Bored pile retaining wall

Cantilever wall of piles at spacing s: embedment, moment per pile and the asymmetry between the loading width and the resisting width.

Wall geometry

H — excavation depth [m]

D — diameter [m]

s — spacing [m]

Centre-to-centre spacing. s < D = secant piles (watertight), s = D = tangent, s > D = contiguous, with a clear gap.

Soil

γ [kN/m³]

φ [degrees]

q — surcharge [kPa]

Calculation model

Factor of safety on K_p Effective width factor The passive resistance mobilises over a width larger than the diameter, because of the three-dimensional effect in front of the pile. The classical value is 3 (Broms), capped at the spacing s. Embedment increase The simplified method neglects the reverse pressure below the point of rotation; the usual convention is to increase the equilibrium embedment by 20%. s/D threshold for arching Above this ratio the gap between piles becomes too large for the soil to arch onto them. This is NOT a code check: EN 1997-1 gives no such criterion, which is why the threshold is an input.

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Tool information

What this page computes

A cantilever retaining wall made of bored piles of diameter \(D\) at spacing \(s\). It gives the required embedment, the maximum moment on one pile, and the classification of the wall — secant, tangent or contiguous.

Why this is not the same as a continuous wall

This is the whole content of the page, and the reason it is not a rename of the diaphragm wall calculation.

The wall is not continuous. The consequence shows up in two different places, and not in the same way:

The load reaches a pile over the full tributary width \(s\). The soil between the piles does not disappear: it arches onto them. So the load on a pile is the active pressure times \(s\), not times \(D\).

The passive resistance below excavation level mobilises over a width larger than \(D\). An isolated pile pushed sideways does not only crush the soil directly in front of it over the diameter: it pushes laterally as well, and the ultimate resistance is appreciably greater. The classical factor is 3D (Broms: \(p_u = 3 K_p \sigma'_v D\)).

But that width is capped at \(s\). Two adjacent piles cannot each mobilise \(3D\) if \(3D > s\) — the zones would overlap and the same soil would be counted twice. Failure then becomes that of a continuous wedge.

\(b_{ef} = \min(3D,\ s)\)

The practical consequence

As long as \(s \le 3D\), the embedment does not depend on the spacing: both the load and the resistance scale with \(s\), and the equilibrium equation is identical. Piles can be spaced further apart with no penalty — up to the limit.

Beyond \(s = 3D\) the situation reverses sharply. The load keeps growing with \(s\), but the resistance stays locked at \(3D\). Increasing the spacing penalises twice over, and the moment on the pile grows faster than proportionally. A test checks exactly this: doubling the spacing from \(3D\) to \(6D\) increases the moment by more than a factor of two.

The plan view on the page shows the two widths side by side. Without it, the fact that \(b_{ef}\) can be smaller than \(3D\) is nowhere visible.

The method

Cantilever, simplified method:

the active pressure acts over the whole pile length, from behind;
the passive pressure acts from excavation level downwards, from the front;
the reverse pressure below the point of rotation is neglected;
moments are taken about the toe and solved for the embedment;
the resulting embedment is increased by 20%, the usual convention to cover the neglected term.

Safety is introduced by reducing \(K_p\), as on the diaphragm wall page. The equilibrium equation is monotonically increasing in the embedment (resistance grows as \(d^3\), load as \((H+d)^2\)), so bisection solves it reliably.

The maximum moment lies below excavation level, not at it: above the excavation there is no passive resistance, so the shear grows monotonically and cannot vanish there.

The gap between piles is not a code check

With contiguous piles a clear gap of \(s - D\) remains. The soil arches onto the piles only if the gap is small enough; otherwise it runs through.

EN 1997-1 gives no criterion for this. That is why the \(s/D\) threshold is an input, not a constant, and the page reports the gap and the ratio and says what they mean — without pretending to have checked something the code does not require.

Independently of the ratio: in clean granular soil below the water table, a facing between the piles or secant piles are needed regardless. Arching does not hold fine particles in place when there is seepage.

What it does not cover

The supported wall (propped or anchored). The model is strictly a cantilever. The widths given here still apply to a supported pile wall, though — they layer on top of the diaphragm wall calculation.
Water pressure and layered soil: a single dry layer with constant \(\varphi\). Below the water table the hydrostatic pressure adds separately and usually dominates.
Design of the reinforced concrete section. The page gives the moment; circular reinforcement is handled on the concrete pages, and the minimum reinforcement and bored-pile detailing rules (Ø16, at least 6 bars, clear spacing ≤ 200 mm) are on the minimum reinforcement page.
Settlements behind the wall and the deflection of the head — the model is limit equilibrium, not deformation.
Cohesion. Rankine with \(\varphi\) is used; for cohesive soils the result is conservative.

Propped diaphragm wall — the same kind of excavation, but with a continuous, supported wall.
Cantilever sheet pile — the same simplified method, but a thin continuous wall.
Wall surcharges — the local surface loads that add on top of the active diagram.
Minimum reinforcement ratios — the "bored pile" element, for reinforcing the circular section.