This document discusses bearing capacity and shallow foundations. It defines bearing capacity as the maximum average pressure a soil can support before failing. There are two failure criteria: shear failure and settlement. Terzaghi's bearing capacity theory is then explained, with soil divided into three zones. Factors influencing bearing capacity are also listed, such as soil type, foundation properties, water table level, and loading eccentricity. Finally, common bearing capacity determination methods are outlined, including analytical calculations, load tests, and laboratory tests.

1. BEARING CAPACITY AND
SHALLOW FOUNDTION
RASHMI VISHWAKARMA
M.TECH (STRUCTURAL ENGINEERING)
ASSISTANT PROFESSOR
DY PATIL SCHOOL OF ENGINEERING &
TECHNOLOGY
LOHEGAON, PUNE

3. BEARING CAPACITY
•Bearing capacity of Foundation or soil is the
maximum average intensity of applied pressure
that a finite loaded area can carry before
underlying material fails.
•In other words it is a load carrying capacity of
soil.

5. Criteria of failure:
There are two criteria for failure of soil in shallow
foundation.
•Shear failure criteria
•Settlement criteria
The design value of bearing capacity would be
the smaller of the two values obtained from the
above two criteria

6. BEARING CAPACITY TERMS
•Gross pressure
•Net pressure
•Ultimate bearing capacity
•Net ultimate bearing capacity
•Net safe bearing capacity
•Safe bearing capacity

9. In structural design SBC shall be used to estimate area of
footing. Also using SBC, safe load on the given footing can be
calculated.

10. 1. SHEAR FAILURE CRITERIA
1. General shear failure.
2. Local shear failure.
3. Punching shear failure.

11. 1. GENERAL SHEAR FAILURE
- It occurs in shallow foundation when placed on medium to
highly dense soil and soils which have a brittle stress-strain
curve.
- At the time of failure foundation will get tilted and large
bulging of soil occurs at one side.
- Before the failure, very small settlement occurs and stress
zone/failure plane will reach up to ground surface.
- The clear failure is observed in load settlement curve.
- This type of failure can be observed in dense sand, stiff
clay.
- ‘c’ and ‘Ø’ are the shear strength parameters of the given
soil in general failure.

12. General shear failure

13. 2. Local shear failure
• It occurs in shallow foundation when placed on loose to medium dense
soil and soils which have elasto-plastic stress-strain curve.
• Before failure larger elastic settlement is observed.
• There is small tilting which causes less bulging or heaving but large
settlement occurs. The stress zone does not extend up to ground level.
• The progressive failure is observed in load settlement curve.
• This type of failure can be observed in loose sand, soft clay and Normally
consolidated clay.
• If ‘c’ and ‘Ø’ are the shear parameters in general shear failure than, ‘Cm’
and ‘Øm’ are the modified shear strength parameters in local shear
failure.
Cm=2C/3 and tanØm=2tanØ/3

14. Local shear failure

15. 3. PUNCHING SHEAR FAILURE
• It occurs in deep footing & piles which are placed in loose
sand, soft clay and soils possessing plastic stress-strain
curve.
• It also occurs in shallow foundation when footing is resting
on very loose/soft soils.
• In this failure soil below the foundation gets cutoff from
adjacent soil by shearing and excessive/large settlement are
observed.
• The adjacent soil mass remains unstressed.
• There will be no tilting & no heaving at the sides.

16. Punching shear failure

18. Three type of shear failures

20. Factor affecting bearing capacity
(i) Type of soil:
(ii) Physical characteristics of foundation
(iii) Soil properties
(iv) Type of foundation
(v) Water table
(vi) Amount of settlement
(vii) Eccentricity of loading.

21. (i) Type of soil:
The bearing capacity of soils depends upon the type of soil. Depending upon the type of soil,
the bearing capacity of soil is different which is clear from Terzaghi bearing capacity equation.
qu = CNC + 0.5 yBNy+ qNq
For purely cohesion less soil
C = 0
Equation (9.1) reduce to
qu = 0.5 yBNy,+ qNq
For purely cohesive soil
φ =0,
the values of bearing capacity factors are
Nc = 5.7
Nq = 1 and Nγ = 0
Equation (9.1) is then
qu = 5.7C+q

22. (ii) Physical characteristics of foundation:
Physical characteristics like width, shape and depth of foundation affect the bearing
capacity of soils. Eq. 9.1 shows that the bearing capacity of soils depends upon the width
B and depth (D) of foundation. So any change in the value of B and D of foundation will
affect the baring capacity.
The shape of foundation also affects the bearing capacity which is as
follows:
For square footings:
qu = 1.2 CNc + 0.4 γBNγ + γDNq …(9.2)
For circular footings:
qu = 1.2 CNC + 0.3 γBNγ + γDNq …(9.3)
where B is the diameter of circular footing.

23. (iii) Soil properties:
Soil properties like shear strength, density, permeability etc.,
affect the bearing capacity of soil. Dense sand will have more
bearing capacity than loose sand as unit weight of dense sand
is more than loose sand.
(iv) Type of foundation:
The type of foundation selected also affects the bearing
capacity of soils. Raft or mat foundation adopted supports the
load of structure safely by spreading the load to a wider area,
even if the soil is having low bearing capacity.

24. (v) Water table:
When the water is above the base of the footing, the submerged unit weight of soil is used to
calculate the overburden pressure and the bearing capacity of the soil reduces by 50%.
(vi) Amount of settlement:
The amount of settlement of the structure also affects the bearing capacity of soil. If the
settlement exceeds the possible settlement, the bearing capacity of soil is reduced.
(vii) Eccentricity of loading:
If the load acts eccentrically in a footing the width ‘B’ and length ‘L’ should be reduced as under
B’ = B – 2e
L’ = L – 2e and
A’ = B’ X L’
The ultimate bearing capacity (qu) of such footings are determined by using B’ and L’ instead of
8 and L. Hence qu is less than that corresponds to actual size of footing

25. METHODS OF DETERMINING BEARING
CAPACITY
(i) Bearing capacity tables in various building codes.
(ii) Analytical methods
(iii) Plate bearing tests
(iv) Penetration test
(v) Model tests and prototype tests
(vi) Laboratory tests

26. TERZAGHI’S BEARING CAPACITY THEORY
Terzaghi gave a general theory of bearing capacity
which is based on the following assumptions:

29. The derivation of this theory is based on limiting equilibrium
condition of the soil in various zones.
Force causing failure : load intensity, which gives ultimate
bearing capacity qu.
Force resisting failure: Shear strength of soil ( c and Ø
parameters)
Zone I : It is in elastic equilibrium, acts as part of footing and
moves downwards.
The downward movement of Zone 1 is resisted by zones 2,3
which offers a passive pressure. The passive pressure has to be
overcome by soil in zone 1, so that it can move down.
Zone II : It is in plastic equilibrium and tends to move radially
outwards since the soil in zone one moves downwards. So it is
called radial shear zone.
Zone III: This is known as linear shear zone and it is in passive
rankine state and also in plastic equilibrium so it makes an angle
45- Ø/2

30. qu
Ø
Ø
Pp Pp
c
c
W
Consider the equilibrium of the
wedge,
x=B/2.tanØ
B
Ø
Ø
𝑞𝑢 𝑥 𝐵 +
1
2
x B x B/2.tanØ xγ = 2𝑃𝑝 + 2𝑐𝑠𝑖𝑛Ø
𝑞𝑢 𝑥 𝐵 = 2𝑃𝑝 + 2𝐶𝑠𝑖𝑛Ø −
1
4
𝛾𝐵2
𝑡𝑎𝑛𝜑
𝑃𝑝 has 3 components: (i) wt of soil in shear zone = 𝑃𝑝γ
(ii) cohesion of soil = 𝑃𝑝𝑐
(iii) surcharge load of soil between G.L and
footing= 𝑃𝑝𝑞
𝑃𝑝 = 𝑃𝑝γ+ 𝑃𝑝𝑐 + 𝑃𝑝𝑞
𝑞𝑢 𝑥 𝐵 = 2(𝑃𝑝γ+ 𝑃𝑝𝑐 + 𝑃𝑝𝑞) + c.BtanØ−
1
𝛾𝐵2
𝑡𝑎𝑛𝜑
ad=(B/2)/cosØ
a
d
a
C = c x ad

31. 2𝑃𝑝γ −
1
4
𝛾𝐵2
𝑡𝑎𝑛𝜑
1
2
𝛾𝐵𝑁𝛾 𝑥 𝐵 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑠𝑜𝑖𝑙 𝑤𝑡 𝑖𝑛 𝑠ℎ𝑒𝑎𝑟 𝑧𝑜𝑛𝑒
2𝑃𝑝𝑐 − 𝐵𝑐𝑡𝑎𝑛𝜑 𝐵. 𝑐𝑁𝑐 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑐𝑜ℎ𝑒𝑠𝑖𝑜𝑛
2𝑃𝑝𝑞 𝐵. 𝑞𝑁𝑞 ( 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑠𝑢𝑟𝑐ℎ𝑎𝑟𝑔𝑒)
Putting these values in the equation,
Net ultimate bearing capacity,
𝑵𝒄, 𝑵𝒒 , 𝑵𝜸 are called Terzaghi’s bearing capacity factors.
𝒒𝒖 = 𝒄𝑵𝒄 + 𝒒𝑵𝒒 +
𝟏
𝟐
𝜸𝑩𝑵𝜸
𝒒𝒖 − 𝒒 = 𝒒𝒏𝒖 = 𝒄𝑵𝒄 + 𝒒(𝑵𝒒 − 𝟏) +
𝟏
𝟐
𝜸𝑩𝑵𝜸
𝒒 = 𝜸𝑫