SHALLOW FOUNDATIONS & SETTLEMENT

ANALYSIS
1. A square foundation of 1.3m x 1.3m size and constructed on a sandy soil at a depth of 1.22m.
The soil has γ = 16.5 kN/m3, γsat = 18.55 kN/m3, φ’ = 340 and water table is at a depth of 0.61m
from the ground level. Determine the allowable/safe load on the foundation.(FOS = 3)
[for φ’ = 340, Nc = 42.16, Nq = 29.44, Nγ = 41.06]
2. A strip foundation of width 2m & the soil supporting the foundation has a friction angle of φ’ =
250 and C’ = 20 kPa. The unit weight of the soil , is 16.5 kN/m3. Determine the allowable gross
load on the foundation with a factor of safety (FS) of 3. Assume that the depth of the foundation
(Df) is 1.5m and that local shear failure occurs in the soil.
[for φ’ = 250, Nc = 25.13, Nq = 12.72, Nγ = 8.34, Nc’ = 14.80, Nq’ = 5.60, Nγ’ = 2.25]
3. A footing of 1.5m wide with its base at a depth of 1m having γ = 17 kN/m3, γsat = 20 kN/m3, φ’ =
380, Unconfined compressive strength of the soil is 50 kPa. Determine the ultimate bearing
capacity of the footing if the ground water table is located (a) at a depth of 0.5m below the
ground surface, (b) at a depth of 0.5m below the base of the footing, (c) at a depth of 2m below
the base of the footing.
[for φ’ = 380, Nc = 77.50, Nq = 61.55, Nγ = 78.61]
4. A footing 4m x 2m in plan, transmits a pressure of 150 kN/m2 on a cohesive soil having E = 6 x104
kN/m2 and ν= 0.50. Determine the immediate settlement of the footing at the center. If = 1.52.
5. Calculate the net safe bearing capacity of a foundation if the ultimate bearing capacity of a soil is
300 kN/m2. The depth of foundation is 1m and unit weight of the soil is 20kN/m3. Choose a
factor of safety of 2.5.
6. A circular raft foundation of 20m diameter and 1.6m thich is provided for a tank that applies a
bearing pressure of 110 kPa on sandy soil with Young’s modulus , Es’ = 30 MPa and Poisson’s
ratio, ν = 0.3. The raft is made of concrete (Ec = 30GPa and νc = 0.15).Considering the raft as
rigid(It = 0.8). Calculate the Elastic settlement in mm.
7. A 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a c-φ soil as
shown in the figure. The water table is at a depth of 5.5 m below ground surface. The soil
properties are: c' = 35 kN/m2, φ' = 28.63°, γsat = 19 kN/m3, γbulk = 17 kN/m3 and γw = 9.81 kN/m3.
The values of bearing capacity factors for different φ' are given below.

φ' Nc Nq Nγ
15° 12.9 4.4 2.5
20° 17.7 7.4 5.0
25° 25.1 12.7 9.7
30° 37.2 22.5 19.7
 Using Terzaghi's bearing capacity equation and a factor of safety FOS= 2.5,
calculate the net safe bearing capacity for General shear failure and local shear failure both(expressed in
kN/m2).

8. Using the properties of the clay layer that γsat = 20.625 kN/m3 , calculate the
consolidation settlement of the same clay layer under a square footing (neglecting its self
weight) with additional data shown in the figure below (assume the stress distribution as
1 H : 2 V from the edge of the footing and γw = 10 kN/m3).

Ÿij

9. A water tank is to be constructed on the soil deposit shown in the figure below. A circular
footing of diameter 3 m and depth of embedment 1 m has been designed to support the
tank. The total vertical load to be taken by the footing is 1500 kN. Assume the unit
weight of water as 10 kN/m3 and the load dispersion pattern as 2V:1H. The expected
settlement of the tank due to primary consolidation of the clay layer is ______ mm.
10. Calculate the consolidation settlement of the clay layer of 5m thickness having coefficient of
volume compressibility as 0.25 m2/MN and the change in effective stress of 80 kN/m2 at the mid
depth of the clay layer due to the lowering of the water table.

PILE FOUNDATIONS
1. A group of 16 piles of 10m length and 0.5m diameter is installed in a 10m thick stiff
clay layer underlain by rock. The pile soil adhesion factor is 0.4, average shear
strength of the of the soil on the sides is 100kPa, undrained shear strength of the soil
at the base is 100 kPa. Calculate the base resistance of a single pile and calculate the
group side friction resistance assuming 100% efficiency of pile groups.
2. For the soil profile shown in Figure below, the minimum number of precast concrete
piles of 300 mm diameter required of safely carry the load for a given factor of safety
of 2.5 assuming 100% efficiency for the pile group) is equal to??
3. The ultimate load capacity of a 10m long concrete pile of square cross section 500mm
x 500mm driven into a homogeneous clay layer having undrained cohesion value of
40kPa is 700 Kn. If the cross section of the pile is reduced to 250mm x 250mm and
the length of the pile is increased to 20m. Then what is the ultimate load capacity of
the pile?
4. A single vertical friction pile of diameter 500 mm and length 20m is subjected to a
vertical compressive load. The pile is embedded in a homogeneous sandy stratum
where angle of internal friction(φ) = 300, dry unit weight = 20 kN/m3 and angle of
wall friction(δ) = 2φ/3. Considering the coefficient of lateral earth pressure(K) = 2.7
and the bearing capacity factor(Nq) = 25. Calculate the ultimate bearing capacity of
the pile in kN.
5. A group of 9 piles arranged in a square pattern with diameter and length of each pile
as 25cm and 10m respectively, is used as a foundation in soft clay deposit. Taking the
unconfined compressive strength of clay as 120 kN/m2 and the pile spacing as 100
cm center to center, the allowable load carrying capacity of the group is??[Assume
the end bearing capacity factor Nc = 9, adhesion factor = 0.75 and factor of safety =
2.5]
6. Pile group is arranged in square pattern consisting of 25 piles. Find the group
efficiency and the safe load which can be applies on the pile group given that
diameter of pile is 0.3m, center to center spacing is 0.9m, length of the piles is 10m,
FOS is 2.5, adhesion factor is 0.45, shear strength at the base of the pile is 180 kN/m2
and average shear strength over the depth of pile is 110 kN/m2 in pure clay.
7. Consider a pile group with 5 rows of piles each row having 5 piles. If the diameter of
pile is same as the spacing between piles then the calculate pile group efficiency
using Converse Labarre formula.
8. A pile group consists of 9 friction piles of 30cm diameter and 10m length and center
to center spacing is 0.75m are driven in clay (Cu = 100 kN/m2, γ = 20 kN/m3) .What
is the safe load for the pile group(Take FOS = 3 and α = 0.6).
9. A wooden pile is being driven with a drop hammer weighing 20 Kn and having a free
fall od 1m. The penetration in the last blow is 5mm, then calculate the load carrying
capacity of the pile according to the Engineering News Formula.(Take FOs = 6)
10. A group of 9 piles, 12m long and 250mm diameter is to be arranged in a square form
in a clay soil with an average unconfined compressive strength of 60 kN/m2.
Calculate center to center spacing of the piles for a group efficiency of 1. Neglect
bearing at the tip of the piles. Take adhesion factor as 0.9.