This document summarizes bearing capacity theory for shallow foundations. It defines key terms like ultimate, net ultimate, and safe bearing capacities. It describes Terzaghi's bearing capacity equation, which considers soil shear strength parameters (c, φ), surcharge loads, and bearing capacity factors (Nc, Nq, Nr). It outlines the failure geometry Terzaghi assumed, with five distinct failure zones. It also distinguishes between general shear, local shear, and punching shear failures based on soil properties and characteristics. Empirical modifications are suggested for local shear failures. Charts summarize the bearing capacity equations for different shaped footings based on experimental results.

1. Bearing Capacity and
Shallow Foundation
Prof. Shivaraj G. Teggi

2. Bearing Capacity Of Shallow Foundation
* A foundation is required for distributing
the loads of the superstructure on a large
area.
* The foundation should be designed
such that
a) The soil below does not fail in shear &
b) Settlement is within the safe limits.

3. Basic Definitions :
1) Ultimate Bearing Capacity (qu) :
The ultimate bearing capacity is the gross
pressure at the base of the foundation at
which soil fails in shear.
2) Net ultimate Bearing Capacity (qnu) :
It is the net increase in pressure at the
base of foundation that cause shear failure
of the soil.
Thus, qnu = qu – γDf (ovrbruden pressure)

4. 3) Net Safe Bearing Capacity (qns) :
It is the net soil pressure which can be
safely applied to the soil considering only shear
failure.
Thus, qns = qnu /FOS
FOS - Factor of safety usually taken as 2.00 -3.00
4) Gross Safe Bearing Capacity (qs) :
It is the maximum pressure which the soil can
carry safely without shear failure.
qs = qnu / FOS + γ Df

5. 5)Net Safe Settlement Pressure (qnp) :
It is the net pressure which the soil can
carry without exceeding allowable
settlement.
6) Net Allowable Bearing Pressure (qna ):
It is the net bearing pressure which can be
used for design of foundation.
Thus,
qna = qns ; if qnp > qns
qna = qnp ; if qns > qnp
It is also known as Allowable Soil Pressure
(ASP).

6. Modes of shear Failure :
Vesic (1973) classified shear failure of
soil under a foundation base into three
categories depending on the type of
soil & location of foundation.
1) General Shear failure.
2) Local Shear failure.
3) Punching Shear failure

7. General Shear Failure
This type of failure is seen in dense and stiff soil.
Characteristics of general shear failure:
• Continuous, well defined and distinct failure surface develops between
the edge of footing and ground surface.
• Dense or stiff soil that undergoes low compressibility experiences this
failure.
• Continuous bulging of shear mass adjacent to footing is visible.
• Failure is accompanied by tilting of footing.
• Failure is sudden and catastrophic with pronounced peak in P – Δ curve.
• The length of disturbance beyond the edge of footing is large.
• State of plastic equilibrium is reached initially at the footing edge and
spreads gradually downwards and outwards.
• General shear failure is accompanied by low strain (<5%) in a soil with
considerable Φ (Φ>36o
) and large N (N > 30) having high relative
density (ID > 70%), e < 0.55.

8. Local Shear Failure
This type of failure is seen in relatively loose and soft soil.
Characteristics of Local shear failure.
• A significant compression of soil below the footing and partial
development of plastic equilibrium is observed.
• Failure is not sudden and there is no tilting of footing.
• Failure surface does not reach the ground surface and slight
bulging of soil around the footing is observed.
• Failure surface is not well defined.
• Failure is characterized by considerable settlement.
• Well defined peak is absent in P – Δ curve.
• Local shear failure is accompanied by large strain (> 10 to
20%) in a soil with considerably low Φ (Φ<28o
) and low N (N
< 5) having low relative density (ID > 20%), e > 0.75.

9. 3) Punching Share failure -
* The loaded base sinks into soil like a punch.
* The failure surface do not extend up to the ground surface.
* No heave is observed.
* Large vertical strains are involved with practically no lateral
deformation.
* Failure planes are difficult to locate

10. Punching Shear Failure
This type of failure is seen in loose and soft soil
and at deeper elevations.
Characteristics of general shear failure.
• This type of failure occurs in a soil of very high
compressibility.
• Failure pattern is not observed.
• Bulging of soil around the footing is absent.
• Failure is characterized by very large settlement.
• Continuous settlement with no increase in P is
observed in P – Δ curve.

11. Footing on ground that experiences a) General shear failure, b)
Local shear failure and c) Punching shear failure
Different failure modes in sandy soil carrying circular footing based
on the contributions from Vesic (1963 & 1973)
P – Δ curve in different
foundation soils
ar failure in foundation soil

13. Distinction between General Shear & Local or Punching Shear
Failures
General Shear Failure Local/Punching Shear Failure
Occurs in dense/stiff soil
Φ>36o
, N>30, ID>70%, Cu>100 kPa
Occurs in loose/soft soil
Φ<28o
, N<5, ID<20%, Cu<50 kPa
Results in small strain (<5%) Results in large strain (>20%)
Failure pattern well defined & clear Failure pattern not well defined
Well defined peak in P-Δ curve No peak in P-Δ curve
Bulging formed in the neighbourhood of
footing at the surface
No Bulging observed in the neighbourhood
of footing
Extent of horizontal spread of disturbance at
the surface large
Extent of horizontal spread of disturbance
at the surface very small
Observed in shallow foundations Observed in deep foundations
Failure is sudden & catastrophic Failure is gradual
Less settlement, but tilting failure observed Considerable settlement of footing
observed

14. Local Shear Failure Mixed Zone General Shear Failure
Φ < 28o
28o
< Φ < 36o
Φ > 36o
Nc
1
, Nq
1
, Nγ
1
Nc
m
, Nq
m
, Nγ
m
Nc, Nq, Nγ
Bearing capacity factors in zones of local, mixed and general
shear conditions.

15. Local shear failure
The equation for bearing capacity explained above is
applicable for soil experiencing general shear failure.
If a soil is relatively loose and soft, it fails in local
shear failure. Such a failure is accounted in bearing
capacity equation by reducing the magnitudes of
strength parameters c and as follows.ϕ
φφ tan
3
2
tan 1
= cc
3
21
=
If Φ is less than 36o
and more than 28o
, it is not sure whether the
failure is of general or local shear type. In such situations, linear
interpolation can be made and the region is called mixed zone.

16. 16
Development of Bearing Capacity
Theory
• Application of limit equilibrium methods first done by
Prandtl on the punching of thick masses of metal.
• Prandtl's methods adapted by Terzaghi to bearing capacity
failure of shallow foundations.
• Vesicʼ and others improved on Terzaghi's original theory and
added other factors for a more complete analysis

17. TERZAGHI’S BEARING CAPACITY THEORY
Terzaghi (1943): Safe bearing capacity of shallow foundation with rough base.
Assumptions
• Soil is homogeneous and Isotropic and semi-infinite.
• Depth of foundation is less than or equal to its width.
• No sliding occurs between foundation and soil (rough foundation)
• The shear strength of soil is represented by Mohr Coulombs Criteria.
• The footing is of strip footing type with rough base. It is essentially a two
dimensional plane strain problem.
• Elastic zone has straight boundaries inclined at an angle equal to Φ to the
horizontal.
• Failure zone is not extended above, beyond the base of the footing. Shear
resistance of soil above the base of footing is neglected.
• Method of superposition is valid.
• Passive pressure force has three components (PPC produced by cohesion, PPq
produced by surcharge and PPγ produced by weight of shear zone).
• Effect of water table is neglected.

18. Assumptions contd..
• Footing carries concentric and vertical loads.
• Footing and ground are horizontal.
• Limit equilibrium is reached simultaneously at all points. Complete shear
failure is mobilized at all points at the same time.
• The properties of foundation soil do not change during the shear failure
• No soil consolidation occurs
• Foundation is very rigid relative to the soil.
Limitations
• The theory is applicable to shallow foundations
• As the soil compresses, Φ increases which is not considered. Hence fully
plastic zone may not develop at the assumed Φ.
• All points need not experience limit equilibrium condition at different
loads.
• Method of superstition is not acceptable in plastic conditions as the ground
is near failure zone.

19. 19
Failure Geometry for Terzaghi's Method

20. Terzaghi’s concept of Footing with five distinct failure
zones in foundation soil

21. * The failure zones do not extend above the horizontal
plane passing through base of footing
* The failure occurs when the down ward pressure
exerted by loads on the soil adjoining the inclined
surfaces on soil wedge is equal to upward pressure.
* Downward forces are due to the load (=qu× B) & the
weight of soil wedge (1/4 γB2
tanØ)
* Upward forces are the vertical components of resultant
passive pressure (Pp) & the cohesion (c’) acting along the
inclined surfaces.

22. For equilibrium:
ΣFv = 0
(1/4) γ B2
tan ø + quxB = 2Pp +2C’ ×
Li sinø’
where Li = length of inclined surface CB
( = B/2 /cosø’)
Therefore,
qu× B = 2Pp + BC’
tanø’
- ¼ γ B2
tanø’ –------ (1)
The resultant passive pressure (Pp) on the surface
CB & CA constitutes three components ie. (Pp)r,
(Pp)c
& (Pp) q
,
Thus,
Pp = (Pp)r
+ (Pp)c
+ (Pp)q

23. qu× B= 2[ (Pp)r
+(Pp)c
+(Pp)q
]+ Bc’tanø’
-¼ γ B2
tanø’
Substituting; 2 (Pp)r - ¼rB2
tanø1
= B × ½ γ BNr
2 (Pp)q = B × γ DNq
& 2 (Pp)c + Bc1
tanø1
= B × C1
Nc;
We get,
qu =C’
Nc + γ Df Nq + 0.5 γ B N γ
This is Terzaghi’s Bearing capacity equation for
determining ultimate bearing capacity of strip footing.
Where Nc, Nq & Nr are Terzaghi’s bearing capacity
factors & depends on angle of shearing resistance (ø)

25. Important points :
* Terzaghi’s Bearing Capacity equation is applicable for general
shear failure.
* Terzaghi has suggested following empirical reduction to actual
c & ø in case of local shear failure
Mobilised cohesion Cm = 2/3 C
Mobilised angle of øm = tan –1
(⅔tanø)
Thus, Nc’
, Nq’
& Nr’
are B.C. factors for local shear failure
qu = CmNc’+ γ Df Nq’
+ 0.5 γ B Nr’

26. γγγ BNDNcNq qcf 5.0++=
imate bearing capacity
[ ] D
F
BNNDcNq qcs γγγ γ ++−+=
1
5.0)1(
afe bearing capacity
γγγ BNDNcNq qcf 3.03.1 ++=Circular footing
Square footing γγγ BNDNcNq qcf 4.03.1 ++=
Rectangular footing γγγ BN
L
B
DNcN
L
B
q qcf 5.0)2.01()3.01( −+++=
Ultimate Bearing Capacity for square, Circular and rectangular
footing -Based on the experimental results, Terzaghi’s suggested
following equations,

27. Effect of water table on Bearing
Capacity:
The equation for ultimate bearing
capacity by Terzaghi has been
developed based on assumption that
water table is located at a great depth .
* If the water table is located close to
foundation ; the equation need
modification.

28. i) When water table is located above the base of
footing –
* The effective surcharge is reduced as the
effective weight below water table is
equal to submerged unit weight.
q = Dw. γ +x. γsub
put x = Df-Dw
q = γsub
Df +(γ - γsub
)Dw

29. Thus,
qu = c’
Nc + [γsub
Df +(γ - γsub
)Dw] Nq + 0.5 γsub
BNr
When, Dw =0
qu =c’
Nc + γsub
Nc + 0.5 γsub
BNr
& when x = 0
qu = c’
Nc + γ
Df Nq + 0.5 γsub
BNr

30. ii) When water table is located at depth y below base :
* Surcharge term is not affected.
* Unit weight in term is γ = γ sub
+ y (γ – γsub
)
B
Thus,
qu = c’
Nc + γ
Df Nq + 0.5B γ
Nr
When y = B ; W.T. at B below base of footing.
qu = c’
Nc + γ Df Nq + 0.5 B γ Nr
Hence when ground water table is at b ≥ B, the equation is not

31. OR EFFECT OF WATER TABLE
FLACTUATION
D
ZW1
B
Influence of RW1
0.5 < RW1 < 1
DD
ZW2B
Influence of RW2
B

32. Ultimate bearing capacity with the effect of water table is given by,
21 5.0 wwqcf RBNRDNcNq γγγ ++=






+=
D
Z
R w
w
1
1 1
2
1






+=
B
Z
R w
w
2
2 1
2
1
ZW1
is the depth of water table from ground level.
•0.5<Rw1
<1
•When water table is at the ground level (Zw1
= 0), Rw1
= 0.5
•When water table is at the base of foundation (Zw1
= D), Rw1
= 1
•At any other intermediate level, Rw1
lies between 0.5 and 1
ZW2
is the depth of water table from foundation level.
•0.5<Rw2
<1
•When water table is at the base of foundation (Zw2
= 0), Rw2
= 0.5
•When water table is at a depth B and beyond from the base of
foundation (Zw2
>= B), Rw2
= 1
•At any other intermediate level, R lies between 0.5 and 1

33. Hansen’s Bearing Capacity Equation :
Hansen’s Bearing capacity equation is :
qu = cNcScdcic + qNqSqdqiq + 0.5 γ BNrSrdr ir
where,
Nc,Nq, & Nr are Hansen’s B.C factors which are
some what smaller than Terzaghi’s B.C. factors.
Sc.Sq &Sr are shape factors which are
independent of angle of shearing resistance;
dc,dq, & dr are depth factors ;
Ic, iq & ir are load inclination factors

34. The bearing capacity factors are given by the following
expressions which depend on .ϕ
φ
φ
φ
γ
φπ
tan)1(5.1
)
2
45(tan)(
cot)1(
2tan
−=
+=
−=
q
q
qc
NN
eN
NN

37. The General Bearing Capacity Equation.

38. The General Bearing Capacity Equation.

39. Other Factors

40. The same form of equation has been
adopted by I.S. 6403 –1971 & may be used
for general form as
qnu = c Nc Sc dc ic + q(Nq-1)Sqdqiq + 0.5 γ BNrSrdr ir

41. Shape sc sq sγ
Strip 1 1 1
Square 1.3 1 0.8
Round 1.3 1 0.6
Rectangle 1)3.01(
L
B
+ )2.01(
L
B
−
Shape factors for different shapes of footing

42. EFFECT OF ECCENTRIC FOUNDATION BASE
Resultant
of
superstructure
pressure
D D
B
Concentric
D D
e
Eccentric
Effect of eccentric footing on bearing capacity
eBB 21
−=
If the loads are eccentric in both the directions, then
BeBB 21
−= LeLL 21
−=

43. Area of foundation to be considered for safe load
carried by foundation is not the actual area, but
the effective area as follows
In the calculation of bearing capacity, width to be
considered is B1
where B1
< L1
. Hence the effect
of provision of eccentric footing is to reduce
the bearing capacity and load carrying capacity
of footing.
111
XLBA =

44. FOOTINGS WITH ECCENTRIC
OR INCLINED LOADINGS
Eccentricity
Inclination

45. FOOTINGS WITH One Way Eccentricity
In most instances, foundations are subjected to moments in addition to the vertical load
as shown below. In such cases the distribution of pressure by the foundation upon the
soil is not uniform.

48. FOOTINGS WITH One Way Eccentricity
• Note that in these equations, when the eccentricity e becomes B/6,
qmin is zero.
• For e > B/6, qmin will be negative, which means that tension will
develop.
• Because soils can sustain very little tension, there will be a
separation between the footing and the soil under it.
• Also note that the eccentricity tends to decrease the load bearing
capacity of a foundation.
• In such cases, placing foundation column off-center, as shown in
Figure is probably advantageous.
• Doing so in effect, produces a centrally loaded foundation with a
uniformly distributed pressure.

49. FOOTINGS WITH One Way Eccentricity

50. Footing with Two-way Eccentricities
• Consider a footing subject to a vertical ultimate load Qult and a moment M as shown in
Figures a and b. For this case, the components of the moment M about the x and y axis
are Mx and My respectively. This condition is equivalent to a load Q placed
eccentrically on the footing with x = eB and y = eL as shown in Figure d.

51. Footing with Two-way Eccentricities

52. FACTORS INFLUENCING BEARING
CAPACITY• Bearing capacity of soil depends on many factors. The
following are some important ones.
• Type of soil
• Unit weight of soil
• Surcharge load
• Depth of foundation
• Mode of failure
• Size of footing
• Shape of footing
• Depth of water table
• Eccentricity in footing load
• Inclination of footing load
• Inclination of ground
• Inclination of base of foundation

53. DETERMINATION OF BEARING
CAPACITY FROM FIELD TESTS
Field Tests are performed in the field.
The biggest advantages are that there is no need to extract soil
sample and the conditions during testing are identical to the
actual situation.
Major advantages of field tests are
• Sampling not required
• Soil disturbance minimum
Major disadvantages of field tests are
• Labourious
• Time consuming
• Heavy equipment to be carried to field
• Short duration behavior

54. Thank You