Bearing Capacity.pptx

7/24/2022 ENGR. ZIA UR RAHMAN 1
BEARING CAPACITY

Bearing capacity Failure and its types
When the bearing pressure of the footing is large enough and the size of the footing is
smaller than the stresses may exceed the shear strength of the soil resulting in the failure
of the soil beneath the foundation called bearing capacity failure/Shear failure.
There are three modes of shear failure described below.
(1) General Shear Failure
It occurs in soil which are comparatively stronger such as stiff clay and dense sand
(Dr>70%). In this type of failure large settlements occur with plastic yielding fully
developed within the soil.

Characteristics of general shear failure are as given below.
i. Well defined failure mechanism
ii. Continuous slip surface from the bottom of the footing to the ground surface.
iii. Sudden catastrophic failure

(2) Local shear Failure
Local shear failure is an intermediate case. The failure surface is well defined
under the foundation but becomes vague near the ground surface. It takes place in
medium sands and clay.
Considerable vertical displacement takes place.
Lower ultimate bearing capacity is observed in such case.

(3) Punching Shear
When the soil is loose one with less compressibility than this type of failure is
likely to occur with the following characteristics.
i. Less well defined failure mechanism.
ii. Large vertical displacements.
iii.Lower ultimate bearing capacity

Key terms and its definitions
Ultimate Bearing capacity (qu)
It is the maximum bearing pressure that the soil can sustain.
Ultimate net Bearing Capacity (qunet)
It is the maximum bearing pressure that the soil can sustain above its current
overburden pressure.
qunet = qu - ɣD
Allowable Bearing Capacity (qall)
The working pressure that would ensure an acceptable margin of safety against
the bearing capacity failure is known as allowable bearing capacity.
qall = qu/FOS

Ultimate Limit State
A state that defines a limit for the shear stress that may not be exceeded by any
conceivable or anticipated loading condition during the life span of the
foundation or geotechnical system.
Serviceability Limit State
It defines the limiting deformation/settlement, if exceeded will impair the
function of the supported structure.
Key terms and its definitions

Terzaghi’s Bearing Capacity Theory

Terzaghi made some assumptions for his analysis which are listed as following
•Soil is is isotropic.
•Soil is homogenous.
•Soil is weightless.
•Soil is rigid plastic material.
•A successful model to predict general shear failure of foundations on medium to
dense sands might be to assume a trapped rigid wedge beneath the footing,
bordering radial shear zone and rankine passive zone.
Terzaghi’s Bearing Capacity Theory

Bearing Capacity Formulas
Terzaghi (1943)
•Terzaghi assumed that this is a strip footing for which L/B>10.
•He assumed general shear failure below the base of the footing and ignored the strength
of the soil lying above the base of the footing.

Terzaghi’s Bearing Capacity Formula
• The soil above the base of the footing may be replaced by a surcharge ɣD.
•The base of the footing is rough.
•The angle θ was taken as φ later on proved as 45+ φ/2.
Based upon effective stress analysis and taking the foundation to be strip footing
terzaghi derived the following formula for finding ultimate bearing capacity (qu).
qu = cNc+qNq+0.5ɣBNɣ
Where Nc, Nq and Nɣ are bearing capacity factors which are the functions of φ
C is the cohesion of the soil and q is the effective overburden pressure of the
surcharge.
B is the width of the foundation.

When the footing is a square footing then the formula will be
qu = 1.3cNc+qNq+0.4ɣBNɣ
While considering a circular footing it will become
qu =1.3 cNc+qNq+0.3ɣBNɣ
If the mode of failure is local shear than the following changes will be
incorporated in the values of c and φ.
͞c =2/3c and tan ͞φ = tan2/3φ
Where ͞c and φ are the shear strength parameters in case of local shear failure.

In case of Total Stress Analysis (TSA) when the loading is rapidly applied so
that the un-drained condition sustains.
Φ=0 =» From table 3.1 in slide. 16 Nɣ =0 and Nq = 1 while Nc = 5.14
qu = 5.14cNc + q
qu – q = 5.14cu
qunet = 5.14cu
In case of local shear failure
qunet = 5.14(2/3)cu
qunet = 3.42cu

Modified Bearing Capacity Equation
Use table 3.3 for the values of Nc
Nq and Ny

Shape Factors

Depth Factors

Inclination Factors

Effect of water table on Bearing capacity
There are three possible cases
(1) Water table lies between the ground surface
and the base of the footing.
q = ɣdw + ɣ´(D – dw)
Where ɣ´ = ɣsat - ɣ
(2) Water table coincides with the base of the
footing.
q = ɣD and ɣ in the third term of the bearing
capacity equation will be replaced by ɣ´

Effect of water Table on Bearing Capacity
(3) Water table lies below the Base of the footing.
There are two sub cases
(a) dw< B in this case q will remain as it is but ɣ in third term will
become
Ɣavg = ɣdw + ɣ´(B-dw)
(b) dw>B In this case no change is required to be incorporated in the
original equation.

Problem and Solution

Fy = 1
q = (0.61)(16.5)+0.61(18.55 – 9.81) = 15.4 KN/m3

Assignment

Try to Practice problems (3.1 to 3.10)
given in Braja. M. Das book

Bearing Capacity.pptx

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