ce5101 lecture 6 - 1d consolidation - terzhagi theory (oct 2013).ppt
DESCRIPTION
CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).pptTRANSCRIPT
![Page 1: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/1.jpg)
1
CE 5101 Lecture 6 – 1D Consolidation
Oct 2013
Prof Harry Tan
![Page 2: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/2.jpg)
2
Outline
• Terzaghi Theory• Useful Elastic Solutions• Oedometer Tests• FEM Theory• FEM compared with Terzaghi• Consolidation of Realistic Soils• Example of Consolidation in Reclaimed Land• Secondary Compression and Creep
![Page 3: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/3.jpg)
3
Terzaghi 1D Vertical Flow
• Formulation of Theory
• Useful Approximations
• Elastic Solutions
![Page 4: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/4.jpg)
4
1D CONSOLIDATION
Assumptions made:
soil is fully saturated
pore water is incompressible
Darcy's law is valid
isotropic (constant) permeability
linear elastic soil behaviour
load applied instantaneously
one-dimensional problem (length of applied load > ∞)
![Page 5: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/5.jpg)
5
1D CONSOLIDATION
soft clay layerfully saturated
z
pw = pw, o
´ = ´
rigid impermeable layer
D
initialground surface apply surcharge loadrapidly
rigid impermeable layer
pw = pw, o + pw, t=o
pw, t=o =
´ = ´
t = 0
rigid impermeable layer
pw = pw, o + pw, t
pw, t = t´
´ = ´ + t´
settlement st
0 < t < ∞
consolidation takes place
rigid impermeable layer
pw = pw, o
´ = ´ +
settlement s
t = ∞
consolidation process completed
![Page 6: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/6.jpg)
6
1D CONSOLIDATION
2w
2
vw
z
pc
t
p
w
oedv γ
Ekc
0m
TMt
v2
eM
21U
the change in pore pressure (pw) with time and position within the layer can be expressed by the partial differential equation
with
cv …. coefficient of consolidation
with boundary conditions:pw = 0 at the top of layer (independent of t)no flow at bottom of layerpw = at t = 0 (independent of z)
pw = 0 at t = ∞ (independent of z)
1m22
1M
![Page 7: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/7.jpg)
7
1D CONSOLIDATION
tDγ
Ek
D
tcT
2w
oed2
v
v
Ut ……… average degree of consolidation
Tv ……… dimensionless time factor
s
s
p
ppU t
0,w
t,wo,wt
NOTE:
D .... drainage path, NOT thickness of layer !
U .... depends on Tv and boundary conditions
Tv ... depends on problem (pw, o - distribution)
![Page 8: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/8.jpg)
8
1D CONSOLIDATION
clay layerfully saturated
z
/ w
t = 0
impermeable
45°
t = t1 t = t2
t = t = t3
horizontal tangent > dv/dz = 0 (no flow) at bottom boundary
slope of Isochrones > hydraulic gradient
t1: bottom of layer not yet influenced by consolidation process
D
surcharge load
![Page 9: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/9.jpg)
9
1D CONSOLIDATION
degree of consolidation Ut
permeable
permeable
D
D
Tv
Isochrones: lines of excess pore pressures (pw, t) at a given time
![Page 10: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/10.jpg)
10
Terzaghi 1D Vertical Flow Consolidation
5.0..,2.0 vv UeiT
21.0
442
22
18
1v
vTT
v eeU
v
v
TU 2
For
Then
For
Then
5.0..,2.0 vv UeiT
Tv is Time factor
cv is Coeficient of Consolidation
wv
vv
vv
m
kc
H
tcT
2
![Page 11: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/11.jpg)
11
Drainage Boundaries
When k is 2 orders smaller it behaves like an impermeable boundary eg
k=1e-8 m/s is an impermeable boundary to sand of k=1e-6 m/s
![Page 12: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/12.jpg)
12
Initial Excess Pore Pressures Distributions
Case 0 Case 0
Case 0
Case 0
Case 1 Case 2
![Page 13: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/13.jpg)
13
Initial Excess PP Distributions
![Page 14: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/14.jpg)
14
Initial Excess PP Distributions
![Page 15: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/15.jpg)
15
Initial Excess PP Distributions
![Page 16: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/16.jpg)
16
Superposition of Elastic Solutions
drained
undrained
= +
Case 0 Case 1
A A0A1
For a given Tv, find U0 and U1
Combined U = U0(A0/A) + U1(A1/A)
What may produce this initial Excess PP??
Reclaimed Clay Fill self weight combined with
Imposed Sand Capping weight above reclaimed clay fill
![Page 17: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/17.jpg)
17
Superposition of Elastic Solutions
• Let ultimate settlement be SAf
• Then degree of consolidation for A is: • By definition:
• Therefore: • Now the amount of settlement is proportional to the area under the
pore pressure isochrones. Thus the ultimate settlement is proportional to the area of the initial excess PP isochrones:
•
• Therefore,
AfAfAfA S
AS
S
AS
S
ASU
)1()0()(
fAA
fAA S
ASU
S
ASU
11
00
)1(;
)0(
Af
fAA
Af
fAAA S
SU
S
SUU 1
10
0
A
A
Af
fA
A
A
Af
fA
A
A
S
S
A
A
S
S1100 ;
A
AA
A
AAA A
AU
A
AUU 1
10
0
![Page 18: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/18.jpg)
18
1D Consolidation Test (Oedometer Test)
Void ratio corresponding to full consolidation for each load increment is calculated backwards from final water content and final thickness readings
![Page 19: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/19.jpg)
19
e vs P curve depends on stress historydeposition gives normal curve (Normally Consolidated Soils)unloading by erosion or removal of soil load gives swelling curve (Over-consolidated Soils)
![Page 20: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/20.jpg)
20
By Eye Method for Determining Pc
![Page 21: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/21.jpg)
21
Casagrande Method for Determining Pc
![Page 22: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/22.jpg)
22
EX Casagrande Method for Determining Pc
![Page 23: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/23.jpg)
23
Log-log Method for Determining Pc
![Page 24: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/24.jpg)
24
Determine Pc - Janbu
Pc
![Page 25: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/25.jpg)
25
Idealized 1D Consolidation e-logP Curve
![Page 26: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/26.jpg)
26
Correction to get Field Curve for NC Clays
![Page 27: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/27.jpg)
27
Correction to get Field Curve for OC Clays
![Page 28: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/28.jpg)
28
Factors Affecting Accuracy of Pc
Sample DisturbanceLoad Increment Ratio
![Page 29: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/29.jpg)
29
Factors Affecting Accuracy of Pc
Load Increment Duration
Related to the influence of secondary compression on test results
![Page 30: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/30.jpg)
30
Taylor Square root time Method for cvExperimental CurveTheory Curve
Correction ratio =0.9209/0.7976=1.15
Tv90 = 0.848
![Page 31: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/31.jpg)
31
Casagrande Log time Method for cv
Correction for U0 based on parabolic relation upto U50
![Page 32: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/32.jpg)
32
Example of Use of Sqrt time and log time methods
![Page 33: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/33.jpg)
33
Rectangular Hyperbolic Method for cvSridharan and Prakash 1981,1985
2972.0B
tfor35.1A
tfor04.2A
where
c
BmHcand
)1A(m
ct
,Therefore
Amt/tcmt
CMT
/t
U/T
90
60
2
v
![Page 34: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/34.jpg)
34
Example of Hyperbolic Method
![Page 35: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/35.jpg)
35
What is a high quality test?
![Page 36: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/36.jpg)
36
Cv is one order larger in OC state compare to NC state
![Page 37: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/37.jpg)
37
FEM Theory
• Formulation
• Stress Equilibrium – Deformation Part
• Continuity Equilibrium – Hydraulic Part
• Global Assembly
• Step by step Integration (Implicit Method)
• Output
![Page 38: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/38.jpg)
38
FINITE ELEMENT FORMULATION FOR CONSOLIDATION (1)
Effective stresses
Constitutive law
Discretization
In terms of excess pore pressure same shape functions for
displacements and pore pressures
![Page 39: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/39.jpg)
39
FINITE ELEMENT FORMULATION FOR CONSOLIDATION (2)
Mechanical problem: equilibrium equation
Stiffness matrix
Coupling matrix
Incremental load vector
![Page 40: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/40.jpg)
40
FINITE ELEMENT FORMULATION FOR CONSOLIDATION (2)
Hydraulic (flow) problem: continuity equation
Flow matrix
Coupling matrix
Water compressibility matrix
![Page 41: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/41.jpg)
41
FINITE ELEMENT FORMULATION FOR CONSOLIDATION (3)
Global system of equations
Step-by-step integration procedure
0 < < 1 ; Generally, fully implicit)
![Page 42: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/42.jpg)
42
FINITE ELEMENT FORMULATION FOR CONSOLIDATION (4)
Time step Automatic time stepping is required Critical time step
Consolidation analysis Prescribed time Maximum excess pore pressure
vc
H
80
2
vc
H
40
2
![Page 43: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/43.jpg)
43
FEM compare Terzaghi
![Page 44: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/44.jpg)
44
Plaxis Model at 1 day
Load = 100 kPa
![Page 45: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/45.jpg)
45
FEM compare Terzaghi
Terzhagi theory
Plaxis Ver 9.0
![Page 46: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/46.jpg)
46
FEM compare Terzaghi
Terzhagi theory
Plaxis
![Page 47: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/47.jpg)
47
Fully Coupled with Unsaturated Soil Model - Plaxis 2010
![Page 48: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/48.jpg)
48
Fully Coupled with Unsaturated Soil Model - Plaxis 2010
![Page 49: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/49.jpg)
49
Fully Coupled with Unsaturated Soil Model - Plaxis 2010
Results for Terzaghi’s 1D Consolidation Test
![Page 50: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/50.jpg)
50
Real Soils Consolidation
• Cv is not constant with consolidation process
• Both kv and mv (or Eoed) are varied as consolidation progress
• Cv is one order larger for OC state compared to NC state
![Page 51: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/51.jpg)
51
1D CONSOLIDATION – NUMERICAL SIMULATION
Investigate influence of:
compressibility of pore water (by means of B-value)
permeability depending on void
ratio
elastic-plastic soil behaviour(by means of changing constitutive model)
applied load = 100 kPasoil layer 2D = 10 mdrainage at top and bottom
![Page 52: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/52.jpg)
52
1D CONSOLIDATION – NUMERICAL SIMULATION
time [days]
0.01 0.1 1 10 100 1000
sett
lem
ent
[mm
]
0
20
40
60
80
100
reference elasticpore water compressible (B=0.85)permeability e-dependentHardening Soil model
![Page 53: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/53.jpg)
53
1D CONSOLIDATION – NUMERICAL SIMULATION
time [days]
0.01 0.1 1 10 100 1000
exce
ss p
ore
pre
ssu
re [
kPa]
-100
-80
-60
-40
-20
0
reference elasticpore water compressible (B=0.85)permeability e-dependentHardening Soil model
![Page 54: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/54.jpg)
54distribution of excess pore pressures at 50% consolidation along centre line
elastic Hardening Soil model
1D CONSOLIDATION – NUMERICAL SIMULATION
![Page 55: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/55.jpg)
55
influence of parameters in HS-model
time [days]
0.001 0.01 0.1 1 10 100
vert
ical
dis
pla
cem
ents
[m
m]
-120
-100
-80
-60
-40
-20
0
HS_ref B=0.85E50 <
E50 >
Ko_nc >
Ko_nc <
![Page 56: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/56.jpg)
56
influence of parameters in HS-model
time [days]
0.01 0.1 1 10 100
exce
ss p
ore
pre
ssu
re [
kPa]
-100
-80
-60
-40
-20
0
HS_ref B=0.85E50 <
E50 >
Eoed <
Ko_nc >
Ko_nc <
![Page 57: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/57.jpg)
57
influence of parameters in HS-model
time [days]
0.001 0.01 0.1 1 10 100
deg
ree
of
con
soli
dat
ion
[%
]
0
20
40
60
80
100
HS_ref B=0.85E50 <
E50 >
Eoed >
Ko_nc >
Ko_nc <
![Page 58: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/58.jpg)
58
Consolidation Modeling in a Reclaimed Land
Why a Mohr-Coulomb Model is grossly incorrect ?
![Page 59: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/59.jpg)
59
Consider a Reclaimed LandSand Loading in 365 days
10m Reclaim Sand
15m Marine Clay
Sea Bed
Closed consolidation boundaries all round
![Page 60: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/60.jpg)
60
Soil Parameters
Equivalent Oedometer Parameters in HS Model:
Cc=1.0 Cs=0.1 eo=2.0 and m=1.0 for logarithmic compression response
![Page 61: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/61.jpg)
61HS Model can produce results very close to Oedometer Test Data
![Page 62: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/62.jpg)
62
Compare Settlements of seabed
MC = 400 mm in 2500 days
HS = 4,350 mm in 12,700 days
Which Model is Correct ?
![Page 63: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/63.jpg)
63
Amount of Settlement
Single layer 1-D compression Estimate:
Cc=1.0, eo=2.0, Ho=15mPo = 7.5m*5 = 37.5 kPaP_inc = 10m*18 = 180 kPaPf = Po+P_inc = 217.5 kPaSett = Ho*Cc/(1+eo)*log(Pf/Po) = 15000*0.254 = 3,817 mm
• This is a single layer computation and it grossly under-estimate amount of settlements; but 3,817 mm >> 400 mm by MC Model, and is much closer to 4,330 mm by HS Model
• Thus HS Model gave realistic answer and MC Model is grossly incorrect
![Page 64: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/64.jpg)
64
Compare with Program UniSettle Using same oedometer parameters of Cc=1.0, eo=2.0;
UniSettle = 4428 mm
HS = 4350 mm
UniSettle 15-layer computation gave same results as Plaxis HS model
![Page 65: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/65.jpg)
65
Conclusions
• MC Model cannot be used for consolidation analysis of soft soils
• The linear elastic model in MC cannot predict both the rate and amount of consolidation settlements of highly nonlinear soft clays
• The HS Model with equivalent oedometer parameters will give very good predictions of both rate and amount of consolidation settlements
![Page 66: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/66.jpg)
66
Secondary Compression - Creep Effects, continued settlements under constant effective stress
![Page 67: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/67.jpg)
67
Definition of Secondary Compression Index
ionconsolidatprimary of end
at timetwhere
tt
log
ee
tlog
eC
p
p
p
![Page 68: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/68.jpg)
68
Bjerrum data on Secondary Compression in 1D Oedometer Test
Apparent Pc
![Page 69: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/69.jpg)
69
Relation between Instantaneous and delayed compression (a) for different thickness (b) for given thickness
Secondary compression index is independent of soil thickness for most cases
![Page 70: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/70.jpg)
70
Effect of Magnitude of Stress Increment: ratio of secondary to primary compression is largest when stress increment to initial stress is small
![Page 71: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/71.jpg)
71
Effects of Pre-consolidation Pressure on cv and C
![Page 72: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/72.jpg)
72
Typical values for C
NC Clays 0.005-0.02
Organic Clays, highly plastic > 0.03
OCR> 2 <0.001
Values of C/ Cc
Organic Silts 0.035-0.06
Peats 0.035-0.085
Canadian Muskeg 0.09-0.1
Singapore MC 0.04-0.06
SF Baymud 0.04-0.06
Leda Clay 0.03-0.06
![Page 73: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/73.jpg)
Creep Settlements by Janbu
73
Can identify 3 different phases for 3 different mechanisms of settlements:
• Immediate is Elastic Undrained Compression• Consolidation is Drained (elastic plus plastic) Cap Compression • Creep is time-dependent secondary compression at constant effective stress
![Page 74: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/74.jpg)
Creep Settlements by Janbu
74
![Page 75: CE5101 Lecture 6 - 1D Consolidation - Terzhagi Theory (OCT 2013).ppt](https://reader034.vdocuments.site/reader034/viewer/2022050802/55cf9b0a550346d033a47fde/html5/thumbnails/75.jpg)
Creep Settlements by Janbu
75