SEMBODAI RUKMANI VARATHARAJAN
ENGINEERING COLLEGE
DEPARTMENT OF CIVIL ENGINEERING
SHALLOW FOUNDATION
BY
KARTHIVELU
Basic Definitions
Footing: Part of foundation that transmit the
load directly to soil.
Foundation : Part of structure which is in direct
contact with & transmit load to ground.
Foundation soil: Upper part of earth mass that
carrying the load of the structure.
Basic Definitions
Foundation
Footing
Foundation
soil
Bearing Pressure intensity
capacity
Ultimate BC
Safe BC
Gross
Total pressure at
base of footing due
to wt of super strct,
self wt of
foundation & earth
fill (q)
The minimum
q at which soil
fails by shear
(qf)
Maximum
pressure, soil can
carry without risk
of shear failure
qs= qns+ YD
Net
pressure at base of
footing due to wt of
super strct, self wt
of foundation
qn = q - YD
The minimum
qn at which soil
fails by shear
qns = qnf / F
(qnf) = qf - YD
* 𝜎 = YD → 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑢𝑟𝑐ℎ𝑎𝑟𝑔𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑎𝑠𝑒 𝑙𝑒𝑣𝑒𝑙
Allowable bearing capacity qa:
The net loading intensity at which the soil fails
neither by shear nor by settlement
Modes of shear Failure
Vesic (1973) classified shear failure of soil
under a foundation base into three categories
depending on the type of soil & location of
foundation.
1) General Shear failure.
2) Local Shear failure.
3) Punching Shear failure
Modes Of Shear Failure
General shear
failure
Local shear
failure
Punching shear
failure
FAILURE
SURFACE
Well defined,
Clearly defined
No failure pattern is
reaching upto ground only immediately observed. Vertical &
surface
below the footing follows the pattern of
base
BULGING
more
slight
FAILURE
Sudden &
accomplished with
tilting of footing
Not sudden & no Only very large
tilting. Only large settlement
settlement
ULTIMATE
BEARING
CAPACITY
Well defined
Not well defined
Not well defined
RELATIVE
DENSITY
OF SOIL
high
35% to 75 %
< 35%
EX
In Very dense sand in In High
In soft clay
shallow footing
compressible soil
nil
Terzaghi’s Bearing Capacity Analysis
Terzaghi (1943) analysed a shallow continuous footing by
making some assumptions.
Plastic Zones Of Failure
• Zone-I :Immediately beneath the footing. Does
not undergo any lateral yield by friction &
adhesion & hence act as part of foundation.
Line db& da are straight &anggle isØ.
• Zone-II : (zone of radial shear) One set of
shear pattern radiates from outer edge of base
of footing. Another set- lograthamic spiral with
center at outer edge of base of footing
• Zone-III : (zone of linear shear) The
∅
o
boundaries rise at 45 2
 The failure zones do not extend above the
horizontal plane passing through base of footing
 The equilibrium occurs when the down ward
pressure exerted by loads on the soil adjoining the
inclined surfaces on soil wedge is equal to upward
pressure.
 Downward forces are due to the load (=qu× B) &
the weight of soil wedge (1/4 γB2 tanØ)
 Upward forces are the vertical components of
resultant passive pressure (Pp) & the cohesion (c’)
acting along the inclined surfaces.
• For equilibrium:
ΣFv = 0
𝟏
γ B2tan ø + quB= 2Pp +2CLi sinø
𝟒
where Li = length of inclined surface CB
( = B/2 /cosø)
quB= 2Pp + BCtanø- ¼ γ B2tanø –------ (1)
The resultant passive pressure (Pp) on the surface
CB & CA constitutes three components ie. (Pp)r,
(Pp)c& (Pp) q,
Thus,
Pp = (Pp)r + (Pp)c + (Pp)q
quB= 2[ (Pp)r +(Pp)c +(Pp)q ]+ BCtanø-¼ γ B2 tanø
Substituting; 2 (Pp)r - ¼rB2tanø
= B × ½ γ BNr
2 (Pp)q
= B × γ D Nq
& 2 (Pp)c + BC tanø
= B × C Nc;
We get,
qu =CNc + γ D Nq + 0.5 γ B N γ
This is Terzaghi’s Bearing capacity equation for
determining ultimate bearing capacity of strip
footing. Where Nc, Nq & Nr are Terzaghi’s bearing
capacity factors & depends on angle of shearing
resistance (ø)
ø
General Shear Failure
Local Shear Failure
Nc
Nq
Nr
Nc’
Nq’
Nr’
0
5.7
1.0
0.0
5.7
1.0
0.0
15
12.9
4.4
2.5
9.7
2.7
0.9
45
172.3
173.3
297.5
51.2
35.1
37.7
ASSUMPTIONS
1. soil is homogeneous, isotropic & its shear strength is
represented by Coulomb’s equation.
2. Strip footing has a rough base, & the problem is two
dimensional.
3. The elastic zone has straight boundaries inclined at ø to
horizontal & plastic zone is fully developed.
4. Pp has 3 components which can be computed and added
separately.
5. The failure zones do not extend above the horizontal
plane passing through base of footing
LIMITATIONS
As soil compresses, Ø changes
Slight downward movement of footing does
not develop fully plastic zones
Error due to assumption 4 is small
Error due to assumption 5 increases with depth
of foundation. Hence suitable for shallow
foundation.
Important points :
* Terzaghi’s Bearing Capacity equation is applicable
for general shear failure.
* Terzaghi has suggested following empirical
reduction to
actual c & ø in case of local shear failure
Mobilised cohesion Cm = 2/3 C
Mobilised angle of øm = tan –1 (⅔tanø)
Thus, Nc’,Nq’ & Nr’ are B.C. factors for local shear
failure
qu = CmNc’+ γ D Nq’+ 0.5 γ B Nr’
Ultimate Bearing Capacity for square & Circular footing
-Based on the experimental results, Terzaghi’s suggested
following equations for UBC –
 Circular footing qu = 1.3 C Nc + γ D Nq + 0.3 γBNr
 Square footing qu = 1.3 C Nc + γ D Nq + 0.4 γ BNr
 Rectgrfootingqu = 1+
𝑩
0.3
𝑳
C Nc+ γ D Nq + 0.4 γ BNr