1. SHALLOW FOUNDATION
MADE BY : MISS.DHARA DATTANI
LECTURER AT ATMIYA INSTITUTE OF TECHNOLOGY AND SCIENCE FOR
Methods to determine bearing capacity
Modes of failures
Effect of eccentric loading
Settlement of foundation
Bearing capacity of raft and its factor affecting
3. Bearing Capacity Of Shallow
* 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.
4. 1. FOOTING :
Lowest part of foundation of the structure that transmits loads directly to soil
It is a part of structure that transmits the load of super structure to the ground
3. BEARING CAPACITY
Load carrying capacity of foundation soil
Expressed as load per unit area kN/m2
4. GROSS BEARING CAPACITY : (q)
Total pressure acting on the base of footing including weight of superstructure
,self weight of footing and weight of fill over the footing called as gross bearing
5. 5. NET BEARING CAPACITY : (qN)
It is defined as gross bearing capacity minus the original overburden pressure
at the foundation level. qn =q-Y *D
6. ULTIMATE BEARING CAPACITY (qu):
It is defined as the gross pressure at the base of foundation at which the soil
fails in the shear
7. NET ULTIMATE BEARING CAPACITY(qnu) :
It is defined as a net pressure in excess of the surcharge pressure at which soil
fails in shear. It is equal to gross pressure minus surcharge pressure.
qnu = qu – γ ∗ 𝐷
6. 8. NET SAFE BEARING CAPACITY : (qns)
It is defined as the maximum load per unit area in excess of surcharge pressure
which the foundation soil or bed can carry safely load without risk or shear
Where, f= Factor of safety taken as 2 to 5.
9. Safe Bearing Capacity: (qs)
It is the maximum gross pressure which the soil can carry safely load without
shear failure. It is equal to net bearing capacity plus the original over burden
+ γ ∗ 𝐷
7. 10. Allowable Bearing Capacity : (qa)
It is the net loading intensity at which the foundation soil
neither fails in shear nor there is excessive settlement ,to the
8. 2. DESIGN CRITERIA
For A Satisfactory Performance, A Foundation Must
Be Following Criteria :
1. Location & Depth Criteria
2. Shear or Bearing Failure Criteria
3. Settlement Criteria
9. 1 . LOCATION AND DEPTH CRITERIA
Foundation must be properly located and at a desired depth that its
performance not affected by factors such as,
Lateral expulsion of soil from beneath the foundation
Seasonal volume changes caused by freezing and thawing
2. SHEAR OR BEARING FAILURE CRITERIA
It is associated with plastic flow of the soil material beneath the foundation,
and lateral expulsion of the soil from underneath the foundation.
A adequate factor of safety is provided to preclude the bearing capacity
3. SETTLEMENT CRITERIA
The settlement of the foundation, especially the differential settlement
must be in permissible limits. Excessive settlement may affect the utility
of structure, spoil the appearance of structure and also damages the
10. Methods of determining the bearing
Methods of determining the bearing capacity
TABLES IN VARIOUS
C) FIELD TEST
1. PLATE LOAD TEST
5. PRESSURE METER
11. Prandtl’s Analysis
This theory is used to determine the ultimate bearing capacity of soil.
The analysis is based on assumptions that a strip footing placed on ground
surface sinks vertically downwards direction in to soil as failure, like a punch.
Fig shows failure zones developed below footing
Zone-1 : immediately under footing subjected with compressive stress.
Zone -2: exerts pressure on side zones II and III
Soil in zone II assumed as in plastic equilibrium
Zone II pushes zone III upwards
13. So prandtls gave an expression for ultimate bearing capacity
for a strip footing using theory of plasticity.
He assumed curved path of a slip surface of the shape of logarithmic spiral.
For purely cohesive soils(ø=0),the spiral becomes circular arc and prandtls analysis
gives the equation :
c=cohesion of the soil.
For cohesion less soil prandtls theory shows that UBC(ultimate bearing capacity)
increases with the width B
For cohesive soil of strip footing the,
It is only applicable for footing with perfectly smooth base, but in actual footing have
rough surface so theory does not gives exact results
qu= 5.14 c + γ ∗ 𝐷
14. Rankine’s analysis
Rankine considered the plastic equilibrium of two soil elements ,one below
(element-I) and the other just outside the footing (element-II) at the base
level of the foundation
15. When the load on the footing increases and approaches a value of qu, a state of
plastic equilibrium is reached under the footing i.e. element I is on the verge of
failure. For element I the vertical stress is the major principal stress ( σ1) and
lateral stress is minor principal stress ( σ3 ).on the other hand , for element II, the
lateral stress is major principal and vertical is minor principal stress.
For the shear failure of element I, element II must fail by lateral thrust from
Element-1,during the state of shear failure the following principal stress relationship
Tan2 α + 2c tan α
For cohesionless soil c=0
σ1= σ3 tan2 α
for element II =
Tan2 α + 2c tan α
σ3 = σv = 𝛾 ∗ 𝐷 Tan2 α
16. For element I
σ3 = σh = σ1 of the element II
= γ ∗ 𝐷 Tan2 α
σ1= σ3 tan2 α
= γ ∗ 𝐷 Tan2 (Tan2 α)
= γ ∗ 𝐷 Tan4 α
But qu = γ ∗DTan4 α
tan2 α =
qu= γ ∗ 𝐷
17. Minimum depth of foundation obtained by
q= intensity of loading at the base of foundation.
18. MODES OF SHEAR FAILURE
When horizontal strip footing resisting on the earth surface,
homogeneous soil is subjected to a gradually increasing load,
characteristic load settlement curves are obtained. The load
settlement behaviour is found to be related to the soil
Three types of failure are considered:
1. GENERAL SHEAR FAILURE
2. LOCAL SHEAR FAILURE
3. PUNCHING SHEAR FAILURE
19. General shear failure
If the soil properties are such that as the footing is loaded to failure a
slight downward movement of the footing develops the fully plastic zone
due to which the entire soil along a slip surface fails in shear and the soil is
bulges out on the sides of the footing , this type of failure is called General
It usually occurs in dense sand or stiff clay.
20. Local shear failure
If the soil properties are such that before the plastic zone are fully developed , large
deformation occur immediately below the footing resulting in the shear failure of the
soil in the potion just below footing is called a Local shear failure
The local shear failure usually occurs in the case of sand or clayey soils of medium
21. Punching shear failure
It occurs when there is a high compression of soil under the
footing,accompanied by shearing in the vertical direction around the
edges of the footing. It is slightly inclined and never reaches to the ground
surface. There is no tilting of the footing.
It is mainly occurred in loose or soft clay.
22. Terzagi’s bearing capacity theory
In 1943 terzagi gave an assumption on bearing capacity of soil
The footing is long : i.e. L/B ratio is infinite
The base of footing is rough
The footing is laid at shallow depth i.e. D<B
The load on footing is vertical and load is uniformly distributed
The shear strength of the base is neglected
Soil above the base is neglected by surcharge pressure
The shear strength of the soil is governed by mohr-Columbus equation.
24. Strip footing of width B subjected to the loading intensity qu to cause failure
The footing is shallow i.e. the depth D of the footing is equal to or less than width of
According to the terzagi the loaded soil fails along the composite surface FGCDE as
shown in fig. this region can be divide into five zones:
Zone I, called zone of elastic equilibrium(ABC)
Zone II, called zone of radial shear
Zone III, called zone of linear shear
When the base of the footing AB sinks into the ground zone I wedge shaped
immediately beneath the footing is prevented from undergoing any lateral yield by
friction and cohesion between the soil and the base of the footing
Thus zone I remains in state of elastic equilibrium and it acts as if it were the part of
Its boundaries assumed as plane surface rising at an angle with the horizontal
25. Zone II (BCD and ACG) are called the zones
of radial shear, because the lines that
constitute one set of shear pattern are
straight radial lines which radiate from the
outer edges of the base of the footing,
while the lines of the other set are
logarithm spirals with their centres located
at the outer edge of the base of the
footing. Thus the boundaries AC,AG,BC and
BD of these zones are the plane surfaces
while the boundaries CG and CD are the
arcs of a logarithm spiral
Zone III AFG,BDE are called the zones of
linear shear and are triangular in shape.
These are passive rankine zone with their
boundaries making an angle
with the horizontal
26. It is assumed that the failure do not extend above the horizontal plane
passing through base of the footing. This implies that the shear resistance
of the soil lying above the horizontal plane passing through the base of
footing is neglected, and the effect of the soil above the plane is taken
equivalent to a surcharge pressure
The application of the zone surface qu on the footing tends to push the
wedge of soil ABC into the ground with lateral displacement of zones II
and III, but this lateral displacement is resisted by forces on the plane AC
27. For ultimate bearing capacity of soil for strip footing
qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N
qu= UBC in kN/m2
γ = unit weight of soil kN/m3
D= depth of footing (m)
B= width of footing(m)
Nc,Nq,Ny = terzagi bearing capacity factors
Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil.
29. For cohesiveless soil ø=0
Thus, for strip footing
If footing located at ground surface D=0
30. Equation for local for shear failure for strip footing can be written as
When local shear failure ø<29
* C*Nc’+ γ ∗ 𝐷*Nq’+0.5 γ*BN γ’
Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil.
Or equal to ø’
31. Terzagi gave different equations for different footing
qu= 1.3cNc+ γ ∗ 𝐷*Nq+0.4 γ*B*Ny
B= dimension of side of footing
qu= 1.3c*Nc+ γ ∗ 𝐷*Nq+0.3 γ*B*Ny
B= diameter of footing
qu= 1.3cNc ( 1+ 0.3
) + γ*D*Nq+0.5 γ*B*Nγ ( 1 – 0.2
B= width or diameter
L= length of footing
32. EFFECT OF WATER TABLE ON BEARING
Terzagi assumed the water table is at greater depth. If the W.T. is located
close to the foundation ,the bearing capacity equation written as follows :
qu=c.Nc+ γ1*D*Nq*Rw1+0.5 γ2*B*N γ*Rw2
Rw1 and Rw2 are the reduction factors for the water table
γ1= average unit weight of the surcharge soil situated above water table
γ2=avg unit weight of the soil in the wedge zone, situated within the depth
below the footing.
34. Case 1 Water table above the base of footing
Rw1 = 0.5 [ 1+
Case 2: Water table below the base of footing
Rw1 = 1
Rw2 = 0.5[ 1+
Case 3: when water table at a depth equal to or greater than the width of
footing below the base of foundation
35. Skempton’s analysis
Skempton’s analysis used for purely cohesive soil ø=0
And for purely saturated soil
Can be used for shallow footing as well as deep footing
For pure cohesive soil :
qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N.. Given by terzagi
36. As per skempton UBC= cNc+ Qu=c*Nc+γ*D
qnu= qu- γ ∗D
Different shape of footing:
(A) STRIP FOOTING:
If Nc value is greater than 7.5 , take Nc=7.5
(B) Square or Circular Footing:
If Nc is greater than 9.0 take Nc=9
B= square of footing or dia of footing
38. I.S. Code Method
As per the Is-code 6403-1981:
qnu= cNc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γ*S γd γi γW’
Nc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γS γd γ i γ W’
Where, dc,dq,dγ= depth factors
Iq,ic,iγ= inclination factors
Nc,Nq,Nγ= bearing factors recommended by Vesic (1973)
q= effective pressure at base
qnu= qu- γ*D
All notation defined earlier.
39. When W.t. is at below depth W’=1.0
If above W’=0.5
If same size or equal to depth
40. Settlement of Foundation
A geotechnical engineer is called upon to predict the magnitude of
settlement and rate of settlement of foundation due to structural loads
There are mainly three types of settlements
1. Immediate settlement
2. primary consolidation
3. Secondary consolidation
41. Immediate settlement
When a partially saturated soil mass is subjected to external loads, a
decrease in volume occurs due to expulsion and compression of air in the
Decrease in volume of soil mass due to compression of solid particles
called as immediate or initial settlement
42. Primary consolidation (sp)
After the initial consolidation, further reduction in volume of soil mass due
to expulsion of water from air voids, called as Primary consolidation.
In fine grained soil, sp occurs for long time where as in coarse grain soil it
takes less time due to high permeability.
43. Secondary consolidation
The reduction in volume continues at a very slow rate even after the excess
pore water pressure developed by the applied pressure is fully dissipated
and the primary consolidation is complete.
This reduction in volume called as Secondary consolidation.
This settlements are important for peats and soft organic clay
Settlement is expressed as S= si+sc+ss
44. Sources of settlement of foundation
Elastic compression of the foundation soil, caused by giving rise to immediate
Plastic compression of the foundation soil, caused by loads giving rise to
consolidation settlement of fine grained soils
Repeated lowering and raising of ground water level in granular loose soils
Under ground erosion may cause cavity in subsoil which collapse and cause
Seasonal swelling and shrinkage and expansion of soil
Vibrations due to pile driving
45. Due to some minerals in soil example-non cohesive soil,gypsum,may result
the settlement of foundation and alsoresponsible for the intergranulars
bond of soil
Frost heave occurs if the structure is not found below the depth of frost
penetration,when thaw occurs the foundation may settle
46. Bearing capacity of Raft
A mat or raft foundation is a thick reinforced concrete slab which supports
all the load of bearing walls columns of structure etc.
When raft should be provided?
Soil pressure is low
Loads of structure are heavy
When columns and walls are so close to structure that individual footing
When there is large variation of load in individual columns
When soil is non homogeneous and also when differential settlements
chances are more.
47. FACTORS AFFECTING BEARING
Position of ground water table
Relative density or angle of shearing resistance
Width of footing
Depth of footing
Unit weight of soil
Eccentricity of load
48. Floating Foundation
Floating foundation is defined as foundation in which the weight of the
building is approximately equal to the full weight of soil and water
removed from the site of the building
49. The principle of floating foundation is explained that a horizontal ground
surface with a horizontal water table at a depth Dw below the ground
surface shows an excavation made in groundto a depth D where D>dw ,fig
shows that structure built in an excavation and completely filling it.
If the weight of the building is equal to weight of soil and water removed
from the excavation ,then it is evident that the total vertical pressure in the
soil below depth D is same as before excavation
Since the water level has not changed neutral pressure and effective
pressure are therefore unchanged. Since the settlements caused by an
increase in vertical pressure the building will not settle at all.
51. While dealing with floating foundation two type of soil are there:
Soil type -1
Shear failure will not occur but settlements or differential settlements will
occur due to building loads.
Soil type 2 :
Shear strength of foundation is low that the rupture of the soil would occur if
the building were founded at ground level
In absence of strong layer at a reasonable depth, the building can only built
on a floating foundation which reduces the shear stresses to an acceptable
value. Solving this problem solves the settlement problem
52. FLOATING FOUNDATION
Floating foundation was a necessary innovation in
the development of tall buildings in the wet soil
of Chicago in the 19th century, floating foundation
was developed by John Wellborn Root.
53. Contact pressure
A vertical pressure acting at the surface of the contact between the base of
footing and the underlying soil mass.
In design it is assumed that the load on footing is uniform also the
distribution of contact pressure is uniform
However this assumption is no always valid, because it depends on elastic
properties of underlying soil mass.
54. Contact pressure on saturated clay
It shows the qualitative contact pressure distribution under flexible and
rigid footing resting on a saturated clay and subjected to uniformly
distributed load q. when the footing is flexile it deforms into shape of a
bowl, with the maximum deflection at the centre.
If the footing is rigid the settlement is uniform.
The contact pressure is more at the centre and maximum deflection at the
56. Contact pressure on sand
in this footing edges of flexible footing undergo a large settlement than at
The soil at the centre is confined and has large modulus of elasticity and
deflects less for the same contact pressure. The contact pressure is uniform.
In case of rigid footing settlement is uniform. the cp increases from zero at
the edges to a maximum at centre.
57. PLATE LOAD TEST
Plate load test is a field test, used to determine the ultimate bearing
capacity of soil
the probable settlement under a given load.
design of shallow foundation.
For performing this test, the plate is placed at the desired depth, then the
load is applied gradually and the settlement for each increment of load is
At one point a settlement occurs at a rapid rate, the total load up to that
point is calculated and divided by the area of the plate to determine
the ultimate bearing capacity of soil at that depth. The ultimate bearing
capacity is then divided by a safety factor (typically 2.5~3) to determine
the safe bearing capacity
59. Plate Load Test Equipment
The following apparatus is necessary for performing plate load test.
Hydraulic jack & pump
Reaction beam or reaction truss
Necessary equipment for loading platform.
Tripod, Plumb bob, spirit level etc
60. Plate Load Test Procedure
The necessary steps to perform plate load test is written below-
Excavate test pit up to the desired depth. The pit size should be at least 5 times the size
of the test plate (Bp).
At the center of the pit, a small hole or depression is created. Size of the hole is same as
the size of the steel plate. The bottom level of the hole should correspond to the level of
actual foundation. The depth of the hole is created such that the ratio of the depth to
width of the hole is equal to the ratio of the actual depth to actual width of the
A mild steel plate is used as load bearing plate whose thickness should be at least 25
mm thickness and size may vary from 300 mm to 750 mm. The plate can be square or
circular. Generally, a square plate is used for square footing and a circular plate is used
for circular footing.
A column is placed at the center of the plate. The load is transferred to the plate
through the centrally placed column.
The load can be transferred to the column either by gravity loading method or by truss
61. For gravity loading method a platform is constructed over the column and
load is applied to the platform by means of sandbags or any other dead
loads. The hydraulic jack is placed in between column and loading
platform for the application of gradual loading. This type of loading is
called reaction loading.
At least two dial gauges should be placed at diagonal corners of the plate
to record the settlement. The gauges are placed on a platform so that it
does not settle with the plate.
Apply seating load of .7 T/m2 and release before the actual loading starts.
Plate Load Test Procedure
62. The initial readings are noted.
The load is then applied through hydraulic jack and increased gradually. The
increment is generally one-fifth of the expected safe bearing capacity or one-
tenth of the ultimate bearing capacity or any other smaller value. The applied
load is noted from pressure gauge.
The settlement is observed for each increment and from dial gauge. After
increasing the load-settlement should be observed after 1, 4, 10, 20, 40 and 60
minutes and then at hourly intervals until the rate of settlement is less than .02
mm per hour. The readings are noted in tabular form.
After completing of the collection of data for a particular loading, the next load
increment is applied and readings are noted under new load. This increment
and data collection is repeated until the maximum load is applied. The
maximum load is generally 1.5 times the expected ultimate load or 3 times of
the expected allowable bearing pressure.
Plate Load Test Procedure
63. Limitation of plate load test
Base plate not less than 30cm not more than 75cm
Soil should be homogeneous, if not then results are incorrect
Suitable for cohesionless soil
It will give immediate settlement