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Vertical Drain
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- 2. Contents • Introduction • InstallationMethod • Prefabricated Vertical Drain(P.V.D) • Design Consideration • Mathematical Example
- 3. Vertical Drain The slowrate of consolidation in saturated clays of low permeability may be accelerated by means of vertical drains which shorten the drainage path within the clay.
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- 5. Vertical Drain Horizontal RadialDrainage Vertical Drainage
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- 13. Installation Method Boreholes Dia= 200~400mm Length= Over 30 m
- 14. Prefabricated Vertical Drain(P.V.D) •Prefabricateddrains are now generally used and tend to be more economic than backfilled drains for a given area of treatment
- 15. Prefabricated Vertical Drain(P.V.D) Sandwick Prefabricated Drain BandPrefabricated Drain
- 16. Sandwick Prefabricated Drain • Sandwick Drainsconsists of a filter stocking, usually of woven polypropylene, filled with sand. • Compressed air is used to ensure that the stocking is completely filled with sand. Geotextile
- 17. Band Prefabricated Drain • Band Drainshave a channeled or studded plastic core wrapped with a geotextile. The plastic core functions as support for the filter. fabric, and provides longitudinal flow paths along the drain length. • It also provides resistance to longitudinal stretching as well as buckling of the drain. Geotextile Plastic Core
- 18. Design Consideration • Therate of soil consolidation or settlement is controlled by how rapidly the pore water can escape from the soil • The controlling variables are the spacing between the drains and the permeability of the soil.
- 19. Design Consideration • Bydeveloping a set of design curves of drain spacing, fill height, and consolidation time, the most economical drain spacing and height of fill can be selected to achieve a given degree of consolidation in a specified time period.
- 20. Vertical Drain Spacing Drains are normallyinstalled in either a square or a triangular pattern.
- 21. Vertical Drain Spacing Drains are normallyinstalled in either a square or a triangular pattern.
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- 28. Z Axis X Axis YAxis
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- 31. This is thebasic differential equation of Terzaghi’s consolidation theory and can be solved with the following boundary conditions : Where, Cv = Coefficient of consolidation (vertical direction)
- 32. 1. Initial Condition, attime t = 0 ; u = Δσ 2. Boundary Conditions at any time where z = 0 ; u = 0 For Double Drainage, z = 2H ; u = 0 The Initial & Boundary Conditions:
- 33. The solution yields, Thetime factor is a non dimensional number. Because consolidation progresses by the dissipation of excess pore water pressure, the degree of consolidation at a distance z at any time t is where, uz= excess pore water pressure at time t.
- 34. Equation and can be combinedto obtain the degree of consolidation at any depth z. This is shown in Figure 1. Figure1: Variation of Uz with
- 35. The average degreeof consolidation for the entire depth of the clay layer at any time t can be written as
- 36. The values ofthe time factor and their corresponding average degrees of consolidation for the case presented in Figure 1 may also be approximated by the following simple relationship:
- 37. The values ofthe time factor and their corresponding average degrees of consolidation for the case presented in Figure 1 may also be approximated by the following simple relationship: Uv = f (Tv)
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- 39. Sand Drain Clay Clay Clay ZAxis Flow of water
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- 43. Design Consideration • Itis essential for a successful design that the coefficients of consolidation in both the horizontal and the vertical directions (ch and cv, respectively) are known as accurately as possible. In particular, the accuracy of ch is the most crucial factor in design.
- 44. In polar coordinatesthe three-dimensional form of the consolidation equation, with different soil properties in the horizontal and vertical directions, is
- 45. The vertical prismaticblocks of soil surrounding the drains are replaced by cylindrical blocks, of radius R, having the same cross-sectional area
- 46. The vertical prismaticblocks of soil surrounding the drains are replaced by cylindrical blocks, of radius R, having the same cross-sectional area c c cc c c
- 47. Equation 1 canbe written in two parts: (1)
- 48. Tr Ur The expression forTr, confirms the fact that the closer the spacing of the drains, the quicker the consolidation process due to radial drainage proceeds. The solution for radial drainage, due to Barron, is given in Figure 7.30, the Ur/Tr relationship depending on the ratio n = R/rd, where R is the radius of the equivalent cylindrical block and rd the radius of the drain.
- 49. The expression forTr, confirms the fact that the closer the spacing of the drains, the quicker the consolidation process due to radial drainage proceeds. The solution for radial drainage, due to Barron, is given in Figure 7.30, the Ur/Tr relationship depending on the ratio n = R/rd, where R is the radius of the equivalent cylindrical block and rd the radius of the drain. It can also be shown that,
- 50. Example 1 Embankment 10 m ClayImpervious Layer Δσv 65 kN/m2 mv 0.25 m2/MN Cv 4.7 m2/year Ch 7.9 m2/year
- 51. Solution: H= 10 m Δσv65 kN/m2 mv 0.25 m2/MN Cv 4.7 m2/year Ch 7.9 m2/year Δσv = 65 kN/m2
- 52. H= 10 m Δσv65 kN/m2 mv 0.25 m2/MN Cv 4.7 m2/year Ch 7.9 m2/year Impervious Layer
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- 61. Reference • Craig, R.F. (2004), “Craig’s Soil Mechanics”, Spon Press, 29 West 35th Street, New York, USA, 7th Edition, pp. 268~274. • Das, B. M. (2009), “Principles of Geotechnical Engineering”, Cengage Learning, Stamford, USA, 7th Edition, pp. 294~364.
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