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Queensferry

Module 12 · Lesson 12.2

Stability, and designing the wall

Three checks before any reinforcement, and the one that usually governs.

Why this matters

A retaining wall can be perfectly reinforced and still slide down the hill. Stability is checked first, on the whole wall as a rigid body, and only then is the concrete designed. It is worth knowing which of the three checks usually governs, because it tells you what to change when the wall does not work — and for a cantilever wall it is almost always sliding, which reinforcement cannot help at all.

By the end of this lesson you should be able to

  • Carry out the overturning, sliding and bearing checks
  • Identify which normally governs and why
  • Say what to change for each
  • Design the stem, using the correct height

What you should already know

  • Earth pressure (previous lesson)
  • Bearing pressure and the middle third (Module 11)
  • Flexural design (Module 4)

Three checks, in order

Overturning about the toe. The earth pressure tries to rotate the wall forward; the weight of the wall and of the soil sitting on the heel resists. A factor of about 2.0 is traditional.

Sliding along the base. The horizontal force tries to push the wall out; friction under the base resists. A factor of about 1.5.

Bearing, under the base. The resultant must stay within the middle third so the heel does not lift, and the peak pressure must be within the allowable bearing resistance.

All three use the same two quantities — the horizontal force and the vertical load — combined differently. And the vertical load is mostly soil sitting on the heel, not the concrete: in the worked example below the soil contributes more than the stem and base together. That is the whole idea of a cantilever retaining wall. It does not resist the earth by being heavy; it resists by using the earth's own weight against it.

Worked example

A 5 m cantilever retaining wall

Given

  • Retained height 5.0 m, base 3.2 m long × 0.4 m thick, stem 0.35 m thick
  • Toe 0.9 m, so the heel is 3.2 − 0.9 − 0.35 = 1.95 m
  • Soil: γ = 18 kN/m³, φ = 30°, so Ka = 1/3
  • Surcharge on the retained surface 10 kPa; base friction coefficient 0.5
  • Drained — the water table is below the base

Find

Whether the wall is stable, and what governs.

Assumptions

  • Free-standing, so the active state applies
  • Characteristic loads against traditional factors of safety, 2.0 and 1.5
  • φ, γ and the base friction are geotechnical inputs, supplied not assumed

    Then, and only then, the concrete

    Once the wall is stable, the three elements are ordinary cantilevers.

    The stem is a vertical cantilever carrying earth pressure over its own height — the height below the top of the stem, not the full wall height. That distinction matters more than it looks: moment goes with the cube of height, so using 5.0 m instead of 4.6 m overstates the stem moment by (5.0/4.6)³ = 28%.

    The heel is a cantilever loaded downward by the soil above it and upward by the bearing pressure. The net load is usually downward, so it needs TOP steel — which surprises people, because every other slab in the building has bottom steel.

    The toe is a cantilever loaded upward by the bearing pressure, so it needs BOTTOM steel.

    The two adjacent elements therefore have their reinforcement on opposite faces, and the bars must be lapped through the base to make the corner work.

    Practice

    A wall has a vertical load of 253 kN/m, a horizontal force of 92 kN/m and a base friction coefficient of 0.5. What is the factor of safety against sliding?

    Practice

    A stem is 4.6 m tall, retaining soil with Ka = 1/3 and γ = 18 kN/m³, with a 10 kPa surcharge. What is the design moment at its base, in kNm/m? Use characteristic values.

    Practice

    By what factor is the stem moment overstated if the full 5.0 m wall height is used instead of the 4.6 m stem height?

    Check yourself

    Which face of the heel slab needs the main reinforcement?

    Summary

    • Overturning, sliding and bearing — all before any reinforcement
    • Sliding usually governs a cantilever wall
    • Fix sliding with a shear key, a wider base or a rougher formation — not with steel
    • The restoring weight is mostly soil on the heel, not concrete
    • The stem cantilevers over its OWN height; using the full wall height overstates it by 28%
    • The heel needs TOP steel and the toe needs BOTTOM steel — opposite faces, lapped through the corner
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    This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint