SOIL MECHANICS AND
FOUNDATION ENGINEERING-II
(CE 311)
BEARING CAPACITY
 Bearing Capacity: Supporting /power of a soil or rock is
referred to as its bearing capacity.
 Gross Bearing Capacity (q): the total pressure at the base of
the footing due to the weight of the superstructure, self
weight of the footing and the earth fill if any.
 Net Bearing Capacity (qn): Excess pressure or the difference
in intensities of the gross pressure after the construction of
the structure and the original overburden pressure.
qn = q – gD
 Ultimate Bearing Capacity (qf): the minimum gross pressure
intensity at the base of the foundation at which the soil fails in
shear.
 Net Ultimate Bearing Capacity (qnf): the minimum net
pressure intensity causing shear failure.
BEARING CAPACITY
qf = qnf + 𝜎
Or
qnf = qf - 𝜎
 Net Safe Bearing Capacity (qns): the net ultimate bearing
capacity divided by a factor of safety F.
𝑞𝑛𝑓
𝑞𝑛𝑠 =
𝐹
 Safe Bearing Capacity (qs): The maximum pressure which
the soil can carry safely without risk of shear failure.
𝑞𝑛𝑓
𝑞𝑠 = 𝑞𝑛𝑠 + 𝛾𝐷 =
+ γ𝐷
𝐹
 Allowable Bearing Capacity (qa): Net loading intensity at
which neither the soil fails in shear nor there is excessive
settlement detrimental the structure.
Terzaghi’s Theory
Terzaghi’s Theory
Parameter
General Shear Failure
Local/ Punching Shear
Failure
Strain Rate
< 5%
10% to 20%
Angle of shearing resistance
> 36º
<28º
Penetration Test
N≥30
N≤5
Plate Load Test
Depends on Shape
Depends on Shape
Density Index
>70
< 20
Equation Parameters
Cohesion c
Friction tan f
2
3
c
2
3
tan f
Terzaghi’s Equations
For Strip footing
𝑞𝑓 = 𝑐𝑁𝑐 + 𝜎𝑁𝑞 + 0.5𝛾𝐵𝑁𝛾
For circular footing
𝑞𝑓 = 1.3 𝑐𝑁𝑐 + 𝜎𝑁𝑞 + 0.3𝛾𝐵𝑁𝛾
For square footing
𝑞𝑓 = 1.3 𝑐𝑁𝑐 + 𝜎𝑁𝑞 + 0.4𝛾𝐵𝑁𝛾
For rectangular footing
𝑞𝑓 = 𝑐𝑁𝑐
𝐵
𝐵
1 + 0.3
+ 𝜎𝑁𝑞 + 0.5𝛾𝐵𝑁𝛾 1 − 0.2
𝐿
𝐿
Effect of Water Table
𝑅𝑤1 = 0.5 1 +
𝑅𝑤2 = 0.5 1 +
𝐷𝑓 −𝑎
𝐷𝑓
𝑏
𝐵
to be applied in second term of equation
to be applied in third term of the equation
Terzaghi’s Bearing Capacity Factors
Terzaghi’s Bearing Capacity
Factors
f
(Degrees)
General Shear Failure
Nc
Nq
Ng
Local Shear Failure
𝑁𝑐
′
𝑁𝑞
′
𝑁𝛾
′
0
5.7
1.0
0.0
5.7
1.0
0.0
5
7.3
1.6
0.5
6.7
1.4
0.2
10
9.6
2.7
1.2
8.0
1.9
0.5
15
12.9
4.4
2.5
9.7
2.7
0.9
20
17.7
7.4
5.0
11.8
3.9
1.7
25
25.1
12.7
9.7
14.8
5.6
3.2
30
37.2
22.5
19.7
19.0
8.3
5.7
34
52.6
36.5
35.0
23.7
11.7
9.0
35
57.8
41.4
42.4
25.2
12.6
10.1
40
95.7
81.3
100.4
34.9
20.5
18.8
45
172.3
173.3
297.5
51.2
35.1
37.7
48
258.3
287.9
780.1
66.8
50.5
60.4
50
347.5
415.1
1153.2
81.3
65.6
87.1
PROBLEMS
1.
A square footing 2.5m x 2.5m is built in a homogenous bed of
sand of unit weight 20 kN/m3 and having an angle of shearing
resistance of 350. The depth of the base of footing is 1.5m
below the ground surface. Calculate the safe load that can be
carried by a footing with a factor of safety of 3 against complete
shear failure. Use Terzaghi’s analysis.
2.
What will be the maximum safe load for problem 1 if the soil is
loose sand of unit weight 16 kN/m3 and the angle of shearing
resistance is 250.
3.
A strip footing, 1m wide at its base is located at a depth of 0.8m
below the ground surface. The properties of the foundation soil
are g=18kN/m3, c=30kN/m2 and f=200. Determine the safe
bearing capacity using a factor of safety of 3. Assume soil fails
by local shear.
PROBLEMS
4. Solve problem 3 if the water table is located at the base of
the footing. Assume saturated unit weight of the soil as
equal to 19.5kN/m3.
5. A strip footing 2m wide carries a load intensity of 400kN/m2
at a depth of 1.2m in sand. The saturated unit weight of
sand is 19.5 kN/m3 and unit weight above water table is
16.8 kN/m3. The shear strength parameters are c=0 and
f=350. Determine the factor of safety with respect to shear
failure for the following cases of location of water table:
a.
b.
c.
d.
e.
water table is 4m below GL
Water table is 1.2m below GL
Water table is 2.5m below GL
Water table is 0.5m below GL
Water table is at GL itself.
PROBLEMS
6. Design a strip footing to carry a load of 750 kN/m at a depth
of 1.6m in c-f soil having a unit weight of 18kN/m3 and
shear strength parameters as c=20kN/m2 and f=250.
Determine the width of footing using factor of safety of 3
against shear failure.
7. A rectangular footing 2m x 3m rests on a c-f soil, with its
base at 1.5m below the ground surface. Calculate the safe
bearing capacity using a factor of safety of 3 on (i) net
ultimate bearing capacity, and (ii) ultimate bearing capacity.
The soil has following parameters: g=18kN/m3, c=10kN/m2,
f=300.