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Chapter 10 of 13

Shallow Foundations

In the NTPC NGEL Engineer Civil syllabus under Soil Mechanics & Foundation Engineering · 2 parts

Shallow Foundations — Types, Proportioning & Rafts · Bearing Capacity of Shallow Foundations

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📑 Contents (19 sections)

Part 1 of 2

Shallow Foundations — Types, Proportioning & Rafts

Last reviewed 16 Sept 2026 · 6 min read

Requirements of a foundation

A foundation must:

be safe against shear failure of the soil (adequate bearing capacity with a factor of safety);
keep total and differential settlement within permissible limits;
be placed at a depth safe from seasonal moisture changes, frost, scour and the effect of adjacent construction;
be structurally strong and durable against aggressive soil and water;
be economical and practical to construct.

Types of shallow foundations

Type	Description	When used
Spread / wall footing (strip)	Continuous footing under a wall	Load-bearing walls
Isolated (pad) footing	Individual footing under a column (plain, stepped or sloped)	Columns spaced well apart on reasonable soil
Combined footing (rectangular or trapezoidal)	One footing for two or more columns	Columns close together, or an exterior column at the property line
Strap (cantilever) footing	Two isolated footings connected by a rigid strap beam	Exterior column at the boundary where a combined footing would be too long
Continuous (strip) footing under columns	One footing under a row of columns	Closely spaced columns in a line
Mat / raft foundation	Single slab under the whole building (or large part)	Weak or variable soils, heavy loads, basements, where footings would cover more than about half the area

Depth of foundation

Factors governing depth

Stratum of adequate bearing capacity and acceptable settlement.
Seasonal volume change zone in expansive clays (often 1.5–3.5 m in black cotton soils).
Frost penetration in cold regions.
Scour depth for bridge foundations near water.
Ground water level, adjacent foundations and future excavations.
A minimum depth of about 0.5 m (practice often uses 0.8–1.0 m for buildings) to remove topsoil and vegetation and protect against weathering.

Rankine's minimum depth (cohesionless soil)

For a footing with pressure $q$ on soil with $γ$ , $ϕ$ :

D_{f, min} = \frac{q}{γ} (\frac{1 - sin ϕ}{1 + sin ϕ})^{2}

Proportioning footings for uniform settlement

Footings of different sizes carrying the same pressure settle differently (larger footings settle more on clay because the pressure bulb is deeper). To reduce differential settlement, footings may be proportioned on the basis of the dead load plus the average (sustained) part of the live load rather than the full design load: the footing with the highest ratio of live to dead load is sized for the allowable pressure under full load, and the same "service" pressure is used for all others.

Combined footings

For two columns with loads $P_{1}$ (exterior, at property line) and $P_{2}$ , spaced $s$ apart:

Locate the resultant: $\overset{x}{ˉ} = \frac{P _{2} s}{P _{1} + P _{2}}$ from column 1.
Make the centroid of the footing coincide with the resultant so pressure is uniform.
Rectangular footing: length $L = 2 \times$ (distance from property line to resultant); width $B = \frac{P _{1} + P _{2}}{q _{a} L}$ .
If the length is restricted at both ends or loads are very unequal, use a trapezoidal footing (wider under the heavier load).
Design longitudinally as an inverted beam (upward soil pressure, columns as supports) and transversely for local bending under each column.

Part 2 of 2

Bearing Capacity of Shallow Foundations

Last reviewed 16 Sept 2026 · 7 min read

Definitions

DefinitionBearing capacity terms

Gross pressure intensity $q$ — total pressure at the base of the footing (structure load + footing + backfill).
Net pressure intensity $q_{n} = q - γ D_{f}$ — excess over the overburden removed.
Ultimate bearing capacity $q_{u}$ — minimum gross pressure that causes shear failure of the supporting soil.
Net ultimate bearing capacity $q_{n u} = q_{u} - γ D_{f}$ .
Net safe bearing capacity $q_{n s} = q_{n u} / F$ ( $F$ = factor of safety, usually 2.5 to 3).
Safe bearing capacity $q_{s} = q_{n s} + γ D_{f}$ .
Safe bearing pressure (net soil pressure for a permissible settlement) — pressure that causes settlement equal to the permissible value.
Allowable bearing pressure — the lesser of the net safe bearing capacity (shear criterion) and the safe bearing pressure (settlement criterion).

$D_{f}$ = depth of foundation below ground; a foundation is shallow when $D_{f} \leq B$ (roughly).

Modes of shear failure

Mode	Soil	Features
General shear failure	Dense sands, stiff clays (low compressibility)	Well-defined slip surfaces to the ground surface; bulging of ground; sudden failure with a clear peak on the load–settlement curve; tilting
Local shear failure	Medium dense sands, medium clays	Slip surfaces not reaching the surface; some bulging; no clear peak
Punching shear failure	Loose sands, soft clays, deep footings	Vertical shearing around the footing edge; large settlement; no heave

Terzaghi's bearing capacity theory

Assumptions: strip footing with a rough base; shallow ( $D_{f} \leq B$ ); soil above the base replaced by a surcharge $q = γ D_{f}$ (its shear strength ignored); homogeneous, isotropic soil; general shear failure; load vertical and concentric; Mohr–Coulomb strength.

The failure zone has three parts: an elastic wedge under the footing (angle $ϕ$ with the base), radial shear zones (log-spiral) and Rankine passive zones.

FormulaTerzaghi's equations (general shear)

Strip: $q_{u} = c N_{c} + q N_{q} + 0.5 γ B N_{γ}$

Square: $q_{u} = 1.3 c N_{c} + q N_{q} + 0.4 γ B N_{γ}$

Circular (diameter B): $q_{u} = 1.3 c N_{c} + q N_{q} + 0.3 γ B N_{γ}$

$N_{c}$ , $N_{q}$ , $N_{γ}$ = bearing capacity factors (functions of $ϕ$ ); $q = γ D_{f}$ .

Local shear failure: use $c^{'} = \frac{2}{3} c$ and $ϕ^{'} = tan^{- 1} (\frac{2}{3} tan ϕ)$ with the same equations.

$ϕ$	$N_{c}$ (Terzaghi)	$N_{q}$	$N_{γ}$
0°	5.7	1.0	0
10°	9.6	2.7	1.2
20°	17.7	7.4	5.0
30°	37.2	22.5	19.7
35°	57.8	41.4	42.4
40°	95.7	81.3	100.4

For $ϕ = 0$ (saturated clay, undrained): strip $q_{u} = 5.7 c + γ D_{f}$ .

IS 6403 general bearing capacity equation

Code ProvisionIS 6403 — net ultimate bearing capacity (general shear failure)

q_{n u} = c N_{c} s_{c} d_{c} i_{c} + q (N_{q} - 1) s_{q} d_{q} i_{q} + 0.5 γ B N_{γ} s_{γ} d_{γ} i_{γ} W^{'}

Shape factors (rectangle $B \times L$ ): $s_{c} = s_{q} = 1 + 0.2 \frac{B}{L}$ ; $s_{γ} = 1 - 0.4 \frac{B}{L}$ (square: 1.2, 1.2, 0.8; circle: 1.3, 1.2, 0.6).

Depth factors: $d_{c} = 1 + 0.2 \frac{D _{f}}{B} N_{ϕ}$ ; $d_{q} = d_{γ} = 1 + 0.1 \frac{D _{f}}{B} N_{ϕ}$ for $ϕ > 10°$ (= 1 for $ϕ < 10°$ ), with $N_{ϕ} = tan^{2} (45° + ϕ /2)$ .

Inclination factors (load inclined at $α$ to the vertical): $i_{c} = i_{q} = (1 - \frac{α}{90})^{2}$ ; $i_{γ} = (1 - \frac{α}{ϕ})^{2}$ .

Water table factor $W^{'}$ : 0.5 if the water table is at or above the base; 1.0 if it is at a depth $\geq B$ below the base; interpolate linearly between.

Bearing capacity factors (IS 6403)

$ϕ$	0°	5°	10°	15°	20°	25°	30°	35°	40°
$N_{c}$	5.14	6.49	8.35	10.98	14.83	20.72	30.14	46.12	75.31
$N_{q}$	1.00	1.57	2.47	3.94	6.40	10.66	18.40	33.30	64.20
$N_{γ}$	0.00	0.45	1.22	2.65	5.39	10.88	22.40	48.03	109.41

Effect of water table

A water table within the zone of shear reduces the effective unit weight: at or above the base, $γ$ in the third term becomes $γ^{'}$ (≈ half), i.e. $W^{'}$ = 0.5; above the base, the surcharge term also uses the effective stress at base level.

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