Settlement of Structures

1
Settlement of Structures

• Elasticity for saturated soils

2
Settlement of a loaded footing
Maximum Settlement
Soil Layer
3
Settlement-time response of a loaded footing
S
Final or long term settlement
Immediate settlement
t
4
Soil deformation - volume change
Ds
Pore water (incompressible)
Voids
Voids
Skeletal Material (incompressible)
Solid
Solid

Water
Initial State
Deformed State
5
Soil deformation - constant volume
Undrained Deformation (no volume change)
Soil Element
Soil Element
6
The soil deformation process

• Deformation of saturated soil can occur due to
• reduction of pore space the squeezing out of
  pore water
• changes in shape at constant volume
• combinations of changes in volume and changes in
  shape
• Pore water can only be squeezed out at a finite
  rate and so immediately after a load is applied
  there is no volume change
• Initially deformation can only take place due to
  changes in shape at constant volume

7
The soil deformation process

• Previously we have been looking at the
  deformation under one-dimensional conditions with
  no lateral strain (confined conditions). For such
  conditions there can be no change in shape and
  hence no immediate deformation.
• In the 1-D analysis of settlement under a footing
  this implies that there can be no immediate
  settlement.
• For more general 3-D conditions there can be
  lateral strains and vertical strains and changes
  in shape can occur at constant volume.
• Thus 3-D analyses of settlement will predict
  immediate settlement.

8
The soil deformation process

• Beneath a loaded footing different points in the
  soil will experience different increases in
  stress
• Immediately after the load is applied deformation
  will be at constant volume, and excess pore
  pressures will develop in the soil
• Excess pore pressures will be greatest at points
  where the increase in stress is greatest

9
Excess pore pressures under a loaded footing
p
Contours of excess pore pressure, Du
Soil Layer
0.5 p
0.3 p
0.1 p
10
Flow of water in a porous soil
As time progresses water will flow until the
excess pore pressures reduce to zero, and
additional deformation will take place in the soil
Region of low excess water pressure
Region of high excess water pressure
Flow
11
Variation of stress and pore pressure with time
Total Stress
Time
Excess Pore Pressure
Time
Effective Stress
Time
12
Typical settlement - time response
Consolidation settlement
Final settlement
Settlement
Initial settlement
Time
13
Analysis of 3-D settlement

• Based on assumption of linear elastic soil
  response
• This is used because
• easily evaluated solutions can be obtained
• complex loadings can be split into simple
  loadings for which solutions can be superimposed
• only 2 material constants need to be specified
• solutions agree with intuition and experience
• despite non-linear real soil behaviour

14
Hookes Law for an Elastic Solid
(1a)
15
Hookes Law for an Elastic Soil
(1b)
16
Relation between total and effective stresses
Increment in effective stress
Increment in total stress
Increment in pore pressure

-
17
Relation between total and effective stresses
Increment in effective stress
Increment in total stress
Increment in pore pressure

-
(1c)
18
Relation between total and effective stresses
Increment in effective stress
Increment in total stress
Increment in pore pressure

-
(1c)
To use Hookes law for a soil it is necessary to
know both the total stress and the pore water
pressure.
19
Relation between total and effective stresses
Increment in effective stress
Increment in total stress
Increment in pore pressure

-
(1c)
To use Hookes law for a soil it is necessary to
know both the total stress and the pore water
pressure. The total stress can be determined
from the theory of elasticity.
20
Relation between total and effective stresses
Increment in effective stress
Increment in total stress
Increment in pore pressure

-
(1c)
To use Hookes law for a soil it is necessary to
know both the total stress and the pore water
pressure. The total stress can be determined
from the theory of elasticity. The pore water
pressure is more difficult to determine. The
only time it is usually known is in the long
term when all excess pore pressures have
dissipated. This implies that only the final long
term settlement can be calculated.
21
Behaviour under undrained conditions
Immediately after a load is applied no water can
drain from the soil and there can be no change in
volume. This is called undrained loading.
22
Behaviour under undrained conditions
Immediately after a load is applied no water can
drain from the soil and there can be no change in
volume. This is called undrained loading. An
alternative form of Hookes Law is useful
D
D
D

-




s
n
s
s
(
)
xx
yy
zz
De

xx
E

D
D
D
D



-






s
n
n
s
s
s
(
)
(
)
1
xx
yy
zz
xx

E

D
D

-
s
n
n
s
(
)
1
3




(2)
xx
m

E

23
Behaviour under undrained conditions
Immediately after a load is applied no water can
drain from the soil and there can be no change in
volume. This is called undrained loading. An
alternative form of Hookes Law is useful
(2)
24
Behaviour under undrained conditions
Hookes law may be used to calculate the volume
strain
(3a)
25
Behaviour under undrained conditions
Hookes law may be used to calculate the volume
strain
(3a)
D
-


3
1
2
(
)
n
s
m
De


0
(3b)
v
E

since the volume strain is zero the change in
mean effective stress must be zero, then
26
Behaviour under undrained conditions
Hookes law may be used to calculate the volume
strain
(3a)
D
-


3
1
2
(
)
n
s
m
De


0
(3b)
v
E

since the volume strain is zero the change in
mean effective stress must be zero, then
(3c)
D
Ds
D
u

-

0
s

m
m
hence the increase in the pore water pressure
must be equal to the increase in mean total stress
27
Behaviour under undrained conditions
Hookes law may be used to calculate the volume
strain
(3a)
D
-


3
1
2
(
)
n
s
m
De


0
(3b)
v
E

since the volume strain is zero the change in
mean effective stress must be zero, then
(3c)
D
Ds
D
u

-

0
s

m
m
hence the increase in the pore water pressure
must be equal to the increase in mean total stress
D
Ds
u

m
28
Behaviour under undrained conditions
Now that the pore pressure increase is known in
terms of the total stress increase, the effective
stress increase can be expressed in terms of the
total stress increase. This leads to a total
stress - strain relationship for undrained
behaviour.
29
Behaviour under undrained conditions
Now that the pore pressure increase is known in
terms of the total stress increase, the effective
stress increase can be expressed in terms of the
total stress increase. This leads to a total
stress - strain relationship for undrained
behaviour. Note that the relations between total
stress changes and strains only apply if the soil
is undrained. This means that they can only be
used to calculate the immediate settlement.
30
Hookes Law for the undrained response of a
saturated elastic soil
(5)
31
Hookes Law for the undrained response of a
saturated elastic soil
(5)
where
(6)
32
Selection of elastic parameters
Soil is not linear elastic. It is therefore very
difficult to select appropriate modulus and
Poisson ratio values.
33
Selection of elastic parameters

• Soil is not linear elastic. It is therefore very
  difficult to select appropriate modulus and
  Poisson ratio values.
• The main factors influencing the modulus are
• the mean effective stress

34
Selection of elastic parameters

• Soil is not linear elastic. It is therefore very
  difficult to select appropriate modulus and
  Poisson ratio values.
• The main factors influencing the modulus are
• the mean effective stress
• the soil stress history
• - Overconsolidation ratio (for clays)
• - Relative density (for sands)

35
Selection of elastic parameters
The other difficulty is that the response is
highly non-linear so that the modulus depends on
strain and load history.
Stress
Slope of this line gives Secant Modulus
Strain
36
Selection of elastic parameters

• Do not use typical values
• Always seek specialist geotechnical advice
• Remember accurate prediction of settlements is
  very difficult. With typical site investigation
  data settlement predictions can easily be out by
  a factor of 2.

37
Example 1
100 kPa
z
y
x
100 kPa
100 kPa
38
Example 1
100 kPa
190 kPa
z
y
x
100 kPa
100 kPa
100 kPa
100 kPa
39
Example 1
100 kPa
190 kPa
z
y
x
100 kPa
100 kPa
100 kPa
100 kPa
Total stress changes Dszz 90 kPa Dsxx 0
kPa Dsyy 0 kPa
40
Example 1
Undrained loading. Total stress and Effective
stress analyses can be used.
41
Example 1
Undrained loading. Total stress and Effective
stress analyses can be used. 1. Total stress
analysis Calculate total stress parameters
42
Example 1
Undrained loading. Total stress and Effective
stress analyses can be used. 1. Total stress
analysis Calculate total stress parameters Use
Hookes law
43
Example 1
Undrained loading. Total stress and Effective
stress analyses can be used. 1. Total stress
analysis Calculate total stress parameters Use
Hookes law
44
Example 1
2. Effective stress analysis Undrained, therefore
Du Dsm 30 kPa
45
Example 1
2. Effective stress analysis Undrained, therefore
Du Dsm 30 kPa
46
Example 1
2. Effective stress analysis Undrained, therefore
Du Dsm 30 kPa
Giving the same answer as before.
47
Example 1
2. Effective stress analysis Undrained, therefore
Du Dsm 30 kPa
Giving the same answer as before.
48
Example 1
2. Effective stress analysis Undrained, therefore
Du Dsm 30 kPa
Giving the same answer as before.
49
Example 2
Sample allowed to drain until all excess pore
pressures dissipated.
50
Example 2
Sample allowed to drain until all excess pore
pressures dissipated. Only Effective Stress
analysis can be used.
51
Example 2
Sample allowed to drain until all excess pore
pressures dissipated. Only Effective Stress
analysis can be used. If total stress remains
constant Ds - Du 30 kPa
52
Example 2
Sample allowed to drain until all excess pore
pressures dissipated. Only Effective Stress
analysis can be used. If total stress remains
constant Ds - Du 30 kPa Then from Hookes
law
53
Example 2
Sample allowed to drain until all excess pore
pressures dissipated. Only Effective Stress
analysis can be used. If total stress remains
constant Ds - Du 30 kPa Then from Hookes
law Note that the combined strains due to
undrained loading and consolidation are identical
to the total strain if the final strains had been
calculated directly using effective stress
analysis with Dszz 90 kPa, Dsxx Dsyy 0
54
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