CE5101 Consolidation and Seepage Lecture 5 Prof Harry Tan SEP 2011 1 CE 5101 Lecture 5 – SETTLEMENTS and Stress Distribution Sep 2011 Prof Harry Tan 1 Outline • Foundation Requirements • Elastic Stress Distribution Elastic Stress Distribution • Concept of Effective Stress • Settlements of Soils - Immediate, Delayed, and Creep Compression • Hand Calculations • SPREADSHEET Calculations (UNISETTLE) • Finite Element Analysis (PLAXIS) 2
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Settlements and Elastic Stress Distribution (SEP 2011)
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CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
1
CE 5101 Lecture 5 –SETTLEMENTS and Stress
Distribution
Sep 2011
Prof Harry Tan
1
Outline• Foundation Requirements
• Elastic Stress DistributionElastic Stress Distribution
• Concept of Effective Stress
• Settlements of Soils - Immediate, Delayed, and Creep Compression
• Hand Calculations
• SPREADSHEET Calculations (UNISETTLE)
• Finite Element Analysis (PLAXIS)2
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
2
Requirements for Foundation Design
• Adequate Safety (degree of utilisation of soil strength)
Acceptable Deformations• Acceptable Deformations(Movements and Settlements limits)
Factor of Safety as Measure of Degree of Utilisation of Soil Strength
2.5
3.0
3.5
4.0
4.5
Point AFS = 4.338; q = 200 kPa; qult = 868 kPa
FS = 2 164; q = 400 kPa; qult = 866 kPa
0 0.05 0.10 0.15 0.20 0.25 0.30 0.35
1.0
1.5
2.0
Settlement (m)
FS = 2.164; q = 400 kPa; qult = 866 kPa
FS = 1.291; q = 670 kPa; qult = 865 kPa
6
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
4
What is Allowable Settlements
Effects on:
• Appearance of Structure
• Utility of Structure
• Damage to Structure
7
Types of Settlements
Uniform settlement
Non-uniform settlement
Angular distortion = /L
L
L
Angular distortion = /(L/2)
8
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
5
Allowable Settlements
Controlled by type of settlements (Sowers 1962)y yp ( )
• Total settlements
• Tilting
• Differential settlements
9
Limiting Angular Distortions (Bjerrum, 1963)
1/150 - Considerable cracking in panel and brick walls, safe limit for flexible brick wall h/l<1/4, limit where structural damage of general buildings is to be feared
1/250 - Limit where tilting of high rigid buildings become visible
1/300 - Limit where first cracking in wall panel expected, difficulties with overhead cranes expected
1/500 - Safe limit for buildings where cracking is not permissible
10
1/600 - Limit of danger for frames with diagonals
1/750 - Limits where difficulties with machinery sensitive to settlements are to be feared (high tech plants)
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
6
Limiting Angular Distortions (Bjerrum ,1963)
Max Distortion (/L) vs Max Differential Settlement :
1/500 vs 25 mm For Stiff Footing,1/500 vs 25 mm
1/300 vs 45 mm
1/200 vs 70 mm
1/100 vs 150 mm
g,
Max Diff Sett = 1/4 Max Sett
For Flexible Footing,
Max Diff Sett = 1/2 Max Sett
Typical Foundation Design,
Max Diff Sett < 25 mm
11
Limiting Angular Distortions (Bjerrum ,1963)
12
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
7
• ER2010 – Review Paper by Ed Cording et al –Assessment of excavation-induced building damage• Damage is due to combined effects of:effects of:• Angular distortion• Lateral strain• Bending strain
13
Basic Soil Phase Relationships
MASSVOLUMEDensities (kg/m3)
Air
Water
Solids
0
Mw Mt
Ms
Mw
Va
Vw
Vs
Vv
Vt
Total, t = Mt/Vt
Dry, d = Ms/Vt
Solids, s = Ms/Vs
Water, t = Mw/Vw
Saturated, sat Ratios
= (Ms+Mw+ w Va)/VtWater content, w = Mw/Ms
Void ratio, e = Vv/Vs
Porosity, n = Vv/Vt
Degree of saturation = Vw/Vv 14
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
8
Basic Soil Phase RelationshipsDefine Vs=1, Vv=e
MASSVOLUMEDensities (kg/m3)
eS w = w s
Air
Water
Solids
0t
s
Mw
(1-e)S
eS
1
e
1+e
Total, t = s (1+w)/(1+e)
= d (1+w)
Dry, d = s /(1+e)
Saturated, sat
= (Ms+Mw+ w Va)/VtRatios
Water content, w = t/ d - 1
Void ratio, e = s/d - 1
Porosity, n = e/(1+e)
Degree of saturation = S = ws / ew 15
Common soil mineral densities
Mineral Type Solid Density, kg/m3
Calcite 2800
Quartz 2670
Mica 2800
Pyrite 5000
Kaolinite 2650
Montmorillonite 2750
Illite 270016
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
9
Typical range of saturated densities
Soil Type Saturated Density, kg/m3
Sands;gravels 1900-2300
Silts 1500-1900
Soft Clays 1300-1800
Firm Clays 1600-2100
Peat 1000-1200
Organic Silt 1200-1900
Granular Fill 1800-220017
The Textbooks on Foundations — They come no better
This is one of the few showingmore than one soil layer
18
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
10
The Reality — With a bit of needed “W” add-on
19
The Reality — Getting closer, at least
20
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
11
So, with this food for thought, , g ,
on to the Fundamental
Principles
21
Determining the effective stress is the key to geotechnical analysis
• The not-so-good method:method:
h ''
)'(' hz
’ = buoyant unit weight
)1(' iwt
22
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
12
It is much better to determine, separately, the total stress and the pore pressure. The effective stress is then the total stress minus the pore pressureminus the pore pressure.
)( hz
uz '
23
Determining pore pressure
u = w hu w hThe height of the column of water (h; the head representing the water pressure)
is usually not the distance to the ground surface nor, even, the distance to the
groundwater table. For this reason, the height is usually referred to as the
“phreatic height” or the “piezometric height” to separate it from the depth below
the groundwater table or depth below the ground surface.
The pore pressure distribution is determined by applying the facts that
(1) in stationary conditions, the pore pressure distribution can be assumed to be
linear in each individual soil layer
SAND Hydrostatic distribution
GW
PRESSURE
(2) in pervious soil layers that are “sandwiched” between less pervious layers,
the pore pressure is hydrostatic (that is, the vertical gradient is unity)
CLAY Non-hydrostatic distribution, but linear
SAND Hydrostatic distribution Artesian phreatic head
DEPTH
24
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
13
Distribution of stress below a a small load area
The 2:1 method
)()(0 zLzB
LBqqz
The 2:1-method can only be used for distributions directly under the centerof the footprint of the loaded area. It cannot be used to combine (add)stresses from adjacent load areas unless they all have the same center. it isthen only applicable under the area with the smallest footprint. 25
Boussinesq Method for stress from a point load
2/522
3
)(2
3
zr
zQqz
26
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
14
Newmark’s method for stress from a loaded area
Newmark (1935) integrated the Boussinesq equation over a finite area and obtained a relation for the stress under the corner of aarea and obtained a relation for the stress under the corner of a
uniformly loaded rectangular area, for example, a footing
40
CBAIqqz
2222
22
1
12
nmnm
nmmnA
(1)
1
222
22
nm
nmB
2222
22
1
12arctan
nmnm
nmmnC
m = x/zn = y/zx = length of the loaded areay = width of the loaded areaz = depth to the point under the corner
where the stress is calculated
27
• Eq. 1 does not result in correct stress values near the ground surface. To represent the stress near the ground surface, Newmark’s integration applies an additional equation:
40
CBAIqqz
F h 2 + 2 + 1 2 2
(2)
For where: m2 + n2 + 1 m2 n2
28
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
15
Stress distribution below the center of a square 3 m wide footing
0 0.25
Eq. (2) Eq. (2)
-4
-2
DE
PTH
(m
)
0.10
0.15
0.20
INF
LUE
NC
E F
AC
TOR
, I
Eq. (1)
Eq. (1)
0 20 40 60 80 100
-6
STRESS (KPa)
0.01 0.10 1.00 10.000.00
0.05
m and n (m = n)
29
0
0 25 50 75 100
STRESS (%)
Boussinesq
Westergaard
0
0 25 50 75 100
SETTLEMENT (%)
Boussinesq
Westergaard
1
2
3
EP
TH
(d
iam
ete
rs)
2:1
1
2
3
EP
TH
(d
iam
ete
rs)
q
2:1
Comparison between Boussinesq, Westergaard, and 2:1 distributions
4
5
DE
4
5
DE
30
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
16
0
0 25 50 75 100
STRESS (%)
Westergaard
0
0 25 50 75 100
SETTLEMENT (%)
Westergaard
1
2
3
PT
H (
dia
me
ters
)
Boussinesq
1
2
3
PT
H (
dia
me
ters
)
Boussinesq
4
5
DE
P
2:1
4
5
DE
P2:1
31
0
1
0 25 50 75 100
STRESS (%)
Westergaard
0
1
0 25 50 75 100
SETTLEMENT (%)
Westergaard
1
2
3
EP
TH
(d
iam
ete
rs)
2:1
Boussinesq
Characteristic Point; 0.37b from center
1
2
3
EP
TH
(d
iam
ete
rs)
Boussinesq
2:1Characteristic Point; 0.37b from center
4
5
D
4
5
D
Below the characteristic point, stresses for flexible and stiff footings are equal 32
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
17
Now, if the settlement distributions are so
similar, why do we persist in using
Boussinesq stress distribution instead of
the much simpler 2:1 distribution?
Because a footing is not alone in this world;
near by, there are other footings, and fills,near by, there are other footings, and fills,
and excavation, etc., for example:
33
The settlement imposed
0
0 25 50 75 100
SETTLEMENT (%)
BoussinesqOutside Point Boussinesq
Center PointThe settlement imposed
outside the loaded
foundation is often critical
1
2
3
PT
H (
dia
me
ters
)
Center Point
4
5
DE
Loaded area
34
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
18
Calculations using Boussinesq distribution can be used to determine how stressapplied to the soil from one building may affect an adjacent existing building.
EXISTING NEW 0 20 40 60 80 100
STRESS (%)
ADJACENT BUILDING
BUILDING WITH LARGE LOAD OVER FOOTPRINT
AREA
2 m2 m 4 m
0
5
10
15
DE
PT
H (
m) STRESSES
UNDER THE FOOTPRINT OT THE LOADED BUILDING
STRESSES UNDER AREA
BETWEEN THE TWO BUILDINGS
20
25
30
STRESSES ADDED TO THOSE UNDER THE FOOTPRINT OF THE ADJACENT BUILDING
Characteristic point is point where vertical stress is equal for both rigid and flexible footing, this point is located at 0.37B and 0.37L from centre of rectangular footing, or 0.37R of 1.10 50.8 0.0 36.7 0.0 53.5 0.0
Approximate Ratio at corner, centre and edge to average settlement
Flexible Load Area RigidgFooting
FoundationDepth
Corner/Ave
Edge/Ave
Centre/Ave
Rigid/Ave
H/L= 0.6 0.9 1.2 0.9
H/L=1 0.5 0.7 1.3 0.8
H/L=1/4 0.4 0.7 1.3 0.8
48
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
25
Elastic Settlement for Other Flexible LoadCorner settlements is given by Terzaghi,1943 as:
B
D =
4.)/(
)1( 2
FigseeLBfisI
IE
qB
Points other than corner for any combination of rectangles can be obtained by superposition
qL
For centre of square loaded area:
)1(12.1 2 E
Bqz
49
Superpostion Principle for Rectangles
= + + +z
- - +=
z
50
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
26
Elastic Settlement for Other Flexible Load
For Flexible Rectangular Loaded area, Corner settlement , g , ,with finite depth of elastic layer, use Steinbrenner chart
)21()1(
)1(
22
2
FFI
IE
qB
B
qL
5.
)21()1(
21
22
12
FigingivenFandF
FFI FiniteD
51
Equivalent Footings for Pile Groups SettlementsGround level
Soft Clay
Ground level
L
2/3L
Equivalent Ftg
L
2/3L
Soft Clay
Equivalent Ftg
2
1Homogeneous Clay
2
1Firm Layer
52
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
27
The end result of a
geotechnical design analysis
is
Settlement
53
Movement, Settlement, and Creep
Movement occurs as a result of an increase of stress, but the term should be reservedto deformation due to increase of total stress. Movement is the result of a transfer ofstress to the soil (the movement occurs as necessary to build up the resistance to theload), and when the involved, or influenced, soil volume successively increases as thestress increases. For example, when adding load increments to a pile or to a plate in astatic loading test (where, erroneously, the term "settlement" is often used). As a term,mo ement is sed hen the in ol ed or infl enced soil ol me increases as the loadmovement is used when the involved, or influenced, soil volume increases as the loadincreases.
Settlement is volume reduction of the subsoil as a consequence of an increase ineffective stress. It consists of the sum of "elastic" compression and deformation due toconsolidation. The elastic compression is the compression of the soil grains (soilskeleton) and of any free gas present in the voids, The elastic compression is oftencalled "immediate settlement”. It occurs quickly and is normally small (theelastic compression is not associated with expulsion of water). The deformation due toconsolidation on the other hand is volume change due to the compression of the soilconsolidation, on the other hand, is volume change due to the compression of the soilstructure associated with an expulsion of water—consolidation. In the process, theimposed stress, initially carried by the pore water, is transferred to the soil structure.Consolidation occurs quickly in coarse-grained soils, but slowly in fine-grained soils. Asa term, settlement is used when the involved, or influenced, soil volume stays constantas the effective stress increases.
54
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
28
Movement, Settlement, and Creep
Creep is compression occurring without an increase of effective stress.Creep is usually small, but may in some soils add significantly to thecompression of the soil skeleton and, thus, to the total deformation of thesoil It is then acceptable to talk in terms of creep settlement
The term "settlement" is normally used for the deformation resulting from thecombined effect of load transfer, increase of effective stress, and creep duringlong-term conditions. It is incorrect to use the term “settlement” to meanmovement due to increase of load such as in a loading test.
soil. It is then acceptable to talk in terms of creep settlement.
55
StrainLinear Elastic Deformation (Hooke’s Law)
E
'
= induced strain in a soil layer
= imposed change of effective stress in the soil layer
E = elastic modulus of the soil layer (Young’s Modulus)
Young’s modulus is the modulus for when lateral expansion is allowed, which may be the case for soil loaded by a small footing, but not when the load is applied over a large area. In the latter case, the lateral expansion is constrained (or confined). The constrained modulus, D, is larger than the E-modulus. The constrained modulus is also called the “oedometer modulus”. For ideally elastic soils, the ratio between D and E is:
'
)21()1(
)1(
E
D
= Poisson’s ratio
56
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
29
Stress-Strain
57
Stress-strain behavior is non-linear for most soils. The non-linearity cannot be disregarded when analyzing compressible soils, such as silts and clays, that is, the elastic modulus approach is not appropriate for these soils.
Non-linear stress-strain behavior of compressible soils, is conventionally modeled as follows.
where = strain induced by increase of effective stress from ‘0 to ‘1
0
1
0
1
0 '
'lg
'
'lg
1
CRe
Cc
y 0 1
Cc = compression indexe0 = void ratio‘0 = original (or initial) effective stress‘1 = final effective stress
CR = Compression Ratio = (MIT)01 e
CCR c
58
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
30
In overconsolidated soils (most soils are)
)'
'lg
'
'lg(
1
1 1
00 pc
pcr CC
e
where ‘p = preconsolidation stressp pCcr = re-compression index
59
The Janbu Method
The Janbu tangent modulus approach, proposed by Janbu (1963; 1965; 1967; 1998),
and referenced by the Canadian Foundation Engineering Manual, CFEM (1985; 1992),
applies the same basic principles of linear and non-linear stress-strain behavior. The
method applies to all soils, clays as well as sand. By this method, the relation between
stress and strain is a function of two non-dimensional parameters which are unique for a
soil: a stress exponent, j, and a modulus number, m.
Janbu’s general relation is
])'
()'
[(1 01 jj
])'
()'
[( 01 j
r
j
rmj
where ‘r is a “reference stress = 100 KPa
j > 0
60
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
31
The Janbu Method
Dense Coarse-Grained Soil j = 1
'1
)''(1
01 mm
'1
)''(1
KPa
ksf
Cohesive Soil j = 00
1
'
'ln
1
m
2)(
2 01 mm
ksf
)''(5
101
m KPa
Sandy or Silty Soils j = 0.5
pm''(
21 ksf
61
There are direct mathematical conversions
between m and the E and Cc-e0
For E given in units of KPa (and ksf), the relation between the modulus number and the E-modulus is
m = E/100 (KPa)
m = E/2 (ksf)
For Cc-e0, the relation to the modulus number is
22
00 69.02lg10ln13.2
110ln
cc C
e
C
em
62
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
32
Typical and Normally Conservative Virgin Modulus Numbers
For clays and silts, the recompression modulus, mr, is often five to tentimes greater than the virgin modulus, m, listed in the table
63
1 00
1.20
p'c 20
25
Evaluation of compressibility from oedometer results
0.40
0.60
0.80
1.00
10 100 1 000 10 000
Voi
d R
atio
(-
-)
m = 12(CR = 0.18)
0
5
10
15
10 100 1,000 10,000
Str
ain
(%
)
p 10p
Cc
Cc = 0.37
e0 = 1.01 p'c
p 2.718p
1/m
Slope = m = 12
10 100 1,000 10,000
Stress (KPa) log scale Stress (KPa) log scale
Void-Ratio vs. Stress and Strain vs. Stress — Same test data
64
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
33
Comparison between the Cc/e0 approachand the Janbu method
0 30
0.35
30
35
m
0.05
0.10
0.15
0.20
0.25
0.30
CO
MP
RE
SS
ION
IN
DE
X, C
c Do these values indicate a
compressible soil, a medium compressible
soil, or a non-compressible soil?5
10
15
20
25
30
VIR
GIN
MO
DU
LU
S N
UM
BE
R, m
Data from a 20 m thick sedimentary deposit of medium compressibility.
0.00
0.40 0.60 0.80 1.00 1.20
VOID RATIO, e0
0
0.400.600.801.001.20
VOID RATIO, e0
65
75
100
125
150
OR
MA
LIZ
ED
C
c (
%)
75
100
125
150
OR
MA
LIZ
ED
m
(%
)
The Cc-e0 approach implies that the the compressibility varies by 30± %.
However, the Janbu methods shows it to vary only by 10± %. The modulus number, m, ranges from 18 through 22; It would be unusual to find a clay with less variation
50
0.40 0.60 0.80 1.00 1.20
VOID RATIO, e0
N 50
0.400.600.801.001.20
VOID RATIO, e0
NO
find a clay with less variation.
What about “Immediate Settlement” and Consolidation? 66
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
34
CE 5101 - SETTLEMENTS AND 1D Compression TheorySettlements of Soils - Immediate, Delayed, and Creep Compressionp p
Terzaghi’s Theory of 1D ConsolidationTerzaghi s Theory of 1D ConsolidationEffects of Drainage and Initial Stress Distribution
SPREADSHEET Calculations (UNISETTLE)Finite Element Analysis (PLAXIS)
67
Foundation Settlement Issues
How Much settlements will occur?
Interested in Ultimate settlements in fully drained state, as well as long-term creep settlements
How Fast and how long will it take for most of settlements to occur?
Involved Consolidation and SecondaryInvolved Consolidation and Secondary Compression theories to estimate rate of settlements, and
Methods to accelerate settlements and minimise long-term settlements
68
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
35
Types of Ground Movements and Causes of Settlements
•Compaction - due to vibrations, pile driving, earthquake
El ti V l t i S ttl t i OC Cl i i•Elastic Volumetric Settlement in OC Clay in recompression, use E’ and ’ or recompression index, Cr or
•Immediate or Undrained Settlement - Distortion without volume change, use Eu and u
•Moisture changes - Expansive soils, high LL and PI, high swelling and shrinkage
S ll P t ti l (%) 0 1(PI 10) l ( / ’)Swell Potential (%) = 0.1(PI-10) log (s/p’)
•Effects of vegetation - related to moisture changes by root system
•Effects of GWT lowering - shrinkage ad consolidation
69
Types of Ground Movements and Causes of Settlements
•Effects of temperatures - Frost heaving, drying by furnace and boilers
•Effects of seepage and scouring - Erosion by•Effects of seepage and scouring - Erosion by piping, scouring and wind action, mineral cement dissolved by GW eg limestone, rock salts and chalk areas
•Loss of lateral support - Footings beside unsupported excavation, movement of natural slopes and cuttings
•Effects of mining subsidence - collapse of ground cavities
•Filled ground - settlements of the fill soils, compaction, consolidation, and creep
70
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
36
Shrink/ swell potential is function of Clay Activity = %clay fraction/ PI
Swell Potential (%) = 0.1(PI-10) log (s/p’)
Where s=suction before construction and p’=final bearing pressure71
1D Settlements
Soil deformations are of two types:• Distortion (change of shape 2D effects)•Compression (change of volume)
Components of Settlements:
distortionsettlementimmediateswhere
ssss
i
scit
,
ncompressiosecondarys
ncompressiosettlementionconsolidats
distortionsettlementimmediateswhere
s
c
i
,
,
72
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
37
Undrained Immediate Settlements
Distortion of clay layer:•Calculate by elastic theory eg JanbuCalculate by elastic theory eg Janbu Chart
by JanbufactorsessdimensionlIandI
arealoadedflexibleforsettlementimmediateswhereE
qBIIs
i
i
)1( 210
layerclay of ratio sPoisson'
layerclay of modulus Undrained E
B dthfootong wi on loadAverage q
by JanbufactorsessdimensionlIandI 10
73
Immediate Settlements in Clays by Janbu
74
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
38
Example on Janbu Chart: Foundation 4x2m with q=150kPa, located at 1m in Clay layer 5m thick with Eu=40MN/m2. Below is second clay layer of 8m thickness and Eu=75 MN/m2.What is average settlement under foundation? Assume =0.5
D:MN/m40Ewithlayer,clay upperConsider(1)
9.0 0.5, 1/2D/B 2;4/2L/B Now2
u
0
H
DB mm5.35.01
40
2*150*7.0*9.0s
7.0 2,4/2L/B and 24/2H/B
y ,ypp( )
21i
1
u
mm3.25.0175
2*150*85.0*9.0s
85.0 2,4/2L/B and 612/2H/B
:MN/m75E withcombined, layers two Consider (2)
22i
1
2u
mm9.15.0175
2*150*7.0*9.0s
7.0 2,4/2L/B and 24/2H/B
:MN/m75E withlayer, upper Consider (1)
23i
1
2u
mm 3.9 1.9 -2.3 5.3s
ssss
;inciplePrionSuperposit By
i
3i2i1ii
75
1D Primary Consolidation Settlements
Time delayed Primary Consolidation Compression:
water
solids
0e
1
e
0H
H
)()(
Δ
00
0
volumeverticalc
0volumevertical
HHHs
e1
e
H
H
'vv P where P), vs(e methodm e
P
e -ility compressib of coeffnav
a1e0e
fe
fP0P P
0
v
0v e1
a
P
1
)e(1
e -change volume of coeffnm
00
vc
0v00
c
HPe1
a s
HPm He1
e sH
76
CE5101 Consolidation and SeepageLecture 5
Prof Harry TanSEP 2011
39
mv and Constrained Modulus D
For wide loaded area, get 1D compression d K diti l ti d l t lunder Ko condition, elastic modulus to apply
is called the Constrained Modulus D defined by:
hlftC ffi ih
211
1E
m
1D
v
0.35)( ratio Poisson drained Soil
elasticity of modulus drained Soil E
changevolume oftCoefficienmwhere v
77
Sc by (e vs logP) Method
Normally Consolidated Clays - non-linear stress strain for soil, but linear in logP