A handy reference for use in geotechnical analysis and design Field  Given Below :

1. 𝐼𝑓=π‘Š1−𝑀2log10𝑁2/𝑁1

2. 𝐼𝑑=𝐼𝑝𝐼𝑓

3. 𝐢𝑒=𝐷60𝐷10

4. 𝐢𝑐=𝐷302𝐷60𝐷10

5. 𝐼𝑃=0.73 (𝑀𝐿−20)

6. 𝐼𝑃=𝑀𝐿−𝑀𝑃

7. 𝐼𝑠=𝑀𝑃−𝑀𝑆

8. 𝐼𝐿=𝑀−𝑀𝑃𝐼𝑃

9. 𝐼𝑐=𝑀𝐿−𝑀𝐼𝑃

10. 𝐴=𝐼𝑝𝐹 where 𝐹 is clay fraction (Activity)

11. 𝑅𝐷=π‘’π‘šπ‘Žπ‘₯−π‘’π‘’π‘šaπ‘₯−π‘’π‘šπ‘–π‘›=1/𝛾𝑑,π‘šπ‘–π‘›−1/𝛾𝑑1/𝛾𝑑,π‘šπ‘–π‘›−1/𝛾𝑑,π‘šπ‘Žπ‘₯

12. π‘˜1π‘˜2=tan𝛼1tan𝛼2 (non homogeneous)

13. π‘˜=πΆπ›Ύπ‘€πœ‡π‘’31+𝑒 𝑑2

14. 𝐾=π‘˜πœ‡π›Ύπ‘€ (absolute permeability)

15. π‘˜=π‘žπœ‹ ln(π‘Ÿ2/π‘Ÿ1)𝑧22−𝑧12 (Permeability in unconfined aquifer)

16. π‘˜=π‘ž2πœ‹π‘ ln(π‘Ÿ2/π‘Ÿ1)𝑧2−𝑧1 (Permeability in confined aquifer)

17. π‘˜β„Ž=π‘˜1𝐻1+π‘˜2𝐻2𝐻1+𝐻2 (effective horizontal permeability in stratified soils)

18. π‘˜π‘£=𝐻1+𝐻2𝐻1π‘˜1+𝐻2π‘˜2 (effective vertical permeability in stratified soils)

19. π‘˜π‘’=√π‘˜β„Žπ‘˜π‘£ (effective permeability)

20. π‘˜=π‘ŽπΏπ΄π‘‘lnβ„Ž1β„Ž2 (falling head permeability test)

21. π‘˜=π‘žπΏπ΄β„Ž (constant head permeability test)

22. π‘ž=π‘˜π‘’ β„Žπ‘π‘“π‘π‘‘ (seepage discharge)

23. πœŽπ‘§=3𝑄2πœ‹1𝑧2 (11+(π‘Ÿπ‘§)2 )52 (Boussinesq’s formula)

24. πœŽπ‘§=𝑐𝑄2πœ‹1𝑧2 (1𝑐2+(π‘Ÿπ‘§)2 )32 where 𝑐=√1−2πœ‡2−2πœ‡ (Wesrwegaard’s formula)

25. πœŽπ‘§=2π‘žπœ‹π‘§ (11+(π‘₯𝑧)2)2 (line load)

26. πœŽπ‘§=π‘žπœ‹(2πœƒ+sin2πœƒ) where πœƒ=tan−1𝑏𝑧 (stress under centre of strip load of width 2𝑏 )

27. πœŽπ‘§=π‘žπœ‹(2πœƒ+sin2πœƒsin2∅) where 2πœƒ=𝛽1−𝛽2 π‘Žn𝑑 2∅=𝛽1+𝛽2 ( strip eccentric point)

28. πœŽπ‘§=π‘ž(1−cos3πœƒ) where πœƒ=tan−1𝑅𝑧 (stress under centre of circular load)

29. sin∅=𝜎1−𝜎3𝜎1+𝜎3 (for cohesion less soils)

30. sin∅=(𝜎1−𝜎3)/2𝑐cot∅+(𝜎1+𝜎3)/2 (for cohesive soils)

31. 𝜎1=2𝑐tan𝛼+𝜎3tan2𝛼 where 𝛼=45+∅2

32. tan∅=𝜏𝜎 (shear box test for cohesion less soils)

33. 𝑇=𝑐 πœ‹π·2(𝐻2+𝐷6) (if both top and bottom surfaces contributes)

34. 𝑇=𝑐 πœ‹π·2(𝐻2+𝐷12) (if only bottom surface contribute)

35. 𝑆𝑖=π‘ž 𝐡 1−πœ‡2𝐸 𝐼𝑓 (immediate settlement )

36. 𝑆𝑓=𝑆𝑝(𝐡𝑓𝐡𝑝 𝐡𝑝+0.3𝐡𝑓+0.3)2 (settlement of footing based on plate settlement)

37. Δ𝑒=𝐡(Ξ”πœŽπ‘)+𝐴𝐡 (Ξ”πœŽπ‘‘) (Skempton’s pore pressure parameters)

38. π‘ž=π‘šπ‘ƒ+π‘˜ is stress path equation where ∅=tan−1π‘š and 𝑐=π‘˜/cos∅

39. 𝐢𝑐=Δ𝑒log10𝜎0+Ξ”πœŽπœŽ0

40. 𝐢𝑐=0.009 (𝑀𝐿−10) (for normally consolidated soil)

41. 𝐢𝑐=0.007 (𝑀𝐿−10) (for over consolidated soil)

42. Δ𝑒1+𝑒0=Δ𝐻𝐻

43. π‘šπ‘£=Δ𝐻/π»Ξ”πœŽ0

44. 𝑐𝑣=π‘˜π›Ύπ‘€π‘šπ‘£

45. 𝑇𝑣=𝑐𝑣𝑑𝑑2

46. 𝑇𝑣=πœ‹4π‘ˆ2 when π‘ˆ≤0.6

47. 𝑇𝑣=−0.933 log10(1−π‘ˆ)−0.085 when π‘ˆ>0.6

48. 𝑆𝑓=𝐢𝑐𝐻1+𝑒0 log10𝜎0+Ξ”πœŽπœŽ0

49. 𝑆𝑓=πΆπ‘Ÿπ»1+𝑒0 log10πœŽπ‘πœŽ0+𝐢𝑐𝐻1+𝑒0 log10𝜎0+Ξ”πœŽπœŽπ‘

50. π΄π‘Ÿ=𝐷02−𝐷𝑖2𝐷𝑖2

51. 𝑆𝑛=𝑐𝑒𝐹𝛾𝐻

52. π‘žπ‘’=𝑐𝑁𝑐+π‘ž π‘π‘ž+0.5 𝛾 𝐡 𝑁𝛾 (Terzaghi’s strip)

53. π‘žπ‘’=1.3 𝑐𝑁𝑐+π‘ž π‘π‘ž+0.4 𝛾 𝐡 𝑁𝛾 (Terzaghi’s square)

54. π‘žπ‘’=1.3 𝑐𝑁𝑐+π‘ž π‘π‘ž+0.3 𝛾 𝐡 𝑁𝛾 (Terzaghi’s circle)

55. π‘žπ‘’=(1+0.3𝐡𝐿) 𝑐𝑁𝑐+π‘ž π‘π‘ž+(1−0.2𝐡𝐿)0.5 𝛾 𝐡 𝑁𝛾 (Terzaghi’s rectangle)

56. π‘žπ‘’=𝑐𝑁𝑐𝑆𝑐𝑑𝑐𝑖𝑐+π‘ž π‘π‘žπ‘†π‘žπ‘‘π‘žπ‘–π‘ž+0.5 𝛾 𝐡′ 𝑁𝛾 𝑆𝛾𝑑𝛾𝑖𝛾 (Meyerhof)

𝐡′=𝐡−2𝑒π‘₯ and 𝐿′=𝐿−2 𝑒𝑦

57. π‘žπ‘›π‘’=𝑐𝑁𝑐 (Skempton

𝑁𝑐=5(1+0.2𝐷𝑓𝐡)(1+0.2𝐡𝐿)

Limiting value of 𝐷𝑓/𝐡 𝑖𝑠 2.5

58. 𝑄𝑒=π‘Šβ„Ž πœ‚β„Žπ‘†+𝐢 (ENR) where 𝐢=2.54 π‘π‘š π‘“π‘œπ‘Ÿ π‘‘π‘Ÿπ‘œπ‘ β„Žπ‘Žπ‘šπ‘šπ‘’π‘Ÿ π‘Žn𝑑 0.254 π‘π‘š π‘“π‘œπ‘Ÿ π‘ π‘‘π‘’π‘Žπ‘š β„Žπ‘Žπ‘šπ‘šπ‘’π‘Ÿ

Geotechnical engineering basic formulas
Geotechnical engineering basic formulas

59. 𝑄𝑒=π‘Šβ„Žπœ‚β„Žπœ‚π‘π‘†+𝐢2 (Hiley)

where 𝐢=𝐢1+𝐢2+𝐢3

𝐢1=9.05𝑅𝐴 with dolley and 𝐢1=1.77𝑅𝐴 without dolley and 𝐢2=0.657𝑅𝐿𝐴 𝐢3=3.55𝑅𝐴 𝐿=πΏπ‘’π‘›π‘”π‘‘β„Ž π‘œπ‘“ 𝑃𝑖𝑙𝑒 𝑖𝑛 π‘š 𝑅=𝑃𝑖𝑙𝑒 π‘π‘Žπ‘π‘Žπ‘π‘–t𝑦 𝑖𝑛 π‘‘π‘œπ‘›π‘›π‘’π‘ =0.1𝑄 𝐴=π‘π‘Ÿπ‘œπ‘ π‘  π‘ π‘’π‘π‘‘π‘–π‘œπ‘› π‘Žπ‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝑝𝑖𝑙𝑒 𝑖𝑛 π‘π‘š2

πœ‚π‘=π‘Š+𝑒2π‘ƒπ‘Š+𝑃 when π‘Š>𝑃

πœ‚π‘=π‘Š+𝑒2π‘ƒπ‘Š+𝑃−(π‘Š−𝑒𝑃𝐸+𝑃)2 when π‘Š<𝑃𝑒

60. 𝑄𝑒=π‘Šβ„Žπœ‚β„Žπ‘†+𝑆02 (Danish) 𝑆0=√2πœ‚β„Žπ‘Šβ„ŽπΏπ΄πΈ

61. 𝑄𝑒=𝐴𝑝𝑐𝑁𝑐+𝐴𝑠𝛼 𝑐 (clays)

62. 𝑄𝑒=𝐴𝑝𝑐𝑁𝑐+𝐴𝑠 πœ†(𝜎̅+2𝑐) (clays)

63. 𝑄𝑒=π΄π‘πœŽ̅ π‘π‘ž+π΄π‘ πœŽ̅ π‘˜tan𝛿 (sands) 𝜎̅ π‘–π‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ π‘’π‘π‘‘π‘œ 15 𝑑 π‘‘π‘’π‘π‘‘β„Ž

64. 𝑄𝑒=𝑁(𝐴𝑝𝑐𝑁𝑐+𝐴𝑠𝛼 𝑐) or 𝑄𝑒=(𝐴𝑔𝑝𝑐𝑁𝑐+𝐴𝑔𝑠 𝑐) (Group)

65. π‘π‘Ž=π‘˜π‘ŽπœŽ̅−2𝑐√π‘˜π‘Ž+𝑒

66. 𝑝𝑝=π‘˜π‘πœŽ̅+2𝑐√π‘˜π‘+𝑒 

67. π‘˜π‘Ž=1−sin∅1+sin∅ and π‘˜π‘=1+sin∅1−sin∅

 68. 𝐻𝑐=2𝑐𝛾√πΎπ‘Ž and unsupported vertical cut =2𝐻𝑐

69. π‘˜π‘Ž=sin2(𝛽+∅)sin2𝛽sin(𝛽−𝛿) (1+√sin(∅+𝛿)sin(∅−𝑖)sin(𝛽−𝛿)sin(𝛽+𝑖))2 (Coulomb’s active )

70. π‘˜π‘=sin2(𝛽−∅)sin2𝛽sin(𝛽+𝛿) (1−√sin(∅+𝛿)sin(∅+𝑖)sin(𝛽+𝛿)sin(𝛽+𝑖))2 (Coulomb’s passive )

71. π‘˜π‘Ž=cos𝛽−√cos2𝛽−cos2∅cos𝛽+√cos2𝛽−cos2∅ and π‘ƒπ‘Ž=π‘˜π‘Žπ›Ύβ„Ž22cos𝛽 (Inclined backfill)

72. π‘˜π‘=cos𝛽+√cos2𝛽−cos2∅cos𝛽−√cos2𝛽−cos2∅ and 𝑃𝑝=π‘˜π‘π›Ύβ„Ž22cos𝛽 (Inclined backfill)

73. 𝑁𝑐=15+12(𝑁−15) π‘€β„Žπ‘’π‘› 𝑁>15 π‘Žπ‘›π‘‘ 𝑁𝑐=𝑁 π‘€β„Žπ‘’π‘› 𝑁≤15 (dilatancy)

74. 𝑖𝑐=𝐺−11+𝑒 (Quick sand condition)