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Vertical Drain
- 2. Contents • Introduction • Installation Method • Prefabricated Vertical Drain(P.V.D) • Design Consideration • Mathematical Example
- 3. Vertical Drain The slow rate of consolidation in saturated clays of low permeability may be accelerated by means of vertical drains which shorten the drainage path within the clay.
- 5. Vertical Drain Horizontal Radial Drainage Vertical Drainage
- 13. Installation Method Boreholes Dia= 200~400 mm Length= Over 30 m
- 14. Prefabricated Vertical Drain(P.V.D) •Prefabricated drains 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 Band Prefabricated Drain
- 16. Sandwick Prefabricated Drain • Sandwick Drains consists 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 Drains have 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 • The rate 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 • By developing 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 normally installed in either a square or a triangular pattern.
- 21. Vertical Drain Spacing Drains are normally installed in either a square or a triangular pattern.
- 24. Z Axis
- 26. Z Axis X Axis
- 28. Z Axis X Axis Y Axis
- 30. Z Axis
- 31. This is the basic 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, at time 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, The time 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 combined to obtain the degree of consolidation at any depth z. This is shown in Figure 1. Figure1: Variation of Uz with
- 35. The average degree of consolidation for the entire depth of the clay layer at any time t can be written as
- 36. The values of the 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 of the 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)
- 39. Sand Drain Clay Clay Clay Z Axis Flow of water
- 43. Design Consideration • It is 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 coordinates the three-dimensional form of the consolidation equation, with different soil properties in the horizontal and vertical directions, is
- 45. The vertical prismatic blocks of soil surrounding the drains are replaced by cylindrical blocks, of radius R, having the same cross-sectional area
- 46. The vertical prismatic blocks 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 can be written in two parts: (1)
- 48. Tr Ur The expression for Tr, 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 for Tr, 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 Clay Impervious 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 Δσv 65 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 Δσv 65 kN/m2 mv 0.25 m2/MN Cv 4.7 m2/year Ch 7.9 m2/year Impervious Layer
- 54. 1 0.17
- 55. 1 0.17
- 56. Tr Ur
- 57. Tr Ur 0.82
- 58. Tr Ur 0.82 0.2
- 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.