prefabricated vertical drains

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DESIGN OF VERTICAL DRAINS

Ground Improvement: CE

6060

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Outline

Introduction

Design Methods

Conclusions

References

2 2

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PVDs for soil improvement

PVDs are artificially-created drainage

paths which are inserted into the soft

clay subsoil for

accelera

ting

consolidation of fine-grained soils by

promoting radial flow/drainage

3

(4)

PVDs can be used:

To shorten the consolidation time



To lead to

increased subsoil bearing

capacity and shear strength

4

PVDs for soil improvement

(5)

Prefabricated vertical Drains

PVD

for soil improvement

PVDs are a composite geosynthetic

system consisting of:



An inner core and an outer filter

jacket

 

Width = 100 mm,

 

Thickness = 6 mm



Flexible core: With formed flow

path grooves on both sides along

its length



Jacket: Filter to maintain the

hydraulic capacity of the grooves

and allowing passage of fluids into

the drain core while preventing

clogging by soil intrusion

5

(6)

Cross section of

PVD

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W

W ic

ick d

k d ra

ra in

in ss

E m b a n k m e n E m b a n k m e n

Surcharge

Core

Sleeve

SS oft

oft so

so iill

D

D etai

etail A

l A

V

(8)

Theoretical considerations

The problem of

designing a vertical drain

scheme is to

determine the

drain spacing

which will give the required degree

of consolidation in a specified time for any given drain type and

size in the ground conditions prevail



Drainage will take place in

both the vertical and horizontal

planes

and therefore any design methods should take this into

account if it is to model the real situation properly



The design of vertical sand drain system is generally based on

the classical theoretical solution developed by

Barron (1948)

in

which the drains are assumed to be functioning as

ideal wells

,

i.e., their permeability is considered infinitely high as compared

with that of the soil in which the drains are placed



The above assumption is justified when the drain sand fulfills

the requirements of an

ideal filter

, but in practice it can never

be achieved

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Methods Available for PVD

Design

Barron, R. A. (1944). The influence of drain wells on the

consolidation of fine-grained soils.

Barron, R. A. (1947). Consolidation of fine –grained soils by

drain wells.

Hansbo, S. (1960). Consolidation of clay, with special reference

to the influence of vertical sand drains.

Hansbo, S. (1981). Consolidation of fine-grained soils by

prefabricated drains.

Zhou, W., Hong, H. P., & Shang, J. Q. (1999). Probabilistic

design method of prefabricated vertical drains for

soil

improvement.

9

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Vertical Consolidation Theory

The evaluation of the

vertical consolidation due to vertical

drainage only is

based on the

one-dimensio

nal consolidation

theory set out



The assessment of the average degree of consolidation due to

horizontal drainage to the drain is

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Radial Consolidation Theory



The equatıon whıch governs the relatıonshıp between pore

pressure, u, radıal dıstance from the draın (r), and tıme (t)

(ın fact k

_h_h

= f(t) and c

_h_h

=f(t)) ıs gıven below.



Draın effects, smear dısturbance, well resıstance, loadıng

rate, creep effects, approprıate hydraulıc flow formulatıon

can all be ıncluded ın the analyses.



The combined equation for both radial and vertical

drainage:

u=u

₀₀

at t=0 at all place

u=u

₀₀

In the draIn at any tIme

t

u

z

u

c

x

u

x

u

c

_h_h _v_v

∂∂

==

∂∂

++













∂∂

++

∂∂

2

2 ..

1

1 t

t

u

r

u

r

u

c

h h

∂∂

==













∂∂

++

∂∂

1

2

(12)



Overall, the degree of

consolıdatıon is three dımensıonal.



The combined degree of

consolidation due to radial(horizontal)

and vertical drainage is given (

Barron’s solution and Carillo’s

equation

)

U

_hv_hv

= 1- (1-U

_h_h

)(1-U

_v_v

)

where, Uv ıs the

average vertıcal degree of consolıdatıon,

Uh ıs the

average horizontal degree of consolıdatıon

12

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Choice of parameters

13

D = diameter of cylindrical soil mass

dewater by a drain

d

_w_w

= drain diameter

d

_s_s

= diameter of the zone of smear

2l = depth of drain installation

k

_h_h

= permeability of the soil in the

horizontal direction

k

_v_v

= permeability of the soil in the

vertical direction

k

_s_s

= permeability of the soil of the

smear zone

q

_w_w

= k

_w_w

d

_w_w22

_{/4 = discharge capacity of}

the drain in the vertical direction

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Choice of parameters

Drain Installation Pattern & D

(a) Square pattern, D/2 = 0.565 s ; (b) triangular pattern D/2 = 0.525 s

14

D

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Choice of parameters

Equivalent diameter of PVD (d

_w_w

)

 

(Hansbo, 1979)



(Atkinson & Eldred, 1981)



(Long & Covo, 1994)

d

w

= diameter of drain well and

ww

and

t t

= width and thickness of PVD

π

))

((

2

2 w

w

t

d

w w

++

==

2

2 ))

((

w

t

d

w w

++

==

15 15

t

w

d

w w

==

0

0 ..

5

5 ++

0

0 ..

7

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Barron’s Theory for Pure

Radial Drainage (1944)

Assumptions



Darcy´s flow law is valid



The soil is saturated and homogeneous



Displacements due to consolidation take place in vertical

direction only



Excess pore water pressure at the drain well surface is

zero



The cylindrical boundary of the soil mass is impervious



Excess pore water pressure at the upper and lower

boundaries of the soil mass is zero



No vertical flow at half the depth of soil mass



No smear zone & well resistance

16

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17 17 P P V V D D

b

a

E E q q u u i i v v a a l l e e n n t t c c y y l l i i n n d d r r i i c c a a l l d d r r a a i i n n

d

_w_w

d

_e_e T T r r i i b b u u t t a a r r y y c c l l a a y y c c y y l l i i n n d d e e r r

))

((

8

1

F F nn T T h h h h

e

U

−−

==

( (

))

75

75 ..

0

0 ))

ln(

4

1

3

3 ))

ln(

1

1 ))

((

₂

2

2 −−

≈≈

−−













−−

==

n

F

Π

++

==

2

2 ((

a

b

))

//

d

w w

2

2 ..

e e h h h h

d

t

c

T

==

w w e e

d

n

==

(18)

Solution to Vertical and Radial

Drainage

18

(19)

Design Charts for Vertical and

Radial Drainage

19

(20)

Solution to Combined Drainage

20

Note:

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Example 1

Given:

Saturated clay layer 8 m thick,

impermeable lower

boundary, PVD size: 104 mm x 5

mm at 2m c/c

spacing in

square pattern, c

_v_v

= 2 m

22

_{/year, c}

h

= 3 m

2

_/year.



Find:

Calculate the time required for 90% degree of

consolidation of the clay layer as a result

of an extensive fill?



Solution:

21

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Model for Vertical Drain with

Smear Zone

22

(23)

Smear Effect

23 23

))

ln(

75

75 ..

0

0 ln

ln

))

((

s

k

s

n

F

s s h h s s













++

−−













==

An annulus of smeared clay

around the drain. Within this

annulus of diameter

d

_s_s

, the remolded soil has a coefficient of

permeability

k

_s_s

which is lower than the

k

_h_h

of the

Undisturbed clay.

Where, s is smear zone ratio = d

_s_s

/d

_w_w

d

_s_s

k

_s_s

k

_h_h

(24)

24

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Choice of parameters

The zone of smear (d

_s_s

)

The effect on the consolidation parameters for the

disturbance caused by the installation of drains

depend on:



Method of drain installation



Size and shape of mandrel



Soil structure

Two problems exists:



To find the correct diameter value ds



To evaluate the effect of smear on

the permeability

25

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Choice of parameters

The zone of smear (d

_s

)



To find the correct diameter value d

s

A

_s_s

= 1.6 A

_cross-_cross-_secti_secti_ona_ona_{l m}_{l m}_and_and_rel_rel

(Hird & Moseley, 1997)



To evaluate the effect of smear on the permeability

(Terzaghi et al. 1996)

2

2 ==

s s h h

k

26 26

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Choice of parameters

Other parameters



(Terzaghi et al. 1996)



The coefficient of horizontal consolidation (c

v v

&

c

_h_h

)

(Rixner et al. 1986)

v

h

c

k

c

==

5

1

−−

==

v

h

k

27 27

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Vertical Drains: Design Criteria

Steps: (Assuming no smear zone)

1.

1. Calculate T

Calculate T

_v_v

; for given c

_v_v

, H, and t.

2.

2. We know, U

We know, U

v,rv,r

= 0.9

3.

3. Find U

Find U

_h_h

from steps 1 & 2. use U

_v,r_v,r

= 1-(1-U

_h_h

)(1-U

_v_v

)

4.

4. Assume spacing ‘s’, calculate d

Assume spacing ‘s’, calculate d

ee

, n, F(n) and T

hh

(use c

hh

t/d

ee

2

₎

5.

5. Then, find U

Then, find U

_h;_h;

U

_h_h

= 1-exp(-8T

_h_h

/F(n))

1.

1. Compare U

Compare U

_h_h

from steps 5 with step 3.

2.

2. If they are not equal, change the spacing and repeat step 5.

If they are not equal, change the spacing and repeat step 5.

When U

_h_h

matches with that calculated in step 3,

then that is the

design spacing.

28 28

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Steps: (if smear zone presents)



Proposed method derived from Equal-Strain consolidation.



Given conditions are c

_v_v

, c

_h_h

, t, k

_h_h

, k

_v_v

, k

_s_s

(smear permeability in horizontal

direction), d

_s_s

, d

_w_w

. Spacing has to be found out.



1. Calculate T

_v_v

; for given c

_v_v

, H, and t.



We know, U

_v_v_,_,_r_r

= 0.9



Find U

_h_h

from steps 1 & 2. use U

_v_v_,_,_r_r

= 1-(1-U

_h_h

)(1-U

_v_v

)



U

_h_h

= 1-exp(-8T

_h_h

/

m

)



Assume spacing ‘s’, calculate d

_e_e

, find ‘m’ from Figure (m vs

k

_h_h

/k

_s_s

for

various n= d

_e_e

/d

_w_w

values and S = d

_s_s

/d

_w_w

), and T

_h_h

(use c

_h_h

t/d

_e_e22

₎



Then, find U

_h_h



Compare U

_h_h

from both the methods.



If they are not equal, change the spacing and repeat

the steps. When U

_h_h

matches with that calculated in the first method, then that is the design

spacing.

29 29

Vertical Drains: Design Criteria

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Where,

30 30

))

ln(

))

((

4

75

75 ..

0

0 ln

ln

))

((

₂

2

2 s

s

n

k

n

s

n

s

n

m

s s h h

−−













++

−−













−−

==

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REFERENCES

McGown, A. & Hughes, F. H.; “

McGown, A. & Hughes, F. H.; “Practical aspects of vertical drain design and installation of Practical aspects of vertical drain design and installation of

deep vertical drains

deep vertical drains”; Vertical Drains, Thomas Telford Publications Ltd., London, 1982”; Vertical Drains, Thomas Telford Publications Ltd., London, 1982 

 Atkinson, M. A. & Eldred, P. J. L.; “Atkinson, M. A. & Eldred, P. J. L.; “Consolidation of soil using vertical drainsConsolidation of soil using vertical drains”; Vertical Drains,”; Vertical Drains,

Thomas Telford Publications Ltd., London, 1982

Thomas Telford Publications Ltd., London, 1982 

 Hansbo, S., Jamiolkowski, M. & Kok, L.; “Hansbo, S., Jamiolkowski, M. & Kok, L.; “Consolidation by vertical drainsConsolidation by vertical drains”; Vertical Drains,”; Vertical Drains,

Thomas Telford Publications Ltd., London, 1982

Thomas Telford Publications Ltd., London, 1982 

 Sharma, J. S. & Xiao, D.(2000); “Sharma, J. S. & Xiao, D.(2000); “Characterisation of a smear zone around vertical drains byCharacterisation of a smear zone around vertical drains by

largescale laboratory tests

largescale laboratory tests”; Canadian Geotechnical Journal, Vol. 37, pp. 1265-1271”; Canadian Geotechnical Journal, Vol. 37, pp. 1265-1271 

 Chai, Jun-Chun & Miura, Norihiko(March, 1999); “Chai, Jun-Chun & Miura, Norihiko(March, 1999); “Investigation of the factors affecting verticalInvestigation of the factors affecting vertical

drain behaviour

drain behaviour”; Journal of Geotechnical and Environmental Engineering, Vol. 125, No. 3, pp. 216-”; Journal of Geotechnical and Environmental Engineering, Vol. 125, No. 3, pp.

216-226

226 

 Onoue, Atsuo (December, 1998); “Onoue, Atsuo (December, 1998); “Consolidation by vertical drains taking well resistance andConsolidation by vertical drains taking well resistance and

smear into consideration

smear into consideration”; Soils and Foundation, Japanese society of SMFE, Vol. 28, No. 4, pp.”; Soils and Foundation, Japanese society of SMFE, Vol. 28, No. 4, pp.

165-1

165-1 

 Indraratna, B. & Redana, I. W. (February, 1998); “Indraratna, B. & Redana, I. W. (February, 1998); “Laboratory determination of smear zone dueLaboratory determination of smear zone due

to vertical drain installation

to vertical drain installation”; Journal of Geotechnical and Environmental Engineering, Vol. 124,”; Journal of Geotechnical and Environmental Engineering, Vol. 124,

No. 2, pp. 180-184

No. 2, pp. 180-184 

 Mitchell, J. K.(1980); “Mitchell, J. K.(1980); “Soil improvement – State-of-the-art reportSoil improvement – State-of-the-art report”; Proceedings of the Tenth”; Proceedings of the Tenth

International Conference on Soil Mechanics and Foundation Engineering, Stockholm, 15-19 June, pp.

509-565

509-565 

 Lorenzo, G. A., Bergado, D. T., Bunthai, W., Hormdee, D., & Phothiraksanon, P. (Article in Press);Lorenzo, G. A., Bergado, D. T., Bunthai, W., Hormdee, D., & Phothiraksanon, P. (Article in Press);

“Innovations and performances of PVD and dual function geosynthetic applications”

“Innovations and performances of PVD and dual function geosynthetic applications”;;

Geotextiles and Geomembranes

Geotextiles and Geomembranes 

 Jeon, H. Y., Kim, S. H., Chung, Y. I., Yoo, H. K. & Mlynarek, J. (October 2003); “Jeon, H. Y., Kim, S. H., Chung, Y. I., Yoo, H. K. & Mlynarek, J. (October 2003); “Assesments of longAssesments of long

term filtration performance fo degradable prefabricated drains”

term filtration performance fo degradable prefabricated drains”; Polymer Testing, Vol. 22,; Polymer Testing, Vol. 22,

Iss. 7, pp. 779-784

Iss. 7, pp. 779-784 

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