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Design of Foundations and Retaining Structures

A foundation passes the building load to the ground without the soil failing or sinking too much. A spread footing makes the area big so the bearing pressure q = Q ÷ A is small. A pile reaches deeper, strong soil and carries load by skin friction and end bearing. A retaining wall holds soil back against earth pressure P = ½ Ka γ H², and must not slide, tip over or overload the soil.

🎬 Step-by-step story

  1. A wall stands next to a heap of soil. The soil wants to spread out, like a pile of sand.
  2. Red arrows show the soil pushing on the wall. Like water, the push is bigger lower down. Together they make the force P.
  3. Make the soil higher. The force P grows very fast, because it depends on H squared.
  4. Make the soil stronger and rougher (bigger friction angle). The arrows get shorter. Strong soil pushes less.
  5. On the right, a column stands on a footing. Make the footing wider and the pressure on the soil, q, drops.
  6. Now three piles go deep under the footing. They reach strong soil far down. Move the sliders and explore.

Tip: drag the 3D scene to turn it. Use two fingers to zoom.

🤔 Common doubts, cleared

Why would soil push on a wall at all?

Loose soil wants to spread out until its slope is gentle. The wall stops that, so it feels the push.

Why are the arrows longer at the bottom?

More soil sits above a deep point, so it pushes harder there.

Why does doubling the soil height make P four times?

The pressure doubles and the pushed height doubles too, so P goes with H².

What does the friction angle mean?

It is the steepest slope a dry heap of that soil can keep. A bigger angle means the soil is more self-supporting and pushes less.

Does a wide footing really help on soft soil?

Yes, it lowers q so that the soil is not overloaded. Very soft layers deeper down may still need piles.

Why do the piles go so deep?

To reach strong soil and to grip more soil along their sides, which adds skin friction.

Design of spread foundations

A spread footing (shallow foundation) is a wide concrete pad under a column or a long strip under a wall. It spreads the load over more soil.

The bearing pressure is q = Q / A (load ÷ footing area). The soil has a safe allowable bearing capacity qa (for example 150–300 kPa for firm soil). Design rule: q ≤ qa. So the needed area is A = Q ÷ qa; for a square footing, B = √A.

Also check: settlement (the footing must not sink unevenly), the depth (below soft top soil, frost and moving soil), and the concrete thickness against punching and bending. Footings are made of reinforced concrete with bars at the bottom.

Design of pile foundations

When the top soil is soft, we use piles: long columns of concrete or steel driven or bored deep into the ground. A pile cap on top joins the piles and takes the column.

A pile carries load in two ways. Skin friction is the grip of soil along the sides: Qs = π D L fs (D diameter, L length, fs friction per area). End bearing is the push of strong soil under the tip: Qb = qb × π D² / 4.

Ultimate capacity = Qs + Qb. Allowable capacity = ultimate ÷ safety factor (about 2.5). For a group of piles, add the single-pile loads, then check that the group as a whole does not fail or settle.

Design of retaining structures

A retaining wall holds back soil that is higher on one side. The soil pushes sideways with an earth pressure. For dry sand-like soil (Rankine): Ka = (1 − sin φ) / (1 + sin φ), where φ is the friction angle (30° gives 0.33). Pressure at depth z is Ka γ z, a triangle like water. Total push per metre of wall: P = ½ Ka γ H², acting at H/3 above the base.

Three stability checks: (1) Overturning: FS = resisting moment ÷ overturning moment, aim for at least 2. (2) Sliding: friction under the base ÷ P, aim for at least 1.5. (3) Bearing: the pressure under the base must stay below qa. Put drainage (weep holes and gravel) behind the wall, because trapped water adds large pressure.

Try it

At home: fill a tray with dry sand and stand a book upright against a side. Pile more sand behind it: the book tips. Now put a wide flat board under a heavy stone on soft sand: it sinks less than a narrow stick does.

In the 3D: predict, then check. If H goes from 3 m to 6 m, how many times does P grow?

Key formulas and definitions

Worked examples

1. Find K_a for a soil with φ = 30°.

sin 30° = 0.5. K_a = (1 − 0.5) / (1 + 0.5) = 0.5 / 1.5 = 0.333.

2. A wall holds H = 3 m of soil, γ = 18 kN/m³, K_a = 0.333. Find P and where it acts.

P = ½ × 0.333 × 18 × 9 = 27 kN per metre. It acts at H/3 = 1 m above the base.

3. The wall weighs 60 kN per metre, with its weight 1.0 m from the toe (tipping point). P = 27 kN acts 1 m above the base. Find the overturning FS.

Resisting moment = 60 × 1.0 = 60 kNm/m. Overturning moment = 27 × 1 = 27 kNm/m. FS = 60 / 27 = 2.22, which is above 2. OK.

4. A column load of 600 kN sits on a 2 m × 2 m footing. Find q. What footing is needed if q_a = 200 kPa?

q = 600 / 4 = 150 kPa, which is below 200. OK. Needed area = 600 / 200 = 3 m², so B = √3 = 1.73 m.

5. A pile has D = 0.4 m, L = 10 m, f_s = 30 kPa and q_b = 2000 kPa. Find Q_s and Q_b.

Q_s = π × 0.4 × 10 × 30 = 377 kN. Tip area = π × 0.16 / 4 = 0.1257 m². Q_b = 2000 × 0.1257 = 251 kN.

6. For that pile find the allowable load (FS = 2.5). How many piles carry a 1000 kN column?

Ultimate = 377 + 251 = 628 kN. Allowable = 628 / 2.5 = 251 kN. Piles = 1000 / 251 = 3.98, so use 4 piles.

Common mistakes

Practice quiz

1. Bearing pressure under a footing is:
2. Earth pressure on a wall grows with:
3. A pile carries load by:
4. A stronger soil (larger φ) gives a K_a that is:
5. Weep holes in a retaining wall:

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Frequently asked questions

When do we use piles instead of footings?

When the soil near the surface is soft or loose, and strong soil lies deeper.

Why is the soil force a triangle?

Deeper soil has more soil above it, so it pushes harder. The push is zero at the surface and biggest at the base.

Is a heavier wall always better?

A heavier wall resists tipping and sliding, but it presses harder on the soil under it. Check bearing pressure too.

Where this is taught

Japan高校（専門学科）1〜3年Civil Structural Design

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