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 Page 1


 PRESSURE ISOBARS
Definition
An isobar  i s a  lin e whic h connect s al l point s o f equa l stres s belo w th e groun d surface . I n othe r
words, a n isoba r i s a  stres s contour . W e ma y dra w an y numbe r o f isobar s a s show n i n Fig . 6.1 9 fo r
any give n loa d system . Eac h isoba r represent s a  fractio n o f th e loa d applie d a t th e surface . Sinc e
these isobar s for m close d figure s an d resembl e th e for m o f a  bulb , the y ar e als o terme d bulb  o f
pressure o r simpl y th e pressure bulb.  Normall y isobars  ar e draw n fo r vertical , horizonta l an d shea r
stresses. Th e on e tha t i s mos t importan t i n th e calculatio n o f settlement s o f footing s i s th e vertica l
pressure isobar .
Page 2


 PRESSURE ISOBARS
Definition
An isobar  i s a  lin e whic h connect s al l point s o f equa l stres s belo w th e groun d surface . I n othe r
words, a n isoba r i s a  stres s contour . W e ma y dra w an y numbe r o f isobar s a s show n i n Fig . 6.1 9 fo r
any give n loa d system . Eac h isoba r represent s a  fractio n o f th e loa d applie d a t th e surface . Sinc e
these isobar s for m close d figure s an d resembl e th e for m o f a  bulb , the y ar e als o terme d bulb  o f
pressure o r simpl y th e pressure bulb.  Normall y isobars  ar e draw n fo r vertical , horizonta l an d shea r
stresses. Th e on e tha t i s mos t importan t i n th e calculatio n o f settlement s o f footing s i s th e vertica l
pressure isobar .
Lines o f
equal vertica l
pressure o r
isobars
Figure 6.19 Bulb of pressure
Significant Depth
In hi s openin g discussio n o n
settlement o f structure s a t th e
First Internationa l Conferenc e
on Soi l Mechanic s an d
Foundation Engineerin g (hel d i n
1936 a t Harvar d Universit y i n
Cambridge, Mass , USA) ,
Terzaghi stresse d th e
importance o f th e bul b o f
pressure an d it s relationshi p
with th e sea t o f settlement . A s
stated earlie r w e ma y dra w an y
number o f isobar s fo r an y give n
load system , bu t th e on e tha t i s
of practica l significanc e i s th e
one whic h enclose s a  soi l mas s whic h i s responsibl e fo r th e settlemen t o f th e structure . Th e dept h o f
this stresse d zon e ma y b e terme d a s th e significant depth  D
S
 whic h i s responsibl e fo r th e settlemen t
of th e structure . Terzagh i recommende d tha t fo r al l practica l purpose s on e ca n tak e a  stress  contour
which represent s 2 0 pe r cen t o f th e foundatio n contac t pressur e q , i.e , equa l t o Q.2q.  Th e dept h o f
such a n isoba r ca n b e take n a s th e significant depth  D
s
 whic h represent s th e sea t o f settlemen t fo r
the foundation . Terzaghi' s recommendatio n wa s base d o n hi s observatio n tha t direc t stresse s ar e
considered o f negligibl e magnitud e whe n the y ar e smalle r tha n 2 0 pe r cen t o f th e intensit y o f th e
applied stres s fro m structura l loading , an d tha t mos t o f th e settlement , approximatel y 8 0 pe r cen t o f
the total , take s plac e a t a  dept h les s tha n D
s
. Th e dept h D
s
 i s approximatel y equa l t o 1. 5 time s th e
width o f squar e o r circula r footing s [Fig . 6.20(a)] .
If severa l loade d footing s ar e space d closel y enough , th e individua l isobar s o f eac h footin g
in questio n woul d combin e an d merg e int o on e larg e isoba r o f the_intensit y a s show n i n
[Fig. 6.20(b)] . Th e combine d significan t dept h D  i s equa l t o abou t 1. 5 B .
a
z
 =  Q.2q
D<=\.5B\ Stresse d zon e
Isobar
(a) Significan t dept h o f stresse d zon e
for singl e footin g
Isobar
Combined stresse d zon e
(b) Effec t o f closel y place d footing s
Page 3


 PRESSURE ISOBARS
Definition
An isobar  i s a  lin e whic h connect s al l point s o f equa l stres s belo w th e groun d surface . I n othe r
words, a n isoba r i s a  stres s contour . W e ma y dra w an y numbe r o f isobar s a s show n i n Fig . 6.1 9 fo r
any give n loa d system . Eac h isoba r represent s a  fractio n o f th e loa d applie d a t th e surface . Sinc e
these isobar s for m close d figure s an d resembl e th e for m o f a  bulb , the y ar e als o terme d bulb  o f
pressure o r simpl y th e pressure bulb.  Normall y isobars  ar e draw n fo r vertical , horizonta l an d shea r
stresses. Th e on e tha t i s mos t importan t i n th e calculatio n o f settlement s o f footing s i s th e vertica l
pressure isobar .
Lines o f
equal vertica l
pressure o r
isobars
Figure 6.19 Bulb of pressure
Significant Depth
In hi s openin g discussio n o n
settlement o f structure s a t th e
First Internationa l Conferenc e
on Soi l Mechanic s an d
Foundation Engineerin g (hel d i n
1936 a t Harvar d Universit y i n
Cambridge, Mass , USA) ,
Terzaghi stresse d th e
importance o f th e bul b o f
pressure an d it s relationshi p
with th e sea t o f settlement . A s
stated earlie r w e ma y dra w an y
number o f isobar s fo r an y give n
load system , bu t th e on e tha t i s
of practica l significanc e i s th e
one whic h enclose s a  soi l mas s whic h i s responsibl e fo r th e settlemen t o f th e structure . Th e dept h o f
this stresse d zon e ma y b e terme d a s th e significant depth  D
S
 whic h i s responsibl e fo r th e settlemen t
of th e structure . Terzagh i recommende d tha t fo r al l practica l purpose s on e ca n tak e a  stress  contour
which represent s 2 0 pe r cen t o f th e foundatio n contac t pressur e q , i.e , equa l t o Q.2q.  Th e dept h o f
such a n isoba r ca n b e take n a s th e significant depth  D
s
 whic h represent s th e sea t o f settlemen t fo r
the foundation . Terzaghi' s recommendatio n wa s base d o n hi s observatio n tha t direc t stresse s ar e
considered o f negligibl e magnitud e whe n the y ar e smalle r tha n 2 0 pe r cen t o f th e intensit y o f th e
applied stres s fro m structura l loading , an d tha t mos t o f th e settlement , approximatel y 8 0 pe r cen t o f
the total , take s plac e a t a  dept h les s tha n D
s
. Th e dept h D
s
 i s approximatel y equa l t o 1. 5 time s th e
width o f squar e o r circula r footing s [Fig . 6.20(a)] .
If severa l loade d footing s ar e space d closel y enough , th e individua l isobar s o f eac h footin g
in questio n woul d combin e an d merg e int o on e larg e isoba r o f the_intensit y a s show n i n
[Fig. 6.20(b)] . Th e combine d significan t dept h D  i s equa l t o abou t 1. 5 B .
a
z
 =  Q.2q
D<=\.5B\ Stresse d zon e
Isobar
(a) Significan t dept h o f stresse d zon e
for singl e footin g
Isobar
Combined stresse d zon e
(b) Effec t o f closel y place d footing s
Pressure Isobars for Footings
Pressure isobar s o f square , rectangula r an d circula r footing s ma y convenientl y b e use d fo r
determining vertica l pressure , (J
z
, a t an y depth , z , belo w th e bas e o f th e footings . Th e depth s z  fro m
the groun d surface , an d th e distanc e r  (o r jc ) fro m th e cente r o f th e footin g ar e expresse d a s a
function o f th e widt h o f th e footin g B . I n th e cas e o f circula r footin g B  represent s th e diameter .
The followin g pressur e isobar s ar e give n base d o n eithe r Boussines q o r Westergaard' s
equations
1. Boussines q isobar s fo r squar e an d continuou s footings , Fig . 6.21 .
2. Boussines q isoba r fo r circula r footings , Fig . 6.22 .
3. Westergaar d isobar s fo r squar e an d continuou s footings , Fig . 6.23 .
B/2=b BI2=b
Continuous
25
Figure 6.21 Pressure isobars based on Boussinesq equation for square and
continuous footings
Page 4


 PRESSURE ISOBARS
Definition
An isobar  i s a  lin e whic h connect s al l point s o f equa l stres s belo w th e groun d surface . I n othe r
words, a n isoba r i s a  stres s contour . W e ma y dra w an y numbe r o f isobar s a s show n i n Fig . 6.1 9 fo r
any give n loa d system . Eac h isoba r represent s a  fractio n o f th e loa d applie d a t th e surface . Sinc e
these isobar s for m close d figure s an d resembl e th e for m o f a  bulb , the y ar e als o terme d bulb  o f
pressure o r simpl y th e pressure bulb.  Normall y isobars  ar e draw n fo r vertical , horizonta l an d shea r
stresses. Th e on e tha t i s mos t importan t i n th e calculatio n o f settlement s o f footing s i s th e vertica l
pressure isobar .
Lines o f
equal vertica l
pressure o r
isobars
Figure 6.19 Bulb of pressure
Significant Depth
In hi s openin g discussio n o n
settlement o f structure s a t th e
First Internationa l Conferenc e
on Soi l Mechanic s an d
Foundation Engineerin g (hel d i n
1936 a t Harvar d Universit y i n
Cambridge, Mass , USA) ,
Terzaghi stresse d th e
importance o f th e bul b o f
pressure an d it s relationshi p
with th e sea t o f settlement . A s
stated earlie r w e ma y dra w an y
number o f isobar s fo r an y give n
load system , bu t th e on e tha t i s
of practica l significanc e i s th e
one whic h enclose s a  soi l mas s whic h i s responsibl e fo r th e settlemen t o f th e structure . Th e dept h o f
this stresse d zon e ma y b e terme d a s th e significant depth  D
S
 whic h i s responsibl e fo r th e settlemen t
of th e structure . Terzagh i recommende d tha t fo r al l practica l purpose s on e ca n tak e a  stress  contour
which represent s 2 0 pe r cen t o f th e foundatio n contac t pressur e q , i.e , equa l t o Q.2q.  Th e dept h o f
such a n isoba r ca n b e take n a s th e significant depth  D
s
 whic h represent s th e sea t o f settlemen t fo r
the foundation . Terzaghi' s recommendatio n wa s base d o n hi s observatio n tha t direc t stresse s ar e
considered o f negligibl e magnitud e whe n the y ar e smalle r tha n 2 0 pe r cen t o f th e intensit y o f th e
applied stres s fro m structura l loading , an d tha t mos t o f th e settlement , approximatel y 8 0 pe r cen t o f
the total , take s plac e a t a  dept h les s tha n D
s
. Th e dept h D
s
 i s approximatel y equa l t o 1. 5 time s th e
width o f squar e o r circula r footing s [Fig . 6.20(a)] .
If severa l loade d footing s ar e space d closel y enough , th e individua l isobar s o f eac h footin g
in questio n woul d combin e an d merg e int o on e larg e isoba r o f the_intensit y a s show n i n
[Fig. 6.20(b)] . Th e combine d significan t dept h D  i s equa l t o abou t 1. 5 B .
a
z
 =  Q.2q
D<=\.5B\ Stresse d zon e
Isobar
(a) Significan t dept h o f stresse d zon e
for singl e footin g
Isobar
Combined stresse d zon e
(b) Effec t o f closel y place d footing s
Pressure Isobars for Footings
Pressure isobar s o f square , rectangula r an d circula r footing s ma y convenientl y b e use d fo r
determining vertica l pressure , (J
z
, a t an y depth , z , belo w th e bas e o f th e footings . Th e depth s z  fro m
the groun d surface , an d th e distanc e r  (o r jc ) fro m th e cente r o f th e footin g ar e expresse d a s a
function o f th e widt h o f th e footin g B . I n th e cas e o f circula r footin g B  represent s th e diameter .
The followin g pressur e isobar s ar e give n base d o n eithe r Boussines q o r Westergaard' s
equations
1. Boussines q isobar s fo r squar e an d continuou s footings , Fig . 6.21 .
2. Boussines q isoba r fo r circula r footings , Fig . 6.22 .
3. Westergaar d isobar s fo r squar e an d continuou s footings , Fig . 6.23 .
B/2=b BI2=b
Continuous
25
Figure 6.21 Pressure isobars based on Boussinesq equation for square and
continuous footings
Figure 6.22 Pressure isobars based on Boussinesq equation for uniformly loaded
circular footings
B/2=b B/2=b
5b
6b
Continuous
IB 2 B 3 5
Figure 6.23 Pressure isobars based on Westergaard equation for square and
continuous footing
Page 5


 PRESSURE ISOBARS
Definition
An isobar  i s a  lin e whic h connect s al l point s o f equa l stres s belo w th e groun d surface . I n othe r
words, a n isoba r i s a  stres s contour . W e ma y dra w an y numbe r o f isobar s a s show n i n Fig . 6.1 9 fo r
any give n loa d system . Eac h isoba r represent s a  fractio n o f th e loa d applie d a t th e surface . Sinc e
these isobar s for m close d figure s an d resembl e th e for m o f a  bulb , the y ar e als o terme d bulb  o f
pressure o r simpl y th e pressure bulb.  Normall y isobars  ar e draw n fo r vertical , horizonta l an d shea r
stresses. Th e on e tha t i s mos t importan t i n th e calculatio n o f settlement s o f footing s i s th e vertica l
pressure isobar .
Lines o f
equal vertica l
pressure o r
isobars
Figure 6.19 Bulb of pressure
Significant Depth
In hi s openin g discussio n o n
settlement o f structure s a t th e
First Internationa l Conferenc e
on Soi l Mechanic s an d
Foundation Engineerin g (hel d i n
1936 a t Harvar d Universit y i n
Cambridge, Mass , USA) ,
Terzaghi stresse d th e
importance o f th e bul b o f
pressure an d it s relationshi p
with th e sea t o f settlement . A s
stated earlie r w e ma y dra w an y
number o f isobar s fo r an y give n
load system , bu t th e on e tha t i s
of practica l significanc e i s th e
one whic h enclose s a  soi l mas s whic h i s responsibl e fo r th e settlemen t o f th e structure . Th e dept h o f
this stresse d zon e ma y b e terme d a s th e significant depth  D
S
 whic h i s responsibl e fo r th e settlemen t
of th e structure . Terzagh i recommende d tha t fo r al l practica l purpose s on e ca n tak e a  stress  contour
which represent s 2 0 pe r cen t o f th e foundatio n contac t pressur e q , i.e , equa l t o Q.2q.  Th e dept h o f
such a n isoba r ca n b e take n a s th e significant depth  D
s
 whic h represent s th e sea t o f settlemen t fo r
the foundation . Terzaghi' s recommendatio n wa s base d o n hi s observatio n tha t direc t stresse s ar e
considered o f negligibl e magnitud e whe n the y ar e smalle r tha n 2 0 pe r cen t o f th e intensit y o f th e
applied stres s fro m structura l loading , an d tha t mos t o f th e settlement , approximatel y 8 0 pe r cen t o f
the total , take s plac e a t a  dept h les s tha n D
s
. Th e dept h D
s
 i s approximatel y equa l t o 1. 5 time s th e
width o f squar e o r circula r footing s [Fig . 6.20(a)] .
If severa l loade d footing s ar e space d closel y enough , th e individua l isobar s o f eac h footin g
in questio n woul d combin e an d merg e int o on e larg e isoba r o f the_intensit y a s show n i n
[Fig. 6.20(b)] . Th e combine d significan t dept h D  i s equa l t o abou t 1. 5 B .
a
z
 =  Q.2q
D<=\.5B\ Stresse d zon e
Isobar
(a) Significan t dept h o f stresse d zon e
for singl e footin g
Isobar
Combined stresse d zon e
(b) Effec t o f closel y place d footing s
Pressure Isobars for Footings
Pressure isobar s o f square , rectangula r an d circula r footing s ma y convenientl y b e use d fo r
determining vertica l pressure , (J
z
, a t an y depth , z , belo w th e bas e o f th e footings . Th e depth s z  fro m
the groun d surface , an d th e distanc e r  (o r jc ) fro m th e cente r o f th e footin g ar e expresse d a s a
function o f th e widt h o f th e footin g B . I n th e cas e o f circula r footin g B  represent s th e diameter .
The followin g pressur e isobar s ar e give n base d o n eithe r Boussines q o r Westergaard' s
equations
1. Boussines q isobar s fo r squar e an d continuou s footings , Fig . 6.21 .
2. Boussines q isoba r fo r circula r footings , Fig . 6.22 .
3. Westergaar d isobar s fo r squar e an d continuou s footings , Fig . 6.23 .
B/2=b BI2=b
Continuous
25
Figure 6.21 Pressure isobars based on Boussinesq equation for square and
continuous footings
Figure 6.22 Pressure isobars based on Boussinesq equation for uniformly loaded
circular footings
B/2=b B/2=b
5b
6b
Continuous
IB 2 B 3 5
Figure 6.23 Pressure isobars based on Westergaard equation for square and
continuous footing
Example 6.12
A singl e concentrate d loa d o f 100 0 k N act s a t th e groun d surface . Construc t a n isoba r fo r
<7 =  4 0 kN/m
2
 b y makin g us e o f th e Boussines q equation .
Solution
From Eq . (6.la ) w e hav e
3(2
1
We ma y no w writ e b y rearrangin g a n equatio n fo r th e radia l distanc e r  a s
 1
Now fo r Q  =  100 0 kN , cr , =  4 0 kN/m
2
, w e obtai n th e value s o f r
p
 r
2
, r
y
 etc . fo r differen t
depths z, , z
2
, z
v
 etc . Th e value s s o obtaine d ar e
z(m)
0.25
0.50
1.0
2.0
3.0
3.455
r(m)
1.34
1.36
1.30
1.04
0.60
0.00
g=1000kN
a, =  4 0 kN/m
J
Isobar
3.455
Figure Ex. 6.12

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Document Description: Pressure Bulbs for Civil Engineering (CE) 2024 is part of Foundation Engineering preparation. The notes and questions for Pressure Bulbs have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Pressure Bulbs covers topics like and Pressure Bulbs Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Pressure Bulbs.

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