Shallow foundation design, bearing capacity of soil.

1. BEARING CAPACITY OF
SHALLOW FOUNDATION
by
Dr. V. Vignesh
Assistant Professor
Sanjivani College of Engineering, Kopargaon

2. INTRODUCTION
The Foundation should be designed such that (1) the soil below
does not fail in shear and (2) the settlement is within the safe limits.
The pressure which the soil can safely withstand is known as the
allowable bearing pressure.
 This chapter gives the methods for the determination of allowable
bearing pressure.
Foundations may be broadly classified into two categories: (1)
Shallow foundations, (2) Deep foundations.
A shallow foundation transmits the loads to the strata at a
shallow depth.
A deep foundation transmits the load at a considerable depth
below the ground surface.

3. BASIC DEFINITIONS
(1) Ultimate Bearing Capacity (qu).
• The ultimate bearing capacity is the gross pressure at the
base of the foundation at which the soil fails in shear.
(2) Net Ultimate Bearing Capacity (qnu).
• It is the net increase in pressure at the base of foundation
that causes shear failure of the soil. It is equal to the
gross pressure minus overburden pressure.
Thus, qnu = qu - γDf
where qu= ultimate bearing capacity (gross), γ = unit
weight of foundation soil, and Df= depth of foundation.

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. It is obtained by dividing the net
ultimate bearing capacity by a suitable factor of safety.
Thus, qns = qnu / F
Where, F = factor of safety, which is usually taken as 3.
(4) Gross Safe Bearing Capacity (qs).
It is the maximum gross pressure which the soil can carry safely
without shear failure. It is equal to the net safe bearing capacity
plus the original overburden pressure.
qs = qns + γDf
or qs = qnu / F + γDf
(5) Net Safe Settlement Pressure (qnp)
It is the net pressure which the soil can carry without exceeding the
allowable settlement. The maximum allowable settlement generally
varies between 25 mm and 40 mm for individual footings.
Also called unit soil pressure or safe bearing pressure.

5. (5) Net Allowable bearing pressure (qna)
The net allowable bearing pressure is the net bearing pressure which
can be used for the design of foundations.
It is the smaller of the net safe bearing capacity (qns) and the net safe
settlement pressure (qnp).

6. Types of Shear or Bearing Capacity Failure
There are three categories of bearing capacity failure,
1. General Shear Failure.
2. Local Shear Failure.
3. Punching Shear Failure.
General Shear Failure.
At a certain load intensity equal to qu, the settlement increases suddenly.
A shear failure occurs in the soil at that load and the failure surfaces
extend to the ground surface. This type of failure is known as general
shear failure.
A heave on the sides is always observed in general shear failure.
Example: Strip footing in Dense sand or stiff clay.

7. Local Shear Failure.
When the load is equal to certain value qu(1), the foundation movement
is accompanied by sudden jerks. The failure surfaces gradually extend
outwards from the foundation. The load at which the considerable
movement of foundation happens is equal to qu. Beyond this point, an
increase of load is accompanied by a large increase in settlement. This
type of failure is called local shear failure.
Example: Strip footing on medium dense sand or clay with medium
consistency.

8. Punching Shear Failure.
In this case, the failure surfaces do not extend up to the ground surface.
There are jerks in foundation at a load of qu(1) The footing fails at a
load of qu, at that stage the load- settlement curve becomes steep and
practically linear. This type of failure is called the punching shear
failure.
No heave is observed. There is only vertical movement of footing.
Example: Strip footing on loose sand or soft clay.

9. Rankine’s Analysis
Rankine (1885) considered the plastic equilibrium of two adjacent soil
elements, one immediately beneath the footing and the other just
beyond the edge of the footing.
For element I beneath the footing, the vertical stress is the major
principal stress and the lateral stress is the minor principal stress.
However, for element II, the lateral stress becomes the major stress,
and the vertical stress becomes the minor principal stress.

10. TERZAGHI’S BEARING CAPACITY THEORY
Terzaghi (1943) gave a general theory for the bearing capacity of soils
under a strip footing, making the following assumptions:
(1) The base of footing is rough.
(2) The footing is laid at a shallow depth, i.e. Df ≤ B.
(3) The shear strength of the soil above the base of the footing is
neglected. The soil above the base is replaced by a uniform surcharge
γDf.
(4) The load on the footing is vertical and is uniformly distributed.
(5) The footing is long, i.e., L/B ratio is infinite, where B is the width and
L is the length of the footing.
(6) The shear strength of the soil is governed by the Mohr-Coulomb
equation.

11. (1) For Strip footing:
The ultimate capacity is given by,
Where, Nc, Nq, and Nγ are the bearing capacity factor which are
dimensionless numbers and are depends on the angle of shearing
resistance of soil.

12. where Kp = Coefficient of passive earth pressure.
The bearing
capacity
factors are
also given by
Hasen

14. (b) For Square Footing
(c) For Circular Footing

15. Problem Solving:
1. A strip footing is 1.5m wide and its base rests 1m below the ground surface. The
soil below the ground level is dense with c = 100 kN/m2
, φ = 38o . Determine the
ultimate bearing capacity of footing. Assume the unit weight of soil γ = 20 kN/m3.
Solutions:
Nq= 48.93, Nc=61.35, Nγ=67.40
qu=8124.6kN/m2
.
2. Determine the ultimate bearing capacity and net safe bearing capacity of a strip
footing 1.2m wide and hving the depth of foundation of 1m. Take φ = 35o , unit weight
of soil as 18 kN/m3 and c = 15kN/m2 and F = 2.5.
Solutions:
Nq= 33.3, Nc=46.13, Nγ=40.71
qu=1769.51 kN/m2
.

16. 3. A 2mx2m footing is located at a depth of 1.5 m from the ground
surface in dense sand. The shear strength parameters are c = 0 and φ =
36o Determine the ultimate bearing capacity of the soil, if (i) the water
table is well below the base of the footing i.e., 2m or more, (ii) the water
table is at ground surface, (iii) the water table is at the base of the
foundation. The unit weight of the soil above water table may be taken as
18 kN/m3 and saturated unit weight as 20kN/m3.(iv) Also compute the
ultimate bearing capacity when the water table is 0.5m below the base of
the foundation.
Solution:
Nq=37.75, Nγ=48.06
Case 1: Rw1=Rw2=1 qu=1711.31kN/m2
Case 2: Rw1=Rw2=0.5 qu=950.73kN/m2
Case 3: Rw1=1,Rw2=0.5 qu=1403.73kN/m2
Case 4: Rw1=1,Rw2=0.625 qu kN/m2

17. 4. What is the ultimate bearing capacity of the circular footing 1m
diameter resting on the surface of a saturated clay of UCS of 100 kN/m2 .
What is the safe value if the factor of safety is 3.
Solution:
Note for φ =0, Nc=5.7, Nq=1, Nγ=0
qu=370.5 kN/m2
qs=123.5 kN/m2
5. Determine the diameter of the circular footing resting on a stiff
saturated clay with unconfined compressive strength of 250 kN/m2, the
depth of foundation is 2m, the bulk unit weight of the soil is 20 kN/m3,
the load of the column is 700kN and assume a factor of safety as 2.5.
Solution: qu= 966.25 kN/m2
. d=1.52m.

18. Ultimate bearing capacity in case of Local Shear failure
Terzaghi (1943) has suggested the following empirical reduction to the
actual cohesion and the angle of shearing resistance in case of local shear
failure:
The equation for strip footing can be written as

19. •IS Code Method:
IS : 6403—1981 gives the equation for the net ultimate bearing capacity as,

20. Depth Factor
Inclination Factor
where α° is the inclination of the load with vertical.
Effect of Water table: (W’)

22. 6. A footing 2m in square is laid at a depth of 1.3 m below the ground
surface. Determine the net ultimate bearing capacity using IS code
method, Take unit weight as 20 kN/m3
, angle of shearing resistance as
30o and cohesion c = 0.
Also Determine the net ultimate bearing capacity for the following
cases
(i) The water table raises to the level of base
(ii) The water table raises to the ground level
(iii) Water table is 1m below the base of the footing
7. Determine the net ultimate bearing capacity of a rectangular footing
1.8m x 3.6m in plan founded at a depth of 1.6m below the ground
surface. The load at the footing acts at a angle of 16o to the vertical and
its eccentric in the direction of width is by 15 cm. The unit weight of soil
is 18 kN/m3 . The rate of loading is sloped and hence the effective shear
strength parameters are c’=15kN/m3, φ=30o. Natural water table is at a
depth of 2m below the ground surface. Use BIS-6403 recommendations.

23. PLATE LOAD TEST:
The allowable bearing pressure can be determined by conducting a plate load test at the
site.
• To conduct a plate load test, a pit of the size 5Bp X 5Bp, where Bp is the size of the
plate, is excavated to a depth equal to the depth of foundation (Df).
• The size of the plate is usually 0.3 m square. It is made of steel and is 25 mm thick.
Occasionally, circular plates are also used.
• Sometimes, large size plates of 0.6 m square are used.

26. • A central hole of the size Bp x Bp is excavated in the pit.
• The depth of the central hole (Dp) is obtained from the following
relation :
Dp/Bp = Df/Bf
or Dp = (Bp/Bf) x Df
where Bf is the width of the pit, and Bp is the size of plate.
• For conducting the plate load test, the plate is placed in the central hole
and the load is applied by means of a hydraulic jack.
• A seating load of 7 kN/m2 is first applied, which is released after some
time.
• The load is then applied in increments of about 20% of the estimated
safe load or one-tenth of the ultimate load.
• The settlement is recorded after 1, 5, 10, 20, 40, 60 minutes, and further
after an interval of one hour. These hourly observations are continued
for clayey soils until the rate of settlement is less than 0.2 mm per hour.
• The test is conducted until failure or at least until the settlement of
about 25 mm has occurred

27. • The ultimate bearing capacity of the proposed foundation qu(f) can be obtained from
the following relations:
For clayey soils: qu(f) = qu(p)
For sandy soils: qu(f) = qu(p) x (Bf/Bp)
The plate load test can also be used to determine the settlement for a given intensity of
loading (qo). It is given as,
For clayey soils,
For Sandy soils,

28. • Problem Solving:
8. A plate load test using a plate size 30cm x 30cm was carried out at the
level of the proposed foundation. The soil at the site is cohesionless with
the water table at greater depth. The plate settled by 10mm at a loading
intensity of 160 kN/m2
. Determine the settlement of a square footing of
size 2m x 2m under the same load intensity.

29. Standard Penetration Test (SPT):
• The standard penetration test is the most commonly used in-situ test,
especially for cohesionless soils that cannot be easily sampled.
• The test is extremely useful for determining the relative density and
the angle of shearing resistance of cohesionless soils.
• It can also be used to determine the UCS of cohesive soils.
• The SPT is conducted in a borehole using a standard split-spoon
sampler.
• When the borehole has been drilled to the desired depth, the drilling
tools are removed and the sampler is lowered to the bottom of the
hole.
• The sampler is driven into the soil by a drop hammer of 63.5 kg mass
falling through a height of 750 mm at the rate of 30 blows per
minute. (IS : 2131—1963).
• The number of hammer blows required to drive 150 mm of the sample
is counted.

31. • The number of blows recorded for the first 150 mm is disregarded.
• The number of blows recorded for the last two 150 mm intervals are
added to give the standard penetration number (N).
• In other words, the standard penetration number is equal to the number
of blows required for 300 mm of penetration beyond a seating drive of
150 mm.
• If the number of blows for 150 mm drive exceeds 50, it is taken as
refusal and the test is discontinued.
• The standard penetration number is corrected for
• Dilatancy correction
• Overburden correction

32. (a) Dilatancy Correction.
• Silty fine sands and fine sands below the water table develop pore
pressure which is not easily dissipated. The pore pressure increases the
resistance of the soil and hence the penetration number (N).
• Terzaghi and Peck (1967) recommend the following correction in the
case of silty fine sands when the observed value of N exceeds 15.
• The corrected penetration number,
where NR is the recorded value, and Nc is the corrected value.
• If NR ≤15, Nc = NR

33. (b) Overburden Correction.
• In granular soils, the overburden pressure affects the penetration resistance.
• As the confining pressure in cohesionless soils increases with the depth, the
penetration number for soils at shallow depths is underestimated and that at
greater depths is overestimated.
• Gibbs and Holtz (1957) recommend the use of the following equation
𝑁𝑐 = 𝑁𝑅
350
𝜎𝑜+70
�
Where σo= Effective overburden pressure
• This equation is applicable for σo ≤ 280 kN/m2.

35. CONE PENETRATION TESTS
• The cone test was developed by the Dutch Government, and so it is also called
Dutch cone test.
• The test is conducted either by the static method or by dynamic method.
Static cone penetration test:
The Dutch cone has an apex angle of 60° and an overall diameter of 35.7 mm, giving an
end area of 10 cm2.

36. • For obtaining the cone resistance, the cone is pushed downward at a steady rate of
10 mm/sec through a depth of 35 mm each time. The cone is pushed by applying
thrust and not by driving.
Dynamic cone Test:
• The test is conducted by driving the cone by blows of a hammer.
• The number of blows for driving the cone through a specified distance is a measure
of the dynamic cone resistance.
• The driving energy is given by a 65 kg-hammer falling through a height of 75 cm.
• The number of blows for every 10 cm penetration is recorded.
• The number of blows required for 30 cm of penetration is taken as the dynamic cone
resistance

38. BEARING CAPACITY FROM STANDARD PENETRATION TEST
• The ultimate bcarin6 capacity of cohesionless soils may be determined from the
standard penetration number (N).
• An average value of N is obtained between the level of the base of the footing and
the depth equal to 1.5 to 2.0 times the width of the foundation.
Formula
HOUSEL’S METHOD FOR DESIGN OF FOUNDATION :
Housel's method can be used for the design of a shallow foundation for a given safe
settlement
Let Qi and Q2 be the loads for the plates of size BY and B2 respectively.

39. 9. Two plate load tests were conducted at the level of proposed
foundation on cohesionless soil close to each other. The following details
are given
Size of the plates Load applied Settlement recorded
0.3x0.3m 30kN 25mm
0.6x0.6m 90kN 25mm
If a footing is to carry a load of 1000 kN, determine the required size of
the footing for the settlement of 25mm.