Bearing Capacity of Shallow Foundation

BEARING
CAPACITY OF
SHALLOW
FOUNDATION
Prepared By:
Arbaz Kazi
Asst. Prof.
VCET, Vasai (W)

WHAT IS FOUNDATION?
• Foundation is one of the element of the structure, the one
responsible for transmitting load from superstructure to the soil
beneath including its own self weight.
• Foundations are designed to have an adequate load capacity
depending on the type of subsoil supporting the foundation.
• The primary design concerns are settlement and bearing capacity.
When considering settlement, total settlement and differential
settlement is normally considered.
• Foundation are generally classified into two types:
SHALLOW FOUNDATION
DEEP FOUNDATION

SHALLOW FOUNDATION:
• A shallow foundation is a type of foundation which transfers building loads
to the nearest earth surface
• In this type of foundation generally width is greater then the depth i.e. Df/B
<= 1
• Shallow foundations include spread footing foundations, raft foundations,
strap footing foundation etc.
DEEP FOUNDATION:
• A deep foundation is a type of foundation which transfers building loads to
the earth farther down from the surface than a shallow foundation does, to
a subsurface layer or a range of depths.
• In this type of foundation generally width is greater then the depth i.e. Df/B
> 1
• Pile foundation & Well foundation are types of deep foundation.

1. SPREAD FOOTING:
• This type of foundation supports
one column only as shown below.
• This footing is also known as Pad
footing or isolated footing.
• It can be square or rectangular in
shape.
• This type of footing is the easiest
to design and construct and most
economical therefore
• For this type of footing , Length to
Breadth ratio (L/B) < 5.
SHALLOW FOUNDATION

2. CONTINUOUS FOOTING:
• If a footing is extended in one
direction to support a long
structure such as wall, it is called
a continuous footing or a wall
footing or a strip footing as
shown below.
• Loads are usually expressed in
force per unit length of the
footing.
• For this type of footing , Length
to Breadth ratio (L/B) > 5.

An example of Continuous Footing

3. COMBINED FOOTING:
• A combined footing is a larger
footing supporting two or more
columns in one row.
• This results in a more even load
distribution in the underlying soil or
rock, and consequently there is less
chances of differential settlement to
occur.
• While these footings are usually
rectangular in shape, these can be
trapezoidal (to accommodate unequal
column loading or close property
lines)

4. STRAP FOOTING:
• Two or more footings joined by a beam
(called Strap) is called Strap Footing.
• This type is also known as a cantilever
footing or pump-handle foundation. This
form accommodates wide column spacing's
or close property lines. Strap is designed as
a rigid beam to with stand bending
moments, shear stresses.
• The strap simply acts as a connecting beam
and does not take any soil reaction.
• To make this sure, soil below is dug and
made loose.

5. RAFT FOOTING:
• A large slab supporting a number of
columns not all of which are in a
straight line is known as Mat or Raft or
Mass foundation.
• These are usually considered where the
base soil has a low bearing capacity and
/or column loads are so large that the
sum of areas of all individual or
combined footings exceeds one half the
total building area.
• A particular advantage of mat for
basement at or below ground water
table is to provide a water barrier

BASIC DEFINATIONS
1. Gross Bearing Pressure (𝒒 𝒈𝒓𝒐𝒔𝒔): The intensity of vertical loading at the
base of foundation due to all loads above that level.
2. Net Bearing Pressure: (𝒒 𝒏𝒆𝒕): The difference between q gross and the
total overburden pressure Po at foundation level (i.e. q net = q gross –
Po). Usually q net is the increase in pressure on the soil at foundation
level.
3. Ultimate Bearing Pressure (𝒒 𝒖): The value of bearing pressure at which
the ground fails in shear. It may be expressed as gross or net or total
effective pressure.
4. Safe Bearing Capacity (𝒒 𝒔): The maximum pressure which the soil can
carry without risk of shear failure. (i.e. qs = qns + ϒ*Df)
5. Net Safe Bearing Capacity (𝒒 𝒏𝒔): It is the ratio of net bearing pressure
to factor of safety

GENERAL SHEAR FAILURE:
• Results in sudden catastrophic associated
with plastic flow and lateral expulsion of
soil.
• Failure usually accompanied by tilting and
failure signs are imminent around the
footing.
• The soil adjacent to the footing bulges
• Failure load is well defined on the load
settlement graph.
• Shallow foundations on dense/hard soil and
footing on saturated NCC under undrained
loading.
• Relative density RD > 70%
• Void Ratio < 0.55 dense.

PUNCHING SHEAR FAILURE:
• Failure Mechanism, relatively slow, no lateral
expulsion, failure is caused by compression of
soil underneath the footing.
• Failure is confined underneath the footing and
no signs of failure are visible around the
foundation.
• No tilting the footing settle almost uniformly.
• Failure load is difficult to be defined from the
shape of load-settlement graph. There is
continuous increase in load with settlement.
• Foundation in and/or on loose/soft soils placed
at relatively shallow depth undergoes such type
of failure.
• RD < 20%, Void Ratio > 0.75 loose.

LOCAL SHEAR FAILURE:
• Failure is between the General shear and Punching shear.
• Footing on saturated NCC under drained loading undergoes such type
of failure.
• RD < 20%, Void ratio > 0.75, loose

TERZAGHI’S THEORY
• Analysis of complete bearing capacity failure termed as general shear
failure can be made by assuming soil behaves as a plastic material.
Theory was first proposed by Prandtl’s theory and later modified by
Terzaghi’s which is still in use in its original form and in many modified
forms proposed by various research workers:
• ASSUMPTIONS:
1. Footing base is rough and problem is 2D
2. Footing is shallow; i.e. Df / B <= 1.
3. Continuous footing is used having L > 5B
4. Shear resistance of the soil above the base is neglected.
5. The soil is homogeneous and isotropic and it’s shear strength is
represented by coulomb’s method.

Zones below base of footing as explained by Terzaghi

• When footing sinks into ground, zone 1 (abd) immediately beneath
the footing is prevented from undergoing any lateral yield by
friction and adhesion between base of footing and soil.
• Hence Zone 1 is in state of elastic equilibrium and act as if it was a
part of footing.
• Zone 2 is called as zone of radial shear, as line constitute one set in
shear pattern that radiate from outer edge of footing
• The radial lines are straight and other set are logarithmic spiral
• Zone 3 is zone of linear shear and is identified with passive
Rankine state, i.e. boundaries rises with 45°-Ø/2 with horizontal.
• The failure zones are assumed not to extend horizontal plane.
TERZAGHI’S THEORY

• When load is applied, footings tend to push wedge abd into ground by lateral
displacement of zone 2 and zone 3
• But lateral displacement is resisted by plane surfaces db and da. The forces are:
1. Resultant of Passive Pressure (Pp)
2. Cohesion (C) acting along da and db.
• At instant of failure of wedge abd, the downward and upward forces must balance
• Downward forces acting are:
1. Qu x B
2. Weight of wedge (1/4 x ϒ x B x B)
• Upward forces acting are:
1. Resultant Pp on surfaces db and da
2. Vertical component of cohesion along length ad and bd
db = da =
𝐵/2
𝑐𝑜𝑠∅
Ø
ØØ
B/
2
B
PpPp
a
d
b
TERZAGHI’S THEORY

Hence vertical component of cohesion da = C x
𝐵/2
𝑐𝑜𝑠∅
x sinØ = C x B/2 x tanØ
qu x B + 1/4 x ϒ x B x B x tanØ = 2 x Pp +2 x C x B/2 x tanØ
qu x B = 2 x Pp +2 x C x B/2 x tanØ - 1/4 x ϒ x B x B x tanØ
Resultant Pp can be divided into 3 categories
1. Ppϒ (produced by weight of shear zone dbfe)
2. Ppc (produced by soil cohesion)
3. Ppq (produced by surcharge)
qu x B = 2 x (Ppϒ + Ppc + Ppq ) +2 x C x B/2 x tanØ - 1/4 x ϒ x B x B x tanØ
qu x B = (2 x Ppϒ - 1/4 x ϒ x B x B x tanØ) + (2 x Ppc + C x B x tanØ )+ 2 x Ppq -- 1
TERZAGHI’S THEORY

Let, (2 x Ppϒ - 1/4 x ϒ x B x B x tanØ) = B x 0.5 x ϒ x Nϒ
(2 x Ppc + C x B x tanØ ) = B x C x NC
2 x Ppq = B x ϒ x D x Nq
Hence rewriting equation 1,
qu = C x NC + ϒ x D x Nq + 0.5 x ϒ x B x Nϒ ------------ 2
qnu = C x NC + ϒ x D x (Nq -1) + 0.5 x ϒ x B x Nϒ -------------------3
For purely cohesive soil,
qu = C x NC + ϒ x D x Nq ------------ 4
Equation 2 is called Terzaghi’s bearing capacity equation
NC,Nϒ andNq are dimensionless number known as Terzaghi’s bearing capacity factors.
TERZAGHI’S THEORY

Terzaghi’s Bearing capacity factors for different ϕ

Equation is only valid for General shear failure hence for local shear
failure,
qu = C x NC ‘+ ϒ x D x Nq’ + 0.5 x ϒ x Nϒ’ ----------- 5
Points to decide General Shear failure or local shear failure:
• Ø > 36° , general shear failure & Ø < 28°, local shear failure
• Lateral strain < 5%, general shear failure & Lateral strain > 5%,
local shear failure
• N >= 30 , general shear failure & N <= 5, local shear failure
• RD > 70, general shear failure & RD < 20, local shear failure

LIMITATIONS OF TERZAGHI’S THEORY
• Slight downward movement of footing may not develop fully
plastic zones.
• Theory is suitable only for shallow foundation
• No provision of shape of footing taken into consideration
• Base of footing cannot always be rough.
Later on Terzaghi proposed shape factors Sc and Sγ for the first and
last terms of equation to account for the different shapes of the
footings such as circular, square, rectangular etc.
Shape Factor Strip Circular Square Rectangular
Sc 1 1.3 1.3 1 + 0.3 (B/L)
Sγ 1 0.6 0.8 1- 0.3 (B/L)

For square foundation:
qu = 1.3 x C x NC + ϒ x D x Nq + 0.4 x ϒ x B x Nϒ
For circular foundation:
qu = 1.3 x C x NC + ϒ x D x Nq + 0.3 x ϒ x B x Nϒ
For Rectangular foundation:
qu =1 + 0.3 (B/L) x C x NC + ϒ x D x Nq + 0.4 x ϒ x B x Nϒ

Brinch Hansen’s Bearing Capacity equation
The bearing capacity equation is given by:
 idsBNidsqNidscNq qqqqccccu 5.0





tan)1(5.1
)
2
45(tan)(
cot)1(
2tan



q
q
qc
NN
eN
NN

Sc 1 1.3 1.3 1 + 0.2 (B/L)
Sq 1 1.2 1.2 1 + 0.2 (B/L)
Sγ 1 0.6 0.8 1 - 0.4 (B/L)
Following are the shape factors adopted:
Following are the depth
factors adopted:
Depth Factor Values
dc 1 + 0.35*(Df/B)
dq 1 + 0.35*(Df/B)
dγ 1
Inclination Factor Values
ic 1 – (H/2*c*B*L)
iq 1 – 1.5*H/V
iγ iq*iq
Following are the inclination
factors adopted:

Vesic’s Bearing Capacity Equation
Vesic (1973) confirmed that the basic nature of failure surfaces in soil as suggested by
Terzaghi to be correct. However, the angle which the inclined surfaces AC and BC
make with the horizontal was found to be (45+∅ 2) . Hence the changes in bearing
capacity factors are to be incorporated as given below:





tan*)1(2
)(*)
2
45(tan
cot*)1(
tan2



q
q
qc
NN
eN
NN
The Equation is similar to the one which is proposed by Hansen, but the variation in
the values of shape, depth and inclination factors
The bearing capacity equation is given by:
 idsBNidsqNidscNq qqqqccccu 5.0

Sc 1 1 + (Nq/Nc) 1 + (Nq/Nc) 1 + (B/L)*(Nq/Nc)
Sq 1 1 + 𝐭𝐚𝐧 ∅ 1 + 𝐭𝐚𝐧 ∅ 1 + (B/L)* 𝐭𝐚𝐧 ∅
Sγ 1 0.6 0.6 1 - 0.4 (B/L)
Following are the shape factors adopted:
Following are the depth factors adopted:
Depth
Factor
Values
dc 1 + 0.40*(Df/B)
dq 𝟏 + 𝟐 ∗ tan ∅ ∗ (𝟏 − sin ∅)2
∗ 𝑫𝒇/𝑩
dγ 1
Inclination Factor Values
ic = iq (𝟏 − 𝛂/𝟗𝟎)2
iγ (𝟏 − 𝛂/∅)2
Following are the inclination factors adopted:

IS Code Method
IS: 6403-1981 gives the equation for net ultimate bearing capacity which is similar to
one proposed by Vesic:
WidsBNidsNqidscNq qqqqccccnu
'
5.0)1( 
The second term has been changed, because:
D* fnu quqquq 
• The bearing capacity factors and inclination factors are same as that of one given by
Vesic’s
• The shape factors are same as proposed by Hansen
Following are the depth factors adopted:
Depth
Factor
Values
dc
dq = dγ 1 for ∅ ≤ 10°
dq = dγ
1+0.20∗(Df B)∗ tan2 (45+
∅
2
)
1+0.20∗(Df B)∗tan2 (45+
∅
2
) for ∅ > 10°

Standard Penetration Test
This test is the most common used in-
situ test, especially for cohesion less
soils which cannot be easily sampled.
The test is extremely useful for
determining the relative density and
angle of shearing resistance of cohesion
less soils. It can also determine the
unconfined compressive strength of
cohesive soils..

Apparatus of SPT
1) Tripod stand
2) Standard split-spoon sampler.
 It consists of three parts:-
 Driving shoe, about 75 mm long.
 Steel tube about 450mm long, split longitudinally in two halves having inner
diameter as 38mm & outer diameter as 50mm.
 Coupling at the top of the tube about 150 mm long.
3) Guide pipe
4) Drill rod
5) Drop hammer weighing 63.5kg.

TRIPOD HOIST
• The drop hammer is attached to the rope of tripod hoist. By
operating winch the weight is lifted.
TRIPOD HOIST
The drop hammer is attached to the
rope of tripod hoist. By operating
winch the weight is lifted.

Split Spoon Sampler
Coupling
150mm long
Driving shoe
75mm long
Split Tube,450mm long

Drop Hammer
• Hammer with a weight of 63.5 kg falling from a distance of 750 mm (30 in)

Equipment making bore hole
It is used to keep the bore hole of 150 mm, 300mm, 450 mm upto desired depth
at which sample is taken

Driving head Lifting bail
It is screwed on sampler
& the hammer is fallen
on it to driven the
sampler in ground.
It is used to lift up the
sampler from the ground
after driven it to 30 cm

Procedure of SPT
 The bore hole is to be drilled up to the desired depth.
 The drilling tools are removed & sampler is lowered to the bottom of the
hole.
 Three markings @ 150 mm are made on the rod of sampler.
 The sampler is driven into the soil by drop hammer falling through the
height of 150 mm @ 30 blows/min.
 The number of blows required to drive each 150 mm of the sampler is
counted.
 The number of blows recorded for the first 150 mm is disregarded.
 The number of blows recorded for the last two 150mm intervals are added
to give the standard penetration number (N)
 Likewise, the another samples of soil are collected at the interval of 1.67
m or where the soil profile or strata changes (IS 6403:1981).

Corrections
DILATANCY CORRECTION:-
• Silty fine sands & fine sands below the water table develop
pore pressure which is not easily dissipated. The pore
pressure increases the resistance of the soil & hence the
penetration. The following correction is applied when the
observed value of N exceeds 15. The corrected penetration
number, Nc = 15 + 0.5(Nr-15), where Nr is the recorded
value of N.
• If Nr is less than or equal to 15, then Nc = Nr.

DILATANCY CORRECTION:-
If the two soils having same relative density but different
confining pressure one with a higher confining pressure
gives a higher penetration number.
𝑁𝑐 = 𝑁𝛾 ∗ 0.77 ∗ log10(2000 𝜎)
where, 𝑁𝑐 = corrected penetration number
 = effective overburden pressure
𝑁𝛾 = recorded value of N.

Hammer rod showing markings @
150mm

PLATE LOAD TEST (IS:1888-1982)
I. Plate Load Test is a field test for determining the ultimate bearing
capacity of soil and the likely settlement under a given load.
II. Circular or square bearing plates of mild steel not less than 25mm
in thickness and varying in size from 300 - 750mm.
III. The subgrade modulus is defined as the load intensity ‘p’ applied
on the standard plate per unit deflection i.e. k=p/d, value of d
=1.25mm. The test load is gradually increased till the plate starts
to sink at a rapid rate.
IV.The ultimate bearing capacity of soil is divided by suitable factor
of safety (which varies from 2 to 3) to arrive at the value of safe
bearing capacity of soil.

APPARATUS
(i) Test plate of square size
(ii) Hydraulic jack & pump
(iii) Pressure gauge
(iv) Proving ring or load cell
(v) 4 no of dial gauges & dial gauge stands
(vi) Magnetic bases for dial gauges & supporting channels
(vii) Loading platform equipment or Truss with anchor rods
(viii) Plumb bob
(ix) Sprit level
(x) Tripod
(xi) Pulley block

PROCEDURE
1. To conduct the plate load test a pit of size 5Bp x 5Bp where Bp = width
of plate, is excavated up to a depth of Df where Df=depth of proposed
foundation.
2. Generally 0.3 sq.m plate is used and sometimes 0.6 sq.m plate are also
used. so Bp = 0.3 or 0.6.
3. A central hole of depth Dp is made at the bottom of the test pit where,
Dp = (Bp/5Bp)x Df
4. The plate is placed in the central hole and load is applied on it by a
hydraulic jack system.
5. A seating load of 7 kN/sq.m is first applied and released after some time.
After that load is increased in increment of 20% of rate estimated load
or 1/10th of ultimate load.

USES
1. To find out the ultimate
bearing capacity of the
proposed foundation.
2. To determine the settlement
of a footing under a given
load intensity.
3. We can design a shallow
footing for any allowable
settlement.

Advantages
• Time-saving and cost saving
• No vehicle required
• On-site evaluation of test result
• Easy to handle
• Reliable and precise
• Understanding of foundation behaviour

Limitations
 The Plate Load Test being of short duration , does not
give the ultimate settlements particularly in case of
cohesive soils.
 The width of the plate should not be less than 30cm. It is
experimentally shown that the load settlement behaviour
of soil is qualitatively different for smaller width.
 The foundation settlements is loose sands are usually
much larger than what is predicted by plate load test.
 The settlement influence zone is much larger for the real
foundation sizes than that for the test plate.

Bearing Capacity of Shallow Foundation

Bearing Capacity of Shallow Foundation

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Bearing Capacity of Shallow Foundation

Similar to Bearing Capacity of Shallow Foundation (20)

More from Arbaz Kazi

More from Arbaz Kazi (14)

Recently uploaded

Recently uploaded (20)

Bearing Capacity of Shallow Foundation