Prof. Samir P ParmarAssociate Professor, Dharmasinh Desai University, Nadiad, Gujarat, INDIA& Research Scholar, Geotechnical Engineering, IIT Kanpur, Uttar Pradesh, INDIAMail: samirddu@gmail.com

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Design of Vertical Drains

Outline

Introduction Design Methods Design Procedures Design Problem References

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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

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PVDs for soil improvement

PVDs can be used: To shorten the consolidation time To lead to increased subsoil bearing capacity

and shear strength

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Prefabricated vertical Drains PVD for soil improvement5

PVDs are a composite Geosynthetic system consisting of:

An inner core and an outer filter jacket Width = 100 mm, Thickness = 3 - 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

Cross section of PVD

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Wick drain(s) Embankment

Surcharge

Core

Sleeve

Soft soil

Detail A

Vertical flow Radial flow

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Theoretical considerations

Design drain spacing

Consider the drainage in both vertical and horizontal planes

The design of vertical sand drain system Based on the classical theoretical solution

developed by Barron (1948) The drains were assumed as ideal wells The drain sand should fulfill the requirements of

an ideal filter

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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.

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10 Vertical Consolidation Theory  

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:

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u=u0 at t=0 at all placeu=u0 In the draIn at any tIme

tu

zuc

ru

rruc 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

12 Radial Consolidation Theory cont…

Choice of parameters13

• D = diameter of cylindrical soil mass dewater by a drain

• dw = drain/well diameter

• ds = diameter of the smear zone

• 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 = kwpdw

2/4 = 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

p)(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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PV

D

wt

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

p/)(2 twdw

2

.e

hh d

tcT w

e

ddn

Solution to Vertical and Radial Drainage18

Solution to Vertical and Radial Drainage (Free-Strain Consolidation with No Smear)

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Design Charts for Vertical and Radial Drainage20

Solution to Combined Drainage21

Note: is zero if no horizontal drainage

Problem 1 Average permanent load on clay is about 115kN/m2. The avg.

eff. overburden pressure at the middle of clay layer is 210kN/m2. H = 6 m, cc = 0.28, e0 = 0.8 and cv = 0.36 m2/mo. Clay is normally consolidated.

Part B: With the addition of some sand drains, assume that rw = 0.1 m,

de= 3 m, and cv = ch. What is the surcharge, s, needed for 9 months period? Assume both free-strain and equal-strain methods. Find out the height of the surcharge if the bulk unit weight of the surcharge, bulk, sur = 20 kN/m3.

Comment on the results!

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Model for Vertical Drain with Smear Zone

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Smear Effect24

)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 the Undisturbed 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)v

v

hh ckkc

51v

h

kk

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Vertical Drains: Design CriteriaSteps: (Assuming no smear zone)1. Calculate Tv; for given cv, H, and t.2. We know, Uv,h = 0.93. Find Uh from steps 1 & 2. use Uv,h = 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))

Compare Uh from steps 5 with step 3. 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,h = 0.9 Find Uh from steps 1 & 2. use Uv,h = 1-(1-Uh)(1-Uv) Uh = 1-exp(-8Th/m) Assume spacing ‘s’, calculate de, find ‘m’ from the equation given in next slide 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.

30 Vertical Drains: Design Criteria

Where,

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)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

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Thank You !

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