Settlement of Shallow Foundations

SETTLEMENT OF SHALLOW FOUNDATION
Created By-
Md. Ragib Nur Alam
130095
Civil Engineering
Ragibnur.ce@gmail.com

SHALLOW FOUNDATION
 General
 Immediate Settlement
 Consolidation Settlement
CREATED BY- RAGIB NUR ALAM CE13 EMAIL: RAGIBNUR.CE@GMAIL.COM

GENERAL
The settlement of shallow foundation may be divided into three broad
categories:
1. Immediate settlement, which is caused by the elastic deformation of dry
soil and of moist and saturated soils without any change in the moisture
content. Immediate settlement are generally based on equations derived
from the elasticity theory
2. Primary consolidation settlement, which is the result of a volume
change in saturated cohesive soils because of expulsion of the water that
occupies the void spaces.
3. Secondary consolidation settlement, which is observed in saturated
cohesive soils and is the result of the plastic adjustment of soil particles.

IMMEDIATE SETTLEMENT

General Equation (Harr, 1966)
 Flexible Foundation
 At the corner of foundation
 At the center of foundation
 Average
 Rigid Foundation
 2
1
. 2 
s
s
o
e
E
qB
S 
 2
1
.
s
s
o
e
E
qB
S 
Es = Modulus of elasticity of soil
B = Foundation width L = Foundation length
  rs
s
o
e
E
qB
S 2
1
.































11
11
ln.
1
1
ln
1
2
2
2
2
m
m
m
mm
mm


  avs
s
o
e
E
qB
S 2
1
.

B
L
m ; ; H = 

If Df = 0 and H < , the elastic settlement of foundation can be
determined from the following formula:
      
     2
2
1
22
2
2
1
2
2
2111
.
2
211
1
.
FF
E
qB
S
FF
E
qB
S
ssss
s
o
e
sss
s
s
o
e





 (corner of rigid foundation)
(corner of flexible foundation)
The variations of F1 and F2 with H/B are given in the graphs of next slide

CREATED BY- RAGIB NUR ALAM CE13
EMAIL: RAGIBNUR.CE@GMAIL.COM

EXAMPLE
Problem:
A foundation is 1 m x 2 m in plan and carries a net load per unit
area, qo = 150 kN/m2. Given, for the soil, Es = 10,000 kN/m2, s
0.3. Assuming the foundation to be flexible, estimate the elastic
settlement at the center of the foundation for the following
conditions:
a. Df = 0 and H = 
b. Df = 0 and H = 5 m

EXAMPLE
Solution:
Part a.
Part b.
  2
s
s
o
e 1
E
q.B
S
  mmmSe 9.200209.0)53.1(3.01
000,10
)150)(1( 2

For L/B = 2/1 = 2    1.53, so
     2
2
1
22
2111
'.
FF
E
qB
S ssss
s
o
e  
For L’/B’ = 2, and H/B’ = 10  F1  0.638 and F2  0.033, so
      mmmxSe 3.160163.04)033.0()3.0(23.01)638.0(3.013.01
000,10
)150)(5.0( 222


General Equation (Bowles, 1982)
2
'
B
B 
2
'
L
L 
1
2
.
1
'.. F
E
BqS
s
s
oe


 
 
 














1
11
ln
11
11
ln.
1
22
22
22
222
1
NMM
NMM
NMM
NMM
MF

'
'
B
L
M 
'B
H
N 
Es = Modulus of elasticity of soil
H = effective layer thickness, ex. 2 - 4B below foundation
At the center of Foundation and F1 time by 4
BB 'At the corner of Foundation LL ' and F1 time by 1

 For saturated clay soil
s
o
21e
E
B.q
A.AS 

 For sandy soil
where:
 Iz = factor of strain influence
 C1 = correction factor to thickness of embedment
foundation = 1 – 0.5x[q/(q-q)]
 C2 = correction factor due to soil creep
= 1+0,2.log(t/0,1)
 t = time in years
 q = stress caused by external load
 q =  . Df
  
2
0
21.
z
s
z
e z
E
I
qqCCS

Young Modulus
Circle Foundation or L/B =1
z = 0  Iz = 0.1
z = z1 = 0,5 B  Iz = 0.5
z = z2 = 2B  Iz = 0.0
Foundation with L/B ≥ 10
z = 0  Iz = 0.2
z = z1 = B  Iz = 0.5
z = z2 = 4B  Iz = 0.0

EXAMPLE
A shallow foundation 3 m x 3 m (as shown in the following drawing). The subgrade
is sandy soil with Young modulus varies based on N-SPT value (use the following
correlation: Es = 766N)
Determine the settlement
occur in 5 years (use strain
influence method)

EXAMPLE

EXAMPLE
Depth
(m)
z
(m)
Es
(kN/m2)
Iz
(average) (m3/kN)
0.0 – 1.0 1.0 8000 0.233 0.291 x 10-4
1.0 – 1.5 0.5 10000 0.433 0.217 x 10-4
1.5 – 4.0 2.5 10000 0.361 0.903 x 10-4
4.0 – 6.0 2.0 16000 0.111 0.139 x 10-4
 1.55 x 10-4
z
E
I
s
z

 
9.0
5.18.17160
5.18.17
5.015.011 














x
x
qq
q
C 34.1
1.0
5
log.2.01
1.0
log.2.012 












t
C
 
mmS
xxS
z
E
I
qqCCS
e
e
B
s
z
e
8.24
)1055.1)(5.18.17160)(34.1)(9.0(
...
4
2
0
21






CONSOLIDATION SETTLEMENT

 Normal Consolidation
 Over consolidation
oc   or 1
o
c


o
o
c
o
c
c H
e
C
S

 

 log..
1
oc   or 1
o
c


𝜎o +  𝜎 < 𝜎c
o
o
c
o
s
c H
e
C
S

 

 log..
1
𝜎o < 𝜎c < 𝜎o+ 𝜎
c
o
c
o
c
o
c
c
o
s
c H
e
C
H
e
C
S



 



 log..
1
log..
1

where:
 eo = initial void ratio
 Cc = compression index
 Cs = swelling index
 pc = preconsolidation pressure
 po = average effective pressure on the clay layer before the construction of the foundation
=  ’.z
 p = average increase of pressure on the clay layer caused by the foundation construction
and other external load, which can be determine using method of 2:1, Boussinesq,
Westergaard or Newmark.
Alternatively, the average increase of pressure (p) may be approximated by:
 bmt pppp  4
6
1
pt = the pressure increase at the top of the clay layer
pm = the pressure increase at the middle of the clay layer
pb = the pressure increase at the bottom of the clay layer

EXAMPLE
A foundation 1m x 2m in plan is shown in the following figure. Estimate the
consolidation settlement of the foundation.
Assume the clay is normally consolidated.

EXAMPLE
o
o
cc
p
pp
H
eo
Cc
S


 log..
1
  
  
2
/45.13
25.3225.31
2.1.150
..
mkNp
zLzB
LBq
p o





mmxSc 44
5.52
45.135.52
log5.2
8.01
32.0




po = (2.5)(16.5) + (0.50)(17.5-10) +(1.25)(16-10) = 52.5 kN/m2
2:1 method

ALLOWABLE SETTLEMENT

Settlement of Shallow Foundations

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