Propped diaphragm wall — preliminary sizing

What this page computes

The page determines the embedment depth and the prop force for a diaphragm wall with a single level of support, in cohesionless soil. Plus the maximum bending moment and the total wall length.

What the prop changes

It is worth comparing directly with the cantilever wall, because it is the same mechanics with one difference.

For a cantilever, the only thing balancing the moment from active pressure is the soil in front of the wall, and the lever arm of that resistance is short — it develops right next to the point of rotation. That is why D comes out on the order of 1.5–2 × H.

With a prop near the top, the moment closes between two well-separated supports. The embedment depth typically drops to 0.3–0.5 × H, and the moment in the wall drops accordingly. On a 6 m excavation the difference is several metres of wall — and a much lighter section.

The price is the prop force. It does not disappear: it is transferred into a real structure — a steel strut, a ground anchor, or the slab cast before excavation. The page reports it explicitly, per metre run of wall, because it sizes that element.

The free earth support method

The toe of the wall is assumed free to rotate: the soil in front pushes it, but does not fix it. Equilibrium is written about the prop, not about the toe as for a cantilever:

\(M_{passive/prop} = M_{active/prop}\)

The equation is of high order in D and is solved by bisection. The net moment increases monotonically with D over the physical range — the passive contribution grows as D³ about the prop, the active one only as D² — so the solution is unique.

The prop force then follows from horizontal equilibrium:

\(F = R_{active} - R_{passive}\)

The alternative: fixed earth support

There is also the fixed earth support method, which assumes the toe is fully restrained. It gives a greater depth but a smaller moment, because the wall acts as a continuous beam on two supports rather than a simply supported one.

The trade-off is economic: less steel, more excavation. The choice depends on local costs and on how deep the bearing stratum lies. The method requires an iterative analysis and is not implemented here — the page uses free earth support, which is the standard for preliminary sizing and is conservative on moment.

The factor of safety goes on K_p

As for the cantilever sheet pile: the passive coefficient is reduced, K_p,d = K_p/FS, and only then is equilibrium written. The alternative — equilibrium with the full K_p, then increasing the depth — gives a different answer, because the relationship between D and moment is non-linear.

The physical reason safety sits on the passive side: passive resistance is the uncertain part of the scheme. It only mobilises at large displacements, it can be compromised by accidental over-excavation in front of the wall, and it depends on a φ known less precisely than the loading.

When a second level of support is worth it

If D/H exceeds about 0.8, the page flags it. At that depth, the extra excavation and the extra wall usually cost more than a second row of props. Below 5–6 m of excavation a single level is generally enough; beyond 8–10 m, two or three become normal.

A wall with several levels of support has a different structural scheme — a continuous beam on several supports — and is not covered by this page.

What it does not cover

• Verification of the wall section — the page gives M_max; choosing the thickness and reinforcement is left to the user.
• Displacements, which for deep excavations next to existing buildings are often the governing criterion rather than strength.
• Construction stages. The wall is checked in its final state; but it passes through a cantilever phase before the prop is installed, and that phase can govern.
• Groundwater, base heave and hydraulic failure.
• Layered soil and cohesion.
• Multiple prop levels, as noted above.

The method is standard (Das, chapter 14), but it has not been checked against a published worked example. The internal tests cover equilibrium, trends and the comparison with a cantilever wall — not a reference value. Read the result as preliminary sizing.