prefabricated vertical drains
TRANSCRIPT
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.
9
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
12
Choice of parameters
13
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
14
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
15
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
16
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
18
Design Charts for Vertical and Radial Drainage
19
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:
21
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
24
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
25
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
26
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
27
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.
28
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.
29
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