dokumen.tips_consolidation-of-soil-558467a7416fa.ppt

1
Consolidation of Soil
DR. M. Zayed

‫التربة‬‫تصلب‬

‫التر‬‫إلى‬ ‫حمآلهآ‬‫ا‬‫التربة‬‫على‬‫المقآمة‬ ‫ت‬‫المنشآ‬ ‫تنقل‬
‫سفلهآ‬‫ا‬‫بة‬
‫حبيب‬‫تيب‬‫ر‬‫لت‬‫إعآدة‬‫عنهآ‬‫ينتج‬ ‫إجهآدات‬‫شكل‬‫على‬
‫التربة‬ ‫آت‬
‫يحدث‬‫ي‬‫ا‬ ‫مكآنهآ‬‫من‬ ‫اح‬‫ز‬‫ت‬‫و‬‫ا‬ ‫بعضهآ‬‫من‬ ‫تتقآرب‬‫بحيث‬
‫في‬
‫التربة‬
”
‫تشكل‬
“
‫وبآل‬‫سآس‬‫ال‬ ‫يتحرك‬‫لذلك‬ ‫ونتيجة‬
‫المنشآ‬ ‫تآلي‬
‫التربة‬ ‫تشكل‬‫شكآل‬‫ا‬‫من‬ ً‫شكال‬ ‫يمثل‬‫وهذا‬‫سفل‬‫ل‬

‫التربة‬‫تصلب‬
Types of ground movements
‫بة‬‫ر‬‫ألت‬‫تشكالت‬ ‫نوأع‬‫أ‬

*
‫التصلب‬
:
‫تغير‬‫بهآ‬‫يحدث‬‫اإلجهآد‬‫في‬‫لزيآدة‬‫تعرضهآ‬‫عند‬‫فإنهآ‬‫ومشبعة‬‫نآعمة‬‫التربة‬‫كآنت‬‫إذا‬
‫يصآحبه‬‫الحجم‬‫في‬
‫ت‬‫عند‬‫ان‬‫ز‬‫الت‬‫درجة‬‫إلى‬‫الوصول‬‫إلى‬‫المآء‬‫ج‬‫و‬‫خر‬‫مع‬ ً‫تدريجيآ‬‫الحجم‬‫في‬‫التغير‬‫ويكون‬،‫ميآه‬‫ج‬‫و‬‫خر‬
‫الميآه‬ ‫ج‬‫و‬‫خر‬‫وقف‬
.

*
‫الدمك‬
.

*
‫الرطوبة‬‫تغير‬
.

*
‫الجوفية‬‫الميآه‬‫مستوى‬‫تفآع‬‫ر‬‫وا‬‫انخفآض‬
.

*
‫ارة‬‫ر‬‫الح‬‫درجة‬‫في‬‫تغير‬
.

*
‫والنحر‬‫التسرب‬
.

*
‫الزلزل‬
.

*
‫الهندسية‬‫عمآل‬‫ال‬
(
‫نفآق‬‫ال‬
.)

Compressibility ‫النضغآطية‬
 The volume of soil mass is decreased under stress.
this decrease is known as Compression, and the
copacity of soil to decrease in volume under stress
is known as compressibility.

‫خآرجي‬‫ضغط‬‫تحت‬ ‫الحجمي‬ ‫النقص‬‫هي‬‫النضغآطية‬
.
‫نت‬‫النضغآطية‬‫وتحدث‬
‫النقص‬‫يجة‬
‫الحبيبآت‬‫حجم‬‫في‬
(
‫نآدر‬
)
‫اغآت‬‫ر‬‫الف‬‫في‬ ‫النقص‬‫وكذلك‬ ،
.
‫ال‬ ‫إليه‬‫يعول‬‫وهذا‬
‫كبر‬‫ال‬‫جآنب‬
‫ا‬‫الجآفة‬‫التربة‬‫في‬ ‫اغآت‬‫ر‬‫الف‬‫من‬ ‫الهواء‬‫يهرب‬‫حينمآ‬ ‫النضغآطية‬‫من‬‫والمؤثر‬
‫تهرب‬‫حينمآ‬‫و‬
‫المشبعة‬‫التربة‬‫اغآت‬‫ر‬‫ف‬‫من‬‫الميآه‬
.

Mechanical modeling of the
consolidation process
piston
Water
Spring
10kg
10kg
10kg
10kg
10kg
Stop
cock Water
out Water
out Water
out
(a) (b) (c) (d) (e) (f)
Spring load (kg): 0 2.5 5 7.5 10
Water load (kg): 10 7.5 5 2.5 0
Consolidation %: 0 25 50 75 100

Consolidation
When soil is loaded undrained, the pore pressures
increase. Then, under site conditions, the excess pore
pressures dissipate and water leaves the soil, resulting
in consolidation settlement. This process takes time,
and the rate of settlement decreases over time.
1
eo
Time = 0+ Time = 

What is Consolidation?
When a saturated clay is loaded externally,
saturated clay
GL
the water is squeezed out of the clay over a long time
(due to low permeability of the clay).

What is Consolidation?
This leads to settlements occurring over a long time,
which could be several years.
time
settlement

In granular soils…
Granular soils are freely drained, and thus the
settlement is instantaneous.
time
settlement

During consolidation…
Due to a surcharge q applied at the GL,
GL
saturated clay
q kPa
A
the stresses and pore pressures are increased at A.

u
’-
..and, they vary
with time.

During consolidation…
 remains the same (=q) during consolidation.
GL
saturated clay
q kPa
A

u
’
-
u decreases (due to drainage)

u
’
q
transferring the load from water to the soil.
while ’ increases,

One Dimensional Consolidation
• drainage and deformations are vertical (none laterally)
saturated clay
GL
q kPa
• a simplification for solving consolidation problems
reasonable
simplification if the
surcharge is of
large lateral extent
water squeezed out

H -e Relation
saturated clay
GL
q kPa
saturated clay
GL
q kPa
Ho
Time = 0+
e = eo
H
Time = 
e = eo - e
average vertical strain =
o
H
H


H -e Relation
Consider an element where Vs = 1 initially.
e
1
eo
Time = 0+ Time = 
average vertical strain =
o
e
e


1

H -e Relation
Equating the two expressions for average
vertical strain,
o
e
e


1


o
H
H
consolidation
settlement
initial thickness of
clay layer
initial void ratio
change in void ratio

Definitions ‫تعآريف‬

Coefficient of compressibility ‫النضغآطية‬ ‫معآمل‬
• denoted by av
• is the ratio of change in void ratio to the
corresponding chang in stress
•‫الضغط‬‫في‬‫الزيآدة‬‫لوحدة‬‫اغآت‬‫ر‬‫الف‬‫نسبة‬‫في‬‫النقص‬‫هو‬
volume
original
volume
in
change

Change void
Change stress



 V
V
mv
no
units
a
e
e
e0
e1
ờ0 ờ1 ờ

Coefficient of volume compressibility
• denoted by mv
• is the volumetric strain per unit increase in stress
•‫الفعال‬ ‫الضغط‬ ‫وحدة‬ ‫لزيادة‬ ‫المقابل‬ ‫الحجم‬ ‫في‬ ‫التغير‬ ‫كمية‬ ‫هي‬
volume
original
volume
in
change




 V
V
mv =
av
1+e0

Compression index Cc
‫النضغآط‬‫معآمل‬
void
ratio
-
e
pressure kNm-2
1000
100
1.0
0.6
straight line
phase
e = e0 - Cc log10 [ /  0]
‫بين‬‫العالقة‬ ‫رسم‬‫يمكن‬‫المعملية‬‫العالقة‬‫من‬
e, log10
‫النضغآط‬‫معآمل‬‫ميله‬‫يسمى‬‫مستقيم‬‫بخط‬‫العالقة‬‫هذه‬‫فتنتهي‬
cc
Cc =
-e
 Log 
e0-e1
log10 [ / 0]
=

‫اند‬‫ر‬‫كآزج‬‫طريقة‬
Casagrande
‫سآبق‬‫مؤثر‬‫إجهآد‬ ‫قصى‬‫ا‬‫لتحديد‬
pressure kNm-2
1000
100
1.0
0.6
straight line phase
lab. virgin curve
tangent to max curvature
line from tangent
bisector
pc
p0
P Q
T
R
C
B
S

‫اند‬‫ر‬‫كآزج‬‫طريقة‬Casagrande

‫تية‬‫ال‬‫الخطوات‬‫في‬‫وتتلخص‬‫بيآنية‬‫اند‬‫ر‬‫اج‬‫ز‬‫كآ‬ ‫طريقة‬
:
1
-
‫العالقة‬ ‫رسم‬
e - log
2
-
‫نقطة‬‫تحديد‬
p
‫للمنحنى‬‫تحدب‬ ‫قصى‬‫ا‬‫عندهآ‬‫التي‬
(
‫انحن‬‫قطر‬‫نصف‬ ‫صغر‬‫ا‬‫عند‬ ‫ي‬‫ا‬
‫آء‬
.)
3
-
‫فقي‬‫ال‬‫الخط‬‫يرسم‬
PQ
‫نقطة‬‫عند‬
P
‫وليكن‬ ‫عندهآ‬‫للمنحنى‬‫ممآس‬‫وكذلك‬
PT
.
4
-
‫اوية‬‫ز‬‫ال‬‫منصف‬‫يرسم‬
QPT
‫الخط‬‫وهو‬
PR
.
5
-
‫النضغآط‬‫منحنى‬ ‫امتداد‬‫مع‬‫المنصف‬‫تقآطع‬
CB
‫نقطة‬‫يعطي‬
S
‫قصى‬‫ا‬‫يقآبلهآ‬ ‫والتي‬
‫سآبق‬‫مؤثر‬‫إجهآد‬
 PC
.

‫اند‬‫ر‬‫كآزج‬‫طريقة‬Casagrande
‫قيمة‬‫نة‬‫ر‬‫وبمقآ‬
 PC
‫تية‬‫ال‬‫الحآلت‬‫إحدى‬‫في‬‫التربة‬‫تكون‬‫الحآلي‬‫المؤثر‬ ‫الضغط‬‫قيمة‬‫مع‬
:
-
‫التصلب‬‫عآدل‬‫طين‬
Normally consolidated clay
‫حيث‬
ờ0=ờPC
‫طينية‬‫نربة‬‫ي‬‫ا‬
‫اء‬‫ر‬‫عذ‬‫تربة‬‫نهآ‬‫ا‬‫ي‬‫ا‬‫عليهآ‬‫المؤثر‬‫الحآلي‬ ‫الضغط‬‫تفوق‬‫لضغوط‬‫تعرضت‬‫ن‬‫ا‬‫لهآ‬‫يسبق‬‫لم‬
‫تصلبهآ‬‫يسبق‬‫لم‬
.
-
‫التصلب‬‫سآبق‬‫طين‬
Preconsolidated clay
‫حيث‬
ờPC>ờ0
‫ن‬‫ا‬‫سبق‬‫تربة‬‫ي‬‫ا‬
‫ا‬‫تصلب‬‫في‬‫تسبب‬‫قد‬ ‫الضغط‬‫وهذا‬ ً‫حآليآ‬‫عليهآ‬‫المؤثر‬ ‫الضغط‬‫يفوق‬‫لضغط‬‫تعرضة‬
‫لتربة‬
.
-
-
‫التصلب‬‫تحت‬‫طين‬
underconslidsted clay
‫حيث‬
ờPC<ờ0
‫ي‬‫ا‬
‫التربة‬‫ن‬‫ا‬
‫وقيمة‬ ‫التصلب‬‫احل‬‫ر‬‫م‬‫في‬‫الت‬‫ز‬‫مآ‬
ờPC
‫التصل‬ ‫عملية‬ ‫ألن‬ ‫نهائية‬ ‫تعتبر‬ ‫ال‬
‫ب‬
‫مستمرة‬ ‫مازالت‬
.

Coefficient of volume compressibility
Soil Type mv (cm2/kg)
Very highly compressible >0.1
highly compressible 0.1 – 0.02
Med. compressible 0.02 – 0.005
Low compressible 0.005 – 0.002
Very low compressible <0.002

Terzaghi’s theory of consolidation
‫للتصلب‬‫اجي‬‫ز‬‫تر‬‫نظرية‬
‫البيني‬‫الميآه‬ ‫ضغط‬‫قيمة‬‫بحسآب‬ ‫اجي‬‫ز‬‫تر‬‫نظرية‬‫تعني‬
‫عند‬‫ة‬
‫نتيج‬‫معين‬‫زمن‬‫بعد‬‫التربة‬‫في‬‫معين‬ ‫عمق‬‫على‬‫نقطة‬
‫ة‬
‫إضآفي‬‫لجهد‬‫التربة‬‫تعرض‬
.
‫حسآب‬‫ذلك‬‫ويتبع‬
‫رض‬‫ال‬‫لسطح‬‫المقآبل‬ ‫والهبوط‬‫بآلتدعيم‬‫النضغآط‬
.

Terzaghi’s theory of consolidation
‫للتصلب‬‫اجي‬‫ز‬‫تر‬‫نظرية‬
‫اجي‬‫ز‬‫تر‬ ‫اضآت‬‫ر‬‫افت‬

ً‫تمآمآ‬ ‫ومتجآنسة‬ ‫مشبعة‬ ‫العينة‬‫إن‬
.

‫لالنضغآط‬‫قآبلة‬‫غير‬‫التربة‬ ‫حبيبآت‬‫وكذلك‬ ‫الميآه‬
.

‫دارس‬‫قآنون‬
Darcy’s low
‫للتطب‬‫صآلح‬‫التربة‬‫خالل‬ ‫الميآه‬‫لسريآن‬
‫يق‬
.

‫التصلب‬ ‫عملية‬‫خالل‬‫ثآبت‬‫يظل‬ ‫النفآذية‬ ‫معآمل‬
.

‫ثآبت‬‫يظل‬‫اغآت‬‫ر‬‫الف‬‫نسبة‬‫في‬‫للتغير‬ ‫المقآبل‬‫الحجمي‬‫التغير‬
.

Consolidation Test

Consolidation Test
Increment of load
Topcap
porous stone
sample
water confining
ring
settlement
dial gauge

Consolidation Test

‫مقلقلة‬‫غير‬‫التربة‬‫من‬ ‫عينة‬‫تجهز‬
Undisturbed
‫حلقة‬‫في‬‫وتوضع‬
‫قطرهآ‬ ‫الختبآر‬
75
‫تفآعهآ‬‫ر‬‫وا‬‫مم‬
15
–
20
‫بين‬ ‫الحلقة‬‫هذه‬‫توضع‬ ‫حيث‬‫مم‬
‫نآفذين‬‫حجرين‬
Porous Stones
‫يمكن‬ ‫كمآ‬ ‫متر‬‫و‬‫يدر‬‫ال‬ ‫خلية‬‫داخل‬
‫مشكلة‬ ‫عينآت‬ ‫اختبآر‬ ‫حيآن‬‫ال‬‫بعض‬‫في‬
Remoulded
‫التجربة‬‫وتعمل‬
‫يعمل‬ ‫فقط‬ ‫سي‬‫ا‬‫ر‬‫ال‬‫التجآه‬‫قي‬ ‫العينة‬‫تشكل‬‫يكون‬ ‫ن‬‫ا‬‫على‬
Porous
Plate
‫خآرجه‬‫وإلى‬ ‫العينة‬‫داخل‬ ‫من‬‫بآلحركة‬ ‫للميآه‬‫السمآح‬‫على‬
‫آ‬
.

Consolidation Test

Double drainge
‫ال‬‫يقآس‬ ‫سي‬‫ا‬‫ر‬‫إستآتيكي‬‫حمل‬ ‫العينة‬‫على‬‫يؤثر‬ ‫كمآ‬
‫في‬ ‫هبوط‬
‫ق‬‫تستغر‬‫احل‬‫ر‬‫م‬ ‫على‬‫التجربة‬‫اء‬‫ر‬‫إج‬‫ويتم‬ ‫النفعآل‬‫بمقيآس‬ ‫العينة‬‫سمك‬
24
‫و‬‫ا‬ ‫سآعة‬
48
‫سآعة‬

‫حمآل‬‫بآ‬
0.25,1,2,4,8 kg/cm2

‫ت‬‫ا‬‫ر‬‫وق‬
½, 1,2,4,8,15,30 min,1,2,4,8,24 hours

‫م‬ ‫سي‬‫ا‬‫ر‬‫ال‬ ‫الحمل‬‫ال‬‫ز‬‫ي‬ ‫حمل‬ ‫خر‬‫ا‬‫تحت‬ ‫التصلب‬‫عملية‬‫في‬‫التجربة‬‫إتمآم‬‫وبعد‬
‫و‬‫ا‬‫واحدة‬ ‫رة‬
‫النتفآخ‬‫ومنحنى‬ ‫النهآئي‬‫المآئي‬‫المحتوى‬‫يعين‬‫ثم‬‫احل‬‫ر‬‫م‬ ‫على‬
.

Consolidation Test

‫والجهآد‬ ‫اغآت‬‫ر‬‫الف‬‫نسبة‬‫بين‬ ‫العالقآت‬‫ترسم‬ ‫الختبآر‬‫نتآئج‬ ‫من‬
e- 
‫كمآ‬
‫تعي‬ ‫ويمكن‬ ‫سي‬‫ا‬‫ر‬‫ال‬ ‫والنفعآل‬‫المؤثر‬ ‫اإلجهآد‬‫بين‬ ‫العالقآت‬‫ترسم‬
‫العوامل‬ ‫ين‬
k & mv & cv
 Cv = coefficient of consolidation
 Mv = coefficient of volume change
 K = coefficient of permeability

Consolidation Test
• simulation of 1-D field consolidation in lab.
field
GL
lab
undisturbed soil
specimen
Dia = 50-75 mm
Height = 20-30 mm
metal ring
(oedometer)
porous stone

Consolidation Test
H1
q1
eo- e1
)
1
(
1
1 o
o
e
H
H
e 



eo
Ho
q2
loading in increments

 2
e
allowing full consolidation before next increment

Consolidation Test
unloading

e – log v’ plot
log v’
void
ratio
loading
v’ increases &
e decreases
unloading
v’ decreases &
e increases (swelling)
- from the above data

Compression and recompression indices
log v’
void
ratio
1
Cc
Cc ~ compression index
Cr ~ recompression index
(or swelling index)
1
Cr
1
Cr

SIVA Copyright©2001
Preconsolidation pressure
log v’
void
ratio
p’
preconsolidation pressure
is the maximum
vertical effective
stress the soil
element has
ever been
subjected to

Virgin Consolidation Line
log v’
void
ratio
virgin consolidation line
p’
vo’
eo
eo, vo’
original
state

Overconsolidation ratio (OCR)
log v’
void
ratio
virgin consolidation line
p’
vo’
eo
original
state
Field
vo’
'
'
vo
p
OCR




Overconsolidation ratio (OCR)
log v’
void
ratio
OCR=1
OCR=2
OCR=2
OCR=13
OCR=13
~current state
VCL
Normally
consolidated
clay
Slightly
overconsolidated clay
Heavily
overconsolidated clay

More to come…

Settlement computations
eo, vo’, Cc,
Cr, p’, mv
-oedometer
test
=q
q kPa
H
Two different ways to estimate the
consolidation settlement:
(a) using mv
(b) using e-log v’ plot
settlement = mv  H
H
e
e
settlement
o



1
next slide

~ computing e using e-log v’ plot
'
'
'
log
vo
vo
c
C
e


 



initial
vo’
eo
vo’+ 
e
If the clay is normally consolidated,
the entire loading path is along the VCL.

'
'
'
log
vo
vo
r
C
e


 



vo’
initial
eo
vo’+ 
If the clay is overconsolidated, and remains so by
the end of consolidation,
e
VCL
note the use of Cr

'
'
'
log
'
'
log
p
vo
c
vo
p
r C
C
e




 




vo’
initial
eo
vo’+ 
If an overconsolidated clay becomes normally
consolidated by the end of consolidation,
VCL
p’
e

One-dimensional
consolidation theory

One-dimensional
consolidation theory
A simple one-dimensional consolidation model consists of rectilinear
element of soil subject to vertical changes in loading and through
which vertical (only) seepage flow is taking place.
There are three variables:
1. the excess pore pressure ()
2. the depth of the element in the layer (z)
3. the time elapsed since application of the loading (t)
 The total stress on the element is assumed to remain constant.
 The coefficient of volume compressibility (mv) is assumed to be
constant.
 The coefficient of permeability (k) for vertical flow is assumed to be
constant.

Mathematical model and equation
Consider the element of consolidating soil. In time dt:
· the seepage flow is dq
(q = A k i = A k dh/dz)
· the change in excess pressure is

 By defining the coefficient of consolidation
as

this can be written:


Terzaghi's solution
 General solution
 Drainage path length
 The basic equation is
 (z,t) is excess pore pressure at depth z after time t.
The solution depends on the boundary conditions:
The general solution is obtained for an overall (average)
degree of consolidation using non-dimensional factors.

Terzaghi's solution
 General solution
 The following non-dimensional factors are used in order to obtain a
solution:
 · Degree of consolidation at depth z
 · Time factor

 · Drainage path ratio

Terzaghi's solution
 The differential equation can now
be written as:
 If the excess pore pressure is
uniform with depth, the solution is:
 Putting Ut = rt/r¥ = average degree
of consolidation in the layer at
time t:


Drainage path length
During consolidation water escapes from the soil to the surface or to
a permeable sub-surface layer above or below (where = 0). The rate
of consolidation depends on the longest path taken by a drop of
water. The length of this longest path is the drainage path length, d.
Typical cases are:
An open layer, a permeable layer both above and below (d = H/2)
A half-closed layer, a permeable layer either above or below (d = H)
Vertical sand drains, horizontal drainage (d = L/2)

Determination of cv from test results
The Root-Time method
The Log-Time method

The Root-Time method
‫الزمن‬ ‫جذر‬ ‫طريقة‬


‫النفعآل‬‫مقيآس‬‫اءة‬‫ر‬‫ق‬‫بين‬‫العالقة‬‫توقيع‬‫وهي‬
dial gauge
‫والجذر‬‫العينة‬‫سمك‬ ‫تغير‬‫عن‬‫المعبرة‬
‫المقآبل‬‫التربيعي‬
(
‫بآلدقيقة‬
)

‫ـ‬‫ل‬‫المقآبل‬‫الزمن‬‫يعين‬‫ة‬‫ر‬‫المذكو‬‫العالقة‬‫من‬
90
%
‫بمقدار‬‫المنحني‬‫على‬‫يصعد‬‫الذي‬‫تصلب‬
1.15
‫الخط‬‫عن‬
‫عند‬‫المستقيم‬
90
%
‫ذلك‬‫بعد‬‫ويعين‬‫تصلب‬
cv
 where d = drainage path length
[d = H for one-way drainage, d = H/2 for two-way
drainage]

The Log-Time method
‫الزمن‬‫لوغآريتم‬ ‫طريقة‬

dokumen.tips_consolidation-of-soil-558467a7416fa.ppt

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