Soil mechanics a[1].ppt

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Soil mechanics a[1].ppt

  1. 1. Basic Definitions and Terminology
  2. 2. Va Solid Vw Water Air Vs • Soil is generally a three phase material • Contains solid particles and voids • Voids can contain liquid and gas phases
  3. 3. Va Solid Vw Water Air Vs • Soil is generally a three phase material • Contains solid particles and voids • Voids can contain liquid and gas phases
  4. 4. Va Solid Vw Water Air Vs • Soil is generally a three phase material • Contains solid particles and voids • Voids can contain liquid and gas phases Phase Volume Mass Weight Air Va 0 0 Water Vw Mw Ww Solid Vs Ms Ws
  5. 5. Units • Length metres • Mass tonnes (1 tonne = 103 kg) • Density t/m3 • Weight kilonewtons (kN) • Stress kilopascals (kPa) 1 kPa= 1 kN/m2 • Unit weight kN/m3 • Accuracy Density of water, w = 1 t/m3 Stress/Strength to 0.1 kPa
  6. 6. Weight and Unit weight • Force due to mass (weight) more important than mass • W = Mg • Unit weight
  7. 7. Weight and Unit weight • Force due to mass (weight) more important than mass • W = Mg W • Unit weight V Mg V = g
  8. 8. Weight and Unit weight • Force due to mass (weight) more important than mass • W = Mg W • Unit weight V Mg V = g z v = gz v v = z
  9. 9. Specific Gravity This is defined by Density of Material G Density of Water w Unit Weight of Material G Unit Weight of Water w • Gs 2.65 for most soils • Gs is useful because it enables the volume of solid particles to be calculated from mass or weight
  10. 10. Specific Gravity This is defined by Density of Material G Density of Water w Unit Weight of Material G Unit Weight of Water w • Gs 2.65 for most soils • Gs is useful because it enables the volume of solid particles to be calculated from mass or weight Ms Ms Ws Ws Vs s Gs w s Gs w
  11. 11. Voids ratio • It is not the actual volumes that are important but rather the ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.
  12. 12. Voids ratio • It is not the actual volumes that are important but rather the ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S. Vv • The voids ratio is defined as e Vs
  13. 13. Voids ratio • It is not the actual volumes that are important but rather the ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S. Vv • The voids ratio is defined as e Vs Vv • and the porosity as n V
  14. 14. Voids ratio • It is not the actual volumes that are important but rather the ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S. Vv • The voids ratio is defined as e Vs Vv • and the porosity as n V The relation between these quantities can be simply determined as follows Vs = V - Vv = (1 - n) V
  15. 15. Voids ratio • It is not the actual volumes that are important but rather the ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S. Vv • The voids ratio is defined as e Vs Vv • and the porosity as n V The relation between these quantities can be simply determined as follows Vs = V - Vv = (1 - n) V Hence Vv Vv n e Vs (1 n )V 1 n
  16. 16. Degree of Saturation • The degree of saturation, S, has an important influence on soil behaviour Vw Vw • It is defined as S Va Vw Vv
  17. 17. Degree of Saturation • The degree of saturation, S, has an important influence on soil behaviour Vw Vw • It is defined as S Va Vw Vv • The phase volumes may now be expressed in terms of e, S and Vs • Vw = e S Vs Va = Vv - Vw = e Vs (1 - S)
  18. 18. Degree of Saturation • The degree of saturation, S, has an important influence on soil behaviour • It is defined as Vw Vw S Va Vw Vv • The phase volumes may now be expressed in terms of e, S and Vs • Vw = e S Vs Va = Vv - Vw = e Vs (1 - S) Assuming Vs = 1 m3, the following table can be produced Phase Volume Mass Weight Air e (1 - S) 0 0 Water eS eS w eS w Solid 1 Gs w Gs w
  19. 19. Unit Weights • The bulk unit weight W w Gs Vs w e S Vs w ( Gs e S) bulk V Vs eVs 1 e
  20. 20. Unit Weights • The bulk unit weight W w Gs Vs w e S Vs w ( Gs e S) bulk V Vs eVs 1 e • The saturated unit weight (S = 1) w ( Gs e) sat 1 e
  21. 21. Unit Weights • The bulk unit weight W w Gs Vs w e S Vs w ( Gs e S) bulk V Vs eVs 1 e • The saturated unit weight (S = 1) w ( Gs e) sat 1 e • The dry unit weight (S = 0) w Gs dry 1 e
  22. 22. Unit Weights • The bulk unit weight W w Gs Vs w e S Vs w ( Gs e S) bulk V Vs eVs 1 e • The saturated unit weight (S = 1) w ( Gs e) sat 1 e • The dry unit weight (S = 0) w Gs dry 1 e • The submerged unit weight ' sat w
  23. 23. Moisture Content • The moisture content, m, is defined as Weight of Water Ww m Weight of Solids Ws
  24. 24. Moisture Content • The moisture content, m, is defined as Weight of Water Ww m Weight of Solids Ws In terms of e, S, Gs and w Ww = w Vw = w e S Vs Ws = s Vs = w Gs Vs
  25. 25. Moisture Content • The moisture content, m, is defined as Weight of Water Ww m Weight of Solids Ws In terms of e, S, Gs and w Ww = w Vw = w e S Vs Ws = s Vs = w Gs Vs hence eS m Gs
  26. 26. Example 1 • Distribution by mass and weight Phase Trimmings Mass Sample Mass, M Sample Weight, Mg (g) (g) (kN) -6 Total 55 290 2845 10 -6 Solid 45 237.3 2327.9 10 -6 Water 10 52.7 517 10
  27. 27. Example 1 • Distribution by mass and weight Phase Trimmings Mass Sample Mass, M Sample Weight, Mg (g) (g) (kN) -6 Total 55 290 2845 10 -6 Solid 45 237.3 2327.9 10 -6 Water 10 52.7 517 10 • Distribution by volume (assume Gs = 2.65) Total Volume V = r2 l
  28. 28. Example 1 • Distribution by mass and weight Phase Trimmings Mass Sample Mass, M Sample Weight, Mg (g) (g) (kN) -6 Total 55 290 2845 10 -6 Solid 45 237.3 2327.9 10 -6 Water 10 52.7 517 10 • Distribution by volume (assume Gs = 2.65) Total Volume V = r2 l Ww Water Volume Vw w
  29. 29. Example 1 • Distribution by mass and weight Phase Trimmings Mass Sample Mass, M Sample Weight, Mg (g) (g) (kN) -6 Total 55 290 2845 10 -6 Solid 45 237.3 2327.9 10 -6 Water 10 52.7 517 10 • Distribution by volume (assume Gs = 2.65) Total Volume V = r2 l Ww Water Volume Vw w Ws Solids Volume Vs w Gs
  30. 30. Example 1 • Distribution by mass and weight Phase Trimmings Mass Sample Mass, M Sample Weight, Mg (g) (g) (kN) -6 Total 55 290 2845 10 -6 Solid 45 237.3 2327.9 10 -6 Water 10 52.7 517 10 • Distribution by volume (assume Gs = 2.65) Total Volume V = r2 l Ww Water Volume Vw w Ws Solids Volume Vs w Gs Air Volume Va = V - Vs - Vw
  31. 31. Ww 10 Moisture content m 0.222 22.2 % Ws 45
  32. 32. Ww 10 Moisture content m 0.222 22.2 % Ws 45 Vv Va Vw Voids ratio e 0.755 Vs Vs
  33. 33. Ww 10 Moisture content m 0.222 22.2 % Ws 45 Vv Va Vw Voids ratio e 0.755 Vs Vs Vw Vw Degree of Saturation S 0.780 78.0 % Vv Va Vw
  34. 34. Ww 10 Moisture content m 0.222 22.2 % Ws 45 Vv Va Vw Voids ratio e 0.755 Vs Vs Vw Vw Degree of Saturation S 0.780 78.0 % Vv Va Vw W Bulk unit weight bulk 181 kN / m3 . V
  35. 35. Ww 10 Moisture content m 0.222 22.2 % Ws 45 Vv Va Vw Voids ratio e 0.755 Vs Vs Vw Vw Degree of Saturation S 0.780 78.0 % Vv Va Vw W Bulk unit weight bulk 181 kN / m3 . V Ws Dry unit weight dry 14.8 kN / m3 V
  36. 36. Ww 10 Moisture content m 0.222 22.2 % Ws 45 Vv Va Vw Voids ratio e 0.755 Vs Vs Vw Vw Degree of Saturation S 0.780 78.0 % Vv Va Vw W Bulk unit weight bulk 181 kN / m3 . V Ws Dry unit weight dry 14.8 kN / m3 V 6 (W 14.9 10 9.81) Saturated unit weight sat 19.04 kN / m3 V Note that dry < bulk < sat
  37. 37. Example 2 Volume and weight distributions Phase Volume Dry Weight Saturated Weight 3 (m ) (kN) (kN) Voids 0.7 0 0.7 9.81 = 6.87 Solids 1.0 2.65 9.81 = 26.0 26.0
  38. 38. Example 2 Volume and weight distributions Phase Volume Dry Weight Saturated Weight 3 (m ) (kN) (kN) Voids 0.7 0 0.7 9.81 = 6.87 Solids 1.0 2.65 9.81 = 26.0 26.0 26.0 kN Dry unit weight, dry 153 kN / m3 . 17 m3 .
  39. 39. Example 2 Volume and weight distributions Phase Volume Dry Weight Saturated Weight 3 (m ) (kN) (kN) Voids 0.7 0 0.7 9.81 = 6.87 Solids 1.0 2.65 9.81 = 26.0 26.0 26.0 kN Dry unit weight, dry 153 kN / m3 . 17 m3 . (26.0 6.87 ) kN Saturated unit weight sat 19.3 kN / m3 17 m3 .
  40. 40. Example 2 Volume and weight distributions Phase Volume Dry Weight Saturated Weight 3 (m ) (kN) (kN) Voids 0.7 0 0.7 9.81 = 6.87 Solids 1.0 2.65 9.81 = 26.0 26.0 26.0 kN Dry unit weight, dry 153 kN / m3 . 17 m3 . (26.0 6.87 ) kN Saturated unit weight sat 19.3 kN / m3 17 m3 . 6.87 Moisture content (if saturated) m 0.264 26.4% 26.0
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