Footing & Retaining Wall

In the MP Vyapam Sub Engineer Civil syllabus under RCC Design · 2 parts

Design of Footings · Retaining Walls

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📑 Contents (15 sections)

Part 1 of 2

Design of Footings

Last reviewed 16 Sept 2026 · 6 min read

Purpose and types

A footing spreads the concentrated column or wall load over a larger area of soil so that the soil pressure stays within the safe bearing capacity (SBC) and settlement is acceptable.

Footing	Use
Wall (strip) footing	Continuous strip under a load-bearing wall
Isolated (pad) footing	Single column; square, rectangular or circular; flat, stepped or sloped top
Combined footing	Two or more columns close together, or a column near the property line
Strap (cantilever) footing	Two isolated footings joined by a stiff strap beam to balance an eccentric boundary column
Strip footing under columns	A row of columns on a continuous footing
Raft (mat) foundation	Whole building on one slab; for weak soils or heavy loads where footings would cover > about 50% of the plan
Pile cap	Transfers column load to a group of piles

Sizing

Area required uses service (unfactored) loads:

A_{r e q} = \frac{P + self-weight of footing and backfill}{q _{s a f e}}

Self-weight is commonly taken as 10% of the column load for a first estimate. Choose convenient dimensions ≥ $A_{r e q}$ .

For structural design use factored loads and the net upward pressure (self-weight of the footing does not bend the footing since it is supported directly by the soil beneath):

q_{u} = \frac{P _{u}}{A _{p r o v i d e d}}

IS 456 provisions for footings

Code ProvisionIS 456 — critical sections and minimum requirements

Thickness at the edge: not less than 150 mm for footings on soil (300 mm above the tops of piles for pile caps).
Bending moment is taken at the face of the column, pedestal or wall (for a masonry wall: halfway between the centre line and the edge of the wall; for a steel column with base plate: halfway between the column face and the edge of the plate).
One-way (beam) shear: at a distance $d$ from the face of the column.
Two-way (punching) shear: on a perimeter at $d /2$ from the column face; $τ_{v} \leq k_{s} τ_{c}$ with $τ_{c} = 0.25 f_{c k}$ and $k_{s} = 0.5 + β_{c} \leq 1$ .
Development length of bars must be available from the critical section for moment.
Minimum cover: 50 mm.
Minimum steel: 0.12% (HYSD) as in slabs.

Distribution of steel in rectangular footings

Long direction: spread uniformly across the full width.
Short direction: a central band of width equal to the short side of the footing gets

\frac{steel in central band}{total steel in short direction} = \frac{2}{β + 1}, β = \frac{long side}{short side}

The rest is spread uniformly in the outer portions.

Transfer of load at the base of the column

Compressive stress at the column–footing interface must not exceed the permissible bearing stress:

f_{b r} = 0.45 f_{c k} \frac{A _{1}}{A _{2}}, \frac{A _{1}}{A _{2}} \leq 2

$A_{1}$ = supporting area (largest area of the footing geometrically similar to the column and concentric with it, within the footing); $A_{2}$ = loaded area (column). If exceeded, provide dowels (starter bars) or extend column bars into the footing; dowel area at least 0.5% of the column cross-section and at least four bars, extending the development length into both members.

Part 2 of 2

Retaining Walls

Last reviewed 16 Sept 2026 · 6 min read

Purpose and types

A retaining wall holds back soil (or other material) at a slope steeper than it would naturally stand. Used for basements, road cuttings and embankments, bridge abutments, wing walls, and terraced sites.

Type	Description	Economical height (typical)
Gravity wall	Masonry or plain concrete; stability from its own weight	Up to about 3 m
Cantilever wall (T or L shaped)	RCC stem cantilevering from a base slab (toe + heel); soil on the heel adds stability	About 3–6 m
Counterfort wall	Cantilever wall with vertical counterforts at intervals on the backfill side tying stem to heel	Above about 6 m
Buttress wall	Like a counterfort wall but the supports (buttresses) are on the front (exposed) side	Where the front space is available
Crib, gabion, reinforced-earth walls	Modular or soil-reinforced systems	Varies

Earth pressure

(See Earth Pressure Theories in Soil Mechanics for derivations.)

For a wall that yields slightly away from the soil (active case), Rankine's theory with a horizontal backfill, cohesionless soil:

K_{a} = \frac{1 - sin ϕ}{1 + sin ϕ}, p_{a} = K_{a} γ h, P_{a} = \frac{1}{2} K_{a} γ H^{2} at \frac{H}{3} above the base

Uniform surcharge $q$ : extra rectangular pressure $K_{a} q$ , total $K_{a} q H$ at $H /2$ .
Submerged backfill: use submerged unit weight $γ^{'}$ for soil pressure plus full hydrostatic pressure $γ_{w} h$ — water pressure can double the thrust, which is why drainage is essential.
Sloping backfill at angle $β$ : $K_{a} = cos β \frac{cos β - cos ^{2} β - cos ^{2} ϕ}{cos β + cos ^{2} β - cos ^{2} ϕ}$ , thrust parallel to the slope.
Passive pressure in front of the toe ( $K_{p} = 1/ K_{a}$ ) is usually ignored or taken only partly, because the soil there may be removed.

Stability requirements

Code ProvisionIS 456 cl. 20 — stability of the structure as a whole

Overturning: the restoring moment must be not less than 1.2 × overturning moment from characteristic dead loads + 1.4 × overturning moment from characteristic imposed loads. Where dead load provides the restoring moment, only 0.9 times the characteristic dead load is taken.
Sliding: the structure must have a factor against sliding of not less than 1.4 under the most adverse combination of characteristic forces, taking only 0.9 times the characteristic dead load.
Probable variation in dead load during construction, repair or temporary works must be considered.

Classical checks (older practice, still asked): factor of safety ≥ 2.0 against overturning and ≥ 1.5 against sliding.

Bearing pressure: with total vertical load $W$ , base width $B$ and eccentricity $e$ of the resultant from the base centre:

p_{ma x, min} = \frac{W}{B} (1 \pm \frac{6 e}{B})

Keep $p_{ma x}$ ≤ SBC.
Keep $e \leq B /6$ (resultant in the middle third) so there is no tension (no loss of contact) at the heel.

Shear key: if sliding resistance is insufficient, a key projecting below the base mobilises passive resistance and increases the sliding path.

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