Stone column

1
 What is Stone Column?
A stone column is a cylindrical element constructed by drilling a hole in
ground and back filling the same with compacted granular material.

2
 Stone Columns
 Amongst various techniques for improving in-situ
ground conditions, stone columns are probably the most
versatile, due to their ability to perform a variety of
important geotechnical functions.

 Load bearing columns of well compacted coarse

aggregate installed in the ground to serve various
purposes such as reinforcement, densification and
drainage.
Purpose
• To carry most of the super structure load
(surrounding ground also takes load 10 to 20 %
of Δp)
• To improve average stiffness of ground
Due to high angle of internal friction and stiffness of stone
column when compared to that of in-situ weak soil,
majority of applied load is transferred to stone column.
As a result, less load is transferred to surrounding weak
soil which leads to reduction in settlement.
 Applicable Soil Types
 Soft,Non-Compactible, Weak Soils
 Granular Soils with High Fines Content (in
excess of 15%)
 Organic Soils
 Marine/Alluvial Clays
 Liquefiable Soils
 Reclaimed Fly Ash/Pond Ash Ponds
 Functions
 Improve the bearing capacity of weak soils.
 Carry high shear stresses by acting as stiff elements and
hence increase the stability of embankments founded on
soft ground.
 Facilitate radial drainage (by acting as vertical drains)
and dissipate rapidly the excess pore water pressure
leading to acceleration of consolidation process and
reduced post-construction settlements.
 Mitigate the potential for liquefaction and damage by
preventing build up of high pore pressure, providing a
drainage path and increasing the strength and stiffness
of the ground.
 Settlement Control
 Stone columns should extend through weak soil to
harder firm strata to control settlements.
 Provision of stone columns does not reduce the entire
consolidation settlement. The reduction depends on the
spacing of stone columns (generally 2.0 to 3.0 m c/c
over the site). (1.5D to 3.0 D where D = dia. of stone
column)
 Maximum percentage reduction of settlement is 75%.
Advantages (Slocombe, 2000) of the stone columns over conventional
methods of ground improvement technique may be described as follows:

Increase in load carrying capacity

Significant reduction of settlement
Being granular and free draining , consolidation settlement will be minimum
Installation is relatively simple and involves low energy input or moderate
labour
Increase in resistance to liquefaction
Cost effective

9
 History

 In France in 1830 (Adalier, 2004) stone column was applied to

improve native soil.

 Stone columns (Black et al., 2006) have been in limited use in the
U.S. since 1972.

 This method has been used extensively in Europe for site

improvement since the late 1950.

 First recorded use of vibro float (Basarkar, 2009) in India was at

Madras in 1961.

 In Gujarat, at Kandla, stone column first applied for oil storage tank
foundation (Desai et al. 1990).
10
 Applications of Vibro Replacement

Tank foundations Highway embankments Railway embankments

Others
• Industrial structures
• Bridge approaches

Reinforced earth walls Individual footings • Runways

 GPS Antenna

Vibrator String +
Stone Feeder Pipe

Seabed

Very Soft to Med. Stiff Clay

Marine Deep Vibratory

Stiff to Very Stiff Clay Replacement Columns
 Ground Improvement below RE wall

qL
qD
Backfill soil
Reinforced
soil

H
0.6 m Granular Blanket
(clean medium to coarse
GL sand)
1.0 m

Foundation soil
Depth of improvement

Stone column
Dia. = 0.6 m to 1.0m , c/c spacing = 1.5 to 3 times dia.
Filling material in stone column = 20 mm to 60mm size aggregate
 Putrajaya Bridge Approach
Embankment
R.C. Structure
RL +32.0 Top of Bridge Deck

Water Lev. RL +21.5

Embankment
RL +12.0 Pile cap

Bored piles
Stone columns Stone columns
 Storage Tanks

Hazira LNG Terminal, Gujarat

 Clay Silt Sand Gravel Stone

100 100

80 80

60 Vibro Replacement 60
Percentage Passing

Vibro Compaction
40 40

20 20

0 0,002 0,006 0,02 0,06 0,2 0,6 2,0 6,0 20 60 0

Grain size [mm]

Figure Range of Soils Suitable for Treatment

Installation Technique
(A) Vibro-compaction process

Figure The Vibro-compaction Process

 soils containing less than 30-40% of fines
 vibration and water jet
Relative density 70-90%
 non cohesive soil 20
Effect of Vibro Compaction
In non-cohesive granular soils, such as sand and
gravel, the passage of the vibrating probe causes a
liquefaction and an almost immediate densification
and settlement.
(B)Vibro-replacement process

Figure Vibro-replacement process

 suitable for cohesive soil

Stone 12 -75 mm
No vibration
Water jet or air jet 23
Vibro-Replacement Procedures:

Stage1: The jet at the bottom of the

Vibroflot is turned on and lowered
into the ground
Stage2: The water jet creates a quick
condition in the soil. It allows the
vibrating unit to sink into the ground
Vibro-Replacement Procedures (cont.):

Stage 3: Granular material is poured from the

top of the hole.
Vibro-Replacement Procedures (cont.):

Stage 4: The vibrating unit is gradually raised

in about 0.3-m lifts and held vibrating for
about 30 seconds at each lift. This process
compacts the soil to the desired unit
weight.
 Method of installation
Different methods of
making hole
Filling hole
Compacting the stone
 Installation Techniques
1. Rammed Stone Column Technique
Wet Top-Feed Method
2. Vibro-Replacement
Dry Bottom-Feed Method
Rammed Stone Column by Cased Borehole Method (Datye and Nagaraju, 1975)

 Rammer wt 15 kN to 20 kN
 Height of fall 1 m to 1.5 m
 Rammed Stone column (Rao 1982)

Figure Rammed stone column process

 Rammer wt 125 kg
 Height of fall 0.75m
32
Installation Methods – Wet & Dry
Installation Process (Wet Top Feed Method)

Penetration & Column

Completion
Flushing Construction
Installation Process (Dry Bottom Feed Method)

Delivery and Compaction

Penetration Completion
Process of Stones
Typical Exposed Vibro Stone column
Typical Exposed Vibro Stone column
Stone Column after Installation
Post-Installation Quality Control (Load Test)
Depth Vibrators (Electrically Powered)
 Depth Vibrator (Courtesy of Keller Group)
Air Chamber and Lock

Extension Tube

Flexible Coupling

Electric Motor

Stone Feeder Pipe

Eccentric Weight

Top-Feed Vibrator Bottom-Feed Vibrator

Advantages

 More economical than piling

 pile cap be eliminated as just granular layer is enough to transfer the load
to the stone column
 Significantly reduces consolidation settlement
 Immediate Increase of shear strength and friction angle of treated soil
 No waiting period after installation as compared to PVD. Embankment
construction can commence immediately after installation of stone column
to full height of embankment.
 Better performance in liquefaction mitigation as compare to pile

56
Stone column

57
 Cu = 10 kPa
Cu = 30 kPa

Stone column

58
 σrL σrL

15 m
11 m
Stone column

D= 1m 59
 NUMERICAL ANALYSIS

Deformed shape of Stone column

60
In the SC, vertical settlements are negligible after a depth of 2.5 m (i.e., 4.17d) from the
top of the column.
61
62
 Drainage Function of Stone Columns
 Load carrying capacity of stone columns is generated by
the top section of the column which extends to about 4
times the diameter of the stone column.
 The length below 4d allows for radial drainage and
acceleration of settlements.
 To retain continuity of drainage path, it is necessary to
provide a 150 mm thick drainage blanket on top of the
stone columns.
Difference between pile and stone
column
 Flexible Rigid

Stone Column Pile

Stone column Pile
 Limitation

 In soft clay soils, the bulging of stone columns will occur

 Normally not adequate for shear strength of the soil in the range of 5-20
kN/m2
 The stone column / vibrocompaction is brittle material which will not take
any tensile or lateral forces and will take care of only vertical compressive
loads.
 Though stone columns /vibrocompaction points are carried out at regular
intervals, it shall be assumed as the whole soil mass has been improved and
same property need to be considered for design.

67
 NUMERICAL ANALYSIS

Deformed shape of Stone column

68
In the SC, vertical settlements are negligible after a depth of 2.5 m (i.e., 4.17d) from the
top of the column. This is caused by the lateral deformation failure mechanism in the
stone column, which occurs in the top portion of the column. 69
70
71
BASIC DESIGN PARAMETERS

(1) Stone Column Diameter (D)

Due to lateral displacement of the stones during vibrator/ramming, the
completed diameter of the stone column is always greater than initial
diameter of the hole. (in field diameter increase10-20% more)(Normally
diameter range from 0.6 to 1 m)

G.L. D

De
D
De

72
Borehole Method (Datye and Nagaraju,
1975)
(2) Pattern
Stones columns should be installed preferably in an equilateral triangular which is the
most dense packing, although a square pattern may also be used. A typical triangular
and square pattern is shown in figure.

(b) Square arrangement of

stone columns

(a) Triangular arrangement

of stone columns

75
(3) Spacing (S)

Mitchell (1985)

(for stone column in a square pattern) ei=initial void ratio

e = required void ratio

Mitchell (1985)

(for stone column in a triangular pattern)

 (1.5D to 3.0 D where D = dia. of stone column)

83
(4) Equivalent diameter (De)

The tributory area of the soil surrounding each stone column forms regular
hexagon around the column. It may be approximated by an equivalent circular
area having the same total area.

De=1.05 × S
D (for an equivalent triangular pattern)

De=1.13 × S
(for a square pattern)
De

84
(5) Replacement Ratio ( as)
To quantify the amount of soil replaced by stone column, the term
replacement ratio, as ,is used. Replacement ratio (as) is given by:

Ag

AS
as 
A As
A

A = As + Ag A = S2 sin60 for triangular pattern

85
 As D2
as  as  2
A g  AS De

De  1.13 x S for square pattern

De  1.05 x S for triang le pattern
 C1=0.783
(for a square pattern )

C1=0.907
(for triangular pattern)
 (6) Stress concentration ratio (n)
s σs
σ n σg
g

The value of n generally (IS 15284 (Part 1), 2003) lie between 2.5 to 5
at the ground surface.
92
(6) Stress concentration ratio (n)
s σs
σ n σg
g

The stress concentration factor (η) decreases along the length of the stone
column.

95
A   s As   g Ag

A  As  Ag

g  ?
σ A   s As   g Ag


g 
1  as (  1)
σ A   s As   g Ag
s

A  ( g )As   g A g g

A
g 
(A g  A s )


g 
(A g  A s )
A
  
g  g 
(A g  A s ) A g A s
A (  )
A A

g  
A - A s As g 
(  ) 1  as  as
A A


g 
1  as (  1)
σ A   s As   g Ag

s  ?
σ A   s As   g Ag


s 
1  as (  1)

g 
1  as (  1)
1) Stone column are said to be possible (and beneficial) in thin layers of cohesive soil with an
undrained cohesion of
a) < 10 kPa
b) 10 to 20 kPa
c) 20 to 60 kPa
d) > 150 kPa
2) For construction of stone column near Athwagate in Surat which method is more suitable?
a) Wet top feed method
b) dry bottom feed method
c) none of the two option
3) Equivalent diameter is
a) diameter of stone column
b) Diameter of unit cell
c) diameter of tank for which ground improvement by stone column is required
d) none of the three option
4) Determine diameter of unit cell if , c/c spacing between stone column = 1.5m
a) 1.575 m for triangular pattern and 1.695 m for square pattern
a) 1.695 m for triangular pattern and 1.575 m for square pattern
c) 1.695 m for both triangular and square pattern
d) 1.575 m for both triangular and square pattern
5) Calculate area replacement ratio, c/c spacing between stone column = 1.5m
and diameter of stone column =0.9m
a) 0.283 m for triangular pattern and 0.326 m for square pattern
a) 0.326 for triangular pattern and 0.283 m for square pattern
c) 4.08 m for both triangular and square pattern
d) 4.08 m for triangular pattern and 3.26 m for square pattern
State whether the following statements are true or false. Justify your
answers with reasons.
1. At the edge of unit cell, axial deformation will be zero
2. Penetration of surrounding soft soil into the stone column reduces
the load carrying capacity of stone column.
DESIGN APPROACHES
Table : Various design approaches for bearing capacity
Sr Approach Author
No.
1 Passive pressure approach Greenwood (1970)
2 General shear failure approach Madhav and Vitkar (1978)
3 Lateral limit state or Gibson and Anderson (1961)
Pressuremeter theory approach Amar and Jezequel (1972)
Peteur (1973)
Hughes & Withers (1974)
Hughes et al.(1975)
Mori (1979), Aboshi et al (1979)
4 Empirical approaches Thorburn & McVicar (1968)
Greenwood (1970)
Thorburn (1975)
Smoltzyk (1979) 106
Failure mechanics
 Load

Stone column

108
 Load

Stone column

109
 Load

σrL σrL

Q1 =
resistance
against
bulging
Stone column
As the column simultaneously bulges and moves downward, the granular
material presses into the surrounding soft soil and transfers stress to the soil
through shear.
The lateral confining stress σ3 which supports the stone column is usually taken in
these methods as the ultimate passive resistance which the surrounding soil can
mobilize as the stone column bulges outward against the soil.
Since the column is assumed to be in a state of failure, the ultimate vertical stress σ1,
which the column can take is equal to the coefficient of passive pressure of the stone
column Kp times the lateral confining stress σ3 , which from classical plasticity
theory can be expressed as:

 1  Kp σ3

1 1  sin c

σ3 1  sin c
Stone column in cohesive soil IS : 15284 (part  I)

 v  σrl Kpcol
 v  (σro  4 Cu ) Kpcol

 (σro  4 Cu )
121
122
123
Stone column in C and ϕ soil

Bell’s formula
125
127
128
Calculate the ultimate load carrying capacity of stone column based on bulging criteria.
Considering following data.
a) Undisturbed undrained shear strength of clay = 28 kPa; Bulk unit weight of soil =
17 kN/m3; Submerged unit weight of soil= 8 kN/m3; Ground water table at 1 m
below ground level. Diameter of the stone column = 0.9 m; angle of internal
friction of stone column Øc = 40°; angle of internal friction of soil Ø = 11°.
b) Undisturbed undrained shear strength of clay = 25 kPa; Bulk unit weight of soil =
18 kN/m3; Submerged unit weight of soil= 12 kN/m3; Ground water table at 1.8 m
below ground level. Diameter of the stone column = 1.0 m; angle of internal
friction of stone column Øc = 41°.

129
Design example as per IS 15284 (Part 1) (2003)

Data:
A stone column is to be designed for the foundation of oil storage tank considering the
following given data:
Depth of soft clay: H = 7 m,
undrained shear strength of clay: Cu = 30 kN/m2,
Bulk density of clay: γb = 17.65 kN/m3,
Submerged density of surrounding soil: γsub = 7.85 kN/m3,
ground Water Table (G.W.T.) at 1 m below Ground Level (G.L.),
Tank diameter: d =79 m,
Load intensity from tank σ = 147 kN/m2,
Tank
Diameter of the stone column: D = 0.9 m,
Angle of internal friction of stone column: Øc = 42°. Sand pad

D
Hard strata

De

130
Figure : Illustration of stone column parameter
For solution refer class notes
 Load

Stone column

132
 Load

Stone column

133
 Load

σrL σrL

Q1=
resistance
Stone column against
bulging

134
γb =
17.65 kN/m3
2D
γsub =
7.85 kN/m3

135
 Q2 =Bearing
capacity
provided by
surrounding
soil
Stone column

136
Equivalent diameter (De)

The tributory area of the soil surrounding each stone column forms regular
hexagon around the column. It may be approximated by an equivalent circular
area having the same total area.

De=1.05 × S
D (for an equivalent triangular pattern)

De=1.13 × S
(for a square pattern)
De

137
Assume S = 2.0 m

De=1.05 × S
(for an equivalent triangular pattern)
D
Ag

De

As
A
138
 Q 3=
Resistance
offered by
Stone column surcharge

139
141
142
 Assumed S = 2.0 m

Revise Assume spacing

S = 1.8 m
Recalculate Q2, total Q, Nos. of stone column and Spacing
143
 Dia = 0.9m
1.5 D to 3 D

Assumed De Area of Ag Q2 Total safe load Area Spacing Remarks

Spacing (m) unit cell (kN) Q = per in m
in m m2 Q1+Q2+Q3 colum
n m2
2.0 2.1 3.46 174.55 463.31 3.15 1.90 Revise

1.80 1.89 2.80 2.164 133.47 215.82+133.47+ 2.87 1.82 Ok

72.94 = 422.23
 147
g   88.23kPa
1  0.222(4  1)

145
 Es  250 to300 Cu

Es  250 x 30  7500 kPa

1 1
mv    0.000133 m 2 /kN
Es 7500
Settlement of soil (before improvemen t)  mvσH  136.85mm
Settlement of soil (after improvemen t)  m v σg H
Settlement of soil  0.000133 x88 .30 x7 x1000  82 .20 mm 146
Settlement of soil (before improvemen t)  mvσH  136.85mm

Settlement of soil  0.000133 x88 .30 x7 x1000  82 .20 mm

82.20
  0.60
136.85

147
Thornburn (for vibroflot)

allowable stress on stone column

25.2Cu
qa   8.4Cu
3

s 
1  as (  1)

147x4
s   354.216kPa
1  0.22x(4  1)

allowable stress on stone column 

q a  8.4 x30  252kPa

148
Provide additional 2 rows of stone column around periphery of tank
Provide additional 2 rows of stone column around periphery of tank
For 001,003,005…… odd registration numbers

Data:
A stone column is to be designed for the foundation of oil storage tank considering the
following given data:
Depth of soft clay: H = 7 m,
undrained shear strength of clay: Cu = 25 kN/m2,
Saturated unit wt. of clay: γb = 18.5 kN/m3,
ground Water Table (G.W.T.) at Ground Level (G.L.),
Tank diameter: d =45 m,
Load intensity from tank σ = 100 kN/m2,
Diameter of the stone column: D = 0.9 m, Tank
Angle of internal friction of stone column: Øc = 40°.
Permissible settlement = 100 mm Sand pad

Es = 7000 kN/m2

D
Hard strata

De

151
Figure : Illustration of stone column parameter
For 0012,004,006…… even registration numbers

Data:
A stone column is to be designed for the foundation of oil storage tank considering the
following given data:
Depth of soft clay: H = 8 m,
undrained shear strength of clay: Cu = 28 kN/m2,
Saturated unit wt. of clay: γb = 18.5 kN/m3,
ground Water Table (G.W.T.) at Ground Level (G.L.),
Tank diameter: d =52 m,
Load intensity from tank σ = 120 kN/m2,
Diameter of the stone column: D = 0.6 m, Tank
Angle of internal friction of stone column: Øc = 44°.
Permissible settlement = 100 mm Sand pad

Es = 7800 kN/m2

D
Hard strata

De

152
Figure : Illustration of stone column parameter
Encased Stone Column
 Load

4d σrL σrL

Stone column

4
 Limitation

 In soft clay soils, the bulging of stone columns will occur

 Normally not adequate for shear strength of the soil in the range of 5-20
kN/m2
 The stone column / vibrocompaction is brittle material which will not take
any tensile or lateral forces and will take care of only vertical compressive
loads.
 Though stone columns /vibrocompaction points are carried out at regular
intervals, it shall be assumed as the whole soil mass has been improved and
same property need to be considered for design.

155
When such columns are installed in very soft clays, we may encounter the
following problems.

(i) Loss of Stones: The stones charged in to the column may squeeze out of the
column due to low lateral confinement from the surrounding soft clay. Due to this
squeezing, the quantity of stone required to form the stone column may be much
higher than anticipated.

(ii) Contamination of Stone Aggregate: The surrounding soft clay soil may intrude
or penetrate into the stone aggregate leading it to the reduction in frictional
strength of the aggregate besides impeding the drainage function of the stone
column.

(iii) Limited Bearing Capacity: As the stone columns largely depend on the lateral
passive support from the surrounding soil, the load carrying capacity of the stone
column can not be improved more than 25 times the strength of the soft clay and
the control over settlement is also limited (Chummar 2000)
Greenwood (1991) and Chummar (1993)
Site
 Near by Bombay, India
 LNG storage tank
 The soil was very soft silty clay of liquid
limit 95-124 %, plasticity index 55-76%,
undrained cohesion 3-30 kN/m2 and
sensitivity 3-14

Figure 2. 9 Soil profile at the LNG tank foundation

(Chummar 1993)
8
Stone column details
The stone columns of 0.9 m diameter and
length between 10 and 12 m, square pattern
at 1.2 apart
Vibro-floatation technique using
replacement method
At this site, the design of the stone column
was made by computing the load carrying
capacity of each stone column using the
lateral deformation theory. The allowable
capacity was worked out as 275 kN
considering cohesion of clay 20 kN/m2. Figure LNG tank foundation system (Chummar 1993)

9
Figure Full-scale water test loading record of LNG tank
(Greenwood 1991)

10
Problems
When the tank was half-full
with the load intensity of 120
kN/m2, the raft tilted at one
side about 91 mm with an
average settlement of 300 mm
and the entire tank collapsed Figure Foundation failure of LNG tank (Greenwood 1991)
(Figure 2.11).

This was accomplished by

ground heave and cracking of
the surface crust (Figure 2.12)
over a distance of about 3 m.

11
Figure Heaving of soil at LNG tank (Greenwood 1991)
Reasons

Vibro-flotation had disturbed the very sensitive clay,

which results in to reduction in radial restrain . The
storage tank was filled at a fast rate not going any
time for possible pore pressure dissipation. Vibro-floatation

Chummar (1993) further added that considering the

theory of Hughes and Withers (1974), and Thorburn
and Mcvicar (1968), the maximum bearing capacity
to which the ground can be improved only 25 times
the cohesion of clay.
Stone column technique itself was not justified when
the initial value of cohesion is less than 10 KPa
Chummar (1993).
12
Thornburn (for vibroflot)

allowable stress on stone column

25.2Cu
qa   8.4Cu
3

s 
1  as (  1)

159x4
s   383 kPa
1  0.22x(4  1)

allowable stress on stone column 

q a  8.4 x30  252kPa

163
 Remedial measure to overcome the problems of ordinary stone column

Skirted granular pile/stone column Nailing (Shivashankar, 2010)

(Rao and Ranjan, 1989)

Geogrid/Steel disc in horizontal plane Geosynthetic reinforced stone column

(Ayadat and Hanna, 2005) 18
(Raithel et al. 2000)
 Advantages of Encasement

Encasing the column with geosynthetic would be an ideal form since it also offers
otherbenefits as follows (Raithel et al. 2002, Alexiew et al. 2005)

i) Additional lateral confinement

ii) Making the stone column to act as a semi-rigid element enabling the load
transfer to deeper depths.
(iii) Preventing the lateral squeezing of stones in to surrounding soft clays thereby
minimising the loss of stones.
(iv) Enabling higher degree of compaction compared to the conventional stone
columns.
(v) Promoting the vertical drainage function of the column by acting as a good
filter (if encased by geotextile)
(vi) Preserving the frictional properties of the aggregates
(vii) Increasing the shear resistance of the stone column (Murugesan & Rajagopal
2009).
Fig. 1. Welded geogrid
encasement.
• • •
.....
• • •
•
• •
• •
• •
• •
•
Installation methods of RSC

(i) Displacement method (ii) Replacement method

36
 The first foundation system “geotextile
encased columns (GEC)” for widening an
about 5 m high railroad embankment on
peat and clay soils in Hamburg was
carried out in 1996.

 Airplane dockyard (EADS) in Hamburg-

Finkenwerder new Airbus A 380 in 2002.

Courtesy: Raithel et al. 2008

34
Comparison with Analytical Solution

Comparison is done with the analytical solution proposed by Murugesan and

Rajagopal based (2007).

pd
H 
2t

 H 2t 2T
p 
d d

37
Computation for Ordinary Stone Column

Diameter of stone column = 50 mm

undrained shear strength of clay: Cu = 9 kN/m2,
Unit weight of clay: γ = 17 kN/m3,
Angle of internal friction of stone column: Øc = 30°.

 v  (σro  4 Cu ) Kpcol
Diameter of stone column = 50 mm
undrained shear strength of clay: Cu = 9 kN/m2,
Unit weight of clay: γ = 17 kN/m3,
Angle of internal friction of stone column: Øc = 30°.

 v  (σ ro  4 Cu ) Kpcol  111.06 kN/m 2

Computation for Encased Stone Column
Diameter of stone column = 50 mm
undrained shear strength of clay: Cu = 9 kN/m2,
Unit weight of clay: γ = 17 kN/m3,
Angle of internal friction of stone column: Øc = 30°
Settlement of stone column = 50 mm

 v  (σro  4 Cu  pc ) Kpcol
Computation for Encased Stone Column

 v  (σro  4 Cu  pc ) Kpcol
S
vertical strain of stone column  a 
4d
hoop strain (or circumfere ntial strain) developed in the geosynthet ic
1 1  a
c 
1  a

2T
additional lateral confining stress pc 
d
Computation for Encased Stone Column

 v  (σro  4 Cu  pc ) Kpcol

2T
additional lateral confining stress pc 
d

T = Tensile load in the encasement corresponding to hoop strain ε c

2T
additional lateral confining stress pc 
d
 8
7
6

Tensile load (kN/m)

5
4
3
2
1
0
0 10 20 30 40 50 60 70
Strain (%)

Nonwoven

T = Tensile load in the encasement corresponding to hoop strain ε c

2T
pc 
d 42
Computation for Encased Stone Column

 v  (σro  4 Cu  pc ) Kpcol
0.05
a   0.25
4x0.05

1 1  a 1  1  0.25
c    0.1547
1  a 1  0.25

2T
additional lateral confining stress pc 
d
 8
7

T  1.6kN/m 6

Tensile load (kN/m)

5
2x1.6
pc   64 kN/m2
4

0.05 3
2
1
0
0 10 20 30 40 50 60 70
Strain (%)

Nonwoven
 v  (σro  4 Cu  pc ) Kpcol

σ v  303.06 kN/m2

42
Geogrid Encased Stone column
 Geogrid Encased Stone column

Geogrid