prefabricated vertical drains

DESIGN OF VERTICAL DRAINS

Ground Improvement: CE 6060

Outline Introduction Design Methods Conclusions References

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PVDs for soil improvement

PVDs are artificially-created drainage paths which are inserted into the soft clay subsoil for accelera accelerating ting 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

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capacity and shear strength

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Prefabricated vertical Drains PVD for soil improvement PVDs are a composite geosynthetic system consisting of: 

An inner core and an outer filter jacket

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Width = 100 mm,

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Thickness = 6 mm

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Flexible core: With formed flow path grooves on both sides along its length

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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

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Cross section of  PVD

Surcharge Embankmen

W ick ick d ra in s Core Sleeve

D etail etail A V ert ica l flo

R ad ial flow

S oft so il

Theoretical considerations

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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, 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, 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-dimensio one-dimensional nal consolidation theory set out

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

Radial Consolidation Theory 

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The equatıon whıch governs the relatıonshıp between pore pressure, u, radıal dıstance from the draın (r), and tıme (t) (ın fact k  = f(t) and ch=f(t)) ıs gıven below. h Draın effects, smear dısturbance, well resıstance, loadıng rate, creep effects, approprıate hydraulıc flow formulatıon can all be ıncluded ın the analyses.

ch 

2   ∂ u 1 ∂u  ∂u  2 +   =   ∂r  r ∂r  ∂t   

The combined drainage: 2

ch

equation

for

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

both

radial

2     1 ∂u ∂ ∂ ∂ u u u  2 + .   +c 2 =   ∂x x ∂x   ∂z  ∂t    v

and

vertical

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Overall, the degree of consolıdatıon is three dımensıonal. The combined degree of consolidation due to radial(horizontal) and vertical drainage is given (Barron’s (Barron’s solution and Carillo’s equation)) 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 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 =  k dw2/4 = discharge capacity of  w the drain in the vertical direction 13

Choice of parameters Drain Installation Pattern & D

D

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

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Choice of parameters Equivalent diameter of PVD (d w)

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=

(Hansbo, d  1979) w

π 

+

w t  ) 1981) (Atkinson &(Eldred, d  w

=

2

(Long & Covo, 1994)

d  w

d  = w

2( w + t  )

= 0.5w + 0.7t 

diameter of drain well and

w

and

t  =

width and thickness of PVD

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Barron’s Theory for Pure Radial Drainage (1944) Assumptions 

Darcy´s flow law is valid

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The soil is saturated and homogeneous

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Displacements due to consolidation take place in vertical direction only

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Excess pore water pressure at the drain well surface is zero

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The cylindrical boundary of the soil mass is impervious

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Excess pore water pressure at the upper and lower boundaries of the soil mass is zero

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No vertical flow at half the depth of soil mass

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No smear zone & well resistance

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de a

b

d  w

= 2(a + b) / Π −8T  h

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

= 1− e

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

P  V  D

(n) F 

 n 2   ( 3n 2 − 1)   (n) =  2 ln(n) − F  2   4n n − 1     ≈ ln(n) − 0.75 =

T  h

ch .t  2

d  e

n

=

d  e d  w

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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

Note: λ is zero if no horizontal drainage

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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, 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?

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Solution:

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Model for Vertical Drain with Smear Zone

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Smear Effect 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.

  n   k     − 0.75 +    ( n) = ln   ln( s ) F    s   k       h

ds

s

s

kh Where, s is smear zone ratio = ds/dw

ks

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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

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Size and shape of mandrel

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Soil structure

Two problems exists: 

To find the correct diameter value ds

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To evaluate the effect of smear on the permeability

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Choice of parameters

The zone of smear (d s) 

To find the correct diameter value ds

As = 1.6 Across-s-sectioionalmandrel

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(Hird & Moseley, 1997)

To evaluate the effect of smear on the permeability k  h

k  s

=2

(Terzaghi et al. 1996)

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Choice of parameters

Other parameters

k  h k  v

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= 1− 5

(Terzaghi et al. 1996)

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The coefficient of horizontal consolidation (cv & ch)

k  h ch cv (Rixner et al. 1986) k  v

=

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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 = 0.9 3.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/de2) 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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Vertical Drains: Design Criteria 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.

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1. Calculate Tv; for given cv, H, and t.

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We know, Uv,r = 0.9

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Find Uh from steps 1 & 2. use Uv,r = 1-(1-Uh)(1-Uv)

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Uh = 1-exp(-8Th/m)

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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)

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Then, find Uh

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Compare Uh from both the methods.

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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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Where, 2     n n   s k  n   ) ln   ( 2 ) ln(s ) − 0.75 + 2 +    m=( 2 2 2   4n n −s s   k   n −s     2

2

h s

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REFERENCES 

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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. 216226 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