Chapter 4. Bearing Capacity of Soil.pdf

1
CHAPTER 4
BEARING CAPACITY OF SOIL
By Gashaw H.(@wku-2022)

1. Types of Foundations
Foundations can be broadly classified into the following
two categories(According to Terzhagi)
Shallow foundations (Df/B<1)
bed rock
firm ground
The foundations provided immediately
beneath the lowest part of the structure,
near to the ground level are known as
shallow foundations.
Shallow foundations are further classified into the
following types:
A. Spread/Isolated/pad footings
B. Combined footing
C. Strap/Cantilever footing
D. Strip /Continuous or wall footing
E. Raft/Mat foundation
By Gashaw H.(@wku-2022) 2

3
Deep foundations(Df/B>1)
bed rock
The most common types of
deep foundations are
 Piles
 piers and
 caissons.
When the soil at or near the ground
surface is not capable of supporting a
structure, deep foundations are required
to transfer the loads to deeper strata.
By Gashaw H.(@wku-2022)

*The following are a few important terminologies related to bearing capacity of soil.

Therefore, the bearing strength characteristics of foundation soil are major design
criterion for civil engineering structures.
Bearing capacity is the power of foundation soil to hold the forces from the
superstructure without undergoing shear failure or excessive settlement. The
maximum load per unit area which the soil or rock can carry without yielding or
displacement is termed as the bearing capacity of soils.

 Modes of shear failure
Depending on the stiffness of foundation soil and depth of foundation, the
following are the modes of shear failure experienced by the foundation soil.

1. Continuous, well defined and distinct failure surface develops between the edge
of footing and ground surface.
2. Dense or stiff soil that undergoes low compressibility experiences this failure.
3. Continuous bulging of shear mass adjacent to footing is visible.
4. Failure is accompanied by tilting of footing.
5. Failure is sudden.
6. The length of disturbance beyond the edge of footing is large.
7. State of plastic equilibrium is reached initially at the footing edge and
spreads gradually downwards and outwards.
The following are some characteristics of general shear failure.
(Dense and stiff soils)

1. A significant compression of soil below the footing and partial
development of plastic equilibrium is observed.
2. Failure is not sudden and there is no tilting of footing.
3. Failure surface does not reach the ground surface and slight
bulging of soil around the footing is observed.
4. Failure surface is not well defined.
5. Failure is characterized by considerable settlement.
6. Well defined peak is absent in P – Δ curve
This type of failure is seen in relatively loose and soft soil.
The following are some characteristics of local shear failure

This type of failure is seen in loose and soft soil and at deeper
elevations.
The following are some characteristics of Punching shear failure.
1. This type of failure occurs in a soil of very high compressibility.
2. Failure pattern is not observed.
3. Bulging of soil around the footing is absent.
4. Failure is characterized by very large settlement.
5. Continuous settlement with no increase in P is observed in P – Δ
curve.

4.2 Bearing capacity theories
4.2.1 Rankine’s

Terzaghi’s bearing Capacity Theory
Terzaghi (1943) was the first to propose a comprehensive theory for evaluating
the safe bearing capacity of shallow foundation with rough base. This theory states that a
foundation is shallow if its depth is less than or equal to its width.
Assumptions
1. Soil is homogeneous and Isotropic.
2. The shear strength of soil is represented by Mohr Coulombs Criteria.
3. The footing is of strip footing type with rough base. It is essentially a two
dimensional plane strain problem.
4. Elastic zone has straight boundaries inclined at an angle equal to Φ to the
horizontal.
5. Failure zone is not extended above, beyond the base of the footing. Shear
resistance of soil above the base of footing is neglected.
6. Effect of water table is neglected.
7. Footing carries concentric and vertical loads.
8. Footing and ground are horizontal.
9.The properties of foundation soil do not change during the shear failure

Terzhagi (1943) improved the Prandtl equation to include the
roughness of the footing and the weight of the failure zone. The failure
mechanism in a c’-φ’ soil for Terzhagi’s ultimate bearing capacity
equations are given as follows:
where Nc, Nq and Nγ are called the bearing capacity factors and are
obtained as follows:

Figure: Terzhagi’s bearing capacity coefficients.
Based on this figure, Aysen (2002) proposed the following equation to obtain
the value of Kpγ in the Nγ equation:
where φ' in the first term is in radians. In the undrained conditions (cu and φu = 0):

 Meyerhof’s General Bearing Capacity equation
Meyerhof (1951) developed a bearing capacity equation by extending Terzhagi’s
failure mechanism and taking into account the effects of footing shape, load
inclination and footing depth by adding the corresponding factors of s, d, and i.
For a rectangular footing of L by B (L > B) and inclined load:
qu = c'Nc sc ic dc + γDNq sq iq dq + 0.5γBNγ sγ iγ dγ
For vertical load, ic = iq = iγ = 1
qu = c'Nc sc dc + γDNq sqdq + 0.5γBNγ sγ dγ
*For the eccentric load, the length and width of the
footing rectangle are modified to:
L’ = L – 2eL and B’ = B – 2eB
where eL and eB represent the eccentricity along the appropriate
directions.
4.3 General form of Bearing capacity equations
qu = c'Nc + γDNq + 0.5γBNγ

The bearing capacity factors are graphically
Figure: Meyerhof’s bearing capacity coefficients.
5.14

 Hansen’s General Bearing Capacity Equation
Hansen (1961) extended Meyerhof’s solutions by considering the effects of
sloping ground surface and tilted base, as well as modification of Nγ and other
factors.
For a rectangular footing of L by B (L > B) and inclined ground surface,
base and load:
This equation is sometimes referred to as the
general bearing capacity equation.
In these special case of a horizontal ground surface
where the suffix i stands for B or L. 2 ≤ α1 ≤5. 2 ≤ α2 ≤5. A is the area of the footing base and cb is the cohesion mobilized in
the footing-soil contact area.
For the tilted base:

Figure: Hansen’s bearing capacity coefficients.
The bearing capacity factors Nc and Nq are identical with Meyerhof’s
factors. Nγ is defined by:

Since failure can take place either along the long side or along the short
side, Hansen proposed two sets of shape, inclination and depth factors.
The shape factors are:
For the tilted base:

In the above equations, B and L may be replaced by their effective values (B’
and L’)
For the sloping ground and tilted base, the ground factors gi and base factors
bi are proposed by the following equations. The angles β and η are at the same
plane, either parallel to B or L.

A comparative summary of the three bearing capacity equations
 Terzaghi’s equations were and are still widely used, perhaps because
they are somewhat simpler than Meyerhof’s and Hansen’s.
 Practitioners use Terzaghi’s equations for a very cohesive soil and
D/B < 1.
However, Terzaghi’s equations have the following major drawbacks:
 Shape, depth and inclination factors are not considered.
 Terzaghi’s equations are suitable for a concentrically loaded horizontal
footing but are not suitable for eccentrically (for example, columns with
moment or titled forces) loaded footings that are very common in practice.
 The equations are generally conservative than Meyerhof’s and Hansen’s.
Currently, Meyerhof’s and Hansen’s equations are more widely
used than Terzaghi’s. Both are viewed as somewhat less
conservative and applicable to more general conditions.
Hansen’s is, however, used when the base is tilted or when the
footing is on a slope and for D/B > 1.

Factors influencing Bearing Capacity
Bearing capacity of soil depends on many factors. The following are some
important ones.
1. Type of soil
2. Unit weight of soil
3. Surcharge load
4. Depth of foundation
5. Mode of failure
6. Size of footing
7. Shape of footing
8. Depth of water table
9. Eccentricity in footing load
10.Inclination of footing load
11.Inclination of ground
12.Inclination of base of foundation

Effects of Groundwater Table on Bearing Capacity
For all the bearing capacity equations, you will have to make some
adjustments for the groundwater condition.
The term D in the bearing capacity equations refers
to the vertical stress of the soil above the base of the footing.
The last term B refers to the vertical stress of a soil mass of
thickness B, below the base of the footing.
qu = c'Nc sc ic dc + γDNq sq iq dq + 0.5BγNγ sγ iγ dγ
B
B
D =unit weight of
soil
G.s

We need to check which one of the three groundwater situations is
applicable to your project.
Situation 1:
Groundwater level at a depth B below the base of the footing. In this
case no modification of the bearing capacity equations is required.
B
B
Beyond depth B
qu = c'Nc sc ic dc + γDNq sq iq dq + 0.5BγNγ sγ iγ dγ
No modification of B.C
Figure : Groundwater at a depth B below base

Situation 2:
Groundwater level within a depth B below the base of the footing.
If the groundwater level is at a depth z below the base, such that z < B,
then the term γB is γz +γ '(B - z) or γsat z + γ '(B - z) .
The later equation is used if the soil above the groundwater level
is also saturated. The term γD remains unchanged.
qu = c'Nc sc ic dc + γDNq sq iq dq + 0.5(γz +γ '(B - z)) Nγ sγ iγ dγ OR
qu = c'Nc sc ic dc + γDNq sq iq dq + 0.5(γsat z + γ '(B - z)) Nγ sγ iγ dγ
Figure : Groundwater within a depth B below base

Situation 3:
Groundwater level within the embedment depth. If the groundwater
is at a depth z within the embedment such that z < D, then the term γD
is γz +γ '(D - z) or γ sat z + γ '(D - z) .
Figure: Groundwater within a depth embedment depth.
The latter equation is used if the soil above the groundwater level is
also saturated.
The term γB becomes γ'B .
qu = c'Nc sc ic dc + (γz +γ '(D - z))Nq sq iq dq + 0.5(γ'B)Nγ sγ iγ dγ OR
qu = c'Nc sc ic dc + (γ sat z + γ '(D - z))Nq sq iq dq + 0.5(γ'B)Nγ sγ iγ dγ

Allowable bearing capacity and factor of safety
The allowable bearing capacity, qa is calculated by dividing the
ultimate bearing capacity by a factor, called the factor of safety, FS.
The FS is intended to compensate for assumptions made in developing
the bearing capacity equations, soil variability, inaccurate soil data,
and uncertainties of loads.
The magnitude of FS applied to the ultimate bearing capacity may be
between 2 and 3. The allowable bearing capacity is:
Alternatively, if the maximum applied foundation stress (σa )max is
known and the dimension of the footing is also known then you
can find a factor of safety by replacingqa by (σa )max

Eccentric Loads
Meyerhof (1963) proposed an approximate method for loads that are
located off-centered (or eccentric loads).

Since the tensile strength of soils is approximately zero, σmin should
always be greater than zero. Therefore, eB& eL should always be less
than B/6 & L/6, respectively.
The bearing capacity equations are modified for eccentric loads by
replacing B with B’.

Field Tests
Often, it is difficult to obtain undisturbed samples of especially
coarse-grained soils for laboratory testing and one has to use results
from field tests to determine the bearing capacity of shallow
foundations.
 Some of the most common methods used for
field tests are
1. Plate Loading Test
Tests on full sized footings are desirable but expensive. The
alternative is to carry out plate loading tests. The plate loading test
is carried out to estimate the bearing capacity of single footings.
The plates that are used in the field are usually made of steel and
are 25 mm thick and 150 mm to 762 mm in diameter. A circular
plate of 300 mm is commonly used in practice. Occasionally,
square plates that are 300 mm× 300 mm are also used.

 To conduct a plate load test, a hole is excavated with a minimum
diameter 4BP (BP = diameter of the test plate) to a depth of D (D =
depth of the proposed foundation).
 Each load increment is held until settlement ceases. The final
settlement at the end of each loading increment is recorded. The
test should be conducted until the soil fails, or at least until the
plate has gone through 25 mm of settlement.
 The plate is placed at the center of the hole. Load is applied to
the plate in increments of 10% to 20% of the estimated
ultimate load.

A. For tests in clay,
where qu(F) & qu(P) are ultimate bearing capacity of foundation and plate,
respectively. The above eqn. implies that the bearing capacity in clays is
independent of plate size.
B. For tests in sandy soil,
where BF and BP stand for width of
foundation and plate, respectively.
There are several problems associated with the plate load test.
 The test is reliable if the soil layer is thick and homogeneous.
 Local conditions such as a pocket of weak soil near the surface of plate can affect the test
results but these may have no significant effect on the real footing.
 The correlation between plate load results and real footing is problematic.
 and performance of the test is generally difficult.

2. Standard Penetration Test (SPT)
 The Standard Penetration Test (SPT) is used to determine the
allowable bearing capacity of cohesionless coarse-grained soils
such as sands.
 The N values obtained from SPT are usually corrected for various
effects such as overburden pressure and energy transfer.
 The following are two of the most commonly used methods in practice
for correcting the N values.
where CN is a correction factor for overburden pressure, and
σz'0 is the effective overburden pressure in kPa.

A further correction factor is imposed on N values if the groundwater level
is within a depth B below the base of the footing.
The groundwater correction factor is:
where z is the depth to the groundwater table,
and D and B are the footing depth and width. If
the depth of the groundwater table is beyond B
from the footing base cW =1.
The corrected N value is:

Meyerhof (1956-1974) proposed the following equations to
determine the allowable bearing capacity qa from SPT values.
where Se is the elastic settlement of the layer in mm and kd = 1 + 0.33D/B ≤ 1.33.
In practice, each value of N is a soil layer up to a depth B below the footing base is
corrected and an average value of Ncor is used
Bowles (1996) modified Meyerhof’s equations by 50% increase
in the allowable bearing capacity. Bowles’s equations are:

 Field Tests are performed in the field. You have understood the advantages of field tests
over laboratory tests for obtaining the desired property of soil.
 The biggest advantages are that there is no need to extract soil sample and the
conditions during testing are identical to the actual situation.
 Major advantages of field tests are
 Sampling not required
 Soil disturbance minimum
•
 Major disadvantages of field tests are
 Labourious
 Time consuming
 Heavy equipment to be carried to field
 Short duration behavior

Eurocode Bearing Capacity Analysis Equations – Drained Conditions
The Eurocode method for drained conditions includes the following equations
Eurocode 7 Bearing Capacity

A’ is the effective plan area of the foundation
B’ is the effective foundation width
L’ is the effective foundation length
D is the embedment depth
q’ is the desive effective overburden pressure at the foundation base
V is the total vertical load acting on the foundation
α is the inclination of the foundation base relative to the horizontal
γ’ is the design effective unit weight of the soil
c’ is the effective cohesion
where;

Eurocode 7 Bearing Capacity Analysis Equations – Undrained
Conditions
The Eurocode 7 bearing capacity method for undrained conditions
includes the following equations where;
cu is the undrained shear strength

Thank you

Chapter 4. Bearing Capacity of Soil.pdf

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