DESIGN OF VERTICAL DRAINSDESIGN OF VERTICAL DRAINS

Ground Improvement: CE 6060

Outline

Introduction

Design Methods

Conclusions

References

2

PVDs for soil improvement

PVDs are artificially-created drainage paths which are inserted into the soft clay subsoil for accelerating consolidation of fine-grained soils by promoting radial flow/drainage

3

PVDs can be used:To shorten the consolidation timeTo lead to increased subsoil bearing capacity and shear strength

4

PVDs for soil improvement

Prefabricated vertical Drains PVD for soil improvementPVDs 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

Cross section of PVD

Wick drain(s) Embankment

Surcharge

Core

Sleeve

Soft soil

Detail A

Vertical flow Radial flow

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

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.

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Vertical Consolidation Theory

The evaluation of the vertical consolidation due to vertical drainage only is based on the one-dimensional consolidation theory set out

The assessment of the average degree of consolidation due to horizontal drainage to the drain is more difficult.

Radial Consolidation Theory

The equatıon whıch governs the relatıonshıp between pore pressure, u, radıal dıstance from the draın (r), and tıme (t) (ın fact kh = f(t) and ch=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=u0 at t=0 at all placeu=u0 In the draIn at any tIme

tu

zuc

xu

xxuc vh

2

2

2

2

.1

tu

ru

rruch

1

2

2

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)

Uhv= 1- (1-Uh)(1-Uv) where, Uv ıs the average vertıcal degree of consolıdatıon,

Uh ıs the average horizontal degree of consolıdatıon

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Choice of parameters

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D = diameter of cylindrical soil mass dewater by a drain

dw = drain diameter

ds = diameter of the zone of smear

2l = depth of drain installation

kh = permeability of the soil in the horizontal direction

kv = permeability of the soil in the vertical direction

ks = permeability of the soil of the smear zone

qw = kwdw2/4 = discharge capacity of

the drain in the vertical direction

Choice of parameters

Drain Installation Pattern & D

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

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D

Choice of parameters

Equivalent diameter of PVD (dw)

(Hansbo, 1979)

(Atkinson & Eldred, 1981)

(Long & Covo, 1994)

dw = diameter of drain well and w and t = width and thickness of PVD

)(2 twdw

2)( twdw

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twdw 7.05.0

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

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17

PV

D

ba

Equivalent cylindrical

drain

dw

de

Tributary clay cylinder

)(8

1 nFT

h

h

eU

75.0)ln(4

13)ln(1

)( 2

2

2

2

nnnn

nnnF

/)(2 badw

2

.e

hh d

tcT w

e

ddn

Solution to Vertical and Radial Drainage

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Design Charts for Vertical and Radial Drainage

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Solution to Combined Drainage

20Note: is zero if no horizontal drainage

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, cv = 2 m2 /year, ch = 3 m2 /year.

Find: Calculate the time required for 90% degree of consolidation of the clay layer as a result of an extensive fill?

Solution:

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Model for Vertical Drain with Smear Zone

22

Smear Effect

23

)ln(75.0ln)( skk

snnF

s

hs

An annulus of smeared clay around the drain. Within this annulus of diameter ds, the remolded soil has a coefficient of permeability ks which is lower than the kh of theUndisturbed clay.

Where, s is smear zone ratio = ds/dw

ds

ks

kh

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Choice of parameters

The zone of smear (ds)

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

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Choice of parameters

The zone of smear (ds)

To find the correct diameter value ds

As = 1.6 Across-sectional mandrel (Hird & Moseley, 1997)

To evaluate the effect of smear on the permeability

(Terzaghi et al. 1996)2

s

h

kk

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Choice of parameters

Other parameters

(Terzaghi et al. 1996)

The coefficient of horizontal consolidation (cv & ch)

(Rixner et al. 1986)

vv

hh ckkc

51v

h

kk

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Vertical Drains: Design Criteria

Steps: (Assuming no smear zone)1.Calculate Tv; for given cv, H, and t.2.We know, Uv,r = 0.93.Find Uh from steps 1 & 2. use Uv,r = 1-(1-Uh)(1-Uv)4.Assume spacing ‘s’, calculate de, n, F(n) and Th (use cht/de

2) 5.Then, find Uh; Uh = 1-exp(-8Th/F(n))

1.Compare Uh from steps 5 with step 3.2.If they are not equal, change the spacing and repeat step 5. When Uh matches with that calculated in step 3, then that is the design spacing.

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Steps: (if smear zone presents)Proposed method derived from Equal-Strain consolidation.Given conditions are cv, ch, t, kh, kv, ks (smear permeability in horizontal

direction), ds, dw. Spacing has to be found out.1. Calculate Tv; for given cv, H, and t.We know, Uv,r = 0.9Find Uh from steps 1 & 2. use Uv,r = 1-(1-Uh)(1-Uv)Uh = 1-exp(-8Th/m)Assume spacing ‘s’, calculate de, find ‘m’ from Figure (m vs kh/ks for

various n= de/dw values and S = ds/dw), and Th (use cht/de2)

Then, find Uh

Compare Uh from both the methods. If they are not equal, change the spacing and repeat the steps. When Uh

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

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Vertical Drains: Design Criteria

Where,

30

)ln()(4

75.0ln)( 22

2

2

2

22

2

ssn

nkk

ns

sn

snnm

s

h

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

of deep vertical drains”; Vertical Drains, Thomas Telford Publications Ltd., London, 1982 Atkinson, M. A. & Eldred, P. J. L.; “Consolidation of soil using vertical drains”; Vertical

Drains, Thomas Telford Publications Ltd., London, 1982 Hansbo, S., Jamiolkowski, M. & Kok, L.; “Consolidation by vertical drains”; Vertical Drains,

Thomas Telford Publications Ltd., London, 1982 Sharma, J. S. & Xiao, D.(2000); “Characterisation of a smear zone around vertical drains

by largescale laboratory tests”; Canadian Geotechnical Journal, Vol. 37, pp. 1265-1271 Chai, Jun-Chun & Miura, Norihiko(March, 1999); “Investigation of the factors affecting

vertical drain behaviour”; Journal of Geotechnical and Environmental Engineering, Vol. 125, No. 3, pp. 216-226

Onoue, Atsuo (December, 1998); “Consolidation by vertical drains taking well resistance and smear into consideration”; Soils and Foundation, Japanese society of SMFE, Vol. 28, No. 4, pp. 165-1

Indraratna, B. & Redana, I. W. (February, 1998); “Laboratory determination of smear zone due to vertical drain installation”; Journal of Geotechnical and Environmental Engineering, Vol. 124, No. 2, pp. 180-184

Mitchell, J. K.(1980); “Soil improvement – State-of-the-art report”; Proceedings of the Tenth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, 15-19 June, pp. 509-565

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”; Geotextiles and Geomembranes

Jeon, H. Y., Kim, S. H., Chung, Y. I., Yoo, H. K. & Mlynarek, J. (October 2003); “Assesments of long term filtration performance fo degradable prefabricated drains”; Polymer Testing, Vol. 22, Iss. 7, pp. 779-784

Advanced soil mechanics by B. M. Das