Transcript CE-632 Geotechnical Engineering

CE-632
Foundation Analysis and
Design
Settlement of Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Settlement
Settlement
S = S e + S c + Ss
Immediate
Settlement
Se
Primary
Consolidation
Sc
Secondary
Consolidation
Ss

Immediate Settlement: Occurs immediately after the construction.
This is computed using elasticity theory (Important for Granular soil)

Primary Consolidation: Due to gradual dissipation of pore pressure
induced by external loading and consequently expulsion of water from
the soil mass, hence volume change. (Important for Inorganic clays)

Secondary Consolidation: Occurs at constant effective stress with
volume change due to rearrangement of particles. (Important for
Organic soils)
For any of the above mentioned settlement calculations, we first need vertical
stress increase in soil mass due to net load applied on the foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Elasticity
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Foundation Analysis and Design: Dr. Amit Prashant
Stress Distribution: Concentrated load
Boussinesq Analysis
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Foundation Analysis and Design: Dr. Amit Prashant
Stress Distribution: Concentrated load
Boussinesq Analysis
Where,
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Concentrated load
0.5
0.4
IB
Influence Factor for
General solution of vertical stress
0.3
0.2
P
 z  2 IB
z
0.1
0.0
0.0
0.2
0.4
0.6
0.8
r z
1.0
1.2
1.4
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Uniformly Distributed Circular Load
Uniformly Distributed Circular Load
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Uniformly Distributed Circular Load
Rigid Plate on half Space
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Rectangular Area
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Rectangular Area
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Foundation Analysis and Design: Dr. Amit Prashant
Pressure Bulb
Square Footing
Strip Footing
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Foundation Analysis and Design: Dr. Amit Prashant
Pressure
Bulb for
Square
Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Pressure
Bulb for
Circular
Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Newmark’s Chart
Influence Value
This Model is good for normally-consolidated, lightly
overconsolidated clays, and variable deposits
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Foundation Analysis and Design: Dr. Amit Prashant
Newmark’s Chart
Point of
stress
calculation
Depth = z2





Determine the depth, z, where you
wish to calculate the stress increase
Adopt a scale as shown in the figure
Draw the footing to scale and place
the point of interest over the center
of the chart
Count the number of elements that
fall inside the footing, N
Calculate the stress increase as:
Depth = z1
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Foundation Analysis and Design: Dr. Amit Prashant
Westergaard’s Method



Provided solution for layered soils
Point Loads
Assumption:
Elastic soil mass is laterally reinfrced by numorous,
closely spaced, horizontal sheets of negligible thickness
but infinite rigidity, that allow only vertical movement but
prevent the mass as a whole from undergoing any lateral
strain.

P 
1
z 
 2
2
2
2 z  C   r z  
3
2
C
1  2
2 1  
This Model is specially good for pre-compressed or
overconsolidated clays
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Foundation Analysis and Design: Dr. Amit Prashant
Westergaard’s influence Chart
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Foundation Analysis and Design: Dr. Amit Prashant
Fröhlich Chart with
concentration factor
m‘ = 4
 z  n  0.005.q
This Model is specially good for
Sands
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Foundation Analysis and Design: Dr. Amit Prashant
Simplified Methods (Poulos and Davis, 1974)
Circular Foundation:
2 1.5 
 

B


 )
 z  1  1      (q   zD
   2z   


Square Foundation:
 
 B

 z  1  1  
  2z f
 



2 1.76





 (q    )
zD


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Foundation Analysis and Design: Dr. Amit Prashant
Simplified Methods (Poulos and Davis, 1974)
Strip Foundation:
 
 B

 z  1  1  
  2z f
 



2 2.60





 (q    )
zD


Rectangular Foundation:
 
 B

 z  1  1  
  2z f
 
1.380.62 B / L  2.600.84 B / L








 (q    )
zD


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Foundation Analysis and Design: Dr. Amit Prashant
Approximate
Methods
Rectangular Foundation:
Square/Circular Foundation:
Strip Foundation:
B.L
 z  q
 B  z  . L  z 
B2
 z  q
2
 B  z
B
 z  q
B  z
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Foundation Analysis and Design: Dr. Amit Prashant
Contact Pressure and Settlement distribution
Cohesive Soil - Flexible Footing
Cohesive Soil - Rigid Footing
Granular Soil Flexible Footing
Granular Soil - Rigid Footing
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of Foundation
H
Elastic settlement:
1
Se    z dz 
Es
0
Es 
H
s 
  
H
z
 s  x  s  y  dz
0
Modulus of elasticity
Thickness of soil layer
Poisson’s ratio of soil
Elastic settlement for Flexible Foundation:


qB
Se 
1  s2 I f
Es
If
Es
= influence factor: depends on the rigidity and shape of the foundation
= Avg elasticity modulus of the soil for (4B) depth below foundn level
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of Foundation
E in kPa
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of Foundation
Soil Strata with
Semi-infinite depth
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Foundation Analysis and Design: Dr. Amit Prashant
Steinbrenner’s Influence Factors for Settlement of the Corners of
loaded Area LxB on Compressible Stratus of  = 0.5, and Thickness Ht
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Foundation Analysis and Design: Dr. Amit Prashant
Strain Influence Factor Method for Sandy Soil: Schmertmann
and Hartman (1978)
Iz
Se  C1C2  q   Df   z
0 Es
z2
C1  Correction factor for foundation depth
1  0.5  Df q   Df 


C2  Correction factor for creep effects



1  0.2log  time in years 0.1
q
For square and circular foundation:
For foundation with L/B >10:
Interpolate the values for 1 < L/B < 10
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Foundation Analysis and Design: Dr. Amit Prashant
Example
Se  C1C2  q   Df  
z2
 Df  31.39 kN m2
0
Iz
z
Es
For square and
circular foundations
Es  2.5qc
For rectangular
foundations
Es  3.5qc
Correlation with SPT data:
Es  800N  in kPa
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Foundation Analysis and Design: Dr. Amit Prashant
Burland and Burbidge’s Method for Sandy Soils
Depth of Stress Influence (z'):
If N60'‘ is constant or increasing with depth, then
z  1.04  B
0.75
,where B is in meters
If N60'‘ is decreasing with depth, use smaller of
z  2B and z  z  Thickness of soft layer below foundation
Elastic Settlement (Se):
1  0.0047 for NC sand
 1.25  L B 
Se  123 Bq 

0.25

L
B
  

Compressibility Index:
0.0016 for OC sand with qna ≤ po‘
0.0047 for OC sand with qna ≤ po‘
z
z
3   2    1
z 
z 
2
where B is in meters
and q is in kPa
2  1.71  N 
1.4
for NC sand
1.4
 0.57  N  for OC sand
q  qna
for NC sand and for OC sand with qna ≤ po‘
q  qna  0.67 po for OC sand with qna ≤ po‘
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Foundation Analysis and Design: Dr. Amit Prashant
Settlement due to Primary Consolidation
For NC clay
 c   o   o   av 
For OC clay
 o   av   c 
For OC clay
 o   c   o   av 
 o 
 
 av
 c 
eo 
Cc 
Cs 
Hc 
     av
 
Cc Hc
log  o


1  eo

o


  o   av
 
Cs Hc
Sc 
log 


1  eo

o


  C H
     av
 
CH
Sc  s c log  c   c c log  o



1  eo

1

e

o
c
 o


Sc 
Average effective vertical stress before construction
Average increase in effective vertical stress
Effective pre-consolidation pressure
Initial void ratio of the clay layer
Compression Index
Swelling Index
Thickness of the clay layer
 
 av
1
 t  4 m  b 
6
 t
 m
 b
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Foundation Analysis and Design: Dr. Amit Prashant
Settlement Correction for Effect of 3-D Consolidation
 Sc 3D    Sc 1D
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Foundation Analysis and Design: Dr. Amit Prashant
Fox’s Depth Correction
Factor for Rectangular
Footings of (L)x(B) at
Depth (D)
 Sc Embedded
 Sc Surface
 Depth factor
Rigidity Factor as per
IS:8009-1976
Total settlement of
rigid foundation
Total settlement at the center
of flexible foundation
Rigidity factor  0.8
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Foundation Analysis and Design: Dr. Amit Prashant
Time Rate of Settlement
St  Si  USc
cvt
T 2
Ht
Assumption of pore pressure
distribution under the given
stress conditions
For open
clay layer
with two
way
drainage
use curve
for V=1
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Foundation Analysis and Design: Dr. Amit Prashant
 t2 
C Hc
Ss 
log  
1  ep
 t1 
C  Secondary Compression Index 
e
log t2 t1 
ep  Void ratio at the end of primary consolidation
Hc  Thickness of Clay Layer
Void Ratio, e
Settlement Due to Secondary Consolidation
ep
e
t1
t2
Time, t (Log scale)
Secondary consolidation settlement is more important in the
case of organic and highly-compressible inorganic clays
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Foundation Analysis and Design: Dr. Amit Prashant
Total Settlement
from SPT Data
for Cohesionless
soil
Multiply the settlement
by factor W'
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Foundation Analysis and Design: Dr. Amit Prashant
Total Settlement from CPT Data for Cohesionless soil
St 
Ht  o   
ln 
C   o 
3  qc 
C  
2  o 

Depth profile of cone resistance
can be divided in several
segments of average cone
resistance

Average cone resistance can
be used to calculate constant of
compressibility.

Settlement of each layer is
calculated separately due to
foundation loading and then
added together
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – IS:1888-1982
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – IS:1888-1982
Bearing Plate:

Rough mild steel bearing plate in circular or square shape

Dimension: 30 cm, 45 cm, 60 cm, or 75 cm.
Thickness > 25 mm

Smaller size for stiff or dense soil. Larger size for soft or loose soil

Bottom of the plate is grooved for increased roughness.

Concrete blocks may be used to replace bearing plates.
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – IS:1888-1982
Test Pit:

Usually to the depth of foundation level.

Width equal to five times the test plate

Carefully leveled and cleaned bottom.

Protected against disturbance or change in natural formation
Plan
Section
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – IS:1888-1982
Procedure:



Selection of Location
 Based on the exploratory boring.
 Test is carried out at the level of proposed foundation. If water table is
below the foundation level but the depth is less than width of plate
then the test is carried out at the level of water table. If the water table
is above the foundation level then the water level is reduced to
proposed foundation level by pumping out the water during the test;
however, in case of high permeability material perform the test at the
level of water table.
 In case the soil is expected to have significant capillary action and the
water table is within 1 m below the foundation, it becomes necessary
to perform the test at the level of water table in order to avoid the
effect of higher effective stresses due to capillary action resulting in
lower values of interpreted settlements.
Reaction supports should be at least (3.5 x width of plate) away from the
test plate location, and loading arrangement should provide sufficient
working space.
Test plate should be placed over a 5 mm thick sand layer and it should be
centered with the loading arrangement.
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – IS:1888-1982
Procedure: (Contd.)

A seating pressure of 7 kPa is applied and then released after some time
before the test.

Loads are applied in the increments of approximately 1/5th of the
estimated ultimate safe load. (Or, one may choose to increase the load at
an increment of 0.5 kN.)

At each load settlement is recorded at time intervals of 1, 2, 4, 6, 9, 16, 25
min and thereafter at intervals of one hour.

For clayey soil, the load is increased when time settlement curve shows
that the settlement has exceeded 70-80% of the probable ultimate
settlement or a duration of 24 Hrs.

For the other soils, the load is increased when the settlement rate drops
below 0.02 mm/min.

The minimum duration for any load should, however, be at least 60 min.

Dial gauges used for testing should have at least 25 mm travel and 0.01
mm accuracy.

The load settlement curve can then be platted from settlement data.
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – Load-Settlement Curve
Zero Correction:
The intersection of the early straight line or nearly straight line with zero load
line shall be determined and subtracted from the settlement readings to allow
for the perfect seating of the bearing plate.
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test – Load-Settlement Curve
Terzaghi and Peck (1948):
S f  Bf  Bp  30 


S p  Bp  Bf  30 


S f  Settlement of a foundation of
2
width Bf (cm)
Sp 
Settlement of the test plate of
width Bp (cm) at the same load
intensity as on the foundation
Bond (1961):
S f  Bf 
 
S p  Bp 
n
Soil
Index - n
Clay
1.03 to 1.05
Sandy clay
1.08 to 1.10
Loose sand
1.20 to 1.25
Medium sand
1.25 to 1.35
Dense sand
1.40 to 1.50
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test: Some Considerations




The width of test plate should not be less
than 30 cm. It is experimentally shown that
the load settlement behavior of soil is
qualitatively different for smaller widths.
The settlement influence zone is much
larger for the real foundation sizes than
that for test plate, which may lead to gross
misinterpretation of expected settlement
for proposed foundation.
Soft soil
layer
The foundation settlements in loose sands are usually much larger than what
is predicted by plate load test.
Plate load test is relatively short duration test and gives mostly the immediate
settlements. In case of granular soils the immediate settlement is close to
total settlements. However, due to considerable consolidation settlement in
case of cohesive soils, the plate load test becomes irrelevant in such case.
Although the following relationship is suggested
S f Bf
for interpreting the settlements in cohesive soils,

it can not be used seriously for design.
S
B
p
p
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test: Bearing Capacity


In case of dense cohesionless soil and highly cohesive soils ultimate bearing
capacity may be estimated from the peak load in load-settlement curve.
In case of partially cohesive soils and loose to medium dense soils the ultimate
bearing capacity load may be estimated by assuming the load settlement curve
so as to be a bilinear relationship.
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Foundation Analysis and Design: Dr. Amit Prashant
Plate Load Test: Bearing Capacity

A more precise determination of
bearing capacity load is possible
if the load-settlement curve is
plotted in log-log scale and the
relationship is assume to be
bilinear. The intersection point is
taken as the yield point or the
bearing capacity load.
For cohesioless soil 
For cohesive soil 
quf Bf

qup Bp
quf  qup
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Foundation Analysis and Design: Dr. Amit Prashant
Modulus of
Sub-grade
Reaction
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Foundation Analysis and Design: Dr. Amit Prashant
Differential Settlement
Terzaghi’s recommendation:
Differential settlement should not exceed 50% of the total settlement calculated for the foundation.
Considering the sizes of different footing, the following criteria is suggested for buildings:
Differential settlement of footing  75% of max calculated settlement of footing
For raft foundation the requirements shall be more stringent and they may designed for the
following criteria
Differential settlement of raft footing  37% of max calculated settlement of raft footing
L

= maximum settlement

d
d= differential settlement
d/ = angular distortion
Allowable maximum and differential settlements as prescribed by
IS:1904-1986 are given on the next slide
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Foundation Analysis and Design: Dr. Amit Prashant
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Foundation Analysis and Design: Dr. Amit Prashant
Rotation of Footings Subjected to Moment

Footings subjected to moment will have the tendency to rotate and
the amount of rotation can be estimated by assuming that the
footing is supported on a bed of springs and using the modulus of
sub-grade reaction theory.
Modulus of sub-grade reaction:
Q
M
L
Es
k
B 1  2


Moment about the base due to
soil reaction:
M  2
B2
0
LB3k
L  k. .dx 
12
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Foundation Analysis and Design: Dr. Amit Prashant
Rotation of Footings Subjected to Moment
12M
 3 
LB k

12M 1  2
LB2 Es
  1 
2
Es
M
I
2 
LB
Influence factor
to compute
rotation of
footing
I values
53
Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing Pressure

Maximum bearing pressure that can be applied on the
soil satisfying two fundamental requirements

Bearing capacity with adequate factor of safety
– net safe bearing capacity

Settlement within permissible limits (critical in most cases)
– net safe bearing pressure
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Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing
Pressure
Terzaghi and Peck (1967):
 B  0.3  
qn  1.37  N   3 
Rw RD1Sa

 2B 
2
kN m
2
Sa in mm and all other
dimensions in meter.
Sa  Permissible settlement in mm.
(25 mm)
 Dw  Df
Rw  0.5 1 

Df




 Rw  1
RD1  depth correction factor
D
 1  0.2 f  1.2
B
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Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing Pressure
Peck, Hanson, and Thornburn (1974):
N-values are corrected for dilatancy and overburden
Initial straight line  safe bearing capacity with FOS =2
Later horizontal portion  permissible settlement of 25 mm.
Allowable bearing pressure from settlement consideration:
Sa  Permissible settlement in mm. (25 mm)
q
 0.44C N S
anet
w
2
kN m
a
 Dw 
Cw  water table correction  0.5  0.5 
 Df  B 


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Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing Pressure
Teng’s (1962) Correlation:
Net safe bearing pressure
 B  0.3  
qn  1.4  Ncor  3 
RwCD Sa

 2B 
2
kN m
2
Sa in mm and all other
dimensions in meter.
Df
CD  depth correction factor  1 
2
B
Ncor  CN .N

CN  
  o

CN  
  o
 o 
1.75 
 for 0   o Pa   1.05
Pa  0.7 

3.5
 for 1.05   o Pa   2.8
Pa  0.7 
Effective Overburden stress
57
Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing Pressure
Meyerhof’s (1974) Correlation:
Net safe bearing pressure
qn  0.49N RD1Sa kN m2 for B  1.2 m
 B  0.3 
2
qn  0.32N RD2 
S
kN
m
for B  1.2 m
a

 B 
2
RD1  depth correction factor
D
 1  0.2 f  1.2
B
RD2  depth correction factor
Df
 1  0.33
 1.33
B
Bowel’s (1982) Correlation:
qn  0.73N RD1Sa kN m2 for B  1.2 m
 B  0.3 
2

qn  0.48N RD2 
S
kN
m
for B  1.2 m
a

 B 
2
N-value corrected for overburden using bazaraa’s equation, but
the N-value must not exceed field value
58
Foundation Analysis and Design: Dr. Amit Prashant
Allowable Bearing Pressure
IS Code recommendation: Use total settlement correlations with SPT
data to determine safe bearing pressure.
Correlations for raft foundations:
Rafts are mostly safe in bearing capacity and they do not show much
differential settlements as compared to isolated foundations.
Teng’s Correlation:
qn  0.7  N   3 Rw CD Sa kN m2
Peck, Hanson, and Thornburn (1974):
qanet  0.88Cw NSa kN m2
Correlations using CPT data:
Meyerhof’s correlations may be used by substituting qc/2 for N,
where qc is in kg/cm2.
59
Foundation Analysis and Design: Dr. Amit Prashant
Net vs. Gross Allowable Bearing Pressure
Soil
Soil
Df
t
Dc
Gross load
Qg  Qc  B2 Dc c  B2  Df  Dc  
Qg Qc
qg  2  2   Df  Dc  c   
B B
Q
qn  qg   Df  c2  Dc  c   
B
 c    is small, so it may be neglected
Q
qn  c2
B
Qc
 qanet
2
B
Qc
 Dc c  t c
2
B
Q
qn  qg   Df  c2   c  Dc  t    Df
B
qg 
Usually Dc+t is much smaller than Df
qn 
Qc
  Df
2
B
Qc
 qanet   Df
2
B
Qc
 qagross
B2
60