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Settlement of soil with sand drains

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Settlement of soil with sand drains

  1. 1. Consolidation Settlement of Sand Drains – Analytical and Numerical Approaches CE 632 INSTRUCTOR: DR. RAJESH SATHIYAMOORTHY 1
  2. 2. Objectives 1. Analytical Approach To review the available literature and theory pertaining to consolidation of clay installed with sand drains. To investigate recent improvements in the popular theory. 2. Numerical Approach To model a drain unit cell in the finite element program Plaxis 2d in order to study – i. Improvement in consolidation time by use of vertical sand drains. ii. Variation of ultimate settlement with loading iii. Variation of consolidation time with diameter of sand drains. 2
  3. 3. PART 1 ANALYTICAL APPROACH 3
  4. 4. Sand Drains  Definition  Fundamental approach 1). Free Strain 2). Equal Strain  Assumptions involved  Smear Consideration  Recent Improvements 4
  5. 5. Nogami & Li (2003) “Consolidation Of Clay With A System Of Vertical And Horizontal Drains.”  Consolidation behavior with the drain system is formulated using the transfer matrix method  Care is given to formulation of thin pervious layers for efficient computation  Can handle the inhomogeneous profile in clay and multiple horizontal drains made of either thin sand layers or geotextile sheets  Developed formulation is verified using available numerical and field information 5
  6. 6. Lekha et. al. (1998) Consolidation Of Clay By Sand Drain Under Time- dependent Loading  Non Linear theory of sand drain consolidation  Took account of effective stress/void ratio/ permeability variations  Closed form solutions are provided for the variation of pore water pressure with a time factor and load increment ratio  Verified with standard results for instantaneous loading, constant permeability, and constant compressibility 6
  7. 7. Indraratna et. al. (2008) Analytical And Numerical Modelling Of Consolidation By Vertical Drain Beneath A Circular Embankment  Consolidation by vertical drains below a circular loaded area where the system of vertical drains in the field was transformed by a series of equivalent concentric cylindrical drain walls.  An equivalent value for the coefficient of permeability of the soil is obtained by matching the degree of consolidation of a unit cell model. 7
  8. 8. Hsu et. al. (2013) Consolidation For Radial Drainage Under Time-dependent Loading  Radial drainage under linear time-dependent loading with varying loading dependent coefficients of radial consolidation by using a visco-elastic approach.  Findings indicate that the predicted consolidation settlements accounting for the loading rate-dependent Cr values more closely match the experimental results than the predictions using an assumed constant Cr. 8
  9. 9. References 1. Leo, C. (2004). ”Equal Strain Consolidation by Vertical Drains.” J. Geotech. Geoenviron. Eng., 130(3), 316–327. 2. Xiao, D., Yang, H., and Xi, N. (2011) Effect of Smear on Radial Consolidation with Vertical Drains. Geo-Frontiers 2011: pp. 4339-4348. doi: 10.1061/41165(397)444 3. Hsu, T. and Liu, H. (2013). ”Consolidation for Radial Drainage under Time- Dependent Loading.” J. Geotech. Geoenviron. Eng., 139(12), 2096–2103. 4. Indraratna, B., Aljorany, A., and Rujikiatkamjorn, C. (2008). ”Analytical and Numerical Modeling of Consolidation by Vertical Drain beneath a Circular Embankment.” Int. J. Geomech., 8(3), 199–206. 5. Nogami, T. and Li, M. (2003). ”Consolidation of Clay with a System of Vertical and Horizontal Drains.” J. Geotech. Geoenviron. Eng.,129(9), 838–848. 6. Lekha, K., Krishnaswamy, N., and Basak, P. (1998). ”Consolidation of Clay by Sand Drain under Time-Dependent Loading.” J. Geotech. Geoenviron. Eng., 124(1), 91–94. 7. Tan, S. (1993). ”Ultimate Settlement by Hyperbolic Plot for Clays with Vertical Drains.” J. Geotech. Engrg., 119(5), 950–956. 8. Das, B. M. (2008). “Advanced Soil Mechanics”, 3rd Ed., Taylor and Francis, London and New York. 9
  10. 10. PART 2 NUMERICAL APPROACH 10
  11. 11. Geometry of the Problem 11
  12. 12. 12
  13. 13. Material Sets Material Set: Dense Sand • Unsaturated unit weight = 17 kN/m3 • Saturated unit weight = 20 kN/m3 • Permeability kx = ky = 1 m/day • Cohesion = 1 kPa • Internal angle of friction = 35 degrees • Angle of dilatancy = 3 degrees • Young’s Modulus = 40000 kPa • Poisson’s ratio = 0.30 • Three material sets were created for this problem – • Dense Sand for Sand Drain • Soft Clay for Clay layer • Stiff Clay for Clay layer 13
  14. 14. Stiff Clay • Unsaturated unit weight = 18 kN/m3 • Saturated unit weight = 19 kN/m3 • Permeability kx = ky = 0.001 m/day • Cohesion = 50 kPa • Internal angle of friction = 0 degrees • Angle of dilatancy = 0 degrees • Young’s Modulus = 50000 Kpa • Poisson’s ratio = 0.35 Soft Clay • Unsaturated unit weight = 15 kN/m3 • Saturated unit weight = 17 kN/m3 • Permeability kx = ky = 0.01 m/day • Cohesion = 15 kPa • Internal angle of friction = 25 degrees • Angle of dilatancy = 0 degrees • Young’s Modulus = 10000 kPa • Poisson’s ratio = 0.25 14
  15. 15. Observations • U vs. Δσ (Taking diameter of sand drain = 0.4 m) Table 2.1 for Stiff Clay Δσ (kPa) Total Consolidation Settlement (m) Total Time with Sand drain, t1 (days) Total Time without Sand Drain, t2 (days) 100 0.019 11.484 122.5 200 0.038 22.972 183.75 300 0.063 19.619 153.13 400 0.09 17.234 157.92 500 0.117 18.006 169.4 600 0.144 20.912 149.3 700 0.171 20.688 172.87 800 0.198 28.395 179.69 900 0.225 30.295 175.62 1000 0.253 30.345 181.9 15
  16. 16. Δσ (kPa) Total Consolidation Settlement (m) Total Time with Sand drain, t1 (days) Total Time without Sand Drain, t2 (days) 100 0.077 22.968 61.25 200 0.169 45.938 91.876 300 0.261 45.938 91.876 400 0.353 45.938 91.876 500 0.445 45.938 91.876 600 0.537 45.938 91.876 700 0.629 45.938 91.876 800 0.721 45.938 91.876 900 0.814 61.251 91.876 1000 0.906 61.251 91.876 U vs. Δσ ; Table 2.2 for Soft Clay 16
  17. 17. U vs. Diameter Table 2.3 for Stiff Clay d (m) Total Consolidation Settlement (m) Total Time (days) 0.1 0.063 91.875 0.2 0.063 42.109 0.3 0.063 31.582 0.4 0.064 15.312 0.5 0.064 12.919 0.6 0.064 10.287 0.7 0.063 8.373 17
  18. 18. U vs. Diameter Table 2.4 for Soft Clay d (m) Total Consolidation Settlement (m) Total Time (days) 0.1 0.265 93.876 0.2 0.265 61.251 0.3 0.263 45.938 0.4 0.261 46.057 0.5 0.259 30.626 0.6 0.261 28.261 0.7 0.253 23.088 18
  19. 19. Results & Discussion • Time vs. Time • From Tables 2.1 and 2.2, it is clear that sand drains effectively reduce the time taken for consolidation of saturated clay for both stiff and soft clays. • As expected, this reduction is much more pronounced in case of stiff clays where the time taken reduces by about 6 to 11 times. While in the case of soft clays, the reduction factor is 1.5 to 3 times. 19
  20. 20. Time with sand drain, t1 (days) Time without sand drain, t2 (days) Reduction Ratio t2/t1 11.484 122.5 10.667 22.972 183.75 7.998 19.619 153.13 7.805 17.234 157.92 9.163 18.006 169.4 9.407 20.912 149.3 7.139 20.688 172.87 8.356 28.395 179.69 6.328 30.295 175.62 5.796 30.345 181.9 5.994 Table 2.5 for stiff clay 20
  21. 21. Time with sand drain, t1 (days) Time without sand drain, t2 (days) Reduction Ratio t2/t1 22.968 61.25 2.66 45.938 91.876 2 45.938 91.876 2 45.938 91.876 2 45.938 91.876 2 45.938 91.876 2 45.938 91.876 2 45.938 91.876 2 61.251 91.876 1.49 61.251 91.876 1.49 Table 2.6 for soft clay 21
  22. 22. • U vs Δσ For both stiff and soft clays, settlement steadily increases with applied load. 0 0.05 0.1 0.15 0.2 0.25 0.3 100 200 300 400 500 600 700 800 900 1000 TotalSettlement(m) Applied Stress (kPa) Fig. 2.3 Settlement vs Loading for Stiff Clay 22
  23. 23. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 200 300 400 500 600 700 800 900 1000 TotalSettlement(m) Applied Stress (kPa) Fig. 2.4 Settlement vs Loading for Soft Clay 23
  24. 24. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 100 200 300 400 500 600 700 800 900 1000 Ratio Applied Stress (kPa) Fig. 2.5 Ratio of Settlement Soft Clay to Stiff Clay 24
  25. 25. • Settlement vs. Diameter of Sand Drain As expected, the final settlement did not vary with the diameter of sand drain. And the time of consolidation steadily decreases with increase in the diameter of drains. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 TotalSettlement(m) Diameter of Sand Drain (m) Fig. 2.6 Settlement vs. Drain Dia for Stiff Clay 25
  26. 26. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 TotalSettlement(m) Diameter of Sand Drain (m) Fig. 2.6 Settlement vs. Drain Dia for Soft Clay 26
  27. 27. 0 10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ConsolidationTime(days) Diameter of Sand Drain (m) Fig. 2.7 Total Time vs. Drain Diameter for Stiff Clay 27
  28. 28. 0 10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ConsolidationTime(days) Diameter of Sand Drain (m) Fig. 2.8 Total Time vs. Drain Diameter for Soft Clay 28
  29. 29. Conclusions 1. Sand drains effectively reduce the time taken for consolidation of saturated clay for both stiff and soft clays. 2. This reduction is much more pronounced in case of stiff clays where the time taken reduces by about 6 to 11 times. 3. For both stiff and soft clays, settlement steadily increases with applied load. 4. The settlement of soft clay was found to be 3 to 5 times more than that for stiff clay. 5. The final settlement does not vary with the diameter of sand drain. 6. And the time of consolidation steadily decreases with increase in the diameter of drains. 29

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