1. Prefabricated vertical drains and Preloading by vacuum
design and performance
University of Shanghai for Science and Technology

2. Presentation Outline
Principal of vacuum consolidation
Efficiency and factors affecting vacuum system
Unit cell analysis
Multi-drain analysis: 2D vs. 3D
Case studies
Conclusion

3. Vertical Drains Shorten the length of the drainage path
Accelerate the rate of pore water pressure dissipation
Accelerate the rate of consolidation / settlement

4. Conventional Surcharge vs Vacuum Preloading (Chu and Yan, 2005; Mohamed-Elhassan and Shang, 2002)
For vacuum application, total stress does not increase.
Staged construction can be avoided.
Lateral displacement can be controlled.
Cost of vacuum pump operation
s’=s - (-u)

5. Inward movement due to VP
Potential benefits of Prefabricated Vertical Drains in Soft Formation clays
Surcharge
With Vertical Drains
Ref: Colbond, The Netherlands
Embankment
Settlement
Without vertical drains
Due to PVDs
Depth
Inward movement due to VP
vertical drains with surcharge
vertical drains with surcharge and
vacuum preloading
Time
Lateral displacement at toe

6. Membrane & Membraneless Systems in Vacuum Preloading
Advantage
Large area
Caution
Membrane leakage
Membrane system
(e.g. Menard)
Advantage
Area can be subdivided
Caution
Significant cost of individual drain connection
Membraneless system
(e.g. Beaudrain)

7. Site preparation for Vacuum Consolidation
Drain Installation
Horizontal drain installation
Peripheral bentonite trench
Connection between horizontal drainage and vacuum pump
Membrane installation

8. Reduction of consolidation time through application of vacuum preloading

9. Efficiency of vacuum preloading depends on
Drain spacing and equivalent drain diameter
Vacuum pressure distribution
Drain core
Lateral confining pressure
Deformation characteristic (folding, bending, crimping)
Installation effects on soil permeability and compressibility
Flow characteristics: Darcian vs. Non-Darcian flow

10. Experimental Evaluation of PVDs
Installation of PVDs by a steel mandrel causes smear – reduced lateral permeability
Large-Scale, Radial Drainage Consolidometer
550mm Diameter
1.2m Height

11. Distributions of vacuum pressure along the drain length
Laboratory scale
20 kPa vacuum pressure
40 kPa vacuum pressure
Field observation
Indraratna, B., Rujikiatkamjorn, C., Kelly, R. and Buys, H. (2012). Soft soil foundation improved by vacuum and surcharge loading. Ground Improvement

12. Effects of vacuum distribution along the drain length
Long Drain
Short Drain
Indraratna, B., Rujikiatkamjorn C., and Sathananthan, I., (2005). Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading. Canadian Geotechnical Journal, 42: 12

13. Determination of consolidation & permeability characteristics
Permeability Approach
Indraratna & Redana, 1998, JGGE, ASCE
Vol. 124(2)
Water Content Reduction upon Vacuum Application
Sathananthan & Indraratna 2006, JGGE, ASCE, Vol. 132(7)

14. Effect of soil disturbance on soil consolidation parameters
Indraratna, B., Perera, D., Rujikiatkamjorn, C., Kelly, R. (2014). Analysis of Soil Disturbance Associated with Mandrel-driven Prefabricated Vertical Drains: Field Experience, Geotechnical Engineering ICE (Accepted)

15. Single drain vs. Multi-drain installation
Indraratna, B., Perera, D., Rujikiatkamjorn, C., Kelly, R. (2014). Analysis of Soil Disturbance Associated with Mandrel-driven Prefabricated Vertical Drains: Field Experience, Geotechnical Engineering ICE (Accepted).

16. Pore pressure variation during mandrel movement
Ghandeharioon, A., Indraratna, B., and Rujikiatkamjorn, C. (2012). Laboratory and Finite-Element Investigation of Soil Disturbance Associated with the Installation of Mandrel-Driven Prefabricated Vertical Drains. J. of Geotechnical & Geoenvironmental Engineering, ASCE. 138(3),
s1=
Locations of pore pressure transducers
Mandrel T1 T2 T3 T4 T5 16

17. Application of Cavity Expansion Theory for Mandrel Driven Vertical Drains
Equations of equilibrium (for elliptical expansion):
Dsr, Dsq and Dtrq are variations in the radial, tangential, and shear stresses
In the plastic region, MCC theory is used with the above equations.
S is the component of body force (per unit volume) radially
T is the tangential component

18. UOW Solution: Elliptical Cavity Expansion Theory for Wick Drains
R = over-consolidation ratio; Other parameters defined by Modified Cam-clay theory
The excess pore water pressure (Du) can be estimated from: ′

19. Finite element mesh for large strain frictional contact
Element type:
CAX4P
Soil and steel mandrel properties
Soil Properties
Value
Slope of unloading-reloading line, 
0.05
Slope of normal compression line, 
0.15
Critical state line slope, M
1.1
Critical state void ratio, ecs
1.55
Poisson’s ratio,  (aasumed)
0.25
Permeability (m/s)
5.1 10-10
Lateral stress coefficient (k0)
0.5
Steel Mandrel Properties
Young modulus (kN/m2)
2108
Poisson’s ratio, 
Interface Properties
Friction coefficient, m
0.24

20. Installation effects by vertical drains

21. Analytical Solutions for Vacuum-assisted Preloading
Assumptions
Rujikiatkamjorn, C. and Indraratna, B. (2014). Analytical Solution for Radial Consolidation Considering Soil Structure Characteristics, Canadian Geotechnical Journal. (Accepted November 2014).

22. Analytical Solutions for Vacuum-assisted Preloading
Effects of soil permeability and compressibility variation
Indraratna, B., Rujikiatkamjorn C., and Sathananthan, I., (2005). “Radial consolidation of clay using compressibility indices and varying horizontal permeability.” Canadian Geotechinical Journal, 42:

23. Installation effects on consolidation responses
CASE A (Single Drain),
CASE B (Multi-drain), and
CASE C (Ideal Case: No smear). 23

24. Analytical Solutions for Vacuum-assisted Preloading: Application to Case histories
Muar Clay Embankment (without vacuum)
Embankment Centre line only
Second Bangkok International Airport (with vacuum)
Indraratna, B., Rujikiatkamjorn C., and Sathananthan, I., (2005). “Analytical modeling and field assessment of embankment stabilized with vertical drains and vacuum preloading.” The Proceedings of the 16th ICSMGE, Osaka, Japan, Edited by the 16th ICSMGE committee, Millpress, Rotterdam, the Natherlands, ( ).

25. Effects of flow behaviour: Darcian and Non Dracian
Flow relationship
Kianfar, K., Indraratna, B. and Rujikiatkamjorn, C. (2013), Radial consolidation model incorporating the effects of vacuum preloading and non-Darcian flow. Geotechnique. 63: p 25

26. 2D FEM Multi-drain Analysis and Plane Strain Permeability Conversion
Field condition: Axisymmetric
2D plane strain FEM
Maintain geometric equivalence
Reduce the convergence time and require less computer memory
Must give the same consolidation response!!

27. The equivalent plane strain permeability is:
After conversion
Before conversion
Indraratna, B., Rujikiatkamjorn C., and Sathananthan, I., (2005). “Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading.” Canadian Geotechinical Journal, 42:

28. Case History: Second Bangkok International Airport, Thailand
Vertical cross section
-60 kPa vacuum and 2.5 m surcharge applied at this site
FEM mesh discretization (ABAQUS)
Indraratna, B., Sathananthan, I., Rujikiatkamjorn C. and Balasubramaniam, A. S. (2005). Analytical and numerical modelling of soft soil stabilized by PVD incorporating vacuum preloading. International Journal of Geomechanics, Vol. 5 No. 2,

29. Case History: Soil Parameters
Case History: Construction Schedule

30. Case History: Vacuum Simulation
Measured vacuum pressure
Indraratna, B., Rujikiatkamjorn C., Balasubramaniam, A. S. and Wijeyakulasuriya, V. (2005). “Predictions and observations of soft clay foundations stabilized with geosynthetic drains and vacuum surcharge.” Ground Improvement: Case Histories, Elsevier,

31. Case History: Vacuum Simulation
Model A: Conventional analysis (i.e., no vacuum application)
Model B: Vacuum pressure is adjusted according to field measurement and reduces linearly to zero at the bottom of the drain (k1= 0)
Model C: Perfect seal (i.e. vacuum pressure was kept constant at -60kPa after 40 days); vacuum pressure varies linearly to zero along the drain length (k1= 0)
Model D: No vacuum loss along the drain length (k1=1)

32. Case History: Results and Discussions
Settlements
Excess pore pressures

33. Case History: Results and Discussions
Lateral Movements at Embankment Toe
Advantages
Embankment height reduction from 4.0m to 2.5 m
Time reduction from 12 months to 4 months

34. Case History at Tianjin Port, China
2D and 3D analysis
Soil Profiles
Embankment plan view
Rujikiatkamjorn C., Indraratna, B. and Chu, J. (2008). 2D and 3D Numerical Modeling of Combined Surcharge and Vacuum Preloading with Vertical Drains. International Journal of Geomechanics, ASCE, 8(2),

35. 2D and 3D FEM mesh discretisation

36. Excess pore water pressure
Ground Settlement

37. Lateral Displacement
Lateral Displacement

38. Effect of vacuum pressure at the border of embankment
Effect of vacuum application (negative movements) may extend more than 10 m from the edge of the embankment
Lateral
movement A A A

39. Case Study: Ballina Bypass
DESIGN APPROACH FOR SOFT CLAY IMPROVED BY VERTICAL DRAINS WITH VACUUM PRESSURE – UoW Method Rujikiatkamjorn and Indraratna (2007, 2008), CGJ. AS8700
Sand layer
Case Study: Ballina Bypass
One way drainage
l =24m
Impermeable layer
qu=80kPa, Ut = 90%, l = 24m,
dw = 0.06 m, ch = 1.8m2/year, uo= -70 kPa,
cv = 0.9m2/year, kh/ks = 5, ds/dw = 3, t = 1.5 year
ds/dw
kh/ks

40. Now determine (a, b) to get spacing parameter, n
g = f (Ut, Tv, u*)
de =n*dw
Drain spacing,
S =de/1.128 for square pattern
S =de/1.05 for triangular pattern
de = POB was justified.
Latest Version:
Rujikiatkamjorn, C. and Indraratna, B. (2007 and 2008). Canadian Geotechnical Journal

41. Conclusions
The effects of permeability and compressibility variation are included in the proposed analytical model
Plane strain with appropriate conversion procedure is useful for multi-drain analysis in terms of calculating time
Vacuum preloading through PVDs applies a direct increase in lateral hydraulic gradient rapidly decreasing the excess pore pressure, thereby effecting rapid consolidation
PVD system subjected to vacuum preloading will only be effective as long as the potential air leaks can be minimized in the field
Factual data from well–monitored site such as measured applied vacuum is important to obtain the accurate predictions