever sheet pile wall calculation has to answer a harder question: "how deep does the wall need to go so the soil below the excavation can hold it up?" There is no footing, no anchor, no strut — the entire wall is held in place by the passive resistance of the soil in front of it, below the dig line.

Below is the method, a complete worked example, and at the end a free cantilever sheet pile calculator that finds the required embedment depth instantly.

How a cantilever sheet pile wall stays up

Picture a wall driven into the ground, with soil excavated on one side down to depth $H$. Above the excavation line, active earth pressure pushes the wall toward the open side. Below the excavation line, the wall is embedded a further depth $D$, and as it tries to rotate, the soil in front resists with passive pressure — while the soil behind, now below the toe, adds a bit more active pressure pushing back.

The wall finds equilibrium when the moments of these pressures, taken about the toe of the wall, balance out. There is no anchor and no strut: embedment depth is the only variable the designer controls, so it has to do all the work.

The equilibrium equation

Using Rankine coefficients for a cohesionless soil:

$K_a = \frac{1 - \sin\varphi'}{1 + \sin\varphi'} \qquad K_p = \frac{1}{K_a}$

A safety factor is applied — but to the passive coefficient, not to the depth found afterward:

$K_{p,d} = \frac{K_p}{FS}$

This matters: reducing $K_p$ first and then solving for $D$ gives a different answer than solving for $D$ with full $K_p$ and inflating the result afterward, because the relationship between $D$ and the resisting moment is not linear. Applying the factor to the coefficient, before solving, is the standard approach for cantilever sheet piles in cohesionless soil (Das, Principles of Foundation Engineering, ch. 9, "Sheet Pile Walls") and the one used here.

The full textbook method works with a more elaborate net-pressure diagram: below the dredge line, the pressure actually reverses sign right at the wall's point of rotation, and the exact solution reduces to a fourth-degree equation in the embedment depth. JointLib's calculator uses a simplified but physically equivalent version — moment equilibrium between a single active triangle (over the full length $L=H+D$) and a single passive triangle (over the embedded depth $D$ only) — good enough for a fast preliminary estimate, but not a substitute for the full check on a final design.

Moment equilibrium about the toe, taking active pressure over the full length $L = H + D$ against passive pressure over the embedded length $D$, gives one equation in $D$:

$M_{passive}(D) = M_{active}(D)$

This equation is not solvable in closed form — it does not simplify to a formula you can rearrange for $D$ — because passive resistance grows with $D^3$ while active thrust grows with $L^2$ where $L$ already contains $D$. The calculator solves it numerically (bisection), the same way any engineer solving it in a spreadsheet would: guess a depth, check whether the passive moment now exceeds the active moment, adjust, repeat.

Worked example, step by step

Take an excavation with:

excavation depth $H = 4$ m
soil unit weight $\gamma' = 18$ kN/m³
friction angle $\varphi' = 32°$
no surcharge
safety factor on the passive coefficient $FS = 1.5$

Step 1 — the coefficients.

$K_a = \frac{1 - \sin 32°}{1 + \sin 32°} = 0.307 \qquad K_p = \frac{1}{K_a} = 3.255$

$K_{p,d} = \frac{3.255}{1.5} = 2.170$

Step 2 — solve for the embedment depth $D$. The calculator finds, by bisection, the depth at which the passive moment about the toe first equals the active moment. For this example:

$D \approx 4.35 \text{ m}$

Step 3 — the ratio that tells you if this is even a reasonable design.

$\frac{D}{H} = \frac{4.35}{4.0} \approx 1.09$

Step 4 — the total length and the forces. Total wall length $L = H + D \approx 8.35$ m. The total active thrust over that length is $P_a \approx 193$ kN/m; the mobilised passive resistance is $P_p \approx 370$ kN/m — larger than $P_a$, as it must be, because it is carrying the safety margin on top of equilibrium.

Step 5 — the maximum bending moment. The moment in the wall peaks where the shear force crosses zero — a bit below the excavation line, once the accumulated passive resistance catches up with the accumulated active thrust. For this example, that point sits about 6.41 m below the top of the wall (2.41 m below the dig line), and the moment there is:

$M_{max} \approx 152 \text{ kNm/m}$

That moment is what sizes the sheet pile section — the depth calculation and the section design are two separate steps, but the first one has to come first.

Suggested figure: the net pressure diagram behind the equilibrium above — a single active triangle growing continuously from the top of the wall to its toe, against a single passive triangle mobilised only over the embedded depth $D$:

Original schematic of the simplified model behind the calculator: active pressure (purple) grows over the full length $L=H+D$; passive pressure (green) is mobilised only over the embedded depth $D$, below the dredge line. The maximum moment occurs where the accumulated shear crosses zero.

Why the embedment depth looks so large

$D/H \approx 1.09$ here — the wall needs to go almost as deep below the excavation as the excavation itself is deep. That is not a calculation error. It is the direct consequence of relying on passive resistance alone: the lever arm the passive pressure has to work with, measured from the toe, is short, so a large volume of soil has to be mobilised to produce enough resisting moment.

This is exactly why cantilever sheet piles are used only for shallow excavations. Past roughly 5 m, the embedment depth (and the section modulus needed to carry the resulting moment) grows fast enough that a cantilever wall stops being economical, and an anchored or propped wall — which redistributes the load instead of relying on embedment alone — takes over.

Common mistake: driving the pile to exactly the theoretical depth

The depth $D$ above solves the moment equilibrium EXACTLY — not a millimetre more. In practice that's a limiting solution, not a design one: the full calculation method (with the net pressure diagram and the sign reversal at the wall's toe) treats the point of rotation as an approximation, and the standard textbook procedure explicitly calls for increasing the theoretical depth by 20–30% before setting the actual pile length — not as an optional safety margin, but as a required step of the method, compensating for exactly that simplification in the net pressure diagram.

For the example above, $D_{theoretical}\approx4.35$ m would become, with a 25% increase, roughly $5.44$ m — over a metre of additional sheet pile that doesn't come from the calculation itself, but from the design rule that completes it.

Practical note: how sensitive the depth is to the friction angle

When the surcharge is zero, the moment equilibrium behind the calculator reduces to a closed form, easily derived directly from the two moment equations:

$D = \frac{H}{\left(\dfrac{K_{p,d}}{K_a}\right)^{1/3} - 1}$

Applying it to the same excavation ($H=4$ m, $\gamma'=18$ kN/m³, $FS=1.5$), but varying $\varphi'$ by just $\pm2°$ around the base example:

φ' (°)	K_a	K_p,d	D (m)
30	0.333	2.000	4.90
32 (base example)	0.307	2.170	4.35
34	0.283	2.359	3.89

A friction angle uncertainty of just ±2° — entirely plausible between a lab test and how the actual sand on site behaves — moves the required depth by nearly ±0.5 m, roughly ±12% of the base value. For a sheet pile wall, that isn't rounding noise: it's the difference between ordering 8 m piles and 9 m piles. Choosing $\varphi'$ conservatively (not the optimistic average of test results) matters here more than the precision of any other step in the calculation.

Assumptions and what this does not cover

Cohesionless soil, Rankine coefficients. No cohesion intercept, no wall friction, vertical wall, horizontal ground on both sides. For layered soils, sloped ground, or wall friction, this simplified method will not match a full limit-equilibrium or FEM analysis.
One effective unit weight for the whole profile. If groundwater is present, you need to account for it yourself when choosing $\gamma'$ — the method here does not take a separate water table depth as input.
This gives the embedment depth, not the section. Once $D$ and $M_{max}$ are known, the sheet pile section still needs to be checked separately against that moment.
Safety factor on $K_p$ only. Some design codes call for a different factoring scheme (e.g. factoring loads instead of, or in addition to, resistance) — check what your project's national annex actually requires before using FS = 1.5 as a default.

Calculate it online

JointLib's cantilever sheet pile calculator runs this exact bisection, instantly, in your browser, and draws the pressure diagrams and the moment location on a scaled section: enter the excavation depth, soil parameters, surcharge, and the safety factor on $K_p$, and get the embedment depth, the total length, the mobilised forces, and the maximum moment.

Active earth pressure calculator — the same Rankine active pressure, for a conventional retaining wall instead of an embedded cantilever
Retaining wall — full check — overturning, sliding, bearing capacity for a gravity or cantilever concrete wall
Boussinesq stress bulb — how stresses spread through the ground under a foundation